U.S. patent application number 10/465123 was filed with the patent office on 2003-11-13 for apparatus for optimized constraint characterization with degradation options and associated methods.
This patent application is currently assigned to Silicon Metrics Corporation. Invention is credited to Howick, E. Keith JR., Rao, Guruprasad G..
Application Number | 20030212964 10/465123 |
Document ID | / |
Family ID | 27402174 |
Filed Date | 2003-11-13 |
United States Patent
Application |
20030212964 |
Kind Code |
A1 |
Rao, Guruprasad G. ; et
al. |
November 13, 2003 |
Apparatus for optimized constraint characterization with
degradation options and associated methods
Abstract
A circuit-characterization system includes a computer. The
computer uses a model of an operation of the circuit to
characterize first and second constraints of the circuit and to
select values for the first and second constraints, respectively.
The computer modifies the values selected for the first and second
constraints to obtain optimized values for the first and second
constraints. The optimized values of the first and second
constraints avoid an invalid region of operation of the
circuit.
Inventors: |
Rao, Guruprasad G.; (Austin,
TX) ; Howick, E. Keith JR.; (Liberty Hill,
TX) |
Correspondence
Address: |
Maximilian R. Peterson
O'KEEFE, EGAN & PETERMAN
Building C, Suite 200
1101 Capital of Texas Highway South
Austin
TX
78746
US
|
Assignee: |
Silicon Metrics Corporation
|
Family ID: |
27402174 |
Appl. No.: |
10/465123 |
Filed: |
June 19, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10465123 |
Jun 19, 2003 |
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09904463 |
Jul 13, 2001 |
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6584598 |
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60269373 |
Feb 16, 2001 |
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60270763 |
Feb 22, 2001 |
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Current U.S.
Class: |
716/113 ;
716/132; 716/136 |
Current CPC
Class: |
G06F 30/367 20200101;
G06F 30/33 20200101 |
Class at
Publication: |
716/1 |
International
Class: |
G06F 017/50 |
Claims
We claim:
1. A circuit-characterization system, comprising: a computer
configured to: characterize, according to a model of an operation
of a circuit, a first constraint of the circuit to select a value
for the first constraint; characterize, according to the model of
the operation of the circuit, a second constraint of the circuit to
select a value for the second constraint; and modify the values
selected for the first and second constraints to obtain optimized
values for the first and second constraints, wherein the optimized
values of the first and second constraints avoid an invalid region
of operation of the circuit.
2. The circuit-characterization system of claim 1, wherein the
computer is configured to characterize the second constraint
independently of the characterization of the first constraint.
3. The circuit-characterization system of claim 2, wherein the
optimized values of the first and second constraints correspond to
a valid meta-stable region of operation of the circuit.
4. The circuit-characterization system of claim 3, wherein the
computer is configured to obtain optimized values of the first and
second constraints by performing searches within, respectively, a
first range and a second range.
5. The circuit-characterization system of claim 4, wherein the
computer is configured to determine at each step of the searches
whether a criterion of circuit operation is met.
6. The circuit-characterization system of claim 1, in which the
computer is configured to: characterize the first constraint by
using a first degraded characteristic of the circuit obtained
according to a first degradation option; and characterize the
second constraint by using a second degraded characteristic of the
circuit obtained according to a second degradation option, wherein
the first and the second degradation options are selected from a
group consisting of an absolute-from-breakdown option, a
unity-slope option, and a normalized intersection option.
7. The circuit-characterization system of claim 3, in which the
computer is configured to: characterize the first constraint by
using a first degraded characteristic of the circuit obtained
according to a first degradation option; and characterize the
second constraint by using a second degraded characteristic of the
circuit obtained according to a second degradation option, wherein
the first and the second degradation options are selected from a
group consisting of an absolute-from-breakdown option, a
unity-slope option, and a normalized intersection option.
8. The circuit-characterization system of claim 5, in which the
computer is configured to: characterize the first constraint by
using a first degraded characteristic of the circuit obtained
according to a first degradation option; and characterize the
second constraint by using a second degraded characteristic of the
circuit obtained according to a second degradation option, wherein
the first and the second degradation options are selected from a
group consisting of an absolute-from-breakdown option, a
unity-slope option, and a normalized intersection option.
9. A computer program product, comprising: a computer application,
adapted for processing by a computer, the computer application
causing the computer to: characterize, according to a model of an
operation of a circuit, a first constraint of the circuit to select
a value for the first constraint; characterize, according to the
model of the operation of the circuit, a second constraint of the
circuit to select a value for the second constraint; and modify the
values selected for the first and second constraints to obtain
optimized values for the first and second constraints, wherein the
optimized values of the first and second constraints avoid an
invalid region of operation of the circuit.
10. The computer program product of claim 9, wherein the computer
application is further adapted to cause the computer to
characterize the second constraint independently of the
characterization of the first constraint.
11. The computer program product of claim 10, wherein the optimized
values of the first and second constraints correspond to a valid
meta-stable region of operation of the circuit.
12. The computer program product of claim 11, wherein the computer
application is further adapted to cause the computer to obtain
optimized values of the first and second constraints by performing
searches within, respectively, a first range and a second
range.
13. The computer program product of claim 12, wherein the computer
application is further adapted to cause the computer to determine
at each step of the searches whether a criterion of circuit
operation is met.
14. The computer program product of claim 9, in which the computer
application is further adapted to cause the computer to:
characterize the first constraint by using a first degraded
characteristic of the circuit obtained according to a first
degradation option; and characterize the second constraint by using
a second degraded characteristic of the circuit obtained according
to a second degradation option, wherein the first and the second
degradation options are selected from a group consisting of an
absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
15. The computer program product of claim 11, in which the computer
application is further adapted to cause the computer to:
characterize the first constraint by using a first degraded
characteristic of the circuit obtained according to a first
degradation option; and characterize the second constraint by using
a second degraded characteristic of the circuit obtained according
to a second degradation option, wherein the first and the second
degradation options are selected from a group consisting of an
absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
16. The computer program product of claim 13, in which the computer
application is further adapted to cause the computer to:
characterize the first constraint by using a first degraded
characteristic of the circuit obtained according to a first
degradation option; and characterize the second constraint by using
a second degraded characteristic of the circuit obtained according
to a second degradation option, wherein the first and the second
degradation options are selected from a group consisting of an
absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
17. A method of characterizing a circuit, comprising:
characterizing, according to a model of an operation of the
circuit, a first constraint of the circuit to select a value for
the first constraint; characterizing, according to the model of the
operation of the circuit, a second constraint of the circuit to
select a value for the second constraint; and modifying the values
selected for the first and second constraints to obtain optimized
values for the first and second constraints, wherein the optimized
values of the first and second constraints avoid an invalid region
of operation of the circuit.
18. The method of claim 17, which further includes characterizing
the second constraint independently of the characterization of the
first constraint.
19. The method of claim 18, wherein the optimized values of the
first and second constraints correspond to a valid meta-stable
region of operation of the circuit.
20. The method of claim 19, which further includes performing
searches within, respectively, a first range and a second range to
obtain the optimized values of the first and second
constraints.
21. The method of claim 20, which further includes determining at
each step of the searches whether a criterion of circuit operation
is met.
22. The method of claim 17, further comprising: characterizing the
first constraint by using a first degraded characteristic of the
circuit obtained according to a first degradation option; and
characterizing the second constraint by using a second degraded
characteristic of the circuit obtained according to a second
degradation option, wherein the first and the second degradation
options are selected from a group consisting of an
absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
23. The method of claim 19, further comprising: characterizing the
first constraint by using a first degraded characteristic of the
circuit obtained according to a first degradation option; and
characterizing the second constraint by using a second degraded
characteristic of the circuit obtained according to a second
degradation option, wherein the first and the second degradation
options are selected from a group consisting of an
absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
24. The method of claim 21, further comprising: characterizing the
first constraint by using a first degraded characteristic of the
circuit obtained according to a first degradation option; and
characterizing the second constraint by using a second degraded
characteristic of the circuit obtained according to a second
degradation option, wherein the first and the second degradation
options are selected from a group consisting of an
absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
25. A system for characterizing an electronic circuit, comprising:
a computer configured to: characterize, according to a model of an
operation of the electronic circuit, a first constraint of the
electronic circuit to acquire a value for the first constraint;
characterize, according to the model of the operation of the
electronic circuit, a second constraint of the electronic circuit
to acquire a value for the second constraint; and obtain optimized
values of the first and second constraints, by modifying the values
acquired for the first and second constraints, so as to avoid an
invalid meta-stable region of operation of the electronic circuit,
wherein the second constraint is characterized independently of the
characterization of the first constraint.
26. The system of claim 25, wherein the computer is configured to
obtain optimized values of the first and second constraints by
performing searches within, respectively, a first range and a
second range.
27. The system of claim 26, wherein the computer is configured to
determine at each step of the searches whether a criterion of
circuit operation is met.
28. The system of claim 27, wherein the electronic circuit
comprises a storage circuit.
29. The system of claim 28, wherein: the first constraint comprises
a setup time of the storage circuit; and the second constraint
comprises a hold time of the storage circuit.
30. The system of claim 25, in which the computer is configured to:
characterize the first constraint by using a first degraded
characteristic of the electronic circuit obtained according to a
first degradation option; and characterize the second constraint by
using a second degraded characteristic of the electronic circuit
obtained according to a second degradation option, wherein the
first and the second degradation options are selected from a group
consisting of an absolute-from-breakdown option, a unity-slope
option, and a normalized intersection option.
31. The system of claim 27, in which the computer is configured to:
characterize the first constraint by using a first degraded
characteristic of the electronic circuit obtained according to a
first degradation option; and characterize the second constraint by
using a second degraded characteristic of the electronic circuit
obtained according to a second degradation option, wherein the
first and the second degradation options are selected from a group
consisting of an absolute-from-breakdown option, a unity-slope
option, and a normalized intersection option.
32. The system of claim 29, in which the computer is configured to:
characterize the first constraint by using a first degraded
characteristic of the storage circuit obtained according to a first
degradation option; and characterize the second constraint by using
a second degraded characteristic of the storage circuit obtained
according to a second degradation option, wherein the first and the
second degradation options are selected from a group consisting of
an absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
33. A computer program product, comprising: a computer application,
adapted for processing by a computer, the computer application
causing the computer to: characterize, according to a model of an
operation of the electronic circuit, a first constraint of the
electronic circuit to acquire a value for the first constraint;
characterize, according to the model of the operation of the
electronic circuit, a second constraint of the electronic circuit
to acquire a value for the second constraint; and obtain optimized
values of the first and second constraints, by optimizing the
values acquired for the first and second constraints, so as to
avoid an invalid meta-stable region of operation of the electronic
circuit, wherein the second constraint is characterized
independently of the characterization of the first constraint.
34. The computer program product of claim 33, in which the computer
application is further adapted to cause the computer to obtain
optimized values of the first and second constraints by performing
searches within, respectively, a first range and a second
range.
35. The computer program product of claim 34, in which the computer
application is further adapted to cause the computer to determine
at each step of the searches whether a criterion of circuit
operation is met.
36. The computer program product of claim 35, wherein the
electronic circuit comprises a storage circuit.
37. The computer program product of claim 36, wherein: the first
constraint comprises a setup time of the storage circuit; and the
second constraint comprises a hold time of the storage circuit.
38. The computer program product of claim 33, in which the computer
application is further adapted to cause the computer to:
characterize the first constraint by using a first degraded
characteristic of the electronic circuit obtained according to a
first degradation option; and characterize the second constraint by
using a second degraded characteristic of the electronic circuit
obtained according to a second degradation option, wherein the
first and the second degradation options are selected from a group
consisting of an absolute-from-breakdown option, a unity-slope
option, and a normalized intersection option.
39. The computer program product of claim 35, in which the computer
application is further adapted to cause the computer to:
characterize the first constraint by using a first degraded
characteristic of the electronic circuit obtained according to a
first degradation option; and characterize the second constraint by
using a second degraded characteristic of the electronic circuit
obtained according to a second degradation option, wherein the
first and the second degradation options are selected from a group
consisting of an absolute-from-breakdown option, a unity-slope
option, and a normalized intersection option.
40. The computer program product of claim 37, in which the computer
application is further adapted to cause the computer to:
characterize the first constraint by using a first degraded
characteristic of the storage circuit obtained according to a first
degradation option; and characterize the second constraint by using
a second degraded characteristic of the storage circuit obtained
according to a second degradation option, wherein the first and the
second degradation options are selected from a group consisting of
an absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
41. A method of characterizing an electronic circuit, comprising:
characterizing, according to a model of an operation of the
electronic circuit, a first constraint of the electronic circuit to
acquire a value for the first constraint; characterizing, according
to the model of the operation of the electronic circuit, a second
constraint of the electronic circuit to acquire a value for the
second constraint; and obtaining optimized values of the first and
second constraints, by optimizing the values acquired for the first
and second constraints, so as to avoid an invalid meta-stable
region of operation of the electronic circuit, wherein the second
constraint is characterized independently of the characterization
of the first constraint.
42. The method of claim 41, which further includes performing
searches within, respectively, a first range and a second range to
obtain the optimized values of the first and second
constraints.
43. The method of claim 42, which further includes determining at
each step of the searches whether a criterion of circuit operation
is met.
44. The method of claim 43, wherein the electronic circuit
comprises a storage circuit.
45. The method of claim 44, wherein: the first constraint comprises
a setup time of the storage circuit; and the second constraint
comprises a hold time of the storage circuit.
46. The method of claim 41, further comprising: characterizing the
first constraint by using a first degraded characteristic of the
electronic circuit obtained according to a first degradation
option; and characterizing the second constraint by using a second
degraded characteristic of the electronic circuit obtained
according to a second degradation option, wherein the first and the
second degradation options are selected from a group consisting of
an absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
47. The method of claim 43, further comprising: characterizing the
first constraint by using a first degraded characteristic of the
electronic circuit obtained according to a first degradation
option; and characterizing the second constraint by using a second
degraded characteristic of the electronic circuit obtained
according to a second degradation option, wherein the first and the
second degradation options are selected from a group consisting of
an absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
48. The method of claim 45, further comprising: characterizing the
first constraint by using a first degraded characteristic of the
storage circuit obtained according to a first degradation option;
and characterizing the second constraint by using a second degraded
characteristic of the storage circuit obtained according to a
second degradation option, wherein the first and the second
degradation options are selected from a group consisting of an
absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This patent application relates to concurrently filed,
commonly owned U.S. patent application Ser. No. ______, Attorney
Docket No. SIME:002, titled "Apparatus and Methods for Constraint
Characterization with Degradation Options."
[0002] Furthermore, this patent application claims priority to the
following U.S. Provisional Patent Applications:
[0003] Application Serial No. 60/269,373, Attorney Docket No.
SIME:002PZ1, titled "Apparatus and Methods for Using Constraint
Dependency to Make Appropriate Performance Risk Tradeoffs Between
Timing, Power and Noise," and filed on Feb. 16, 2001; and
[0004] Application Serial No. 60/270,763, Attorney Docket No.
SIME:005PZ1, titled "Apparatus and Methods for Using Constraint
Dependency to Make Appropriate Performance Risk Tradeoffs Between
Timing, Power and Noise," and filed on Feb. 22, 2001. The present
patent application incorporates by reference the above patent
applications.
TECHNICAL FIELD OF THE INVENTION
[0005] This invention relates to characterizing electronic circuits
and, more particularly, to characterizing constraints of electronic
circuits.
BACKGROUND
[0006] Complexity of a typical electronic circuit, for example, an
integrated-circuit device, has increased dramatically. At the same
time, the length of the design cycle has typically remained
unchanged or has become shorter. To meet the shorter design cycles
for the more complex designs, circuit designers increasingly rely
on characterization of the designs in order to identify any
problems early in the design cycle. The short design cycles and the
complexity of the integrated-circuit devices make cost- and
time-prohibitive an approach that characterizes a design by
actually realizing the design in hardware and testing it in a
laboratory.
[0007] As an alternative to actually building a prototype of the
design, circuit designers have increasingly relied on electronic
design automation (EDA) tools, such as circuit simulation and
characterization tools. Effective circuit simulation tools provide
a way for the designer to simulate the behavior of a complex
design, identify any problems, and make alterations and
enhancements to the circuit before arriving at a final design. That
iterative design process has in turn improved the reliability of
the end-products that incorporate a given circuit design. The
effectiveness of a circuit characterization or simulation tool
depends on several criteria, for example, accuracy, reliability,
and predictability. Traditional approaches to characterizing
circuit constraints or various attributes of circuits, for example,
intrinsic delay, output transition time, or power, sometimes fail
to meet those criteria. In other words, the traditional approaches
may fail to provide results that match the behavior of an actual
prototype relatively closely. The failure of the traditional
characterization techniques results in increased costs, longer
design cycles, less reliable end-products, and/or less-than-optimal
designs. A need therefore exists for accurate and reliable
techniques for circuit characterization and circuit-constraint
characterization.
SUMMARY OF THE INVENTION
[0008] The invention contemplates constraint characterization in
electronic cells or circuits. One aspect of the invention relates
to circuit-characterization systems. In one embodiment of the
invention, a circuit-characterization system includes a computer
configured to characterize a first constraint of a circuit
according to a model of an operation of the circuit to select a
value for the first constraint. The computer characterize a second
constraint of the circuit according to the model of the operation
of the circuit to select a value for the second constraint. The
computer modifies the values selected for the first and second
constraints to obtain optimized values for the first and second
constraints, respectively. The optimized values of the first and
second constraints avoid an invalid region of operation of the
circuit.
[0009] In another embodiment, a circuit-characterization system
includes a computer configured to characterize a first constraint
of an electronic circuit according to a model of an operation of
the circuit to acquire a value for the first constraint. The
computer also characterizes a second constraint of the circuit
according to the model of the operation of the electronic circuit
to acquire a value for the second constraint. The second constraint
is characterized independently of the characterization of the first
constraint. The computer obtains optimized values of the first and
second constraints, by modifying the values acquired for the first
and second constraints, respectively, so as to avoid an invalid
meta-stable region of operation of the circuit.
[0010] More specifically, the computer is configured to
characterize the first constraint by using a first degraded
characteristic of the electronic circuit obtained according to a
first degradation option. The computer is also configured to
characterize the second constraint by using a second degraded
characteristic of the circuit obtained according to a second
degradation option. In exemplary embodiments, the first and second
degradation options are selected from among an
absolute-from-breakdown option, a unity-slope option, and a
normalized intersection option.
[0011] A second aspect of the invention relates to computer program
products for constraint characterization. In one embodiment of the
invention, a computer program product includes a computer
application adapted for processing by a computer. The computer
application causes the computer to characterize first and second
constraints of a circuit according to a model of an operation of
the circuit to select a value for the first and second constraints,
respectively. The computer application also causes the computer to
modify the values selected for the first and second constraints to
obtain optimized values for the first and second constraints,
respectively. The optimized values of the first and second
constraints avoid an invalid region of operation of the
circuit.
[0012] In another embodiment, a computer application, adapted for
processing by a computer, causes the computer to characterize first
and second constraints of an electronic circuit according to a
model of an operation of the circuit to acquire values for the
first and second constraints, respectively. The second constraint
is characterized independently of the characterization of the first
constraint. The computer application further causes the computer to
obtain optimized values of the first and second constraints, by
optimizing the values acquired for the first and second
constraints, respectively, so as to avoid an invalid meta-stable
region of operation of the circuit.
[0013] More specifically, the application causes the computer to
characterize the first and second constraints of the electronic
circuit by using a first degraded characteristic of the circuit
obtained according to a first degradation option, and by using a
second degraded characteristic of the circuit obtained according to
a second degradation option, respectively. In exemplary
embodiments, the first and the second degradation options are
selected from among an absolute-from-breakdown option, a
unity-slope option, and a normalized intersection option.
[0014] A third aspect of the invention relates to methods for
characterizing circuits. In one embodiment of the invention, a
method for circuit characterization includes characterizing a first
constraint of a circuit according to a model of an operation of the
circuit to select a value for the first constraint. The method
further includes characterizing a second constraint of the circuit
according to the model of the operation of the circuit to select a
value for the second constraint. The method modifies the values
selected for the first and second constraints to obtain optimized
values for the first and second constraints, respectively, so as to
avoid an invalid region of operation of the circuit.
[0015] In another embodiment, a method of characterizing an
electronic circuit includes characterizing first and second
constraints of the circuit to acquire values for the first and
second constraints, respectively. The second constraint is
characterized independently of the characterization of the first
constraint. The method further includes obtaining optimized values
of the first and second constraints, by optimizing the values
acquired for the first and second constraints, respectively, so as
to avoid an invalid meta-stable region of operation of the
circuit.
[0016] More specifically, the method includes characterizing the
first constraint by using a first degraded characteristic of the
electronic circuit obtained according to a first degradation
option. The method further includes characterizing the second
constraint by using a second degraded characteristic of the circuit
obtained according to a second degradation option. In exemplary
embodiments, the method includes selecting the first and second
degradation options from among an absolute-from-breakdown option, a
unity-slope option, and a normalized intersection option.
DESCRIPTION OF THE DRAWINGS
[0017] The appended drawings illustrate only exemplary embodiments
of the invention and therefore should not limit its scope. The
disclosed inventive concepts lend themselves to equally effective
embodiments other than the exemplary embodiments shown in the
drawings. The same numerals used in more than one drawing denote
the same, similar, or equivalent functionality, components, or
blocks, unless the description of the drawing states otherwise.
[0018] FIG. 1 illustrates a block diagram of a
circuit-characterization system according to the invention.
[0019] FIG. 2 shows a block diagram of a process flow for a
circuit-characterization system according to the invention.
[0020] FIG. 3 illustrates a general block diagram of a cell or
circuit under test by a circuit characterization system according
to the invention.
[0021] FIG. 4 shows a plot of an intrinsic delay of a circuit as a
function of a constraint time of the circuit.
[0022] FIG. 5 depicts a plot of power consumption by a circuit as a
function of a constraint time of the circuit.
[0023] FIG. 6A illustrates a circuit diagram of a two-input NAND
gate.
[0024] FIG. 6B shows a truth table for the two-input NAND gate of
FIG. 6A.
[0025] FIG. 6C depicts a set of input waveforms and a corresponding
output waveform of the NAND gate of FIG. 6A.
[0026] FIG. 6D illustrates another set of input waveforms and a
corresponding output waveform of the NAND gate of FIG. 6A.
[0027] FIG. 7A shows an inverter circuit that has an input and an
output.
[0028] FIG. 7B depicts a truth table for the inverter of FIG.
7A.
[0029] FIG. 7C illustrates an input waveform and a corresponding
output waveform of the inverter of FIG. 7A.
[0030] FIG. 7D shows another input waveform and a corresponding
output waveform of the inverter of FIG. 7A.
[0031] FIG. 8A depicts a block diagram of a D-type latch.
[0032] FIG. 8B illustrates an exemplary circuit diagram for the
D-type latch of FIG. 8A.
[0033] FIG. 8C shows a circuit diagram of a transmission gate used
in the D-type latch of FIG. 8B.
[0034] FIG. 9A depicts a set of waveforms that correspond to an
operation of the D-type latch of FIG. 8A.
[0035] FIG. 9B illustrates another set of waveforms that correspond
to an operation of the D-type latch of FIG. 8A.
[0036] FIG. 10A depicts a block diagram of a D-type flip-flop.
[0037] FIG. 10B shows a set of waveforms that correspond to an
operation of the D-type flip-flop of FIG. 10A.
[0038] FIG. 10C depicts another set of waveforms that correspond to
an operation of the D-type flip-flop of FIG. 10A.
[0039] FIG. 11 illustrates an exemplary set of waveforms that show
setup time and hold time for a storage circuit.
[0040] FIG. 12 shows an example of intrinsic delay of a storage
circuit as a function of its setup time.
[0041] FIG. 13 depicts an example of power consumption of a storage
circuit as a function of its setup time.
[0042] FIG. 14 illustrates a meta-stable region formed between the
breakdown points of the plots of intrinsic delay as functions of
setup time and hold time.
[0043] FIG. 15A shows a set of waveforms that correspond to the
operation of a D-type flip-flop, indicating that no violation of
the setup constraint has occurred.
[0044] FIG. 15B depicts a second set of waveforms that correspond
to the operation of the D-type flip-flop, showing that no violation
of the setup constraint has occurred.
[0045] FIG. 15C illustrates a third set of waveforms that
correspond to the operation of the D-type flip-flop, indicating
that a violation of the setup constraint has occurred.
[0046] FIGS. 16A and 16B depict a set of waveforms that correspond
to independent characterization of a setup constraint.
[0047] FIGS. 17A and 17B illustrate a set of waveforms that
correspond to independent characterization of a hold
constraint.
[0048] FIG. 17C depicts a negative meta-stable region as a result
of independent characterizations of the setup and hold
constraints.
[0049] FIGS. 18A and 18B show a set of waveforms that correspond to
dependent characterization of a setup constraint according to the
invention.
[0050] FIGS. 19A and 19B depict a set of waveforms that correspond
to dependent characterization of a hold constraint according to the
invention.
[0051] FIGS. 20A-20D illustrate optimized characterization of setup
and hold constraints according to the invention.
[0052] FIG. 21 shows a plot of an exemplary solution path for
inter-dependent characterization of setup and hold constraints
according to the invention.
[0053] FIG. 22 depicts plots that correspond to the
absolute-from-nominal delay degradation option according to the
invention.
[0054] FIG. 23 illustrates plots that correspond to the unity-slope
delay degradation option according to the invention.
[0055] FIG. 24 shows plots that correspond to the
absolute-from-breakdown delay degradation option according to the
invention.
[0056] FIGS. 25A and 25B depict plots that correspond to the
normalized-intersection delay degradation option according to the
invention.
DETAILED DESCRIPTION OF THE INVENTION
[0057] This invention contemplates apparatus and methods for
characterizing constraints of electronic circuits. More
particularly, the invention relates to ways of characterizing
independent as well as dependent constraints in electronic
circuits.
[0058] The apparatus and methods according to the invention provide
novel ways of constraint characterization for electronic circuits,
which include dependent constraint characterization, optimized
constraint characterization, and inter-dependent constraint
characterization. The invention also contemplates degradation
options for use in circuit characterization. The degradation
options include unity slope, absolute-from-breakdown, and
normalized intersection. The apparatus and methods according to
this invention provide circuit designers with tools for improved
circuit constraint characterization and, therefore, solve the
problems of inaccurate or incomplete constraint characterization of
electronic circuits.
CHARACTERIZATION OF ELECTRONIC CIRCUITS
[0059] Design and implementation of a modern electronic circuit
typically involves characterization of the circuit. Generally,
circuit or cell characterization refers to the process of
determining a circuit's or cell's response to various external
conditions. Put another way, characterization constitutes the
acquisition of a set of measurements that predict how a real
implementation (i.e., an implementation in actual hardware, for
example, on an integrated circuit device) of the circuit will
behave in response to a stimulus or stimuli. In a given design, for
example, a circuit designed for implementation on an integrated
circuit device, usually includes modules or cells. Each cell or
module typically constitutes a circuit that includes a collection
of circuit elements, for example, transistors, diodes, resistors,
and the like. One may characterize the cells in a given design to
determine various cell qualities or attributes, such as timing and
power consumption.
[0060] As part of cell characterization, the characterization tool
measures the responses of the cell or circuit at one or more
characterization points and records those responses in the form of
a characteristic equation or, alternatively, a characterization
table. A characterization point refers to a specific voltage or
current, temperature, and process at which the tool characterizes a
cell or circuit. For a given characterization point, the tool
typically measures a cell's response with respect to various input
transition times and capacitive loads to determine the cell's
behavior. A cell's behavior refers to the way the cell or circuit's
output quantity (e.g., voltage) behaves as a function of its input
stimulus or stimuli. For example, an AND gate behaves like a
logical "and" operation. The behavior determines how a designer
will use a cell or circuit, and what measurements a tool should
take to predict how the cell or circuit will operate once
physically implemented.
[0061] The type and amount of measurements a tool takes varies,
usually driven by modeling considerations. The desired models for a
cell or circuit determine what measurements a tool will take.
Measurements may cover various quantities, for example, power and
timing. Power measurements determine how much power a cell or
circuit consumes as it operates. Power measurements may include
leakage power, hidden power, and switching power, etc.
[0062] To generate timing models, the tool performs timing
characterization of the cell or circuit. Similarly, to generate
power models, the tool performs power characterization of the cell
or circuit. Currently in the industry, the main model for cell
characterization is Synopsys Incorporated's Liberty model. This
model encompasses some aspects of timing and power. Other common
models includes ALF, Verilog, VHDL, and VITAL. These models dictate
what measurements the characterization tool should take and how it
should acquire those measurements.
[0063] Timing measurements may include delay measurements and
constraints. Delay measurements determine how fast a signal
propagates through a cell or circuit, and the strength of the
signal from the circuit's output or outputs. Constraint
measurements include setup, hold, recovery, removal, minimum
pulse-width, and non-critical minimum pulse-width, and the like.
These types of measurements determine how close in time various
transitions in the input signals may occur before a cell or circuit
fails to operate predictably.
[0064] To perform timing characterization, tools typically measure
three parameters for each input transition/capacitive load
combination: intrinsic delay, output transition time, and input-pin
capacitance. Intrinsic delay refers to the delay between the time
of input transition and the time of the output transition, often
measured between the 50% points of the waveforms that correspond to
those quantities. Tools usually measure the output transition time
across the most linear region of the output voltage waveform.
Characterization tools typically measure transition times between
the 10% and 90% or between 20% and 80% points of a voltage
waveform.
[0065] The input-pin capacitance refers to the intrinsic effective
capacitance of an input pin of a cell or circuit. Depending on the
cell or circuit, the effective capacitance may vary as a function
of the load that the cell drives, as output capacitance may couple
back to the input leads or pins of the cell or circuit. The varying
effective capacitance changes the amount of time it takes to charge
and discharge the effective capacitance and, therefore, impacts the
timing of the cell or circuit.
[0066] To characterize a given circuit design, one typically uses a
computer system that processes information relating to that
circuit. FIG. 1 shows a block diagram of a system 1000 for
processing information according to the invention. The system 1000
includes a computer device 1005, an input device 1010, a
video/display device 1015, and a storage/output device 1020,
although one may include more than one of each of those devices, as
desired. The computer device 1005 couples to the input device 1010,
the video/display device 1015, and the storage/output device 1020.
The system 1000 may include more that one computer device 1005, for
example, a set of associated computer devices or systems, as
desired.
[0067] The system 1000 operates in association with input from a
user. The user input typically causes the system 1000 to perform
specific desired information-processing tasks, including circuit
characterization and/or circuit simulation. The system 1000 in part
uses the computer device 1005 to perform those tasks. The computer
device 1005 includes an information-processing circuitry, such as a
central-processing unit (CPU), although one may use more than one
CPU or information-processing circuitry, as persons skilled in the
art would understand.
[0068] The input device 1010 receives input from the user and makes
that input available to the computer device 1005 for processing.
The user input may include data, instructions, or both, as desired.
The input device 1010 may constitute an alphanumeric input device
(e.g., a keyboard), a pointing device (e.g., a mouse, roller-ball,
light pen, touch-sensitive apparatus, for example, a
touch-sensitive display, or tablet), or both. The user operates the
alphanumeric keyboard to provide text, such as ASCII characters, to
the computer device 1005. Similarly, the user operates the pointing
device to provide cursor position or control information to the
computer device 1005.
[0069] The video/display device 1015 displays visual images to the
user. The visual images may include information about the operation
of the computer device 1005, such as graphs, pictures, images, and
text. The video/display device may constitute a computer monitor or
display, a projection device, and the like, as persons of ordinary
skill in the art would understand. If a system uses a
touch-sensitive display, the display may also operate to provide
user input to the computer device 1005.
[0070] The storage/output device 1020 allows the computer device
1005 to store information for additional processing or later
retrieval (e.g., softcopy), to present information in various forms
(e.g., hardcopy), or both. As an example, the storage/output device
1020 may constitute a magnetic, optical, or magneto-optical drive
capable of storing information on a desired medium and in a desired
format. As another example, the storage/output device 1020 may
constitute a printer, plotter, or other output device to generate
printed or plotted expressions of the information from the computer
device 1005.
[0071] The computer-readable medium 1025 interrelates structurally
and functionally to the computer device 1005. The computer-readable
medium 1025 stores, encodes, records, and/or embodies functional
descriptive material. By way of illustration, the functional
descriptive material may include computer programs, computer code,
computer applications, and/or information structures (e.g., data
structures or file systems). When stored, encoded, recorded, and/or
embodied by the computer-readable medium 1025, the functional
descriptive material imparts functionality. The functional
descriptive material interrelates to the computer-readable medium
1025.
[0072] Information structures within the functional descriptive
material define structural and functional interrelations between
the information structures and the computer-readable medium 1025
and/or other aspects of the system 1000. These interrelations
permit the realization of the information structures'
functionality. Moreover, within such functional descriptive
material, computer programs define structural and functional
interrelations between the computer programs and the
computer-readable medium 1025 and other aspects of the system 1000.
These interrelations permit the realization of the computer
programs' functionality.
[0073] By way of illustration, the computer device 1005 reads,
accesses, or copies functional descriptive material into a computer
memory (not shown explicitly in FIG. 1) of the computer device
1005. The computer device 1005 performs operations in response to
the material present in the computer memory. The computer device
1005 may perform the operations of processing a computer
application that causes the computer device 1005 to perform
additional operations. Accordingly, the functional descriptive
material exhibits a functional interrelation with the way the
computer device 1005 executes processes and performs
operations.
[0074] Furthermore, the computer-readable medium 1025 constitutes
an apparatus from which the computer device 1005 may access
computer information, programs, code, and/or applications. The
computer device 1005 may process the information, programs, code,
and/or applications that cause the computer device 1005 to perform
additional operations.
[0075] Note that one may implement the computer-readable medium
1025 in a variety of ways, as persons of ordinary skill in the art
would understand. For example, memory within the computer device
1005 may constitute a computer-readable medium 1025, as desired.
Alternatively, the computer-readable medium 1025 may include a set
of associated, interrelated, or networked computer-readable media,
for example, when the computer device 1005 receives the functional
descriptive material from a network of computer devices or
information-processing systems. Note that the computer device 1005
may receive the functional descriptive material from the
computer-readable medium 1025, the network, or both, as
desired.
CHARACTERIZATION PROCESS FLOW
[0076] FIG. 2 shows a block diagram of the architectural process
flow of a characterization tool that facilitates characterization
of circuitry according to the invention. More specifically, one may
use the characterization tool in FIG. 2 to characterize
constraints, implement degradation options, and generally
characterize circuit or cell attributes, such as power consumption
and timing.
[0077] The process flow in FIG. 2 includes using an input file
1100, an auto-mapper 1105, a characterization manager 1110 and
associated simulation managers 1115A-1115N, a characterization
database 1120, a model generator 1125, and model databases
1130A-1130F. The characterization tool may run or execute on a
computer, such as the computer device 1005 in FIG. 1, or on a set
or network of associated computers, as persons skilled in the art
who have read the description of the invention would
understand.
[0078] The characterization tool receives its input via an input
file 1100. The input file 1100 contains a functional or behavioral
specification of the circuitry or cell that the user wishes to
characterize. The input file 1100 may include, for example, the
input and output leads or pins of a cell, the relationship between
the input and output leads or pins of the cell, and the functional
description of the cell, as desired.
[0079] FIG. 3 shows a general block diagram of a cell or circuit
under test 1150. The circuit 1150 may receive power from one or
more positive power supplies or sources 1162A-1162N and one or more
negative power supplies or sources 1164A-1164K, as desired. The
circuit 1150 may also have a signal and/or power ground 1166.
Alternatively, the circuit 1150 may have separate signal and power
ground connections (not shown explicitly in FIG. 3), as
desired.
[0080] Furthermore, the circuit 1150 may have one or more inputs
and one or more outputs. The exemplary circuit 1150 in FIG. 3 has a
number of inputs, generally designated as input X.sub.1 1155A,
input X.sub.2 1155B, input X.sub.3 1155C, . . . , and input X.sub.i
1155D. The circuit 1150 also has a number of outputs, generally
designated as output Y.sub.1 1160A, output Y.sub.2 1160B, output
Y.sub.3 1160C, . . . , and output Y.sub.o 1160D. Thus, the input
file 1100 for circuit 1150 may describe the inputs X.sub.1-X.sub.i,
the outputs Y.sub.1-Y.sub.o, the relationship between the inputs
X.sub.1-X.sub.i and the outputs Y.sub.1-Y.sub.o, and a functional
description of the behavior of circuit 1150.
[0081] The input file 1100 may provide the functional description
of the cell or circuit in a variety of formats. For example, the
input file 1100 may include a functional description of a cell in
the form of the cell's Boolean specifications. The Boolean
specifications may describe combinational or sequential circuits,
as desired. The Liberty (.lib) models generated according to
specifications from the Synopsys, Incorporated (a vendor of EDA
tools), constitute an example of a Boolean input file 1100.
[0082] Alternatively, the input file 1100 may include a functional
description in a description language, for example, Pilot. Silicon
Metrics Corporation, the assignee of this invention, provides the
specifications for Pilot. Among other capabilities, Pilot allows
the user to define cell characterization methodologies, cell
behavior, and modeling properties, as desired.
[0083] Referring to FIG. 2, an auto-mapper 1105 receives the
information in the input file 1100. The auto-mapper 1105 defines
how the tool characterizes the cell. The auto-mapper 1105 processes
the cell information within the input file 1100 and determines an
appropriate methodology for characterizing the cell (unless the
input file 1100 specifies a particular characterization
methodology). Characterization methodology for a cell generally
takes into account the cell's boundary network, e.g., the structure
of the load circuitry applied to the cell's output or outputs and
the structure of the source circuitry applied to the cell's input
or inputs. The auto-mapper 1105 specifies the structure of the
stimuli to apply to the input or inputs of the cell as well which
output or outputs of the cell to observe. In other words, the
auto-mapper 1105 uses the information in the input file 1100 to
generate specifications for simulating the cell's behavior (as
described below in more detail).
[0084] The auto-mapper 1105 provides those specifications to the
characterization manager 1110. The specifications include a list of
arcs for the characterization manager 1110 and the associated
simulation managers 1115A-1115N to use to simulate the cell. The
auto-mapper 1105 can consider a variety of attributes, as desired.
Those attributes include, for example, propagation delay of the
cell, the slew rate of the cell's output, the cell's input
capacitance, and power consumption by the cell.
[0085] Power consumption characteristics may include internal
power, hidden power, switching power, and leakage power. Internal
power refers to the consumption of power within a cell in response
to a change of state on one or more inputs. Hidden power refers to
certain cases of internal power. Hidden power concerns power
consumption within a cell in response to a change of state on one
or more inputs that causes no corresponding change of state on any
of the cell's outputs. Switching power, also known as capacitive or
output power, concerns the consumption of power to charge and
discharge a load capacitance at an output of the cell. Leakage
power, also known as static power, refers to power consumption in a
cell even when no inputs or outputs of the cell change state.
Leakage power arises from deviations of actual circuitry from its
ideal behavior. Leakage power typically results from sub-threshold
leakage and current flow through reverse-biased junctions between
diffusion regions and the substrate in an integrated circuit
device.
[0086] The auto-mapper 1105 provides the list of arcs by examining
the cell's behavioral description. For combinational circuits, the
auto-mapper 1105 may use an expression or equation that describes
the cell's behavior (e.g., the Boolean expression for the cell) or
the cell's truth table. For sequential circuits, the auto-mapper
1105 may use a cell's state table or an expression or set of
expressions of the information that the state table contains. Using
that information, the auto-mapper 1105 determines what changes in
the state of an input or group of inputs of the cell propagate to
an output or outputs of the cell and/or to an internal node or
nodes of the cell. The auto-mapper 1105 determines the arcs that
facilitate the characterization of various properties or
constraints of a cell, for example, setup time, hold time, hidden
power, switching power, minimum pulse-width of the clock signal,
and the like.
[0087] Once it has determined the set of arcs, the auto-mapper 1105
specifies to the characterization manager 1110 the structure of the
stimulus or stimuli that the characterization manager 1110 and the
simulation managers 1115A-1115N use to simulate the cell's
behavior. For example, the auto-mapper 1105 specifies the structure
of the state transitions of the stimuli waveforms to apply to the
cell in order to measure the cell's desired characteristics. The
auto-mapper 1105 also selects a set of measurements of the various
attributes of the cell (e.g., output voltage) that characterize the
cell's behavior, and specifies the set of measurements to the
characterization manager 1110.
[0088] Note that, rather than relying on the auto-mapper 1105 to
provide a characterization methodology, the user may explicitly
specify the methodology, as desired. The user may do so, for
example, by using the Pilot language, as described above. In other
words, the user may provide via Pilot a characterization
methodology that overrides the characterization methodology that
auto-mapper 1105 would have selected if the user had not chosen to
specify a characterization particular methodology.
[0089] The characterization manager 1110 uses the information it
receives from the auto-mapper 1105 to generate input files (not
shown explicitly in FIG. 2) for the set of simulation managers
1115A-1115N. The input files constitute circuit representations of
the circuit-under test or cell-under-test (CUT). The input files
include descriptions of the components or devices within the cell,
the cell's topology (i.e., the connections or couplings among the
components or devices), the input stimuli, the types of simulation
to perform and the parameters for those simulations, and the output
or outputs to observe. In an exemplary embodiment of the invention,
for each cell in a given circuit, a copy of the characterization
manager 1110 runs on a computer device, such as computer device
1005 in FIG. 1. One, however, may use other arrangements for
running the characterization manager 1110, as desired.
[0090] To achieve increased utility and flexibility, in exemplary
embodiments the characterization manager 1110 provides the input
files for a variety of simulators (used within the simulation
managers 1115A-1115N) from a multitude of vendors. For example, the
characterization manager 1110 may provide input files, sometimes
referred to as "SPICE decks" or netlists, suitable for use with
various simulators, for example, HSPICE, SmartSpice, Spectre, MICA,
and the like. "SPICE" constitutes an acronym for Simulation Program
with Integrated Circuit Emphasis, and refers to the generic version
of a commonly used simulator familiar to persons of ordinary skill
in the art. HSPICE (from Avant! Corp.), SmartSpice (from Silvaco
International), Spectre (from Cadence Design Systems, Inc.), and
MICA (from Motorola, Inc.) refer to particular simulators. Note
that, with modifications within the knowledge of persons of
ordinary skill in the art, the characterization manager 1110 can
generally provide input files for virtually any given simulators,
as desired. The simulation managers 1115A-1115N use the input files
they receive from the characterization manager 1110 to simulate the
behavior of the circuit using a given simulator, for example,
SPICE, HSPICE, SmartSpice, Spectre, MICA, and the like.
[0091] The characterization manager 1110 employs a variety of
techniques that tend to reduce the time and resources used during
circuit characterization. Using those techniques, the
characterization manager 1110 provides input files for the desired
simulator or simulators. More specifically, the characterization
manager 1110 employs a technique called auto-ranging to specify the
range of values for the input stimulus or stimuli. The
characterization manager 1110 specifies the range of values to the
simulation managers 1115A-1115N.
[0092] The simulation managers 1115A-1115N use the range of values
to simulate the behavior of the CUT and to generate response
surfaces for the CUT. The response surfaces provide information
about one parameter (e.g., delay through the CUT) as a function of
other parameters (e.g., input transition delay and capacitive
load). Commonly assigned U.S. patent application Ser. No.
09/090,457, titled "Method and System for Creating Electronic
Circuitry," and filed on Jun. 4, 1998, provides more details
regarding the auto-ranging technique.
[0093] In exemplary embodiments of the invention, for each CUT, a
separate copy of the characterization manager 1110 runs on one of
an appropriate number, M, of coupled computer devices (such as
computer device 1005 in FIG. 1). The number M constitute an integer
equal to or greater than unity. Each of the characterization
managers 1110 is responsible for the characterization of one of the
CUTs. In other words, a library of cells that contains M cells
causes the initiation of M characterization managers 1110. Note,
however, that one may use other arrangements, for example, a single
computer device, as desired. The choice of the number and
configuration of the computer devices, as well as the structure and
operation of the couplings among those computer devices (e.g., a
network) depends on a number of considerations specific to each
implementation, as persons of ordinary skill in the art would
understand.
[0094] To characterize a CUT, in exemplary embodiments each
characterization manager 1110 spawns or runs a set of N processes,
where N constitutes an integer equal to or greater than unity. Each
of the N processes corresponds to one of the simulation managers
1115A-1115N. Note, however, that one may use other arrangements for
he simulation managers 1115A-1115N, depending on various factors
(e.g., the speed, traffic level, and implementation of the coupling
among the computer devices as well as the number of the computer
devices), as persons of ordinary skill in the art would understand.
Each of the simulation managers 1115A-1115N performs a simulation
on the CUT using an input file that the characterization manager
1110 provides, as described above. Each of the simulation managers
1115A-1115N provides the results of the simulation to the
characterization manager 1110.
[0095] Once it receives the simulation results from the simulation
managers 1115A-1115N, each characterization manager 1110 determines
the response surface or surfaces of the corresponding CUT. The
characterization manager 1110 does so by causing the simulation
managers 1115A-1115N to take a sufficiently large number of
measurements of the CUT's simulated characteristics to represent
the response with a desired degree of accuracy. In other words, the
characterization manager 1110 uses a technique called over-sampling
to determine the points that tend to increase the accuracy of the
representation of the response surfaces of the CUT. For more
details regarding the over-sampling technique, see U.S. patent
application Ser. No. 09/090,457, cited and discussed above.
[0096] The characterization manager 1110 processes the results of
the simulations that the simulation managers 1115A- 1115N perform
and makes the results available in a characterization database
1120. Thus, the characterization database 1120 includes
characterization results for the cells in the design. A model
generator 1125 uses the data residing within the characterization
database 1120 to generate models (e.g., timing or power models) for
the cells within the circuit. The models that the model generator
1125 produces serve as input files to simulation engines or
simulators (not shown explicitly in FIG. 2).
[0097] The model generator 1125 may use properties that relate to
the characteristics of the cells. The user may specify those
properties in the input file 1100, as desired. The model generator
1125 may also use a technique known as data reduction to reduce the
amount of data that represent the characteristics of the CUTs, as
desired. The data-reduction technique allows the model generator to
reduce the size of tables that represent the response surfaces of
the CUTs. For more details regarding the data-reduction technique,
see U.S. patent application Ser. No. 09/090,457, cited and
discussed above.
[0098] To provide the tool with increased utility and flexibility,
in exemplary embodiments of the invention the model generator 1125
generates models, such as timing or power models, in a variety of
formats. For example, the model generator can generate models in
the following formats: Liberty (from Synopsys, Incorporated),
Advanced Library Format or ALF (from Nippon Electric Corporation),
Timing Library Format or TLF (from Cadence Design Systems, Inc.),
Verilog (also from Cadence Design Systems, Inc.), and/or Very
High-Speed Integrated Circuit (VHSIC) Hardware Description Language
or VHDL. The model generator 1125 may generate models for other
simulators or simulation engines, as persons of ordinary skill in
the art who have read the description of the invention would
understand.
[0099] Moreover, the model generator 1125 may generate models in a
parallel fashion, as desired. In other words, several instances of
the model generator 1125 may run on a number of associated computer
devices to generate the model databases 1130A-1130F. In such an
implementation, each instance of the model generator 1125 receives
the data within the characterization database 1120 and uses those
data to generate a model or models for desired simulation engine or
engines. The model generator 1125 stores the resulting models in
model databases, as described above. The choice of the particular
implementation of the model generator or generators 1125 depends on
a number of considerations (e.g., amount and type of computing and
networking resources, the complexity of the design, and the like),
as persons of ordinary skill in the art understand.
[0100] The model generator 1125 provides the desired models in
model databases 1130A-1130F. Note that the characterization tool
can provide support for a variety of simulators, as desired. The
model generator 1125 may provide models for additional simulators
to other model databases, as denoted by model database 1130F in
FIG. 2. A simulator may subsequently use a model from the
appropriate model database to perform simulation of part or all of
the circuit that contains the CUTs. From the results of the
simulation run or runs, the user may obtain a desired
characterization of the circuit.
[0101] The characterization tool may also perform checks to
determine the relative accuracy of the results of the simulators.
In other words, the tool may receive the results of the simulations
from the simulators and compare those results to the results stored
in the characterization database 1120. The comparison of the
results allows the tool to gauge the accuracy of the models
compared to the circuit-level models (e.g., SPICE models) that the
simulation managers 1115A-1115N use.
CONSTRAINT CHARACTERIZATION
[0102] As noted above, one may use the tool described in connection
with FIG. 2 to perform a variety of circuit characterizations. One
type of circuit or cell characterization involves constraints. A
circuit constraint refers to a limit imposed on an environmental
condition, a stimulus, or stimuli of the circuit to provide for
proper operation of the circuit. Put another way, a circuit
constraint constitutes a specification or limit on a pin or lead of
the circuit or cell (typically an input pin or lead) that should be
true for the behavior of the cell to be valid. Various constraints
include setup time, hold time, recovery, removal, minimum
pulse-width, non-critical minimum pulse-width, etc.
[0103] Traditionally, the limits have been set at or before the
moment of functional failure (also known as the breakdown point or
the pass-fail point) of a circuit. Observing the behavior of a
constraint, however, demonstrates that operating within a circuit's
functional tolerances does not necessarily mean that the circuit
operates in a predictable manner. In other words, the designer may
trade circuit performance for predictability of the operation of
the circuit.
[0104] Circuit attributes often behave non-linearly as a function
of various constraints of the circuit. For example, consider the
intrinsic delay of a sequential circuit, such as a latch. FIG. 4
shows a curve 1170 that plots the intrinsic delay of the latch as a
function of constraint time (the constraint may constitute, for
example, the setup time or hold time of the latch). Note that the
intrinsic delay of the circuit increases non-linearly as a function
of decreasing constraint time. When the constraint time decreases
beyond a certain limit, the intrinsic delay of the circuit reaches
the breakdown point. At the breakdown point, the circuit fails to
operate correctly or as desired.
[0105] FIG. 5 shows a curve 1180 that plots the power consumption
within the latch as a function of constraint time (again, the
constraint may constitute, for example, the setup time or hold time
of the latch). Similar to the intrinsic delay, the power
consumption of the circuit increases non-linearly as a function of
decreasing constraint time. When the constraint time decreases
beyond a certain limit, power consumption within the circuit
reaches the breakdown point, where it fails to operate in a correct
or desired manner.
[0106] Circuit constraints govern the behavior of both
combinational and sequential circuits. As an example, consider the
CMOS two-input NAND gate 1190 shown in FIG. 6A. The NAND gate 1190
includes p-type MOS transistors 1193A and 1193B, as well as n-type
MOS transistors 1196A and 1196B. The NAND gate 1190 has two inputs,
A and B, and one output, Y. FIG. 6B shows the truth table of the
NAND gate 1190.
[0107] Suppose that the NAND gate 1190 inputs, A and B, make a
transition from A=0 and B=0 to A=1 and B=1. When A=0 and B=0,
transistors 1193A and 1193B are on, thus pulling the output Y high
toward the supply voltage, V.sub.DD. Also, the low voltages on
inputs A and B keep transistors 1196A and 1196B off, thus
substantially insulating the output Y from the ground voltage,
V.sub.SS. When A=1 and B=1, however, the reverse situation occurs:
transistors 1193A and 1193B turn off, and transistors 1196A and
1196B turn on. The turning on of transistors 1196A and 1196B pulls
the output Y low toward the ground voltage, V.sub.SS. Also, the
high voltages on inputs A and B keep transistors 1193A and 1193B
off, thus substantially insulating the output Y from the supply
voltage, V.sub.DD.
[0108] The intrinsic delay of NAND gate 1190 depends, among other
things, on the relative points in time when the A and B inputs make
their respective low-to-high transitions. The point in time when
one input makes a transition relative to a transition on the other
input constitutes a constraint of the NAND gate 1190. FIG. 6C shows
a situation where input A makes its transition from low to high
and, within a sufficiently long time, input B makes its low-to-high
transition. (In other words, the transitions on the inputs of the
NAND gate 1190 do not violate the input-transition constraint). As
the plot of the voltage at output Y shows, the output of the NAND
gate 1190 makes a high-to-low transition within a nominal amount of
time.
[0109] Now consider the situation in FIG. 6D. Here, the inputs A
and B make their low-to-high transitions almost simultaneously
relative to each other. Referring to FIG. 6A, the near-simultaneous
low-to-high transitions on inputs A and B cause transistors 1193A
and 1193B to begin to turn off. The transitions on the inputs also
cause transistors 1196A and 1196B to begin to turn on. Because of
the simultaneous turning off of the p-network (i.e., transistors
1193A and 1993B) and the turning on of the n-network (i.e.,
transistors 1196A and 1196B), the NAND gate 1190 takes a longer
time to resolve its output Y. In other words, a violation of the
input-transition constraint occurs. Consequently, as the plot in
FIG. 6D of the voltage at the output Y shows, the high-to-low
transition of output Y takes a longer time compared to its
high-to-low transition in FIG. 6C.
[0110] As another example, consider inverter 1200 in FIG. 7A. The
inverter 1200 includes p-type MOS transistor 1203 and n-type MOS
transistor 1206. The inverter 1200 has one input, A, and one
output, Y. FIG. 7B shows the truth table of the inverter 1200.
[0111] Suppose that the inverter 1200 input A make a transition
from low to high and, some time later, makes a second transition
from high to low. Initially, when A=0, transistor 1203 is on, thus
pulling the output Y high toward the supply voltage, V.sub.DD.
Also, the low voltage on input A keeps transistor 1206 off, thus
substantially insulating the output Y from the ground voltage,
V.sub.SS. When A makes its transition to high, however, the reverse
situation occurs: transistor 1203 turns off, and transistor 1206
turns on. The turning on of transistor 1206 pulls the output Y low
toward the ground voltage, V.sub.SS. Also, the high voltage on
input A keeps transistor 1203 off, thus substantially insulating
the output Y from the supply voltage, V.sub.DD. Finally, when some
time later the input A makes its high-to-low transition, transistor
1203 turns on and transistor 1206 turns off. Consequently, the
voltage at the output Y rises toward the supply voltage,
V.sub.DD.
[0112] The intrinsic delay of inverter 1200 depends, among other
things, on the pulse-width of the low-to-high-to-low transition
applied to input A. In other words, the width of the voltage pulse
applied to input A constitutes a constraint of the inverter 1200.
FIG. 7C shows a situation where the pulse applied to input A has a
sufficiently wide duration. Put another way, the low-to-high and
the high-to-low transitions on input A take place sufficiently
apart in time. As the plot of the voltage at output Y shows, the
output of the inverter 1200 makes a high-to-low transition followed
by a low-to-high transition within a nominal amount of time (the
amount of time corresponds to the nominal intrinsic delay of the
inverter 1200).
[0113] FIG. 7D shows the situation where the high-to-low transition
on input A follows the low-to-high transition on input A almost
instantaneously. Referring to FIG. 7A, the near-instantaneous
high-to-low transition following the low-to-high transition on
input A causes transistor 1203 to begin to turn off and then almost
immediately begin to turn on again. Similarly, transistor 1206
begins to turn on and then almost immediately begins to turn off
again. As a result, the pulse on the input A does not propagate to
the output Y. Referring to the plot of the voltage at output Y, the
low-to-high-to-low transition on input A does not result in a
corresponding set of transitions on output Y. Because of the
violation of the minimum pulse-width constraint on input A, output
Y fails to make any predictable transitions that correspond to the
transitions on input A.
[0114] Examples of sequential circuits that have constraints
include D-type latches and D-type flip-flops. FIG. 8A shows a block
diagram of a D-type latch 1210. The latch 1210 has a D (data)
input, a clock input (labeled CLK), and a Q output. (Note that the
latch 1210 may also have a {overscore (Q)} output, which FIG. 8A
does not depict.) FIG. 8B shows an exemplary, simplified schematic
diagram 1215 of latch 1210. The latch 1210 includes pass gates 1218
and 1227, and buffers 1221 and 1224.
[0115] When the clock input is high, pass gate 1218 conducts, but
pass gate 1227 does not. As a result, the output Q reflects the
signal applied to input D. If input D makes any transitions while
the clock CLK input is high, output Q reflects those transitions.
(Note that with simple modifications, one may implement a latch in
which the output Q reflects input transitions when the clock signal
is low, rather than high, as persons of ordinary skill in the art
would understand. Also note that, for the sake of simplicity, the
circuit diagram 1215 in FIG. 8B does not show buffering of the
various signals, i.e., data and clock signals. The buffering of
those signals may have implications for the constraints of the
latch, as described below.)
[0116] Conversely, when the clock signal is low, pass gate 1218
does not conduct, but pass gate 1227 does. Thus, pass gate 1218
blocks any transitions on input D from reaching the output Q.
Conduction by pass gate 1227 completes a feedback loop that
includes buffer 1224. As a result, the output Q retains the value
that it had just before the clock made its high-to-low transition.
In other words, the latch 1210 has memory and can retain its
previous output value.
[0117] FIG. 8C shows an exemplary schematic diagram for a pass gate
1230 that one may use as each of pass gates 1218 and 1227. The pass
gate 1230 includes an n-type MOS transistor 1233 and a p-type MOS
transistor 1236. An input signal REF drives the gate of transistor
1233. The complement of signal REF, {overscore (REF)}, drives the
gate of transistor 1236. When REF is high, transistors 1233 and
1236 conduct and connect the input IN to the output OUT.
Conversely, when REF is low, both transistors 1233 and 1236 are
off, thus substantially isolating the input IN from output OUT.
[0118] FIGS. 9A and 9B show exemplary waveforms that correspond to
the operation of latch 1210. FIG. 9A shows a situation where the D
(data) input makes a low-to-high transition while the clock signal
is low. Because the clock signal is low, the latch 1210 does not
transmit the transition on the input D to the output Q. When the
clock signal goes high, however, the latch 1210 transmits the high
value on the input D to the output Q. Note that the input D
subsequently makes a high-to-low transition. Because that
transition occurs while the clock input is low, however, the latch
1210 does not transmit the transition to the output Q. Thus, the
output Q retains the value it had just before the clock signal made
its high-to-low transition.
[0119] In contrast, FIG. 9B illustrates a situation where the D
input makes a low-to-high transition while the clock signal is
high. Because the clock signal is high, the latch 1210 transmits
the transition on the input D to the output Q. Thus, the output Q
follows the transitions on input D while the clock signal is high.
Note that, similar to FIG. 9A, the input D subsequently makes a
high-to-low transition. Because that transition occurs while the
clock input is low, however, the latch 1210 does not transmit the
transition to the output Q. Hence, the output Q retains the value
it had just before the clock signal made its high-to-low
transition, in the same manner as in FIG. 9A.
[0120] FIG. 10A shows a block diagram of a D-type edge-triggered
flip-flop 1245. Similar to the latch 1210 in FIG. 8A, the flip-flop
1245 has a D (data) input, a clock input (labeled CLK), and a Q
output. (Note that the flip-flop 1245 may also have a {overscore
(Q)} output, which FIG. 10A does not show.) Unlike the latch 1210
in FIG. 8A, the flip-flop 1245 transmits the value at its D input
to its Q output only when the clock makes a transition. An
edge-triggered flip-flop does not transmit to the Q output those
transitions on the D input that fail to persist until the clock
signal makes a transition. Broadly speaking, two types of
edge-triggered flip-flops exist: positive-edge-triggered flip-flops
and negative-edge-triggered flip-flops. The two types of
edge-triggered flip-flop differ by which clock transition transmits
the value at the D input to the Q output. In a
positive-edge-triggered flip-flop the D-to-Q transmission occurs
when the clock makes a low-to-high transition; the converse occurs
in a negative-edge-triggered flip-flop.
[0121] FIGS. 10B and 10C show exemplary waveforms that correspond
to the operation of a positive edge-triggered flip-flop. FIG. 10B
shows a situation where the D (data) input makes a low-to-high
transition while the clock signal is low. Because the clock signal
is low and not making a transition from low to high, the flip-flop
does not transmit the transition on the input D to the output Q at
the moment that the transition on the D input occurs. When the
clock signal subsequently makes a low-to-high transition, the
flip-flop transmits the high value on the D input to the Q output.
Note that the input D subsequently makes a high-to-low transition.
Because that transition occurs while the clock input is low and not
making a transition from low to high, the flip-flop does not
transmit the transition to the output Q. Thus, the output Q retains
the high value it held.
[0122] FIG. 10C illustrates a situation where the D input makes a
low-to-high transition followed shortly by a high-to-low transition
(shown as pulse 1248 in FIG. 10C) while the clock signal is low.
Because the clock signal is low and not making a transition, the
flip-flop does not transmit the transitions on the input D to the
output Q. In effect, the flip-flop ignores the pulse 1248 on input
D. The input D subsequently makes a high-to-low transition 1250.
Because that transition occurs while the clock input is high,
however, the flip-flop does not transmit the transition to the
output Q. Later, the input D makes a high-to-low transition 1253.
Again, because the transition occurs while the clock is low, the
flip-flop does not transmit it to the output Q. In effect, the
flip-flop ignores the pulse that consists of transitions 1250 and
1253.
[0123] Two constraints one commonly encounters in sequential
circuit design constitute setup time and hold time. Setup time and
hold time are constraints that pertain in particular to latches and
flip-flops. Setup time refers to the time interval between when one
sets a state on the data input before a clock transition occurs
that results in the state's propagation to the output (e.g., the Q
output). Hold time refers to the amount of time after the clock
transition that one should hold the changed state on the data input
in order to preserve that state on the output. Stated differently,
violating setup time results in the failure of the new state on the
input to propagate to the output, whereas violating the hold time
causes the new state to not persist on the output. FIG. 11 shows
setup time, t.sub.S, and hold time, t.sub.H, with respect to a
reference clock transition. Note from FIG. 11 that one measures
setup and hold time with respect to the clock transition to which
the setup and hold times pertain, i.e., the reference clock
transition.
[0124] Like other constraints generally, setup and hold behave in a
non-linear fashion. As an example, FIG. 12 shows the intrinsic
delay of a latch or flip-flop as a function of setup time. Note
that the intrinsic delay increases sharply from a nominal value as
the setup time decreases below a certain point. The increase in
intrinsic delay results from contention among the various circuit
elements within the latch or flip-flop. For example, referring to
FIG. 8B, pass gates 1218 and 1227 contend with each other as they
each drive, and attempt to set, the input voltage to buffers 1221
and 1224. Resolving the contention among the circuit elements takes
longer as setup time decreases with respect to the reference clock
edge, thus giving rise to a higher intrinsic delay. At the limit,
the latch or flip-flop reaches its breakdown point and an input
transition fails to propagate to the output in a predictable
manner.
[0125] As another example of the non-linear behavior of the setup
and hold constraints, FIG. 13 illustrates the power consumed within
a latch or flip-flop as a function of setup time. Note that,
similar to intrinsic delay, power consumption increases sharply as
the setup time decreases below a certain point from its nominal
value. Referring again to FIG. 8B, pass gates 1218 and 1227 contend
with each other as they each drive, and attempt to set, the input
voltage to buffers 1221 and 1224. The contention between pass gates
1218 and 1227 results in increased power consumption in various
parts of the circuit, for example, in buffers 1218 and 1227, as
they operate in their linear regions until the resolution of the
contention. At the limit, the latch or flip-flop reaches its
breakdown point and power consumption within it becomes
unpredictable. Note that, although FIGS. 12 and 13 show intrinsic
delay and power consumption as a function of setup time, similar
results apply to the hold constraint or other constraints
generally.
[0126] FIG. 14 shows plots of intrinsic delay as a function of
setup time, t.sub.S, and hold time, t.sub.H. Note that intrinsic
delay has a nominal value for setup and hold times larger than
certain values (shown as t.sub.S(nominal) and t.sub.H(nominal),
respectively). As setup time and hold time decrease below
t.sub.S(nominal) and t.sub.H(nominal), respectively, intrinsic
delay increases, giving rise to additional timing unpredictability
within the circuit. At the limit, the circuit reaches its breakdown
point, causing the circuit to fail to operate correctly or as
desired. The region between the setup time and the hold time at the
breakdown point constitutes a meta-stable region (MSR). The MSR
typically varies from one cell to the next. No data transition
should occur within the MSR of a given cell.
[0127] To illustrate, FIGS. 15A-15C show the exemplary effects of
setup time and hold time on the operation of a flip-flop, in
particular, a positive-edge-triggered flip-flop. In FIG. 15A, the
flip-flop holds a logic high value following clock transition 1260.
The D input makes a high-to-low transition 1266 during the period
between the two clock transitions 1260 and 1263. The transition
1266 occurs sufficiently long before the clock transition 1263 and
the D input stays at a low level for a sufficiently long time after
the transition 1263 for the flip-flop to exhibit a nominal
intrinsic delay. The flip-flop transmits the transition 1266 to its
output, causing a transition 1269 on the Q output.
[0128] In FIG. 15B, the same set of events occurs, except that the
D input has a transition 1272 closer to the clock transition 1263,
but still without a setup constraint failure. Consequently, the
flip-flop correctly transmits the value at its D input to its
output, Q, although with increased intrinsic delay compared to FIG.
15A. In FIG. 15C, the D input has its transition 1278 sufficiently
close to the clock transition 1263 that a violation of the setup
constraint occurs. As a result, the flip-flop fails to transmit the
transition 1278 on the D-input to its output, Q. Ensuring proper
operation of the flip-flop therefore depends, among other things,
on proper characterization of the setup and hold constraints.
[0129] Characterizing setup and hold constraints for latches and
flip-flops often involves a trade-off between performance and
predictability of the cell's operation. To operate the cell at
higher frequencies, one may use a model that does not accommodate
the non-linear behavior of the constraints. Doing so, however,
reduces the predictability of the operation of the cell. The
traditional approach to constraint characterization, such as setup
and hold characterization, uses independent characterization of
constraints that often produces overly-optimistic results that do
not accommodate the non-linear behavior and the interaction of the
constraints.
[0130] To illustrate, FIGS. 16 and 17 show, respectively,
independent characterization of setup and hold for a latch, for
example, the latch of FIG. 8A. Referring to FIG. 16A, to
characterize the setup time, one sweeps a rising edge 1300 of the
latch's data signal toward a rising edge 1303 of the latch's clock
signal to search for a violation of the setup constraint. At each
position of the rising edge 1300, one performs a simulation of the
latch to determine whether violation of the setup constraint has
occurred. FIG. 16B shows the situation when the data rising edge
1300 has moved close enough in time to the clock rising edge 1303
so as to cause the latch to reach its breakdown point. The time
interval between the data rising edge 1300 and the clock rising
edge 1303 constitutes an independently characterized setup time for
the latch.
[0131] Note that in FIG. 16B, the data rising edge 1300 resides to
the right of the clock rising edge 1303. In other words, the latch
exhibits a negative setup time. This situation illustrates an
example of how different buffering and circuit delays within the
latch may give rise to a negative setup time. Referring to FIG. 8B,
if buffering causes the clock signal to take longer for the clock
signal to travel to pass gate 1218 than it takes the data signal to
arrive at the input of buffer 1221, the latch may exhibit a
negative setup time.
[0132] FIGS. 17A and 17B show independent characterization of the
hold constraint for the latch. Referring to FIG. 17A, to
characterize the hold time, one arranges a rising edge of the data
signal at a sufficiently long time (effectively at infinity) before
a rising edge 1312 of the clock signal so as not to affect the hold
characterization. For example, one may hold the data rising edge
1306 at a point in time that corresponds to a setup time longer
than the nominal setup time shown in FIG. 14 (effectively the
rising edge of the data signal takes place at infinity relative to
the clock rising edge 1312). For sufficiently large values of the
hold time, the output of the latch properly reflects the change in
the D-input. Next, one sweeps a falling edge 1309 of the latch's
data signal toward the clock rising edge 1312. At each position of
the falling edge 1309, one performs a simulation of the latch to
determine whether violation of the hold constraint has
occurred.
[0133] FIG. 17B shows the situation when the data falling edge 1309
has moved close enough in time to the clock rising edge 1312 so as
to cause the latch to fail to preserve the new data state at its
output (i.e., a hold violation occurs). In other words, as a result
of the hold constraint violation, the output of the latch fails to
properly reflect the change in the D-input. The time interval
between the previous successful data falling edge 1309 and the
clock rising edge 1312 constitutes an independently characterized
hold time for the latch. Note that in FIG. 17B, the data falling
edge 1309 resides to the left of the clock rising edge 1312, i.e.,
the latch exhibits a negative hold time. This situation may occur
for reasons similar to those described above with respect to the
negative setup time shown in FIG. 16B.
[0134] Because of the mutually exclusive characterizations of the
setup and hold time in FIGS. 16 and 17, respectively, setup and
hold characterizations using the traditional technique are
independent of each other. In other words, this technique produces
results that tend to be overly optimistic because they correspond
to the best-case setup and hold times. The results produce an
anomaly known as the negative meta-stable region (NMSR). FIG. 17C
shows a plot of setup and hold times acquired using this technique
as in FIGS. 16 and 17, respectively, referenced to the clock's
rising edge.
[0135] The interval between the setup and hold times in FIG. 17C
constitutes a negative number, the NMSR, which does not correspond
to the actual operation of a latch circuitry fabricated and tested
in a laboratory. Note that the interval constitutes a negative
number because, as FIG. 17C shows, the hold time occurs before the
setup time. Note also that FIG. 17C shows one situation where an
NMSR exists. As persons of ordinary skill in the art would
understand, other situations may also exist that give rise to an
NMSR.
[0136] Constraint acquisition techniques according to the invention
overcome the problems associated with the independent acquisition
of constraints. The invention contemplates dependent constraint
acquisition, optimized constraint acquisition, and inter-dependent
constraint acquisition. One aspect of the invention concerns
dependent acquisition of constraints, such as setup and hold
constraints for latches and flip-flops. FIGS. 18 and 19 illustrate
dependent acquisition of setup and hold, respectively. Note that
FIGS. 18 and 19 merely illustrate the principle of dependent
constraint acquisition according to the invention. One may apply
dependent constraint acquisition to related constraints other than
setup and hold, as desired.
[0137] FIG. 18 shows acquisition of dependent setup, which involves
two steps. The first step characterizes the hold constraint in an
independent manner. The second step uses the acquired value of the
hold constraint from the first step to characterize the setup
constraint. Referring to FIG. 18A, to characterize dependent setup,
one arranges the rising edge 1320 of the data signal a sufficiently
long time (effectively infinity) before the rising edge 1326 of the
clock signal that the rising edge 1320 of the data signal does not
affect the acquisition of the hold time. Next, one sweeps (for
example, by using a search mechanism) a falling edge 1323 of the
latch's data signal toward the clock rising edge 1326. At each
position of the falling edge 1323, one performs a simulation of the
latch to determine whether violation of the hold constraint has
occurred. Through repetitive simulations, one obtains the hold
constraint of the latch in an independent manner.
[0138] FIG. 18B shows the second step of dependent setup
characterization according to the invention. Here, one holds the
falling edge 1323 of the data signal at a point in time that
corresponds to the independently characterized value of the hold
constraint in step one. Then, one sweeps (for example, by using a
search mechanism) rising edge 1320 of the latch's data signal
toward the clock rising edge 1326. At each position of the rising
edge 1320, one performs a simulation of the latch to determine
whether violation of the setup constraint has occurred, until one
acquires the setup constraint. Note that the characterization of
the setup constraint in step two depends on the independently
characterized hold constraint in step one. That dependency results
in a positive meta-stable region and, hence, overcomes the negative
meta-stable region problem associated with independent
characterization of setup and hold, discussed above.
[0139] FIG. 19 shows acquisition of dependent hold, which also
involves two steps. The first step characterizes the setup
constraint in an independent manner. The second step uses the
characterization of the setup constraint from the first step to
characterize the hold constraint. Referring to FIG. 19A, to
characterize dependent hold, one arranges the falling edge 1323 of
the data signal a sufficiently long time (effectively infinity)
before the rising edge 1326 of the clock signal that the falling
edge 1323 of the data signal does not affect the acquisition of the
setup time. Next, one sweeps (for example, by using a search
mechanism) a rising edge 1320 of the latch's data signal toward the
clock rising edge 1326. At each position of the rising edge 1320,
one performs a simulation of the latch's behavior to determine
whether violation of the setup constraint has occurred. By using
repetitive simulations, one obtains the setup constraint of the
latch in an independent manner.
[0140] FIG. 19B shows the second step of dependent hold
characterization according to the invention. Here, one holds the
rising edge 1320 of the data signal at a point in time that
corresponds to the independently characterized value of the setup
constraint in step one. Then, one sweeps (for example, by using a
search mechanism) falling edge 1323 of the latch's data signal
toward the clock rising edge 1326. At each position of the falling
edge 1323, one performs a simulation of the latch to determine
whether violation of the hold constraint has occurred, until one
acquires the hold constraint. Thus, the characterization of the
hold constraint in step two depends on the independently
characterized setup constraint in step one. As with dependent setup
characterization described above, the dependent hold
characterization results in a positive meta-stable region. The
positive meta-stable region overcomes the negative meta-stable
region problem associated with independent constraint
characterization, as discussed above.
[0141] Another aspect of the invention concerns optimized
constraint characterization. Under some circumstances, dependent
constraint characterization, for example, the dependent setup
characterization or the dependent hold characterization described
above, may produce somewhat pessimistic results. In other words, it
may produce a meta-stable region that is wider than desired or
necessary. Circuit designers may seek to have a more aggressive
meta-stable region that corresponds to an increased operating
frequency of the latch. Optimized characterization seeks to provide
a more aggressive meta-stable region than does the dependent
constraint characterization techniques discussed above. Optimized
characterization locates the final values of the constraints, such
as the setup and hold constraints, by simultaneously adjusting the
values of the constraints within two respective ranges, as
described below in detail.
[0142] Optimized constraint characterization includes three steps.
In the first step, one characterizes the setup constraint
independently. In the second step, one characterizes the hold
constraints independently. The third step modifies or adjusts the
independently acquired values of the setup and hold constraints so
as to avoid an invalid region of circuit operation, for example, a
negative meta-stable region or an overly optimistic meta-stable
region. Optimized constraint characterization provides more
aggressive, yet realistic, values for the constraints, such as the
setup and hold constraints. FIGS. 20 and 21 correspond to the three
steps of optimized constraint characterization.
[0143] Referring to FIG. 20A, to characterize the setup time in the
first step, one sweeps (for example, by using a search mechanism) a
rising edge 1330 of the latch's data signal toward a rising edge
1333 of the latch's clock signal. At each position of the rising
edge 1330, one performs a simulation of the latch to determine
whether violation of the setup constraint has occurred. At some
point, the data rising edge 1330 moves close enough in time to the
clock rising edge 1333 so as to cause the latch to reach its
breakdown point. The time interval between the data rising edge
1330 and the clock rising edge 1333 constitutes an independently
characterized setup time for the latch.
[0144] FIG. 20B shows independent characterization of the hold
constraint in the second step of optimized constraint
characterization. Here, one arranges rising edge 1330 of the data
signal at a sufficiently long time (effectively infinity) before a
rising edge 1333 of the clock signal so as not to affect the hold
characterization. Next, one sweeps (for example, by using a search
mechanism) falling edge 1336 of the latch's data signal toward the
clock rising edge 1333. At each position of the falling edge 1336,
one performs a simulation of the latch to determine whether
violation of the hold constraint has occurred. At some point, the
falling edge 1336 moves sufficiently close in time to clock rising
edge 1333 that the latch reaches its breakdown point. The time
interval between the data falling edge 1336 and the clock rising
edge 1333 constitutes an independently characterized hold time for
the latch.
[0145] As noted above, independent characterization of setup and
hold constraints may lead to an overly optimistic meta-stable
region or a negative meta-stable region. Referring to FIG. 20C, in
step three, optimized constraint characterization according to the
invention moves data rising edge 1330 and data falling edge 1336
away from the reference clock edge 1333 so as to widen the
meta-stable region. As the edges 1330 and 1336 move away from clock
edge 1333, at some point one observes a transition in the output of
the latch when one simulates the behavior of the latch, i.e., one
obtains a valid meta-stable region. In other words, step three of
the optimized constraint characterization starts with the
constraint characterizations of steps one and two and moves out
edges 1333 and 1336 to provide a valid meta-stable region. In
exemplary embodiments of the invention, if the values of the setup
and hold times acquired in steps one and two correspond to a valid
meta-stable region, step three makes no adjustment to those
values.
[0146] Characterizations of the setup and hold constraints use the
clock edge 1333 in FIG. 20C as a reference point. Thus, FIG. 20C
illustrates positive values for both the setup and hold
constraints, which correspond to a positive meta-stable region.
Although region 1137 in FIG. 20C corresponds to a positive
meta-stable region, under some circumstances the region 1137 may
correspond to a negative meta-stable region (i.e., t.sub.H occurs
before t.sub.S). If t.sub.H occurs before t.sub.S (corresponding to
an NMSR), step three of optimized characterization according to the
invention reverses or switches the positions of t.sub.H and
t.sub.S. Reversing or switching the positions of t.sub.H and
t.sub.S under those circumstances enforces a positive meta-stable
region.
[0147] FIG. 20D illustrates more details of how step three of the
optimized constraint characterization operates. Here, one starts
with setup and hold values of t.sub.S(min) and t.sub.H(min), which
correspond to values of the independently characterized setup and
hold constraints from steps one and two, respectively. Next, one
establishes a first range 1355 and a second range 1358. Optimized
characterization according to the invention searches for the final
values of the setup and hold constraints within the first and
second ranges 1355 and 1358, respectively.
[0148] As FIG. 20D shows, to establish the first and second ranges
1355 and 1358, one uses the values t.sub.S(min) and t.sub.H(min)
together with values t.sub.S(max) and t.sub.H(max). One may obtain
values for, or assign values to, t.sub.S(max) and t.sub.H(max) in a
variety of ways. For example, the user may provide the values of
t.sub.S(max) and t.sub.H(max). As another example, one may use the
rise and fall times of the rising transition 1349 and falling
transition 1352, which correspond, respectively, to the rising and
falling transitions used in steps one and two of optimized
characterization. One may then use
t.sub.S(max)=t.sub.S(min)+k.sub.1.multidot.t.sub.rise and
t.sub.H(max)=t.sub.H(min)+k.sub.2.multidot.t.sub.fall, where
t.sub.rise and t.sub.fall denote the rise time and the fall time,
respectively. Note that k.sub.1 and k.sub.2 represent scaling
factors that may have values less than, equal to, or greater than
unity, as desired.
[0149] As an alternative, one may assign values to the widths of
the first and second ranges 1355 and 1358 and calculate the values
of t.sub.S(max) and t.sub.H(max) accordingly. One may assign the
widths of the first and second ranges 1355 and 1358 in a variety of
ways. For example, one may obtain values from the user that
correspond to the widths of the first and second ranges 1355 and
1358. As another example, one may use a scaled value of the
intrinsic delay of the cell or circuit under test. As yet another
example, one may use a scaled value of the clock period that clocks
the cell or circuit under test.
[0150] After establishing first and second ranges, one starts with
the values of the setup and hold constraints obtained in steps one
and two and re-positions the setup and hold constraints within the
first and second ranges 1355 and 1358, respectively. In other
words, one moves the values of the setup and hold constraints away
from clock edge 1333 in FIG. 20D. To re-position the setup and hold
constraints within the first and second ranges 1355 and 1358,
respectively, one may use any suitable search technique. The
well-known binary search constitutes one such technique, although
one may use other techniques, as desired. Note that the search
proceeds in a dependent fashion, i.e., the estimated values of the
setup and hold constraints move simultaneously as the search
progresses.
[0151] The search typically proceeds in several steps. At each step
of the search within the first and second ranges 1355 and 1358, one
performs a simulation of the circuit to determine whether it
satisfies objective criterion or criteria and/or auxiliary
measurements prescribed by the user. The objective criteria may
include, among others, whether the signal transition at the data
input of the latch causes a corresponding signal transition at the
output of the latch. The auxiliary measurements, may include, for
example, output transition time, slew rate, and switching power of
the latch, and the like, as desired.
[0152] If the output of the latch satisfies the objective criteria
(e.g., if it has a valid transition) and/or the auxiliary
measurements, then the optimized characterization technique has
acquired final values for the setup and hold constraints. On the
other hand, if the output of the latch fails to have a valid
transition, one continues to search and simulate until one reaches
the termination condition, i.e., the output has a valid transition
or the range sizes become smaller than the resolution of the
simulation. At that point, the values of setup and hold constitute
the final values of the setup and hold constraints acquired
according to optimized characterization. In summary, by adjusting
the values of the setup and hold within their respective ranges,
optimized constraint characterization avoids an invalid region of
operation of the circuit.
[0153] Another aspect of the invention concerns inter-dependent
constraint characterization. In inter-dependent constraint
characterization the edges of the meta-stable region move
simultaneously and independently relative to the reference clock
edge. In other words, inter-dependent characterization according to
the invention locates the final values of the constraints, such as
setup and hold, by simultaneously and independently adjusting the
values of the constraints. The name "inter-dependent" denotes the
fact that the technique accounts for both constraints
simultaneously, which permits the two constraints to interact with
each other (i.e., react to each other in a mutually dependent
manner).
[0154] FIG. 21 helps to illustrate inter-dependent constraint
characterization according to the invention. FIG. 21 shows a plot
of an exemplary response-surface 1368 of intrinsic delay as a
function of two constraints, here setup and hold times. The plot
shows that, when considered simultaneously, more than one
combination of the setup and hold times can lead to the same value
for the intrinsic delay for the cell or circuit. The
inter-dependent constraint characterization technique seeks to
locate the smallest possible meta-stable region, given search
conditions set by the user (e.g., delay degradation, described
below in detail).
[0155] The inter-dependent technique uses a search mechanism to
obtain successive values of the setup and hold constraints. The
inter-dependent technique characterizes or seeks to predict the
shape of the intrinsic-delay response plot 1368 as it evaluates
each combination of values for the setup and hold constraints. By
doing so, the inter-dependent characterization technique allows the
search mechanism to traverse the response surface 1368 of the
intrinsic delay, without prior knowledge of the response surface,
to locate an optimal combination of the setup and hold times.
[0156] To begin searching, inter-dependent characterization
according to the invention selects values for the setup and hold
constraints that correspond to the nominal delay of the cell or
circuit (a point at or near the beginning of path 1365 in FIG.
20D). To select those values, one may employ any of a variety of
techniques. For example, one may use a scaled value of the slowest
input slew-rate applied (or expected to be applied) to the cell or
circuit and use a search mechanism to find where the linear nominal
delay region ends. In other words, one locates a point on the
response surface 1368 where a line tangent to the surface 1368 has
a slope of unity or about unity.
[0157] One may then use a suitable search mechanisms to adjust the
values of setup and hold in a manner that generally tends toward
smaller values for setup and hold constraints. Note that generally
one may use any of a variety of suitable search techniques, as
desired. The search mechanism estimates through mathematical
analysis, for example, by using mathematical formulae, the shape of
the response surface 1368. The choice of the mathematical analysis
or formulae used depends on the technology and/or design
methodology used in the cell or circuit under test. The search
mechanism gathers and analyzes trend data to estimate the shape
(e.g., the direction of change and inflection points) of the
response surface 1368. In exemplary embodiments of the invention,
the search mechanism uses a suitable error-estimating techniques to
avoid local minima that may lead to false results.
[0158] The search mechanism in the inter-dependent characterization
technique recognizes the breakdown region of the response surface
1368 (i.e., where the measurement of intrinsic delay fails) and
takes measures to return the search to other parts of the response
surface 1368 if it encounters the breakdown point or region. The
search terminates when the search mechanism locates a valid
solution point, such as point 1371 in FIG. 20D. The valid solution
point 1371 provides valid values for the setup and hold constraints
that represent the smallest meta-stable region found from the
response surface 1368, given the search conditions that the user
has established (e.g., delay degradation, as described below in
detail).
[0159] Note that, generally, either the setup time or the hold time
may have a negative value. Both setup and hold times, however,
should not have negative values, as a negative setup time together
with a negative hold time results in a negative meta-stable region.
To avoid the negative meta-stable region, either the setup time or
the hold time (or both) should have a positive value. In other
words, a positive setup time or a positive hold time (or both)
result in a positive meta-stable region. Note that both the setup
and hold times need not have positive values to avoid the negative
meta-stable region. As long as the setup time is positive, the hold
time may be negative, and vice-versa.
[0160] Constraint characterization according to the invention
produces a positive meta-stable region. In the case of
characterizing dependent constraints, the independently
characterized constraint may have a negative value. The dependent
constraint, however, has a positive value. In the case of optimized
constraint characterization, the independently acquired initial
values of the constraints may have negative values. The third step
of the optimized constraint characterization, however, results in
positive values for one or both of the constraints.
[0161] Note that, generally, two ways exist for determining when
one should cease searching for a constraint (such as setup and
hold), i.e., the termination condition of the constraint
characterization. In other words, two techniques exist for deciding
when one has acquired the desired constraint. The first technique
uses the breakdown in the circuit's or cell's operation. The above
discussion of constraint characterization assumes use of the
breakdown point (e.g., one looks for violation of a constraint in
the form of breakdown in the circuit's response). Rather than using
breakdown, however, one may alternatively use degradation to
determine when to stop searching for a constraint.
[0162] Degradation generally refers to the change in the behavior
of a cell or circuit when an environmental condition or stimulus
approaches the cell's or the circuit's breakdown point. Even when a
circuit or cell operates within its tolerances (i.e., it has not
reached its breakdown point), it may still fail to operate
predictably because of its degraded behavior. For example, as a
cell reaches its breakdown point, it may experience degraded
intrinsic delay. Referring to FIG. 4 or FIG. 14, the cell may take
a longer period of time to produce its output in response to a
change in its inputs as a constraint time exceeds a nominal value.
As another example, the cell may experience degraded (i.e.,
increased) power consumption as it nears its breakdown point. FIG.
5, for example, shows an example of a cell that consumes more power
as the constraint time exceeds a nominal value.
[0163] The choice of using breakdown or degradation as the
termination condition depends on the type of cell or circuit that
one wishes to characterize. Under some circumstances, using
breakdown may be more appropriate, and vice-versa. As an example,
consider the situation where one wishes to characterize the hold
constraint for a latch. In that case, one sets the rising edge of
the data signal sufficiently away in time from the reference clock
edge and then sweeps (for example, by using a search mechanism) the
falling edge of the data signal toward the reference clock edge. At
some point, a violation of the hold constraint occurs. In other
words, the output of the latch shows a first transition that
corresponds to the rising edge of the data signal, but also
includes a second transition that corresponds to the violation of
the hold constraint (i.e., the latch fails to retain its intended
output signal). The second transition therefore denotes an invalid
output value, and one should not apply degradation to it because
the use of degradation implies the existence of a measurable
transition. Thus, in this example, i.e., characterizing the hold
constraint for a latch, one should use breakdown, rather than
degradation, as the termination condition.
[0164] In illustrative embodiments of the invention, the
programming of the characterization tool includes identification
and proper treatment of situations in which use of one or the other
termination condition is more appropriate than using the other
condition. Depending on the type of circuit or cell that it
characterizes, the characterization tool may therefore suggest use
of a particular termination condition to the user or automatically
use a particular termination condition according to its
programming, as desired.
[0165] One may degrade a variety of a cell's or circuit's
attributes. For example, one may degrade intrinsic delay, output
slew-rate, or power consumption. Degrading the intrinsic delay
typically produces more variation than other attributes, such as
power consumption, output slew-rate, etc. Moreover, delay is
typically the attribute of the cell or circuit that designers seek
to characterize. Output slew rate is a more sensitive attribute
than intrinsic delay, and has a relatively narrow band of
variation. The relatively narrow band of variation also typically
leads to longer simulation times because of the increased precision
and less tolerance used during simulation. Degrading the consumed
power allows designers of mobile and battery-powered equipment to
improve their characterizations of the power-consumption of the
circuits they design.
[0166] The user of the characterization tool can use degradation to
trade the predictability of the model used in characterization for
the performance of the cell or circuit characterized. In
characterizing constraints according to the invention, one may use
four degradation options: (1) absolute-from-nominal degradation,
(2) unity-slope degradation, (3) absolute-from-breakdown
degradation, and (4) normalized intersection degradation. The user
may choose any of those degradation options, as desired. In
illustrative embodiments of the invention, once the user has
selected a degradation option, the characterization tool applies
that degradation option to acquisitions of all constraints of a
given cell or circuit.
[0167] FIG. 22 shows an example of how one may use the
absolute-from-nominal degradation option. The plot in FIG. 22
represents the intrinsic delay of the cell or circuit as a function
of constraint time. The cell has a nominal delay denoted at, for
instance, point 1380 on the plot. To use absolute-from-nominal
degradation, the user specifies a scalar, which may represent a
percentage. The characterization tool calculates a degraded delay
(corresponding to point 1383 in FIG. 22) that exceeds the nominal
delay by the user-specified factor. For example, suppose the cell
has a nominal delay of 10 ns, and the user specifies a scalar of
0.1, or 10%. The tool would calculate the degraded delay as
(1.1.times.10 ns), or 11 ns. The tool uses as a target the degraded
delay rather than the nominal delay in simulations used to
characterize the cell. Put another way, the degraded delay becomes
the delay target during simulations of the cell. The
absolute-from-nominal option represents the simplest and fastest of
the degradation options. It has a drawback in that the target cell
or circuit may fail to produce an intrinsic delay equal to the
target delay before it reaches the breakdown point.
[0168] FIG. 23 illustrates an illustrative embodiment of the
unity-slope degradation option according to the invention. The plot
in FIG. 23 represents the intrinsic delay of a cell or circuit as a
function of constraint time. The cell has a nominal delay at, for
example, point 1380 on the plot. The characterization tool locates
a point 1386 where the plot of intrinsic delay has a slope of unity
or substantially close to unity. The point 1386 typically occurs at
the sharp knee in the plot of intrinsic delay. The characterization
tool uses the intrinsic delay at point 1386 as the degraded delay,
or the delay target, during its simulations of the cell or circuit.
This option provides an inherent balance between model
predictability and cell performance because it provides a degraded
delay, yet not too excessive, delay. Note that the user need not
provide a degradation target as is the case with the
absolute-from-nominal option described above; the characterization
tool performs the calculations without user input.
[0169] FIG. 24 provides an illustrative embodiment of the
absolute-from-breakdown option according to the invention. The plot
in FIG. 24 represents the intrinsic delay of the cell or circuit as
a function of constraint time. The cell has a nominal delay at, for
example, point 1380 on the plot. The cell also has a breakdown
point shown as point 1389. To use absolute-from-breakdown
degradation, the user specifies a scalar, which may represent a
percentage. In exemplary embodiments of the invention, the
user-specified scalar or percentage has a value in the range
between the nominal delay of the cell and its delay near the
breakdown point. In alternative embodiments, the user may select a
scalar or percentage that corresponds to a delay below the nominal
delay of the cell. In this scenario, the characterization tool
according to the invention includes programming code to prevent an
infinite loop (i.e., to prevent the absolute-from-breakdown
degradation option within the tool from selecting increasingly
large constraint values in an attempt to find decreasing
delays).
[0170] The characterization tool calculates a degraded delay
(corresponding to point 1392 on the plot) that is lower than
breakdown point 1389 by an amount equal to the user-specified
percentage. In other words, the absolute-from-breakdown option is
similar to the absolute-from-nominal option, except that it
calculates a degraded delay relative to, and below, the breakdown
point. The characterization tool uses the degraded delay rather
than either the nominal delay or the breakdown point in simulations
used to characterize the cell (the degraded delay becomes the delay
target during simulations of the cell). The absolute-from-breakdown
option trades model predictability with some cell performance.
[0171] FIGS. 25A and 25B shows illustrative embodiments according
to the invention of the normalized intersection option.
Conceptually, to use this option one uses values that correspond to
two plots superimposed on each other: the plot of normalized delay
and a plot of normalized constraint time plotted in reverse (i.e.,
a mirror-image plot). To generate the first plot, one normalizes
the plot of intrinsic delay with respect to the breakdown point. In
other words, one divides the values corresponding to the points
along the intrinsic delay plot by the highest delay value, i.e.,
the delay at the breakdown point. FIG. 25A shows a plot 1395 of
normalized intrinsic delay.
[0172] To generate a plot of normalized constraint time, one finds
the constraint time at point 1380, which corresponds to the nominal
delay of the cell or circuit. In other words, one projects point
1380 to the horizontal axis in FIG. 25A to find a value x.sub.1 on
that axis. One also finds the constraint time at breakdown point
1389 by projecting that point to the horizontal axis to find point
x.sub.2. By dividing x.sub.1 and x.sub.2 by x.sub.1 one arrives at
values y.sub.1 (which equals unity) and y.sub.2 (which equals 1 x 2
x 1
[0173] ). The coordinates x.sub.1 and y.sub.1 define a point 1398
in FIG. 25A. Likewise, the coordinates x.sub.2 and y.sub.2 define a
point 1401 in FIG. 25A. Next, one draws a line 1404 between points
1398 and 1401. Note that line 1404 has a mid-point 1407.
[0174] To generate a mirror-image plot, one pivots line 1404 around
its mid-point 1407 to generate line 1410, as FIG. 25B illustrates.
Put another way, line 1410 in FIG. 25B constitutes a mirror-image
with respect to mid-point 1407 of line 1407 in FIG. 25A. Plot 1395
and line 1407 intersect at point 1413, as FIG. 25B illustrates.
Point 1413 provides the value of the constraint determined by the
normalized-intersection option according to the invention. Note
that, under some circumstances, plot 1395 and line 1407 may
intersect more than once. In that scenario, the user and/or the
characterization tool should consistently choose one of the
intersections (e.g., the intersection that provides the most
predictability or the intersection that results in improved
performance of the cell or circuit, as desired). Note also that
FIGS. 22-25 show illustrative application of the degradation
options to a particular attribute, namely intrinsic delay, although
one may apply the degradation options to other attributes of a
circuit or cell, for example, output slew-rate and power
consumption, as desired.
[0175] The description of the invention included here provides
illustrative embodiments of the inventive concepts. One may readily
modify the described embodiments to produce alternative embodiments
that nonetheless fall within the scope of the invention, as persons
of ordinary skill in the art would understand. For example,
although the characterization techniques shown in the appended
figures illustrate the inventive concepts as applied to sequential
digital circuits, one may apply those concepts to combinational
circuits equally effectively. Furthermore, one may apply the
described concepts to sequential circuits other than the particular
circuits (e.g., a latch) used to illustrate the inventive concepts,
as persons skilled in the art would appreciate.
[0176] The appended figures and the description above show the
application of the invention to characterize the setup and hold
constraints. One may apply the described and illustrated inventive
concepts to the characterization of a variety of constraints, for
example, recovery, removal, minimum pulse-width, and non-critical
minimum pulse-width, and the like, by making modifications to the
illustrative embodiments presented here. Those modifications fall
within the knowledge of persons of ordinary skill in the art who
have the benefit of this description of the inventive concepts.
[0177] As noted above, during the characterization of constraints
according to the invention, one simulates the circuit or cell under
test. At each step during the acquisition of constraints where one
performs circuit simulation, one may perform auxiliary
measurements, for example, output transition time, slew rates,
switching power, hidden power, and the like, as desired. Together
with the characterization results according to the invention, the
auxiliary measurements may provide the user with further
information and insights regarding the circuit or cell under test.
The user may use the characterization results, the results of the
auxiliary measurements, or both, to make decisions regarding a
given design, as desired.
[0178] Furthermore, the description of the exemplary embodiments of
the invention refers to performing searches or sweeping various
signal edges, constraints, parameters, or attributes through
techniques that include performing searches. Note that one may use
any suitable search technique, as desired. For example, one may use
binary search, simulated annealing, simplex search, hill climbing,
or the like, as desired. The choice of a search technique or
mechanism depends on the details and desired characteristics of a
particular implementation of the inventive concepts, as persons of
ordinary skill in the art would understand.
[0179] Further modifications and alternative embodiments of this
invention will be apparent to persons skilled in the art in view of
this description of the invention. Accordingly, this description
teaches those skilled in the art the manner of carrying out the
invention and are to be construed as illustrative only.
[0180] The forms of the invention shown and described should be
taken as exemplary embodiments. Persons skilled in the art may make
various changes in the shape, size and arrangement of parts without
departing from the scope of the invention described in this
document. For example, persons skilled in the art may substitute
equivalent elements for the elements illustrated and described
here. Moreover, persons skilled in the art who have the benefit of
this description of the invention may use certain features of the
invention independently of the use of other features, without
departing from the scope of the invention.
* * * * *