U.S. patent application number 13/761679 was filed with the patent office on 2014-08-07 for distortion correction based feedforward control systems and methods for radio frequency power sources.
This patent application is currently assigned to MKS INSTRUMENTS, INC.. The applicant listed for this patent is MKS INSTRUMENTS, INC.. Invention is credited to David J. COUMOU, Larry J. FISK, II.
Application Number | 20140220913 13/761679 |
Document ID | / |
Family ID | 51135734 |
Filed Date | 2014-08-07 |
United States Patent
Application |
20140220913 |
Kind Code |
A1 |
COUMOU; David J. ; et
al. |
August 7, 2014 |
Distortion Correction Based Feedforward Control Systems and Methods
For Radio Frequency Power Sources
Abstract
A distortion module includes a first module, at least one module
and a correction module. The first module is configured to (i)
receive radio frequency signals from radio frequency sensors of a
power amplifier, and (ii) generate a distortion signal indicating
distortion values for the radio frequency signals. The radio
frequency signals are indicative of radio frequency power out of
the power amplifier and received by a transmission line. At least
one module is configured to estimate a phase of the distortion
signal. The phase of the distortion signal is indicative of a phase
of the transmission line. The correction module is configured to
generate a distortion correction signal based on the phase to
correct at least one of the distortion values of the radio
frequency signals.
Inventors: |
COUMOU; David J.; (Webster,
NY) ; FISK, II; Larry J.; (Fairport, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
MKS INSTRUMENTS, INC. |
Andover |
MA |
US |
|
|
Assignee: |
MKS INSTRUMENTS, INC.
Andover
MA
|
Family ID: |
51135734 |
Appl. No.: |
13/761679 |
Filed: |
February 7, 2013 |
Current U.S.
Class: |
455/114.3 |
Current CPC
Class: |
H03H 7/40 20130101; H01J
37/32935 20130101; H01J 37/32183 20130101 |
Class at
Publication: |
455/114.3 |
International
Class: |
H04B 1/04 20060101
H04B001/04 |
Claims
1. A distortion module comprising: a first module configured to (i)
receive radio frequency signals from radio frequency sensors of a
power amplifier, and (ii) generate a distortion signal indicating
distortion values for the radio frequency signals, wherein the
radio frequency signals are indicative of radio frequency power out
of the power amplifier and received by a transmission line; at
least one module configured to estimate a phase of the distortion
signal, wherein the phase of the distortion signal is indicative of
a phase of the transmission line; and a correction module
configured to generate a distortion correction signal based on the
phase to correct at least one of the distortion values of the radio
frequency signals.
2. The distortion module of claim 1, further comprising: a
derivative module configured to, based on the distortion values of
the distortion signal, determine derivative values of a derivative
of a distortion function or the distortion signal to generate a
derivative signal, wherein the first module is configured to
generate the distortion signal based on the distortion function; a
translation module configured to determine an offset translation
based on the derivative values of the derivative signal; and a
phase module configured to determine the phase of the distortion
signal based on the offset translation.
3. The distortion module of claim 2, further comprising: a sampling
module configured to sample the distortion signal to obtain the
distortion values; and a matrix module configured to generate a
matrix based on the derivative values of the derivative signal,
wherein the translation module is configured to generate the offset
translation based on the matrix.
4. The distortion module of claim 3, wherein the offset translation
is determined based on a least squares estimate of the matrix.
5. The distortion module of claim 4, wherein the matrix module
configured to generate the matrix based on: a predetermined number
of samples of the distortion signal; and a predetermined number of
samples of the derivative signal.
6. The distortion module of claim 2, wherein the first module is
configured to generate the distortion signal according to at least
one of (i) a sinusoidal function of the radio frequency signals and
(ii) a cross-correlation function of the radio frequency
signals.
7. The distortion module of claim 2, wherein: the phase module is
configured to generate a phase correction signal based on the
phase; and the correction module is configured to generate the
distortion correction signal based on the phase correction
signal.
8. A radio frequency system comprising: the distortion module of
claim 2; the power amplifier configured to provide an output to a
matching network via the transmission line between the power
amplifier and the matching network; and the radio frequency sensors
configured to (i) monitor the output of the power amplifier, and
(ii) generate the radio frequency signals.
9. The radio frequency system of claim 8, further comprising a
control module configured to (i) generate a impedance tuning value
based on the distortion correction signal, and (ii) provide
feedforward control of impedance matching performed within the
matching network including outputting the impedance tuning value to
one of the power amplifier and the matching network.
10. The radio frequency system of claim 9, further comprising a
gain module configured to determine a gain value based on the
derivative values of the derivative signal to account for a
resolution of an impedance tune space associated with the
transmission line, wherein the control module is configured to
generate the impedance tuning value based on the gain value.
11. The radio frequency system of claim 10, wherein the control
module adjusts coefficients of the impedance tuning value based on
the gain value.
12. A distortion module comprising: a function module configured to
(i) receive radio frequency signals from radio frequency sensors of
a power amplifier, and (ii) generate a distortion signal indicating
distortion values for the radio frequency signals based on a
distortion function; a first derivative module configured to, based
on the distortion values of the distortion signal, determine first
derivative values of a first derivative of the distortion function
or the distortion signal to generate a first derivative signal; a
second derivative module configured to, based on the first
derivative values or the first derivative signal, determine second
derivative values of a second derivative of the distortion signal
to generate a second derivative signal; a phase module configured
to (i) determine a first phase of the first derivative signal and a
second phase of the second derivative signal, and (ii) determine a
first phase correction value based on the first phase and the
second phase; and a correction module configured to generate a
distortion correction signal based on the first phase correction
value.
13. The distortion module of claim 12, further comprising: a first
comparison module configured to compare the first phase of the
first derivative signal to .pi./2 to generate a second phase
correction value; and a second comparison module configured to
compare the second phase of the second derivative signal to .pi. to
generate a third phase correction value, wherein the first phase
correction value is generated based on the second phase correction
value and the third phase correction value.
14. The distortion module of claim 13, further comprising: a first
extrapolation module configured to extrapolate the first phase of
the first derivative signal for an angular position associated with
a maximum amount of power transfer from a power generator to a
transmission line, wherein the first comparison module is
configured to generate the second phase correction value based on
the extrapolated first phase; and a second phase extrapolation
module configured to extrapolate the second phase of the second
derivative signal for the angular position associated with the
maximum amount of power transfer from the power generator to the
transmission line, wherein the second comparison module is
configured to generate the third phase correction value based on
the extrapolated second phase.
15. The distortion module of claim 14, further comprising a third
comparison module configured to compare the second phase correction
value to the third phase correction value to generate the first
phase correction value.
16. A radio frequency system comprising: the distortion module of
claim 12; the power amplifier configured to provide an output to a
matching network via a transmission line between the power
amplifier and the matching network; and the radio frequency sensors
configured to (i) monitor the output of the power amplifier, and
(ii) generate the radio frequency signals.
17. The radio frequency system of claim 16, further comprising a
control module configured to (i) generate a first impedance tuning
value based on the distortion correction signal, and (ii) provide
feedforward control of impedance matching performed within the
matching network including outputting the first impedance tuning
value to one of the power amplifier and the matching network.
18. The radio frequency system of claim 17 further comprising a
gain module configured to determine a gain value based on the
derivative values of the derivative signal to account for a
resolution of an impedance tune space associated with the
transmission line, wherein the control module is configured to
generate the impedance tuning value based on the gain value.
19. The radio frequency system of claim 18, wherein the control
module is configured to adjust coefficients of the impedance tuning
value based on the gain value.
20. A radio frequency system comprising: a power amplifier
configured to output a radio frequency signal to a matching network
via a transmission line between the power amplifier and the
matching network; a sensor configured to monitor the radio
frequency signal and generate first sensor signals based on the
radio frequency signal; a distortion module configured to determine
distortion values according to at least one of (i) a sinusoidal
function of the first sensor signals and (ii) a cross-correlation
function of the first sensor signals; a derivative module
configured to determine derivative values for a derivative of a
distortion function based on the distortion values; a gain module
configured to determine a gain value based on the derivative values
to account for a resolution of an impedance tune space associated
with the transmission line; and a control module configured to (i)
generate an impedance tuning value based on the distortion values
and the gain value, and (ii) provide feedforward control of
impedance matching performed within the matching network including
outputting the impedance tuning value to one of the power amplifier
and the matching network.
21. The radio frequency system of claim 20, wherein the power
amplifier is configured to adjust frequency of the radio frequency
signal to the matching network based on the impedance tuning
value.
22. The radio frequency system of claim 20, further comprising the
matching network, wherein the matching network is configured to
adjust an impedance in the matching network based on the impedance
tuning value.
Description
FIELD
[0001] The present disclosure relates to a radio frequency (RF)
generator and, more particularly, to tuning control of a RF
generator.
BACKGROUND
[0002] The background description provided herein is for the
purpose of generally presenting the context of the disclosure. Work
of the presently named inventors, to the extent the work is
described in this background section, as well as aspects of the
description that may not otherwise qualify as prior art at the time
of filing, are neither expressly nor impliedly admitted as prior
art against the present disclosure.
[0003] A RF power system may include a RF power supply (or RF
generator), a matching network and a load. Guided search techniques
may be used for impedance tuning the RF power supply and/or the
matching network. Impedance tuning is performed to match, for
example, an input impedance of the matching network to an impedance
of a transmission line between the RF power supply and the matching
network. This impedance matching maximizes an amount of power
forwarded to the matching network and minimizes the amount of power
reflected back from the matching network to the RF power
supply.
[0004] An example method for impedance tuning includes coarse and
fine frequency tuning the RF power supply. An objective of a
frequency tuning algorithm is to determine a frequency such that a
magnitude of a reflection coefficient of the RF power supply is at
a minimum value. The smaller the reflection coefficient, the less
power that is reflected back to the RF power supply. FIG. 1
illustrates reflection coefficient responses based on coarse and
fine tuning of the RF power supply. In FIG. 1 a reflection versus
frequency curve is shown. Coarse frequency hops are indicated by
arrows 1-5 and fine frequency hops are indicated by arrows 6-8. For
an operating frequency range F.sub.max-F.sub.min of the RF power
supply, a minimum magnitude of the reflection coefficient is at a
tune frequency F.sub.Tune. The tune frequency F.sub.Tune is located
between two approximately flat (approximately zero slope) regions
of the reflection coefficient versus frequency curve. The flat
regions may have a reflection coefficient value of one.
[0005] Typically, a frequency tuning algorithm may include a
heuristic technique to adjust the frequency to the tune frequency
F.sub.Tune. The heuristic technique commences with a first course
frequency hop as indicated by arrow 1. The first coarse frequency
hop may be performed in either direction. Based on the resulting
reflection coefficient, a next coarse frequency hop is performed.
Since the first frequency hop decreases the frequency of the RF
power, increases the reflection coefficient, and increases the
amount of reflected power, the first coarse frequency hop is not in
the correct direction (i.e. towards F.sub.Tune). The guided-search
method continues with a determination that the decrease in
frequency was inappropriate and the next course frequency hop is
performed to increase the frequency of the RF power supply. This
can return the RF power supply to an initial condition. As a
result, multiple frequency hops are performed, which decreases RF
power efficiency (ideally, reverse power is zero and all of the RF
power is applied to the load) and increases tuning time. For this
reason, a frequency tuning algorithm may be enhanced with an
initial predetermined direction of a frequency hop to provide a
more efficient path toward the minimum reflection coefficient.
[0006] The guided-search method produces subsequent course
frequency hops that increase the frequency of the RF power supply.
The action of increasing the frequency causes both the magnitude of
the reflection coefficient and reverses power to decrease. The
guided-search method continues to increase the frequency with
course updates until a predetermined tune threshold is passed. When
the guided-search method passes the predetermined tune threshold,
the next frequency hop is in a reverse direction and is a fine
frequency hop to proceed toward the tune frequency F.sub.Tune. A
result of driving the frequency past the tune frequency F.sub.Tune
there is an increase in the magnitude of the reflection coefficient
and an increase in reverse power, which decreases RF power
efficiency and increases tuning time. The guided-search method may
continue to reverse the direction and size of frequency hops until
the predetermined tune threshold is met. The frequency tuning may
require multiple passes of the predetermined tune threshold and/or
the tune frequency F.sub.Tune before being completed.
[0007] FIG. 2 provides an example illustrating effects on reverse
power associated with coarse and fine frequency tuning adjustments.
In FIG. 2 a reverse power versus tuning time curve is shown. Coarse
frequency hops are indicated by arrows 9-13. Fine frequency hops
are indicated by arrows 14-16. FIG. 2 illustrates multiple passes
of the tune frequency F.sub.Tune before completing tuning. The
reverse power may not be at a minimum level as shown in FIG. 2 when
the frequency tuning is completed. This is because the tuning is
completed when the predetermined tune threshold is no longer passed
and/or is met, which may not result in the frequency of the power
amplifier being at the tune frequency F.sub.Tune.
SUMMARY
[0008] A distortion module is provided and includes a first module,
at least one module and a correction module. The first module is
configured to (i) receive radio frequency signals from radio
frequency sensors of a power amplifier, and (ii) generate a
distortion signal indicating distortion values for the radio
frequency signals. The radio frequency signals are indicative of
radio frequency power out of the power amplifier and received by a
transmission line. At least one module is configured to estimate a
phase of the distortion signal. The phase of the distortion signal
is indicative of a phase of the transmission line. The correction
module is configured to generate a distortion correction signal
based on the phase to correct at least one of the distortion values
of the radio frequency signals.
[0009] In other features, a distortion module is provided and
includes a function module, a first derivative module, a second
derivative module, and a correction module. The function module is
configured to (i) receive radio frequency signals from radio
frequency sensors of a power amplifier, and (ii) generate a
distortion signal indicating distortion values for the radio
frequency signals based on a distortion function. The first
derivative module configured to, based on the distortion values of
the distortion signal, determine first derivative values of a first
derivative of the distortion function or the distortion signal to
generate a first derivative signal. The second derivative module is
configured to, based on the first derivative values or the first
derivative signal, determine second derivative values of a second
derivative of the distortion signal to generate a second derivative
signal. The phase module is configured to (i) determine a first
phase of the first derivative signal and a second phase of the
second derivative signal, and (ii) determine a first phase
correction value based on the first phase and the second phase. The
correction module is configured to generate a distortion correction
signal based on the first phase correction value.
[0010] In other features, a radio frequency system is provided and
includes a power amplifier, a sensor, a distortion module, a
derivative module, a gain module, and a control module. The power
amplifier is configured to output a radio frequency signal to a
matching network via a transmission line between the power
amplifier and the matching network. The sensor is configured to
monitor the radio frequency signal and generating first sensor
signals based on the radio frequency signal. The distortion module
is configured to determine distortion values according to at least
one of (i) a sinusoidal function of the first sensor signals and
(ii) a cross-correlation function of the first sensor signals. The
derivative module is configured to determine derivative values for
a derivative of a distortion function based on the distortion
values. The gain module is configured to determine a gain value
based on the derivative values to account for a resolution of an
impedance tune space associated with the transmission line. The
control module is configured to (i) generates an impedance tuning
value based on the distortion values and the gain value, and (ii)
provides feedforward control of impedance matching performed within
the matching network including outputting the impedance tuning
value to one of the power amplifier and the matching network.
[0011] Further areas of applicability of the present disclosure
will become apparent from the detailed description, the claims and
the drawings. The detailed description and specific examples are
intended for purposes of illustration only and are not intended to
limit the scope of the disclosure.
BRIEF DESCRIPTION OF DRAWINGS
[0012] FIG. 1 is a reflection coefficient versus frequency plot
associated with a traditional guided-search method;
[0013] FIG. 2 a reverse power versus tuning time plot associated
with a traditional guided-search method;
[0014] FIG. 3 is a functional block diagram of a RF power system
incorporating feedforward control in accordance with the present
disclosure;
[0015] FIG. 4 is a functional block diagram of a RF power system
incorporating feedforward control and power correction feedback
control in accordance with the present disclosure;
[0016] FIG. 5 is a functional block and schematic diagram of a
matching network;
[0017] FIG. 6 is a plot of impedance variability and distortion
function variability in accordance with the present disclosure;
[0018] FIG. 7 is a Smith chart illustrating conductance circle and
frequency tuning with respect to power distortion in accordance
with the present disclosure;
[0019] FIG. 8 is a functional block diagram of a distortion module
in accordance with the present disclosure;
[0020] FIG. 9 illustrates a single derivative based distortion
correction method in accordance with the present disclosure;
[0021] FIG. 10 illustrates a double derivative based distortion
correction method in accordance with the present disclosure;
[0022] FIG. 11 is a derivative plot of distortion functions in
accordance with the present disclosure;
[0023] FIG. 12 is a functional block diagram of a tuning correction
control module in accordance with the present disclosure; and
[0024] FIG. 13 illustrates a distortion correction based control
method in accordance with the present disclosure.
[0025] In the drawings, reference numbers may be reused to identify
similar and/or identical elements.
DESCRIPTION
[0026] Deficiencies of the guided-search method for frequency
tuning can be extended to matching network tuning algorithms.
Matching network tuning may be performed to tune an impedance of a
matching network as described above. Both frequency tuning and
matching network tuning share a mutual objective of impedance
matching such that a maximum amount of RF power is transferred from
a RF power supply to a load. The quicker that impedances are
matched and the fewer steps performed and/or guided conditions
checked, the more efficient the tuning method. For example, a
tuning method may include determining when a peak point of
operation has been met (e.g., frequency of RF power supply matches
tune frequency F.sub.Tune) and indicating when a condition of peak
power transfer no longer exists. These conditions may be checked to
determine whether further tuning is required. In U.S. patent
application Ser. No. 13/339,494, feedforward tuning techniques are
disclosed that eliminate the need to check these conditions.
[0027] The feedforward tuning techniques include correcting power
disturbance by adjusting frequency, load and tune actuators for
impedance matching. The corresponding adjustment of these
actuators, or a subset of these actuators, corrects the power
disturbance for maximum and efficient RF power transfer. The
feedforward tuning techniques include an automated calibration
process to adjust operations of control modules to compensate for
transmission line effects on RF power transfer. Calibration
processes are performed to compute frequency, tune and load
corrections to compensate for changes in a phasor associated with
transmission line effects. The transmission line effects can impair
geometrical orientations of signals originating from RF sensors,
which can increase reflected power and reduce an amount of power
transferred.
[0028] Two approaches can be performed for obtaining a maximum
amount of power transfer between an RF generator and a transmission
line, where the transmission line is used to provide power to a
dynamic load. The first approach is performed by a first RF power
system (shown in FIG. 3) and includes an RF power generator
connected to a matching network with at least two tuning elements.
The RF power generator adjusts the position (or impedance) of the
tuning elements to adjust an impedance of the matching network to
provide a maximum amount of power transfer. The tuning elements can
include variable load and tune capacitors of the matching network.
The second approach may be performed by a second RF power system
(shown in FIG. 4), which uses agile frequency of the RF generator
to adjust impedance seen by the RF generator.
[0029] Feedforward power control methods are disclosed below and in
U.S. patent application Ser. No. 13/339,494 that include frequency,
tune capacitor position and load capacitor position (or impedance)
actuators. The impedance actuators are updated to correct power
distortion, which can prevent a RF power system from transferring a
maximum amount of power with minimal reflected power. The power
control methods determine power distortion based on signals from RF
sensors located in a RF power generator. The power control methods
may be dependent on normalizing a ratio of outputs of RF sensors to
yield cos .theta..+-.jsin .theta., where .theta. is a phase angle
between the outputs of the RF sensors.
[0030] For example, if a RF sensor is a type VI sensor, power
distortion d may be computed as a ratio by relationship
d = z .fwdarw. z = j .theta. , ##EQU00001##
where
z .fwdarw. = v .fwdarw. i .fwdarw. = z j .theta. , ##EQU00002##
z is impedance of the transmission line, v is a voltage output as
detected by the RF sensors, and i is a current output as detected
by the RF sensors. If the RF sensor is a directional coupler, power
distortion d is computed as a ratio by relationship
d = .GAMMA. .fwdarw. .GAMMA. = j .theta. , ##EQU00003##
where
.GAMMA. .fwdarw. = P .fwdarw. r P .fwdarw. f = .GAMMA. j .theta. ,
##EQU00004##
.GAMMA. is a reflection coefficient, P.sub.r is reverse power, and
P.sub.f is forward power. In this normalized form, the feedforward
control module performs a correction by applying an imaginary
quantity (d.sub.f=d.sub.t=sin .theta.) to the tune or frequency
impedance actuators (or tune and frequency elements), and a real
quantity (d.sub.i=cos .theta.) is used to apply a correction to the
load impedance actuator. Directly, determination of impedance (in
the case of the VI sensor) or the reflection coefficient (in the
case of the directional coupler) is not required. The angular
component .theta. may be determined instead.
[0031] The following described techniques include enhancements to
the above-described control method and include adaptation of
parameters of control modules. The adaptation of these parameters
alleviates manual intervention to initiate a corresponding
calibration process. Coefficients of the control modules are
adapted for improved tuning performance.
[0032] In FIG. 3, a RF power system 10 is shown. The RF power
system 10 includes a RF generator 12, a matching network 14, and a
load 16 of the matching network 14. The RF generator 12 generates a
RF power signal 17, which is provided to the matching network 14.
The matching network 14 matches an input impedance of the matching
network 14 to a characteristic impedance of a transmission line 18
between the RF generator 12 and the matching network 14. Put
another way, the matching network 14 matches an impedance of the
load 16 to an impedance as seen by the output of the RF generator
12. The matching network 14 and the load 16 may be considered as
the load on the RF generator 12. The load 16 may be, for example, a
plasma chamber or other RF load. The impedance of the load 16 may
be static (i.e. unchanging over time) or dynamic (i.e. changing
over time).
[0033] The RF generator 12 includes a RF power source 20 (or a
power amplifier) and a feedback loop 22. The power amplifier 20
generates the RF power signal 17, which is outputted to the
matching network 14. The power amplifier 20 may generate the RF
power signal 17 based on a power signal received from a power
source 24 external to the power amplifier 20. Although the power
source 24 is shown as part of the RF generator 12, the power source
24 may be external to the RF generator 12. The power source 24 may
be, for example, a direct current (DC) power source.
[0034] The feedback loop 22 includes one or more sensors (first
sensors) 26, a scaling module 28, a first summer 30, and a power
control module 32. The sensors 26 may include voltage, current
and/or directional coupler sensors. The sensors 26 may detect (i)
voltage V and current/output of the power amplifier 20, and/or (ii)
forward (or source) power P.sub.FWD out of the power amplifier 20
and/or RF generator 12 and reverse (or reflected) power P.sub.REV
received from the matching network 14. The voltage V, current I,
forward power P.sub.FWD, and reverse power P.sub.REV may be scaled
and/or filtered versions of the actual voltage, current, forward
power and reverse power of the output of the power amplifier 20.
The sensors 26 may be analog and/or digital sensors. In a digital
implementation, the sensors 26 may include analog-to-digital (A/D)
converters and signal sampling components with corresponding
sampling rates.
[0035] The sensors 26 generate sensor signals 33, which are
received by the scaling module 28. The scaling module 28 scales the
sensor signals 33 and generates a power feedback signal 34. The
power feedback signal 34 is generated based on the sensor signals
33 and a scaling matrix. The power feedback signal 34 may represent
the forward power for forward power leveling deliver power. The
power feedback signal 34 may represent the RF power transferred to
the matching network 14 or load power P.sub.d and can be
represented by equation 1, where V is voltage output of the power
amplifier 20 and/or RF generator 12, l is current out of the power
amplifier 20 and/or RF generator 12, and .THETA. is a phase
difference between the voltage and the current outputs V, l of the
power amplifier 20.
P.sub.d=|V.parallel.I|cos(.THETA.)=P.sub.FWD-P.sub.REV (1)
[0036] The first summer 30 sums the power feedback signal 34 with a
predetermined power setpoint signal 36, which may be generated by a
power setpoint module 38. The power feedback signal 34 may be
subtracted from the predetermined power setpoint signal 36 to
generate an error signal e.sub.fb.
[0037] The power control module 32 receives the error signal
e.sub.fb and generates a power control signal u.sub.fb.sup.p to
regulate power out of the power amplifier 20. The power control
signal u.sub.fb.sup.p is provided to the power amplifier 20. The
power amplifier 20 adjusts the RF power signal 17 based on the
power control signal u.sub.fb.sup.p. The RF power signal 17 may be
a continuous waveform or a pulsed waveform. The servo control
described herein allows for the RF power signal 17 to be pulsed due
to the update rate associated with the servo control. The power
control module 32 may include a proportional integral derivative
(PID) controller and/or a direct digital synthesis (DDS)
component(s). In one implementation, the power control module 32 is
a first PID controller with a function identified as
D.sub.fb.sup.p(z). The power control signal u.sub.p.sup.fb may be a
drive signal and have a DC offset or rail voltage, a frequency and
a phase. However, the power control signal u.sub.fb.sup.p does not
adjust frequency of the RF power signal 17.
[0038] The RF generator 12 may further include a first feedforward
loop 40 and a second feedforward loop 42. The first feedforward
loop 40 includes a distortion module 44 and a first correction
circuit 46. The distortion module 44 determines a distortion value
d.sub.t (referred to as d or d.sub.i with respect to FIGS. 5-13
below) representative of the distortion as seen at the output of
the power amplifier 20 and/or RF generator 12. The first distortion
value d.sub.t is generated based on the sensor signals 33 and a
distortion function. The distortion function is described in more
detail below. The first correction circuit 46 generates a first
power tuning value (or first impedance tuning value) u.sub.ff.sup.t
based on the first distortion value d.sub.t. The tuning value
u.sub.ff.sup.t is provided to the matching network 14 for frequency
response tuning and impedance adjusting purposes. The distortion
module 44 may determine the first distortion value d.sub.t based on
a sinusoidal function and/or a cross-correlation function.
Sinusoidal Function
[0039] Multiple techniques are disclosed herein that include
maximizing optimal power transfer in an RF power system with a
dynamic load (i.e. a load having varying impedance(s)). A first
technique, which is described with respect to FIG. 3 includes the
RF power source 24 connected to the matching network 14. The
matching network 14 may include an impedance matching circuit 50
with two or more variable tuning elements 52 (e.g., variable
capacitors). The variable tuning elements 52 may be in a
`L`-configuration (one capacitance in parallel with the RF
generator 12 and one capacitance in series with the load 16). The
variable tuning elements 52 are used for adjusting tune and load
parameters of the matching network 14, and may have respectively an
associated tune input 54 and load input 56. The tune and load
parameters refer to impedance adjustments performed in the matching
network 14 via the variable tuning elements 52. As an example, the
tune parameter and the load parameter may be associated with
respective capacitances of capacitors in the matching network
14.
[0040] A second technique, which is described with respect to FIG.
4, introduces a variable frequency adjustment to the power
amplifier 20 and may be used alternatively or in combination with
the first technique. The tune and load parameters may each be
fixed, discretely selectable, and/or adjustable when using the
second technique.
[0041] In both the first and second techniques, the RF power
transferred P.sub.d from the power amplifier 20 to the matching
network 14 is maximized. This may occur when the forward power
P.sub.FWD to the matching network 14 is maximized and/or the
reverse power P.sub.REV from the matching network is minimized. The
RF power transferred P.sub.d may be represented by equation 2. A
maximum RF power transferred P.sub.MAX may be represented by
equation 3.
P.sub.d=|V.parallel.I|cos(.THETA.) (2)
P.sub.MAX=max(|V.parallel.I|cos(.THETA.))=max(P.sub.FWD)-min(P.sub.REV)
(3)
[0042] The RF power transferred P.sub.d is maximized when the phase
.THETA. is as close to zero as systematically achievable for a RF
power system 10 providing power to a reactive load or reactive
impedance (e.g., the load 16). A reactive impedance refers to a
load with changing impedance. The first and second techniques
minimize the phase .THETA. by adjusting the tune and load
parameters of the matching network 14. Since the phase .THETA. is
dependent on the reactive impedance, reduction in the phase .THETA.
is a function of frequency f of the power amplifier 20. As a
result, phase reduction can be performed as a function of the
frequency f or in other words, the phase .THETA. can be reduced to
or nearly 0 by adjusting the frequency f of the power amplifier 20
and thus the output frequency f of the power amplifier 20.
Frequency adjustment is provided by the implementations of FIG.
4.
[0043] Although the first and second techniques can be used to
minimize the phase .THETA., the techniques do not directly detect
or adjust the phase .THETA.. The techniques may include determining
cos (.THETA.) (referred to herein as "the cosine function"), sin
(.THETA.) or 1-sin.sup.2.THETA. (referred to herein as "the sine
function"), and/or another primary and/or sinusoidal function. The
phase .THETA. may be referred to as a secondary function. The first
distortion value d.sub.t is determined via the distortion module 44
using vector calculus without determining the phase .THETA.. The
first distortion value d.sub.t may be equal to and/or be
represented by the sinusoidal function.
[0044] As an example, the cosine function cos (.THETA.) for two
independent variables X, Y may be represented by, for example,
equation 4, where X may be voltage or reverse power, Y may be
current or forward power, and XY is a dot product of X and Y.
cos ( .THETA. ) = XY X 2 Y 2 ( 4 ) ##EQU00005##
The sine function 1-sin.sup.2 .THETA. may be determined based on
one of the equations 5 and 6.
sin ( .THETA. ) = X Y X 2 Y 2 ( 5 ) sin ( .THETA. ) = ( X Y - XY )
1 2 X 2 Y 2 ( 6 ) ##EQU00006##
[0045] One technique disclosed herein includes maximizing power
transfer to the matching network 14 by maximizing the cosine
function cos(.THETA.). As an example, the variables X and Y may be
substituted for voltage V and current l, and cos(.THETA.) may be
calculated directly using a closed form solution to control the
frequency f of the power amplifier 20. The cosine function is
maximized to maximize the power transferred. This technique may be
performed digitally using, for example, digital circuitry and/or a
PID controller.
[0046] An example analog technique includes using directional
coupler sensors to detect the reverse power P.sub.REV and the
forward power P.sub.FWD. The variable X of expression 4 may be
replaced with the reverse power P.sub.REV and the variable Y of
expression 4 may be replaced with the forward power P.sub.FWD. A
reflection coefficient .GAMMA. of the transmission line 18 is a
function of the reverse power P.sub.REV and the forward power
P.sub.FWD. The reflection coefficient .GAMMA. may be represented by
the reverse power P.sub.REV divided by the forward power P.sub.FWD
and or by equation 7, where z.sub.l is the impedance of the load on
the RF generator 12 (i.e. the matching network 14 and the load 16)
and z.sub.0 is the impedance of the transmission line 18.
.GAMMA. = z l - z 0 z l + z 0 ( 7 ) ##EQU00007##
[0047] The techniques disclosed herein enable autonomous servo of
an agile frequency RF power source (power amplifier 20) for
maximized power transfer. Although servo control includes feedback
and feedforward control, the feedforward control provided herein
aids in quickly maximizing the power transferred to the matching
network 14. These techniques include determining distortion of a RF
power system (RF power system 10) and providing feedforward
correction using vector calculus. The distortion refers to the
reflected power due to the reactive change in load impedance, which
is directly related to the sinusoidal function of the phase
.THETA..
Cross Correlation
[0048] As an alternative to and/or in addition to using a
sinusoidal function, a cross-correlation function may be used to
determine the first distortion value d.sub.t. The energy of a
signal s(t) may be represented by equation 8 using vector calculus,
where t is time.
s(t)=.intg..sub.-.infin..sup..infin.s.sup.2(t)dt (8)
[0049] To compute energy for a change in load impedance or an arc
disturbance of a load, the energy exhibited by a RF power system is
based on two parameters. The two parameters may be determined based
on signals from RF sensors (such as the sensors 26). The RF sensors
may be, for example, voltage and current sensors or directional
coupler sensors that are used to acquire voltage, current and/or
power samples of a transmission line. Signals from the RF sensors
are oscillating continuous time signals, which may be arbitrarily
designated as x(t) and y(t), which correspond to the above
variables X and Y. The corresponding digital version of these
oscillating continuous time signals is x(n) and y(n). A
discrete-time cross correlation value r.sub.xy(.tau.) of the
signals x(n) and y(n) may be represented by equation 9, where
.mu..sub.x represents the average of the signal x(n), .mu..sub.y
represents the average of the signal y(n), and .tau. represents an
overlap of and/or shift in time between the signals x(n) and
y(n).
r xy ( .tau. ) = .A-inverted. n ( x [ n ] - .mu. x ) ( y [ n -
.tau. ] - .mu. y ) ( 9 ) ##EQU00008##
[0050] Power p associated with the two signals x(n) and y(n) can be
determined when .tau. is equal to 0. The two signals x(n) and y(n)
completely overlap in time when .tau. is equal to 0. Energy
E.sub.xy for an impedance changing event can be represented by
equation 10 and as a function of the power p, where b identifies a
block number, T.sub.b is a duration time of each block, K is a
total of non-overlapping blocks of samples of the two signals x(n)
and y(n), and k identifies a current block and/or sample.
E xy = T b k = 1 K ( p [ k ] - p [ k - 1 ] ) ( 10 )
##EQU00009##
[0051] The dot product XY may be determined based on the
cross-correlation value when .tau. is equal to 0. The dot product
XY is directly related to the cross-correlation value when .tau. is
equal to 0. Also, the power p (or P.sub.d) is related to the dot
product XY by substituting equation 2 into equation 4. Based on the
discrete-time cross correlation value r.sub.xy(.tau.), the power p
(or P.sub.d), and the dot product XY the distortion value of the
sinusoidal function (e.g., the cosine function or the sine
function) may be determined based on vector calculus.
[0052] The distortion module 44 may determine the first distortion
value d.sub.t based on the discrete-time cross correlation value
r.sub.xy(.tau.) when .tau. is not equal to 0. The distortion module
44 may not determine the first distortion value d.sub.t based on
the discrete-time cross correlation value r.sub.xy(.tau.) when
.tau. is equal to 0. As shown above, this cross-correlation
technique may be used to derive a sinusoidal function between two
wideband signals x(t) (e.g., V or P.sub.REV) and y(t) (e.g., I or
P.sub.FwD), which is representative of characteristics of the
transmission line 18.
[0053] The sinusoidal function may be used as described below for
autonomous control of a variable frequency RF power source to
maximize power transfer. The sinusoidal function is used in
feedforward control to correct distortion impinged on power
regulation when the frequency of the RF power source (or power
amplifier) achieves a power transfer that is less than a maximum
power transfer. This correction is immune to spectral interference
due to harmonics or intermodulation distortion. For this reason,
this technique is useful for dynamic load conditions and RF power
applications requiring frequency tuning responses of a RF power
source within a predetermined period (e.g., less than 3
microseconds (.mu.s)) with a predetermined update rate (e.g., less
than 1 .mu.s). Frequency tuning of a RF power source is described
primarily with respect to FIG. 4.
[0054] Referring again to FIG. 3, in one implementation, the first
correction circuit 46 includes a first input module 60, a second
summer 62 and a tune control module 64 (or D.sub.ff.sup.t (z)). The
first input module 60 may generate a first predetermined value
(e.g., 0 when determining the distortion value d.sub.t according to
the sine function or 1 when determining the distortion value
d.sub.t according to the cosine function). The second summer 62 may
subtract the first distortion value d.sub.t from the first
predetermined value to generate a tuning or first correction value
c.sub.t. The tune control module 64 may include a second PID
controller and generate a power tuning value (or first impedance
tuning value) u.sub.ff.sup.t based on the first correction value
c.sub.t. The tune control module 64 may adjust the impedance tuning
value u.sub.ff.sup.t to match the first distortion value d.sub.t
with the first predetermined value. The tune control module 64 may
generate and/or receive the first predetermined value.
[0055] The second feedforward loop 42 may include the distortion
module 44 and a second correction circuit 72. The distortion module
44 determines a ratio of magnitudes (or second distortion value)
d.sub.l based on the sensor signals 33 and a second distortion
function. The second distortion function may be represented by
equation 11.
d l = X 2 Y 2 ( 11 ) ##EQU00010##
The first and second distortion values d.sub.t,d.sub.l each provide
an indication of distortion and/or associated parameters, as
measured by the sensors 26.
[0056] The second correction circuit 72 may include a load setpoint
module 76, a third summer 78 and a load control module 80, which
may be represented as a function D.sub.ff.sup.t(z). The load
setpoint module 76 may generate a predetermined load setpoint value
(e.g., 50 Ohms(.OMEGA.)). The third summer 78 may subtract the
second distortion value d.sub.l from the load setpoint value to
generate a load correction value (second correction value)
c.sub.l.
[0057] The load control module 80 may include a third PID
controller and may generate a power load value (or second impedance
tuning value) u.sub.ff.sup.t based on the second correction value
c.sub.l. The load control module 80 may adjust the power load value
u.sub.ff.sup.t to match the second distortion value d.sub.l to the
load setpoint value. The load control module 80 may generate and/or
receive the load setpoint value.
[0058] The tune control module 64 and the load control module 80
are coupled, as represented by arrow 82. The arrow 82 represents a
mutual coupling between the tune and the load inputs 54, 56 of the
matching network 14. The power load value u.sub.ff.sup.t is
affected (or indirectly adjusted) when the power tune value
u.sub.ff.sup.t is directly adjusted by the tune control module 64.
Similarly, the power tune value u.sup.t is affected (or indirectly
adjusted) when the power load value u.sub.ff.sup.t is directly
adjusted by the load control module 80. The tune and load inputs
54, 56 are adjusted respectively by the power tune value
u.sub.ff.sup.t and the power load value u.sub.ff.sup.t.
[0059] The matching network 14 may also include second sensors 90.
The second sensors 90 may include phase and magnitude sensors,
which are used by the impedance matching circuit 50 to adjust the
tune and load inputs 54, 56. The impedance matching circuit 50 may
adjust the tune and load inputs 54, 56 such that the load 16 and
the matching network 14 have an impedance as seen by the power
amplifier 20 and/or the RF generator 12 matching the impedance of
the transmission line 18. The tune and load inputs 54, 56 may be
adjusted until phase of the RF power signal 17 is 0 and impedance
of the matching network 14 is at a predetermined impedance (e.g.,
50.OMEGA.). This aids in minimizing the reverse power P.sub.REV,
which maximizes power transferred to the matching network 14. The
second sensors 90 may be electrically coupled to the transmission
line 18 and used to detect the distortion (or P.sub.REV) of the RF
power system 10. The tune and load adjustments performed by the
impedance matching circuit 50 based on the outputs of the second
sensors 90 do not need to fully maximize the power transferred, as
the feedforward loops 40, 42 further aid in maximizing the power
transferred.
[0060] The second sensors 90 may be located at an input of the
matching network 14, not at an output of the matching network 14 to
quantify the distortion of the RF power system 10 as a function of
the reverse power P.sub.REV. The impedance matching circuit 50 may
apply a feedforward match correction u.sup.m.sub.ff to correct an
impedance mismatch between the matching network 14 and the
transmission line 18. Collective power transfer contributions by
the power control module 32 and the matching network 14 (and/or
controller of the matching network 14) to power delivery may be
analytically represented as a vector u including the compensation
(power regulation) and correction (matching network tuning) values
provided by these controllers. This vector is represented by
equation 12.
u=[u.sub.p.sup.fbu.sup.m.sub.ff] (12)
[0061] The tune and load control modules 64, 80 provide the
distortion corrections values u.sub.ff.sup.t and u.sup.l.sub.ff,
which are provided to the tune and load inputs 54, 56. The match
correction value u.sup.m.sub.ff may be expressed as a vector
including quantities, as represented by equation 13.
u.sup.m.sub.ff=[u.sub.ff.sup.tu.sub.ff.sup.t] (13)
Without the distortion correction of the matching network 14, there
can be a loss in the RF power system 10 if feedback control is used
without feedforward control. The second sensors 90 may be coupled
to the transmission line 18 to measure impedance or a reflection
coefficient, which may be used to minimize the reverse power
P.sub.REV. The second sensors 90 may be referred to as phase and/or
magnitude detectors. The matching network 14 may not correct all of
the distortion, as other feedforward control is provided via the
feedforward loops 40, 42. The matching network 14 may adjust the
tune and load inputs 54, 56 based on the measured impedance or
reflection coefficient. The distortion correction as performed by
the matching network 14 may be limited and may not reduce the
reverse power P.sub.REV to 0 due to model imperfections and/or a
measurement error. The feedforward correction provided by the
feedforward loops 40, 42 may further correct the distortion and
reduce the reverse power P.sub.REV to 0.
[0062] To reduce the number of sensors incorporated in the RF power
system 10, the first sensors or the second sensors may not be
included. The remaining sensors included in the RF power system 10
and the corresponding signals and/or parameter actuators are
accessible to the RF generator 12 and the matching network 14. As
an example, sensor and controller consolidation may be achieved by
deploying power delivery feedforward correction within the RF
generator 12.
Autonomous Control of Agile RF Power Source
[0063] The phase of the signals x(t) and y(t) has a relationship,
which may be represented by equation 14, where W is equal to the
dot product XY.
W=.parallel.X.sub.2.parallel.Y.parallel..sub.2 cos(.THETA.)
(14)
The cosine function may be used to represent distortion upon which
feedforward correction is based. This feedforward correction may be
used when the sensors used to determine the distortion value of the
cosine function are (i) voltage and current sensors or (ii)
directional coupler sensors. As an example, the voltage and current
signals are in phase when the load impedance matches the
characteristic impedance of the transmission line 18.
[0064] Based on the complex reflection coefficient .GAMMA., which
is a ratio of the reverse power P.sub.REV to the forward power
P.sub.FWD, a phase difference between the reverse power P.sub.REV
and the forward power P.sub.FWD is minimized and/or P.sub.REV is
reduced to 0. When voltage and current sensors are used, a phase
difference between the voltage and phase signals is also minimized
and/or reduced to 0. This leads to a control law represented by
equation 15, wherein cos(.THETA.).sub.d is a desired or
predetermined value and cos(.THETA.).sub.a is an actual and/or
calculated value.
cos(.THETA.).sub.d-cos(.THETA.)).sub.a=1-cos(.THETA.),.sub.a
(15)
Minimizing the phase difference between the sensor signals
minimizes and/or reduces the distortion to 0.
[0065] In a directional coupler sensor implementation, it is
feasible for an offset to occur in a primary conductance circle
from an admittance grid of a Smith chart. The primary conductance
circle refers to a circle that passes through an origin in a
complex reflection coefficient grid of the Smith chart. The load of
the matching network 14 is set such that the tune input 54 when
adjusted causes the reflection coefficient .GAMMA. as mapped to a
unit circle of the Smith chart to follow a conductance circle and
pass through the origin. At the origin, the impedance of the
matching network 14 matches the characteristic impedance of the
transmission line 18.
[0066] As another example, the frequency of the power amplifier 20
may be servo controlled to adjust the impedance and/or reflection
coefficient .GAMMA. to an intersection of a real axis of the Smith
chart in a complex plane of the reflection coefficient .GAMMA..
Frequency adjustment of the power amplifier 20 is described below
with respect to FIG. 4. For a directional coupler sensor
implementation, the phase difference is adjusted to .+-..pi..
Taking advantage of the symmetrical nature of the cosine function,
the control law is revised and may be represented by equation
16.
cos(.THETA.).sub.d-cos(.THETA.).sub.a=1-|cos(.THETA.).sub.a|
(16)
[0067] For a voltage and current sensor implementation, the primary
conductance circle may not intersect the origin and exhibit a
rotational offset due to systematic variation in the RF power
system 10 and the load to be matched. The cosine function may be
reduced to a non-zero value producing a small error in
cos(.THETA.).sub.d-cos(.THETA.).sub.a. This is one of several
benefits in contrast to measuring the phase directly.
[0068] For an expedient search to a maximum power transfer state,
the feedforward control follows a trajectory along the conductance
circle to minimize the distance to the origin and to assure that
the origin is reached or the real axis is intersected near the
origin. Since the feedforward control includes using vector
calculus to measure the cosine function including determining a
ratio of magnitudes of X and Y, a quantitative measure of
directivity is provided. The ratio of magnitudes provides a
quantitative measure for directivity. Directivity may refer to a
tuning direction or a direction in which a correction value is
adjusted, and be based on an increasing or decreasing distortion
value.
[0069] The use of the sine function instead of the cosine function
can also provide directivity. The cosine function does not directly
imply directivity, whereas the sine function does, as the output of
the sine function may be compared to 0 and the output of the cosine
function may be compared to 1. Equation 13 may be modified as
follows to provide directivity. Both sides of equation 4 may be
squared to provide cos.sup.2(.THETA.). The square of the cosine
function cos.sup.2(.THETA.) is equal to 1 minus the square of the
sine function (1-sin.sup.2(.THETA.)). The control law provided by
equation 16 may then be modified as shown by equation 17.
cos(.THETA.).sub.d-cos(.THETA.).sub.a=1-|sin.sup.2(.THETA.).sub.a|
(17)
[0070] When directional coupler sensors are used, impedance of the
matching network 14 and/or frequency of the power amplifier 20 may
be adjusted such that the ratio of magnitudes is reduced to a
minimum value. Reducing the ratio of magnitudes indicates that the
impedance and/or frequency adjustments are tending to a maximum
power transfer. As an alternative to and/or in addition to
determining the ratio of the magnitudes, a magnitude of the reverse
power P.sub.REV may be monitored and minimized. When voltage and
current sensors are used, the impedance and/or frequency
adjustments are performed such that the ratio of the magnitudes
tends to the characteristic impedance of the transmission line
18.
[0071] As described herein, techniques are provided to correct a
power mismatch using servo tunable elements based on a ratio of
magnitudes of RF sensor outputs and a sinusoidal calculation based
on the RF sensor outputs. Although the update rate is faster in a
digital sampling system than for mechanically tunable circuit
elements, analog components may be used for a frequency tunable
power source.
[0072] Instead of or in addition to adjusting the tune and load
inputs 54, 56, frequency of the power amplifier 20 may be adjusted
within a predetermined frequency range. Agile frequency control may
be provided using feedforward control complementing feedback power
control. If the load impedance of the RF generator 12 varies, the
power control module 32 may not be able to correct for this change
and/or may be limited in correcting for this change. By determining
the sinusoidal function, an estimate of the distortion imposed by
an impedance disturbance is determined. To further correct for the
change in load, the frequency drive of the power amplifier and/or
the frequency of the RF power signal may be adjusted based on the
sinusoidal function to further counter the reactive distortion to
the load. This is described in further detail below with respect to
FIG. 4.
[0073] In FIG. 4, a RF power system 100 is shown. The RF power
system 100 includes a RF generator 102, the matching network 14
with the impedance matching circuit 50 and the second sensors 90,
and the load 16. The RF generator 102 generates a RF power signal
104, which is provided to the matching network 14. The RF generator
102 includes a RF power source (or a power amplifier) 106 and the
feedback loop 22. The power amplifier 106 generates the RF power
signal 104, which is an output to the matching network 14. The
power amplifier 106 may generate the RF power signal 104 based on
(i) a power signal received from the power source 24 external to
the power amplifier 106, and/or (ii) a frequency tuning value
u.sub.ff.sup.t. The power source 24 may be, for example, a direct
current (DC) power source.
[0074] The feedback loop 22 includes the sensors 26, the scaling
module 28, the first summer 30, and the power control module 32.
The sensors 26 generate the sensor signals 33, which are received
by the scaling module 28. The scaling module 28 scales the sensor
signals 33 and generates the power feedback signal 34. The power
feedback signal 34 is generated based on the sensor signals 33 and
the scaling matrix. The first summer 30 sums the power feedback
signal 34 with the predetermined power setpoint signal 36, which
may be generated by the power setpoint module 38. The power
feedback signal 34 may be subtracted from the predetermined power
setpoint signal 36 to generate the error signal e.sub.fb.
[0075] The power control module 32 receives the error signal
e.sub.fb and generates the power control signal u.sub.fb.sup.p to
regulate power out of the power amplifier 106. The power amplifier
106 adjusts the RF power signal 104 based on the power control
signal u.sub.p.sup.fb and the frequency tuning value
u.sub.ff.sup.ff. The RF power signal 104 may be a pulsed waveform
and have a frequency set based on the frequency tuning value
u.sub.ff.sup.ff.
[0076] The RF generator 12 may further include the first
feedforward loop 40, the second feedforward loop 42, and a third
feedforward loop 110. The RF power system 10 may include the third
feedforward loop 110 and not the first and second feedforward loops
40, 42 or may include the first, second and third feedforward loops
40, 42, 110, as shown. The first feedforward loop 40 includes the
distortion module 44 and the first correction circuit 46 with the
first input module 60, the second summer 62 and the tune control
module 64. The second feedforward loop 42 may include the
distortion module 44 and the second correction circuit 72 with the
load setpoint module 76, the third summer 78 and the load control
module 80.
[0077] Although the third feedforward loop 110 may have the
appearance of a feedback loop, the third feedforward loop 110
performs as a feedforward loop and performs a feedforward function
and is thus referred to herein as a feedforward loop. The third
feedforward loop 110 provides the frequency tuning value
u.sub.ff.sup.ff which is used to adjust frequency of the RF power
signal 104. By adjusting the frequency of the RF power signal 104,
frequency responses of the matching network 14 changes, which
alters impedances in the matching network 14. These impedance
changes affect impedance matching between the matching network 14
and the transmission line 18, which affects the amount of reverse
power P.sub.REV and the amount of power transferred P.sub.d.
[0078] The third feedforward loop 110 includes the distortion
module 44 and a third correction circuit 112. The third correction
circuit 112 includes a second input module 114, a fourth summer 116
and a frequency control module 118, which may be represented as a
function D.sup.f.sub.ff(z). The second input module 114 generates a
third predetermined value (e.g., 1). The fourth summer 116 may
subtract the distortion tuning value d.sub.t from the third
predetermined value to generate a third correction value c.sub.f.
The frequency control module 118 may include a fourth PID
controller and generate the frequency tuning value u.sub.ff.sup.ff
based on the third correction value c.sub.f. The frequency control
module 118 may adjust the frequency tuning value u to match the
first distortion value d.sub.t to the third predetermined value.
The frequency control module 118 may generate and/or receive the
third predetermined value.
[0079] Referring also to FIG. 5, an example matching network 150 is
shown, which may be used to replace the matching network 14 of
FIGS. 3-4. The matching network 150 may include a tune variable
impedance 152, a load variable impedance 154, and a load output
impedance 156. The tune variable impedance 152 may be connected to
a transmission line (e.g., the transmission line 18). The tune
variable impedance 152 may include a first variable capacitance.
Impedance of the tune variable impedance and/or capacitance of the
first variable capacitance may be adjusted based on the impedance
tuning value u.sub.ff.sup.t. The load variable impedance 154 may be
connected to the transmission line and the tune variable impedance
152. The load variable impedance may include a second variable
capacitance. Impedance of the load variable impedance and/or
capacitance of the second variable capacitance may be adjusted
based on the power load value u.sub.ff.sup.t.
[0080] The matching network 150 may further include a load
inductance L.sub.l and a tune inductance L.sub.t. The load
inductance L.sub.l may be connected between the load variable
impedance 154 and a ground reference 158. The tune inductance
L.sub.t may be connected between the tune variable impedance 152
and the load output impedance 156. The load output impedance 156
may be connected between the tune inductance L.sub.t and the load
16.
[0081] The above-described feedforward techniques send a power
tuning value and a load tuning value to a matching network for
tuning elements of the matching network and/or a frequency tuning
value to a power amplifier. These feedforward techniques are
dependent on normalizing an impedance measurement to yield cos
.theta.+jsin .theta., where .theta. is the phase angle between
sensor output signals. In this normalized form, control modules
perform corrections by using (i) an imaginary quantity to apply a
correction to a tune element or a frequency element, and (ii) a
real quantity to apply a correction to the load element.
[0082] The feedforward techniques may not include determining
transmission line impedance. The phase angle .theta. may simply be
determined based on a relationship for impedance and a relationship
for a normalized distortion ratio. The impedance relationship
is
z .fwdarw. = v .fwdarw. i .fwdarw. = z j .theta. . ##EQU00011##
The relationship for normalized distortion ratio is
d = z .fwdarw. z = j .theta. . ##EQU00012##
This normalized distortion ratio can include a square root function
in a denominator term. An alternate normalization procedure
includes determining distortion based on
d = z .fwdarw. - x z .fwdarw. + x .apprxeq. j .theta.
##EQU00013##
for a suitable complex quantity x. The complex quantity x is
further defined as a matrix below. The alternate normalization
procedure alleviates use of the square root function for processing
RF sensor signals.
[0083] Processing of the RF sensor signals to determine the
distortion d is dependent on the orientation of the complex
quantity x in a complex plane. Ideally, the trajectory of d lies in
a left-hand portion of the complex plane (i.e., left of a real zero
axis of the complex plane and referred to as the left-hand plane)
and an intersection of the trajectory with the real zero axis
occurs at a location for maximum power transfer. This intersection
corrects the tune impedance element in the matching network or the
frequency element of a RF generator for maximum power transfer.
Impedance of a transmission line between the RF generator and the
matching network affects the trajectory of the distortion d.
Variation in velocity of propagation V.sub.P and/or length l of the
transmission line can rotate orientation of a path of the
distortion d, which is indicated by phase .phi.. The phase .phi.
may be equal to, for example,
30.5 lf V p . ##EQU00014##
[0084] The length l alone does not fully characterize the effect of
the transmission line between the RF generator and the matching
network. The phase .phi. increases proportionally with frequency f
and inversely proportionally with the velocity of propagation
V.sub.p. More importantly to the feedforward control techniques is
the rotational effect the transmission line has on the
normalization procedure. Impedance transformation may not be
performed when performing the feedforward control techniques. The
rotational effect caused by the transmission line is corrected by
estimating a phasor {circumflex over (.phi.)} of the transmission
line and applying this to provide a distortion correction using the
relationship d.sub.c=de.sup.-j.sup.({circumflex over
(.phi.)}+.pi.). The distortion correction d.sub.c is applied such
that the trajectory path of the distortion correction d.sub.c is
contained in the left-hand plane. The estimation of phasor
{circumflex over (.phi.)} may also include systematic effects
contributed by RF sensors and associated signal processing
circuitry. RF sensor signals {right arrow over (v)} and {right
arrow over (i)} may be signals that are calibrated to a common
reference plane and used to determine the distortion d.
[0085] FIG. 6 shows a plot of impedance variability and distortion
function variability. A distortion function can vary for various
reasons, which are disclosed below. The rotational effect of a
transmission line between a RF generator and a matching network is
shown in FIG. 6. Trace 200 is the trajectory of impedance {right
arrow over (z)} of the transmission line with a circle on the
trajectory being associated with a minimum frequency of an
operating bandwidth. Each of the other curves in FIG. 6 are
associated with a respective distortion function and include a
circle corresponding to the minimum frequency of the operational
bandwidth. Trace 202 shows a distortion function without phasor
correction for the transmission line. Trace 204 is the distortion
function with a phasor correction applied along with a distortion
correction d.sub.c. Traces 206, 208 show a minimum and maximum
range for distortion correction for a first or minimum phase
variability. Traces 210, 212 show a minimum and maximum range for a
second or maximum phase variability.
[0086] An increase to a maximum phasor .phi..sub.max that is
applied when determining the distortion d, can lead to a distortion
function with a phase trajectory potentially positive without a
crossing of the real zero axis. The same analogy holds true for a
minimum phasor .phi..sub.min. A phase characterization of the
transmission line is determined to properly orient the distortion
function in the complex plane. Known length of the transmission
line does not alone allow for the proper orientation of the
distortion function. This phase characterization is a function of
transmission line length l and velocity of propagation V.sub.p.
[0087] The feedforward adaptations disclosed herein allow for less
intrusive or manual inputs. For example, the feedforward
adaptations do not include manually entry of a transmission line
phasor or manual initiation of a calibration procedure. The
feedforward adaptations and associated methods include an efficient
phasor estimator without user intervention.
[0088] FIG. 7 shows a Smith chart illustrating a conductance circle
250 and frequency tuning with respect to power distortion. The
Smith Chart in FIG. 7 illustrates a feedforward control strategy
for frequency tuning, which may be used by, for example, the
frequency control module 118 of FIG. 4. The conductance circle 250
is strategically located in the Smith Chart such that d.sub.t>0,
the frequency f of a RF generator is increased to the point where
d.sub.t=0 (shown by arrow 252). In a similar manner, if d.sub.t0,
the frequency of the RF generator is decreased until d.sub.t=0
(shown by arrow 254). When d.sub.t=0, the condition of maximum RF
power transfer occurs.
[0089] Correction to the frequency f of the RF generator is
determined by coefficient terms of the frequency control module
118. The following disclosed techniques include autonomous
adaptation (i) of the proper conductance circle orientation, and
(ii) formulation of coefficients of the frequency control module
118 for different operating conditions and variants of the
corresponding RF power system. The following disclosed techniques
include automated procedures to auto-adjust the phasor .phi. for
properly orienting the conductance circle 250 and adapting the
coefficients of the frequency control module 118 for improved
feedforward performance.
Orientation of the Conductance Circle
[0090] The conductance circle 250 is located in a left-hand plane
of the Smith Chart and oriented with a center of the conductance
circle 250 on a negative real axis. This is an ideal location for
the conductance circle 250 because the trajectory of the distortion
d (also referred to as "the distortion function") includes an odd
and symmetric imaginary quantity sin .theta.. An odd function is
mathematically defined as a function for which f(x)=-f(-x). An odd
and symmetric function is used by one or more of the control
modules 64, 118 and based on the imaginary quantity sin .theta. to
correct the distortion d of the RF power system. This includes
adjusting the frequency f of the RF generator and/or the tune
element of the matching network.
[0091] The transmission line variation (e.g., changes in
transmission line length, frequency and velocity of propagation) as
indicated by trace 200 of FIG. 6 can have an adverse effect on the
orientation of the conductance circle 250. This can be addressed by
(i) manual entry of phase .phi., or (ii) performance of a
calibration and/or estimation procedure to correct the phase .phi.
impinged on the orientation of the conductance circle 250 by the
transmission line. The transmission line (i.e., cable) phasor
{circumflex over (.phi.)} may be estimated and used to determine a
distortion correction d.sub.c=de.sup.-j({circumflex over
(.phi.)}+.pi.) such that the trajectory path of the distortion
correction d.sub.c is contained in the left-hand plane of FIG. 6.
The rotational effect of the transmission line is a function of the
length l of the transmission line, the velocity of propagation
V.sub.p of the transmission line, and the applied frequency f. Any
of these parameters can alter the orientation of the conductance
circle 250 and thereby prevent the distortion function from being
an odd function for maximum power transfer.
[0092] Transmission line effects are described as an exponential
function e.sup..gamma.I=e.sup.l.alpha.e.sup.jl.beta., where .alpha.
is an attenuation constant per meter of the transmission line,
.beta. is a phase constant .beta.=g(V.sub.p,f) per meter of the
transmission line, .gamma.=.alpha.+j.beta., and g identifies a
function. With any variant to the parameters l and .beta., the
orientation of the conductance circle 250 rotates by a proportional
amount or phase .phi.. The calibration process estimates the phase
.phi., which may be an approximation of l.beta..
[0093] In another implementation, the phase (or phasor) .phi. is
estimated while alleviating the calibration process manual input
and/or adjustment of the phasor .phi.. An estimation procedure is
performed that adapts the phasor .phi. in an automated and
autonomous manner that does not require manual input and/or
adjustment of the phasor .phi. each time a variation to the
transmission line occurs. Two estimation procedures for the phasor
.phi. are disclosed with respect to FIGS. 9 and 10 and may be
performed by the distortion module 44 (example of which is provided
in FIG. 8).
[0094] Both the distortion function and corresponding conductance
circle can be described in geometric terms as a parabolic or
circular function with an offset translation a from an origin (0,0)
of, for example, the Smith Chart of FIG. 7. The offset translation
.sigma., which is equal to e.sup.j.phi. has a phase angle that is
equivalent to the phasor .phi. of the transmission line. The phasor
.phi. refers to a rotation angle of the conductance circle about
the origin (0,0). By inspection of the conductance circle (shown in
FIG. 7), the transmission line phasor and the phase angle of the
offset translation .sigma. is .pi..
[0095] Based on this, the i.sup.th quantity of the distortion
function can be represented as
d.sub.i=.xi.e.sup.j.phi..sup.i+.sigma., where
.phi..sub.i=.phi..sub.g(q.sub.i-q.sub.T)+.phi..sub.o. This
characterizes the i.sup.th phase relationship for the first order
distortion function, parameterized by the terms .phi..sub.g and
.phi..sub.o terms. The relationship for .phi..sub.i is a
linearization of the conductance circle, where .phi..sub.g
indicates a point on the conductance circle. The term .phi..sub.g
may be referred to as a gain term. Rotation of the distortion
function occurs at .phi..sub.g radians per step with the initial
offset of .phi..sub.o. The variable q expresses the angular
position for respective frequency f or tune capacitor position
p.sub.t values, where q is directly related and/or analogous to
frequency f or a tune capacitor position p.sub.t for respective
control modules 64, 118 and q.sub.T demarcating the angular
position that will achieve a tune condition for maximum power
transfer. An attenuation or scaling term .xi. is included in the
distortion function d.sub.i to indicate it is unnecessary for the
function to have unity magnitude. The distortion function d.sub.i
is the time index of the distortion d.sub.t, where i is an index
value that maps q.sub.i to a particular distortion value
d.sub.i.
[0096] In summary, the distortion curve with impairment of the
transmission line phasor is defined as
d.sub.i=.xi.e.sup.j.phi..sup.i+.sigma.. The i.sup.th first
derivative of this function is represented by equations 18-20.
{dot over (d)}.sub.i=d.sub.i-d.sub.i-1 (18)
{dot over
(d)}.sub.i=(.xi.e.sup.j.phi..sup.i+.sigma.)-(.xi.e.sup.j.phi..sup.i-1+.si-
gma.) (19)
{dot over (d)}.sub.i=.xi.(e.sup.j.phi..sup.i-e.sup.j.phi..sup.i-1)
(20)
[0097] The first derivative removes the offset translation .sigma.
of the distortion that results from the transmission line phasor
.phi.. The derivative of the distortion {dot over (d)}.sub.i
circumscribes the origin (0,0) and the orientation of the
derivative {dot over (d)}.sub.i is independent of the transmission
line impedance. If K samples of the derivative {dot over (d)}.sub.i
are obtained, an estimate of the offset translation {circumflex
over (.sigma.)} can be determined using a least square method. The
method of FIG. 9 includes obtaining the K samples and determining
the offset translation .sigma. based on the K samples.
[0098] FIG. 8 shows the distortion module 44, which may be used to
replace the distortion module 44 of FIGS. 3-4. The distortion
module 44 includes a trigger module 302, a distortion function
module 304, a first derivative module 306, a sampling module 308, a
matrix module 310, an offset translation module 312, a phase
control module 314 and a distortion correction module 316. The
phase control module 314 includes a phase correction module 318.
These modules are described with respect to the method of FIG. 9
and/or 10 below.
[0099] FIG. 9 illustrates a single derivative based distortion
correction method. Although the following tasks are primarily
described with respect to the implementations of FIGS. 3-4 and 8-9,
the tasks may be easily modified to apply to other implementations
of the present disclosure. The tasks may be iteratively performed.
The method of FIG. 9 may begin at 320.
[0100] At 322, the trigger module 302 may determine whether AC
power to the RF power system (e.g., one of the RF power systems 10,
100 of FIGS. 3 and 4) and/or to a corresponding RF safety interlock
system has been interrupted. If AC power has been interrupted, task
324 is performed. The trigger module 302 may receive a power signal
AC indicting whether AC power has been interrupted and generate a
trigger signal TRIG to initiate the single derivative based
distortion correction method.
[0101] At 324, the sampling module 308 obtains K+1 samples of the
distortion function d.sub.i based on (i) RF sensor output signals
RF.sub.SENS from the RF sensors 26, and (ii) the trigger signal
TRIG. In one implementation K is 4. K is an integer constant. K+1
samples from d.sub.i are acquired when RF output of the RF
generator is enabled with a non-zero setpoint (e.g., the setpoint
provided by the power setpoint module 38). The distortion samples
are collected as a function of frequency or tune capacitor
position.
[0102] At 326, the first derivative module determines K samples of
the first derivative of the distortion function {dot over
(d)}.sub.i. The first derivative module may determine the K samples
of {dot over (d)}.sub.i based on the K+1 samples of {dot over
(d)}.sub.i. From these K samples, the angular rate of change (or
velocity) can be used to characterize a distortion curve and adapt
feedforward control terms.
[0103] In this way, there is no user intervention required and
delay time in obtaining the K samples is negligible (e.g., less
than 500 .mu.s) to acquire distortion values from frequency
operation and process K=4 samples. For matching network tuning, the
time to acquire the distortion samples may be (i) greater than time
associated with the frequency tuning, and (ii) dependent on motor
time constants and communication delays between the matching
network and RF power supply. The motor time constants refer to time
delays associated with adjusting a tune capacitor position, and a
load capacitor position, and/or other impedance elements in a
matching network.
[0104] At 328, a vector element x(2) is determined using a
non-recursive least square method. The vector x is equal to
(A.sup.TA).sup.-1A.sup.Ty, where A is a constructing matrix, and y
is a vector. The constructing matrix A has K rows and two columns.
The first column has K samples of {dot over (d)}.sub.i. Each entry
in the second column is a one. The vector y is a vector containing
K samples from d.sub.i in K rows and a single column. The
constructing matrix A matrix and vector y are constructed to
formulate the least squares estimate of vector x. In one
implementation, the vector x is a 2-by-1 matrix having 2 rows and 1
column, where x(2) refers to the second term in the 2-by-1 matrix.
Although a non-recursive least squares method is used, a recursive
least square estimate may be used.
[0105] At 330, from the vector x, the offset translation module 312
estimates the offset translation {circumflex over (.sigma.)}, which
is equal to x(2).
[0106] At 332, the phase control module estimates the phase
{circumflex over (.phi.)} based on the offset translation
{circumflex over (.sigma.)} and according to equation 21. Phasor
estimates may be determined for cables of various lengths, whether
an initial matching network condition was tuned or not-tuned.
.phi. ^ = tan - 1 ( Im ( .sigma. ^ ) Re ( .sigma. ^ ) ) = tan - 1 (
Im ( x ( 2 ) ) Re ( x ( 2 ) ) ) .apprxeq. l .beta. ( 21 )
##EQU00015##
[0107] At 334, the distortion correction module 316 determines a
distortion correction d.sub.c to rotate the distortion d to the
desired left-hand plane and construct an odd function for
corresponding imaginary components of the distortion d. The
corrected distortion function d.sub.c=de.sup.j{circumflex over
(.phi.)}.sup.c is used to determine the distortion correction
d.sub.c, where {circumflex over (.phi.)}.sub.c=-({circumflex over
(.phi.)}+.pi.). After the estimation and subsequent correction of
distortion is performed, the control modules 64, 118 and
corresponding circuitry may proceed to operate as previously
described.
[0108] At 336, the corrected distortion d.sub.c is then used as the
distortion value for d.sub.t to generate the frequency tuning value
u.sub.ff.sup.ff and the impedance tuning value u.sub.ff.sup.t. The
method may end at 338.
[0109] Referring now to FIGS. 8 and 10. The distortion module 44
may further include a second derivative module 340, a first
extrapolation module 342, and a second extrapolation module 344.
The phase control module 314 may further include a first comparison
module 348, a second comparison module 350, and a third comparison
module 352.
[0110] FIG. 10 illustrates a double derivative based distortion
correction method. The method of FIG. 10 may be used as an
alternative to and/or in addition to the method of FIG. 9. Although
the following tasks are primarily described with respect to the
implementation of FIGS. 3-4, 8 and 10, the tasks may be easily
modified to apply to other implementations of the present
disclosure. The tasks may be iteratively performed and may be
performed as described above. The method may begin at 360.
[0111] At 362, the trigger module 302 may determine whether AC
power to the RF power system (e.g., one of the RF power systems 10,
100 of FIGS. 3 and 4) and/or to a corresponding RF safety interlock
system has been interrupted. If AC power has been interrupted, task
364 is performed. The trigger module 302 may receive a power signal
AC indicting whether AC power has been interrupted and generate a
trigger signal TRIG to initiate the double derivative based
distortion correction method.
[0112] At 364, the sampling module 308 obtains K+1 samples of
d.sub.i as a function of frequency and tune capacitor position. K+1
samples from d.sub.i are acquired when RF output of the RF
generator is enabled with a non-zero setpoint (e.g., the setpoint
provided by the power setpoint module 38).
[0113] At 366, the first derivative module 306 determines K samples
of the first derivative {dot over (d)}.sub.i. From the K+1 samples
of d.sub.i, K values of {dot over (d)}.sub.i are determined. Each
derivative of a sinusoidal function produces a phase shift of
.pi. 2 . ##EQU00016##
The first derivative {dot over (d)}.sub.i has the offset
translation removed and provides a reference to
.pi. 2 . ##EQU00017##
[0114] At 368, the second derivative module 340 determines K-1
values of a second derivative {umlaut over (d)}.sub.i. From the K+1
samples of d.sub.i, K-1 values of the second derivative {umlaut
over (d)}.sub.i are determined. The method of FIG. 10 includes
computation of a second derivative {umlaut over (d)}.sub.i and use
of the relationship q=q.sub.T. The purpose of the second derivative
is for an additional phase datum for a quantitative comparison. The
second derivative yields a reference to .pi.. The first and second
derivatives provide geometrical datums to compare the angular
rotation associated with l.beta. to a corresponding and
predetermined phase.
[0115] At 370, the first extrapolation module 342 extrapolates
phase of the first derivative {dot over (d)}.sub.i for q.sub.T. The
first derivative is extrapolated to the value for d.sub.i with
q=q.sub.T. For example, the phase extrapolated from the first
derivative provides an estimate of a first phase correction
{circumflex over (.phi.)}=.angle.{dot over (d)}(q=q.sub.T).
[0116] At 372, the second extrapolation module 344 extrapolates
phase of the second derivative {umlaut over (d)}.sub.i for q.sub.T.
The second derivative is extrapolated to the value for d.sub.i with
q=q.sub.T. The phase extrapolated from the second derivative
provides an estimate of a second phase correction {circumflex over
(.phi.)}.sub.c2=.angle.{umlaut over (d)}(q=q.sub.T).
[0117] At 374, the first comparison module 348 may compare the
estimated phase for the first derivative to
.pi. 2 ##EQU00018##
to provide a third estimate phase correction
.sigma. ^ c 3 = .angle. d . ( q = q T ) + .pi. 2 . ##EQU00019##
[0118] At 376, the second comparison module 350 may compare the
estimated phase for the second derivative to .pi. to provide a
fourth estimate phase correction {circumflex over
(.phi.)}.sub.c4=.angle.{umlaut over (d)}(q=q.sub.T)+.pi..
[0119] To illustrate the above tasks 370-376, a simulation of a
transmission line phasor effect on a distortion function is shown
in FIG. 11. FIG. 11 shows a derivative plot of distortion
functions. The curve 380 indicates the ideal distortion function
and the curve 382 indicates a distortion function due to an effect
of an example phasor of an arbitrary transmission line. The example
phasor may be, for example, 45.7.degree.. Circle and X symbols on
the curves of FIG. 11 indicate a start of a distortion function
where q is associated with a minimum frequency or minimum tune
capacitor position. The circle symbols are on dashed curves, which
are associated with the ideal distortion function. The Xs are on
solid curves, which are associated with an arbitrary transmission
line. Triangle symbols are included to identify tune positions,
where q=q.sub.T.
[0120] Examining the ideal distortion function and the distortion
function of the arbitrary transmission line, a tune point for the
ideal distortion function has a zero crossing with a real zero
axis. The method of FIG. 10 determines a phasor to apply a
correction to the distortion function of the arbitrary transmission
line, which is indicated by curve 382 such that a point (indicated
by triangle 384) on the curve 382 intersects with the real zero
axis. A first derivative of the ideal distortion function is
indicated by curve 386. A first derivative of the distortion
function of the arbitrary transmission line is indicated by curve
388. Magnitudes of the derivative functions are scaled for the sole
purpose of generating a suitable presentation of the original
distortion functions along with the corresponding derivative
functions. Visually comparing the triangle locations on the curves
386, 388 of the first derivative functions, the ideal derivative
function crosses the imaginary axis leading the derivative function
of the arbitrary transmission line by approximately 45.degree..
[0121] A second derivative of the ideal distortion function is
shown by curve 390. A second derivative of the distortion function
for the arbitrary transmission line is shown by curve 392. The
curve 390 crosses the real axis leading the curve 392 by
45.degree.. The simulation produced estimates of phase correction
{circumflex over (.phi.)}.sub.c=45.75.degree. for the first
derivative and phase correction {circumflex over
(.phi.)}.sub.c=45.68.degree. for the second derivative,
corroborating with the visual estimates and expected result.
[0122] As another example, a transmission line may have a length of
2.5 ft., a transmission line phasor of 18.degree. at 13.56 MHz. For
the first derivative, an estimate phase correction may be
{circumflex over
(.phi.)}.sub.c=108.degree..+-.90.degree.=198.degree., and based on
the second derivative an estimate phase correction may be
{circumflex over
(.phi.)}.sub.c=18.degree..+-.180.degree.=198.degree.. Illustrating
that an estimate phase correction may be based on the first
derivative and/or the second derivative.
[0123] The extrapolation from the second derivative may provide a
more precise phasor for the transmission line than the first
derivative. For this reason, the second derivative may be used to
ensure an accurate estimate of phase correction is obtained.
[0124] At 394, the third comparison module 352 may compare the
third estimate of phase correction {circumflex over (.phi.)}.sub.c3
to the fourth estimate of phase correction {circumflex over
(.phi.)}.sub.c4. A quantitative comparison is made to ensure
.sigma. ^ c = .angle. d . ( q = q T ) + .pi. 2 = .angle. d ( q = q
T ) + .pi. . ##EQU00020##
The estimates may be recalculated if the third estimate of phase
correction {circumflex over (.phi.)}.sub.c3 is not within a
predetermined range of the fourth estimate of phase correction
{circumflex over (.phi.)}.sub.c4.
[0125] At 396, the phase control module 314 and/or the third
comparison module 352 proceeds to task 398 if the third estimate of
phase correction {circumflex over (.phi.)}.sub.c3 is within a
predetermined range of fourth estimate of phase correction
{circumflex over (.phi.)}.sub.c4, otherwise task 400 is
performed.
[0126] At 398, the phase control module 314 and/or the third
comparison module determines a fifth estimate of phase correction
{circumflex over (.phi.)}.sub.c5 based on the third and fourth
estimate of phase correction {circumflex over (.phi.)}.sub.c3,
{circumflex over (.phi.)}.sub.c4. The fifth estimate of phase
correction {circumflex over (.phi.)}.sub.c5 may be, for example,
set equal to one of the third and fourth estimate of phase
correction {circumflex over (.phi.)}.sub.c3, {circumflex over
(.phi.)}.sub.c4, or may be an average of third and fourth estimate
of phase correction {circumflex over (.phi.)}.sub.c3, {circumflex
over (.phi.)}.sub.c3.
[0127] At 400, if the third estimate of phase correction
{circumflex over (.phi.)}.sub.c3 is not within a predetermined
range of the fourth estimate of phase correction {circumflex over
(.phi.)}.sub.c4, the phase control module 314 and/or the third
comparison module 352 may generate an error signal, default to the
method of FIG. 9, use a predetermined estimate of phase correction,
and/or request manual input of a phase correction. Task 402 may be
performed subsequent to task 400.
[0128] At 402, the distortion correction module 316, based on the
fifth estimate of phase correction {circumflex over (.phi.)}.sub.c5
or an estimate of phase correction as determined at 400, determines
a distortion correction d.sub.c to rotate the distortion d to the
desired left-hand plane and construct an odd function for
corresponding imaginary components of the distortion d. To rotate d
to the desired left-hand plane, the corrected distortion function
may be obtained from d.sub.c=de.sup.j{circumflex over
(.phi.)}.sup.c. After the estimation and subsequent correction of
distortion is performed, the control modules 64, 118 and
corresponding circuitry may proceed to operate as previously
described.
[0129] At 404, the corrected distortion d.sub.c is then used as the
distortion value for d.sub.t to generate the frequency tuning value
u.sub.ff.sup.f and the impedance tuning value u.sub.ff.sup.t. The
method may end at 406.
[0130] FIG. 12 shows a functional block diagram of a tuning
correction control module 420. The tuning correction control module
420 may replace one of the control modules 64, 118 of FIGS. 3-4.
The tuning correction control module 420 may be used to determine
one of the frequency tuning value u.sub.ff.sup.f and the impedance
tuning value u.sub.ff.sup.t. The tuning correction control module
420 may determine these values for tasks 336, 404 of the
above-described methods of FIGS. 9 and 10. The tuning correction
control module 420 may include a trigger module 422, a distortion
function module 424, a sampling module 425, a first derivative
module 426, a gain module 428, and a tuning parameter correction
module 430. The modules of the tuning correction control module 420
are described with respect to the method of FIG. 13.
[0131] The control modules 64, 118 of FIGS. 3-4 are allocated to
respectively adjusting frequency of a RF generator and a tune
capacitor position in a matching network. The objective of these
control modules is to correct impedance seen by the RF generator to
achieve maximum RF power transfer. The responses of the control
modules 64, 118 are based on (i) limitations of a frequency
response of a power amplifier in the case of the control module 64,
and (ii) actuator (e.g., motor) time constants and communication
latencies in the case of the control module 118. The responses may
not take into account a resolution of impedance tune space. The
feedforward adjustments made by the control modules 64, 118 target
corrections to remove a distortion; the distortion prevents a
condition for maximum RF power transfer that may not be compensated
by a feedback control method. By knowing the resolution of the tune
space, the coefficients of the control modules 64, 118 can be
adjusted for a single step correction.
[0132] Unfortunately, the elements of matching networks vary and
often are not precisely known for each load. For this reason, an
auto-adaption procedure is disclosed below that tailors coefficient
terms of the control modules 64, 118 to align with an impedance
tune space by accounting for resolution of the impedance tune
space. Similar to the estimation procedures of FIGS. 9 and 10
described for determining a phasor of a transmission line, the
auto-adaption procedure is based on derivatives of a distortion
function.
[0133] A first derivative of the distortion function is analogous
to angular velocity and provides the resolution of the impedance
tune space. The resolution of the impedance tune space is directly
related to .phi..sub.g, which is an unknown parameter that may be
determined and/or accounted for as described below. The parameter
.phi..sub.g is an angular position parameter that indicates where a
distortion value is on a distortion curve for a transmission line.
For a certain change in an impedance actuator (e.g., a change in
the frequency or tune capacitor position), there is a notable
change in distortion. By producing derivatives of the distortion
function with quantifiable control of the impedance actuators, the
actual impedance tune space can be characterized. It is anticipated
that this auto-adaption procedure is performed in parallel with
operations of the control modules 64, 118 and the adapted terms
(e.g., coefficient terms) of the control modules 64, 118 are used
by the control modules 64, 118 to generate the frequency tuning
value u.sub.ff.sup.f and the impedance tuning value
u.sub.ff.sup.t.
[0134] FIG. 13 illustrates a distortion correction based control
method. Although the following tasks are primarily described with
respect to the implementation of FIGS. 3-4 and 12, the tasks may be
easily modified to apply to other implementations of the present
disclosure. The tasks may be iteratively performed and may be
performed as described above. The method may begin at 450.
[0135] At 452, the trigger module 422 may determine whether AC
power to the RF power system (e.g., one of the RF power systems 10,
100 of FIGS. 3 and 4) and/or to a corresponding RF safety interlock
system has been interrupted. If AC power has been interrupted, task
354 is performed. The trigger module 422 may receive a power signal
AC indicting whether AC power has been interrupted and generate a
trigger signal TRIG to initiate the distortion correction based
control method.
[0136] At 454, the distortion function module 424 determines
distortion correction values for a distortion correction function
d.sub.c(i)=.xi.e.sup.j.phi..sup.i based on the impedance and
distortion relationships
z = v .fwdarw. i .fwdarw. = z j .theta. and d c ( i ) = z .fwdarw.
z = j .theta. . ##EQU00021##
At 455, the sampling module 425 obtains K+1 samples of the
distortion correction values.
[0137] At 456, first derivative module 426 determines, for example,
K first derivative correction values based on the K+1 samples of
the distortion correction values. The first derivative module 426
may determine a first derivative function of the distortion
correction function based on an expanded distortion correction
function. The K first derivative correction values may be provided
in terms of cos .theta. and sin .theta.. The distortion correction
function may be expanded as provided by equation 22. The first
derivative function may then be represented by equation 23.
d c ( i ) = .xi. j .PHI. 1 = .xi.cos ( .PHI. g ( q i - q T ) +
.PHI. o ) + j.xi. sin ( .PHI. g ( q i - q T ) + .PHI. o ) ( 22 ) d
. c ( i ) = .differential. d .differential. q = - .xi..PHI. g sin (
.PHI. g ( q i - q T ) + .PHI. o ) + j.xi..PHI. g cos ( .PHI. g ( q
i - q T ) + .PHI. o ) ( 23 ) ##EQU00022##
Trigonometeric identities - sin ( x ) = cos ( x + .pi. 2 ) and
##EQU00023## cos ( x ) = sin ( x + .pi. 2 ) ##EQU00023.2##
may be applied to equation 23 to provide equation 24.
d . c ( i ) = .xi..PHI. g cos ( .PHI. g ( q i - q T ) + .PHI. o +
.pi. 2 ) + j.xi..PHI. g sin ( .PHI. g ( q i - q T ) + .PHI. o +
.pi. 2 ) ( 24 ) ##EQU00024##
[0138] At 458, the gain module 428 may determine a gain value G
(first coefficient term) based on the K first derivative correction
values. The inverse of the first derivative {dot over (d)}.sub.c(i)
is assigned to the gain term. The gain G may be determined based on
an inverse of, for example, one or more of the K first derivative
correction values. The gain term may be represented as provided by
equation 25. Equation 24 is in rectangular form and may be
converted to equation 25, which is in polar form by taking the
inverse of {dot over (d)}.sub.c(i).
G = 1 .xi..PHI. g - j ( .PHI. g ( q i + q T ) + .PHI. o + .pi. 2 )
= 1 .xi..PHI. g - j ( .PHI. i + .pi. 2 ) ( 25 ) ##EQU00025##
The variable .phi..sub.g may be accounted for by determining the
gain G based on the K first derivative correction values and/or may
be determined using equation 25 and the determined value for the
gain G.
[0139] At 460, the tuning parameter correction module 430
determines the frequency tuning value u.sub.ff.sup.f and/or the
impedance tuning value u.sub.ff.sup.t based on the gain G. Each of
the control modules 64, 118 can be generalized as provided by
equation 26, where the parameter q represents (i) the frequency f
for the control module 64, and (ii) the tune parameter t (or tune
capacitor position) for the control module 118. The gain term G is
different for each of the control modules 64, 118, as the terms
q.sub.i and q.sub.T are analogous to frequency for the control
module 64 and to tune capacitor position for the control module
118.
u.sub.ff.sup.q(i+1)=u.sub.ff.sup.q(i)-[G(.alpha..sub.qd.sub.c(i)+.beta..-
sub.qd.sub.c(i-1)+.gamma..sub.qd.sub.c(i-2))] (26)
[0140] By applying the gain G according to equation 26, the
coefficient terms .alpha..sub.q,.beta..sub.q,.gamma..sub.q, are
modified by the gain G. The method may end at 462.
[0141] The above-described tasks of FIGS. 9-10 and 13 are meant to
be illustrative examples; the tasks may be performed sequentially,
synchronously, simultaneously, continuously, during overlapping
time periods or in a different order depending upon the
application. Also, any of the tasks may not be performed or skipped
depending on the implementation and/or sequence of events.
[0142] The foregoing description is merely illustrative in nature
and is in no way intended to limit the disclosure, its application,
or uses. The broad teachings of the disclosure can be implemented
in a variety of forms. Therefore, while this disclosure includes
particular examples, the true scope of the disclosure should not be
so limited since other modifications will become apparent upon a
study of the drawings, the specification, and the following claims.
As used herein, the phrase at least one of A, B, and C should be
construed to mean a logical (A or B or C), using a non-exclusive
logical OR. It should be understood that one or more steps within a
method may be executed in different order (or concurrently) without
altering the principles of the present disclosure.
[0143] In this application, including the definitions below, the
term module may be replaced with the term circuit. The term module
may refer to, be part of, or include an Application Specific
Integrated Circuit (ASIC); a digital, analog, or mixed
analog/digital discrete circuit; a digital, analog, or mixed
analog/digital integrated circuit; a combinational logic circuit; a
field programmable gate array (FPGA); a processor (shared,
dedicated, or group) that executes code; memory (shared, dedicated,
or group) that stores code executed by a processor; other suitable
hardware components that provide the described functionality; or a
combination of some or all of the above, such as in a
system-on-chip.
[0144] The term code, as used above, may include software,
firmware, and/or microcode, and may refer to programs, routines,
functions, classes, and/or objects. The term shared processor
encompasses a single processor that executes some or all code from
multiple modules. The term group processor encompasses a processor
that, in combination with additional processors, executes some or
all code from one or more modules. The term shared memory
encompasses a single memory that stores some or all code from
multiple modules. The term group memory encompasses a memory that,
in combination with additional memories, stores some or all code
from one or more modules. The term memory may be a subset of the
term computer-readable medium. The term computer-readable medium
does not encompass transitory electrical and electromagnetic
signals propagating through a medium, and may therefore be
considered tangible and non-transitory. Non-limiting examples of a
non-transitory tangible computer readable medium include
nonvolatile memory, volatile memory, magnetic storage, and optical
storage.
[0145] Although the terms first, second, third, etc. may be used
herein to describe various elements, components, loops, circuits,
and/or modules, these elements, components, loops, circuits, and/or
modules should not be limited by these terms. These terms may be
only used to distinguish one element, component, loop, circuit or
module from another element, component, loop, circuit or module.
Terms such as "first," "second," and other numerical terms when
used herein do not imply a sequence or order unless clearly
indicated by the context. Thus, a first element, component, loop,
circuit or module discussed herein could be termed a second
element, component, loop, circuit or module without departing from
the teachings of the example implementations disclosed herein.
[0146] In addition, in the above-described description various
variable labels and values are disclosed. The variable labels and
values are provided as examples only. The variable labels are
arbitrarily provided and may each be used to identify or refer to
one or more items. If a variable label is used to refer to more
than one item, the items may be unrelated. As an example, the
variable label is used to refer to a systematic error and is also
used to refer to a scaling term. The systematic error is different
than and unrelated to the scaling term. The values are also
arbitrarily provided and may vary per application.
[0147] The apparatuses and methods described in this application
may be partially or fully implemented by one or more computer
programs executed by one or more processors. The computer programs
include processor-executable instructions that are stored on at
least one non-transitory tangible computer readable medium. The
computer programs may also include and/or rely on stored data.
* * * * *