U.S. patent application number 11/273286 was filed with the patent office on 2007-05-17 for digital saturation handling in integral noise shaping of pulse width modulation.
This patent application is currently assigned to FREESCALE SEMICONDUCTOR, INC.. Invention is credited to John Grosspietsch, Pallab Midya, William J. Roeckner, Anthony R. Schooler.
Application Number | 20070109165 11/273286 |
Document ID | / |
Family ID | 38040230 |
Filed Date | 2007-05-17 |
United States Patent
Application |
20070109165 |
Kind Code |
A1 |
Midya; Pallab ; et
al. |
May 17, 2007 |
DIGITAL SATURATION HANDLING IN INTEGRAL NOISE SHAPING OF PULSE
WIDTH MODULATION
Abstract
An audio amplifier includes a digital signal processor (DSP)
that contains a noise shaping quantizer having an integrating error
amplifier. The integrating error amplifier contains integrators
connected in a feedback loop, a summer supplied with an output of
each of the integrators, and a saturation function module producing
a saturation function. A multiplier is disposed between each pair
of adjacent integrators. The multiplier receives a signal from one
of the adjacent integrators and the saturation function and
supplies a signal to the other of the adjacent integrators. The
saturation function decreases the effect of all of the integrators
except an integrator to which an input signal to the integrating
amplifier is supplied using an input signal to and/or an output
signal from the noise shaping quantizer. This permits the duty
ratio of the output signal from the noise shaping quantizer to
extend from 0% to 100%.
Inventors: |
Midya; Pallab; (Palatine,
IL) ; Roeckner; William J.; (Carpentersville, IL)
; Grosspietsch; John; (Libertyville, IL) ;
Schooler; Anthony R.; (Bartlett, IL) |
Correspondence
Address: |
BRINKS HOFER GILSON & LIONE
P.O. BOX 10395
CHICAGO
IL
60610
US
|
Assignee: |
FREESCALE SEMICONDUCTOR,
INC.
MOTOROLA, INC.
|
Family ID: |
38040230 |
Appl. No.: |
11/273286 |
Filed: |
November 14, 2005 |
Current U.S.
Class: |
341/144 |
Current CPC
Class: |
H03M 3/432 20130101;
H03M 3/452 20130101; H03M 3/366 20130101 |
Class at
Publication: |
341/144 |
International
Class: |
H03M 1/66 20060101
H03M001/66 |
Claims
1. A switching amplifier comprising a noise shaping quantizer, the
noise shaping quantizer having an integrating error amplifier, the
integrating error amplifier containing a plurality of series
connected integrators in a loop and a saturation function module
producing a saturation function, the saturation function
continually decreasing the effect of at least one of the
integrators from the loop when a duty ratio of at least one of an
input signal to or an output signal from the noise shaping
quantizer varies between predetermined values; wherein a frequency
of the input signal to and an output signal from the noise shaping
quantizer is fixed.
2. The switching amplifier of claim 1, wherein the saturation
function is a nonlinear function.
3. The switching amplifier of claim 1, wherein the saturation
function is a piecewise function.
4. The switching amplifier of claim 3, wherein the saturation
function is a nonlinear function.
5. The switching amplifier of claim 1, wherein the saturation
function completely removes the effect of the at least one of the
integrators from the loop only when the duty ratio of the at least
one of the input or output signal is 0% to 100%.
6. The switching amplifier of claim 5, wherein the saturation
function continually reduces the effect of the at least one of the
integrators when the duty ratio varies from a first duty ratio to
0% to 100%.
7. The switching amplifier of claim 6, wherein the first duty ratio
is 50%.
8. The switching amplifier of claim 6, wherein the saturation
function does not change the effect of the at least one of the
integrators from the first duty ratio to the second duty ratio.
9. The switching amplifier of claim 6, wherein the saturation
function is (1-(2x-1).sup.2n), where x is the duty ratio of the
input signal (x=0.5 for a 50% duty ratio and x=1 for a 100% duty
ratio) and n is an integer.
10. The switching amplifier of claim 1, wherein the noise shaping
quantizer is implemented within a digital signal processor
(DSP).
11. The switching amplifier of claim 10, further comprising
oversampling circuitry, natural sampling circuitry connected
between the oversampling circuit and the noise shaping quantizer,
and a pulse-width modulation counter supplied with a signal from
the noise shaping quantizer.
12. A switching amplifier comprising a noise shaping quantizer, the
noise shaping quantizer having an integrating error amplifier, the
integrating error amplifier containing a plurality of series
connected integrators in a loon and a saturation function module
producing a saturation function, the saturation function
continually decreasing the effect of at least one of the
integrators from the loop when a duty ratio of at least one of an
input signal to or an output signal from the noise shaping
quantizer varies between predetermined values; wherein the
integrators are disposed in a feedback loop arrangement and the
integrating error amplifier further comprises a multiplier between
each pair of integrators; and wherein each multiplier supplied with
the saturation function and an output from one of the integrators
between which the multiplier is disposed, an output of the
multiplier supplying the other of the integrators between which the
multiplier is disposed.
13. The switching amplifier of claim 12, wherein the noise shaping
quantizer further comprises: a first comparator to which the input
signal of the noise shaping quantizer and a ramp signal are
supplied, an output of the first comparator supplied to the
saturation function module of the integrating error amplifier, a
second comparator to which the ramp signal is supplied, a duty
ratio quantizer to which an output of the second comparator and a
clock signal are supplied, a fist summer subtracting an output of
the duty ratio quantizer from the output of the first comparator to
produce an error signal that is supplied to a first of the
integrators of the integrating error amplifier, a second summer in
the integrating error amplifier to which outputs from each of the
integrators are supplied, and a third summer to which an output of
the second summer and the input signal of the noise shaping
quantizer are supplied, and an output of the third summer is
supplied to an input of the second comparator.
14. A digital audio amplifier comprising a digital signal processor
(DSP) and a power stage to which an output of the digital signal
processor is supplied, the DSP containing a noise shaping quantizer
having an integrating error amplifier, the integrating error
amplifier containing a plurality of series connected integrators in
a feedback loop, a summer supplied with an output of each of the
integrators, a saturation function module producing a saturation
function, a multiplier disposed between each pair of adjacent
integrators to which an output of one of the adjacent integrators
and the saturation function are supplied and which supplies an
input of the other of the adjacent integrators, the saturation
function decreasing the effect of all of the integrators except an
integrator to which an input signal to the integrating amplifier is
supplied using at least one of an input signal to the integrating
amplifier is supplied using at least one of an input signal to or
an output signal from the noise shaping quantizer such that a duty
ratio of the output signal from the noise shaping quantizer extends
from 0% to 100%.
15. The digital audio amplifier of claim 14, wherein the saturation
function is a nonlinear function.
16. The digital audio amplifier of claim 14, wherein the saturation
function is a piecewise function.
17. The digital audio amplifier of claim 16, wherein the saturation
function is a nonlinear function.
18. The digital audio amplifier of claim 14, wherein the saturation
function completely removes the effect of the integrators from the
loop only when the duty ratio of the at least one of the input or
output signal is 0% to 100%.
19. The digital audio amplifier of claim 18, wherein the saturation
function is (1-(2x-1).sup.2n), where x is the duty ratio of the
input signal (x=0.5 for a 50% duty ratio and x=1 for a 100% duty
ratio) and n is an integer.
20. A method of noise shaping a pulse width modulated signal, the
method comprising: receiving an input signal; generating a first
pulse width modulated (PMW) signal using the input signal and a
second PMW signal using a noise shaped input signal; quantizing the
second PMW signal to produce a quantized signal; subtracting the
quantized signal from the first PWM signal to produce an error
signal; providing a plurality of integrators and multipliers
between each integrator that are series connected such that the
error signal is integrated to produce an integrated signal and
multiplied by a saturation function to provide a multiplied signal
that is integrated, the saturation function decreasing as a duty
ratio of at least one of the input signal to or an output signal
from the noise shaping quantizer extends from 0% to 100%; and
summing all of the integrated signals to generate the noise shaped
input signal.
21. The method of claim 20, wherein the saturation function is a
nonlinear function.
22. The method of claim 20, wherein the saturation function is a
piecewise function.
23. The method of claim 22, wherein the saturation function is a
nonlinear function.
24. The method of claim 20, wherein the saturation function becomes
0 only when the duty ratio of the at least one of the input or
output signal is 0% or 100%.
25. The method of claim 24, wherein the saturation function is
(1-(2x-1).sup.2n), where x is the duty ratio of the input signal
(x=0.5 for a 50% duty ratio and x=1 for a 100% duty ratio) and n is
an integer.
Description
TECHNICAL FIELD
[0001] The present application relates to noise shaping of a pulse
width modulated signal. More specifically, the present application
relates to saturation handling of a pulse width modulated
signal.
BACKGROUND
[0002] Switching amplifiers are used in various electronic
components such as audio amplifiers. A switching amplifier consists
of a network of switching elements that produces a square wave
output and is connected to a load through a power stage. The
switching amplifier typically uses pulse width modulation (PWM).
The MOSFETs are switched either on or off, rather than operated in
linear mode, to convert an input signal to a sequence of pulses (a
PWM signal) whose averaged value is directly proportional to the
amplitude of the input signal at that time. The frequency of the
pulses is typically ten or more times the highest frequency of
interest of the input signal. The switching amplifier is used in
audio equipment, for example, when reproducing analog signals
stored on a compact disc in a digital format.
[0003] The PWM switching period is typically fixed. The ratio of
the time that a PWM signal is high to the switching period is
called the duty ratio. A digital PWM signal is defined by the
switching period and the duty ratios. During digital processing,
the PWM duty ratio is quantized, resulting in a signal-to-noise
ratio that is reduced from that of the original signal. The
quantized PWM signal introduces audible distortion and raises the
noise level of the audible frequency band. Accordingly, noise
shaping is used on the PWM signal to manipulate the signal to
reduce the noise level and force the noise out of the audible
range. Noise shaping uses a noise shaping loop within the digital
processor.
[0004] In audio equipment using the switching amplifier, at peaks
of audio and high volume settings, the desired output voltage
exceeds the capability of the power supply and the power stage.
During these times, the largest output power can be obtained by
stopping switching of the MOSFETs and allowing the entire power
supply across the load. However, large input signals can cause the
noise shaping loop to become unstable.
[0005] One approach to increase the stability is to artificially
limit the amplitude of the input signal to a lower value, and thus
the duty ratio of the PWM signal, before the noise shaping loop
goes unstable. However, this reduces the peak power out of the
amplifier due to both the reduction in duty ratio range and the
relative inefficiency of the power stage when operated with a very
high or low duty ratio. Additionally, artifacts in the audio signal
may be introduced by the transition from the switching mode to the
saturation mode (and back) of the switching amplifier. Further, if
a lookup table is used to provide the amplitude limitation, a large
amount of memory (which is relatively expensive) is used, and the
power consumption and size of the device is increased.
BRIEF DESCRIPTION OF THE DRAWINGS
[0006] The present invention is illustrated by way of example and
not limited to the accompanying figures in which like references
indicate similar elements.
[0007] FIG. 1 illustrates an amplifier according to one
embodiment.
[0008] FIG. 2 illustrates a noise shaping quantizer according to
one embodiment.
[0009] FIG. 3 is an S-domain graph of the poles of a gain function
of the noise shaping quantizer according to one embodiment as the
system moves into saturation.
[0010] FIG. 4 is a graph of a quantized duty ratio when the input
has an amplitude sufficient to drive the system into saturation
according to one embodiment.
[0011] FIG. 5 is a graph showing values from integrators in the
noise shaping quantizer during normal operation and saturation
according to one embodiment.
[0012] FIG. 6 is a typical timing diagram illustrating the input
and output signals as well as the sampling ramp signal.
[0013] FIG. 7 is a typical curve of efficiency vs. duty ratio for a
switching amplifier.
[0014] Skilled artisans appreciate that elements in the figures are
illustrated for simplicity and clarity and have not necessarily
been drawn to scale.
DETAILED DESCRIPTION
[0015] A switching amplifier is presented that does not
artificially limit the duty ratio of the output signal. The
switching amplifier contains a digital signal processor (DSP) that
includes an integrating error amplifier with a noise shaping
quantizer using a saturation function. The saturation function
allows the noise shaping quantizer to use the same algorithm
independent of whether the noise shaping quantizer is in normal
switching mode or in saturation mode. That is, the saturation
function allows the noise shaping quantizer to use the same
algorithm independent of whether the input signal drives the
amplifier into saturation. The switching amplifier can be applied
to audio equipment, for example. The computation engine of the DSP
is a single instruction, multiple data engine with no branching in
the noise shaping loop. This method of saturation handling
maintains a continuous loop as one or more channels of the
amplifier (if the amplifier has multiple channels) may go in and
out of saturation.
[0016] FIG. 1 illustrates one embodiment of a switching amplifier.
Switching amplifier 112 contains digital signal processor 110 and
power stage 124. Digital signal processor (DSP) 110 includes
oversampling circuitry 116, natural sampling circuitry 118, noise
shaping quantizer 120, and pulse-width modulation (PWM) counter
122. Other electronic components known in the art may be present,
but are not shown for clarity.
[0017] Storage device 114 provides uniformly sampled input digital
data 130 to oversampling circuitry 116. Oversampling circuit 116
provides higher frequency uniformly sampled digital data 132, to
natural sampling circuitry 118. Natural sampling circuitry 118
provides naturally sampled digital data 134, to noise shaping
quantizer 120, which in turn provides a duty ratio 136 to PWM
counter 122. PWM counter 122 provides a PWM square wave 138 to
power stage 124, which in turn outputs amplified signal 140.
[0018] In operation, storage device 114 contains input digital data
130 that is uniformly sampled. Storage device 114 can include such
devices as a solid-state memory such as a memory card or other
package that houses one or more non-volatile read-only memories, a
random access memory or other volatile re-writable memory, or a
magneto-optical or optical medium. For example, storage device 114
can include a CD or digital audio tape. Storage device 114 may
also
[0019] be used to broadcast digital data to a receiver for
inputting into DSP 110. This broadcast can be over any wireless
communication protocol such as Bluetooth.
[0020] The uniformly sampled input digital data 130 includes a
stream of values which may include an audio signal. For example, CD
data has a 16-bit resolution signal sampled at a 44.1 kilohertz
frequency. The uniformly sampled input digital data 130 is then
converted to a higher frequency uniformly sampled digital data 132
by oversampling circuitry 116. Effectively, oversampling circuitry
116 is a data rate converter in which data is provided at one rate
and is output at a different rate. In one embodiment, oversampling
circuitry 116 receives uniformly sampled input digital data 130 and
samples it at a rate 16 times greater to produce the higher
frequency uniformly sampled digital data 132. For example, in the
case of the CD where uniformly sampled input digital data 130 is
sampled at a rate of 44.1 kilohertz, oversampling circuitry 116
would sample this signal at a higher frequency of 705.6 kilohertz
to produce the higher frequency uniformly sampled digital data 132.
Natural sampling circuitry 118 then converts the uniformly sampled
digital data signal 132 into a naturally sampled digital data
signal 134.
[0021] Noise shaping quantizer 120, quantizes and noise shapes the
naturally sampled digital data signal 134 to produce a lower
resolution signal such that the noise in the frequency band of
interest is limited. Noise shaping quantizer 120 converts naturally
sampled digital data 134 into duty ratio 136. Duty ratio 136 is
then used by PWM counter 122 to produce PWM square wave 138. The
PWM square wave 138 at the output of PWM counter 122 is amplified
by power stage 124 to produce amplified signal 140 at the output of
switching amplifier 112. When the duty ratio is larger than 50%,
the signal supplied from switching amplifier 112 is positive and
has an increasing amplitude. When the duty ratio is smaller than
50%, the signal supplied from switching amplifier 112 is positive
and has a decreasing amplitude. Note that although the use of
uniformly sampled input digital data is provided in FIG. 1, other
embodiments may use digital signals that are not uniformly sampled.
For example, the frequency may vary over the range of the input
digital data.
[0022] The circuitry and programming of oversampling circuitry 116,
natural sampling circuitry 118, and pulse-width modulation (PWM)
counter 122 are known to those skilled in the art. Thus, circuit
details will not be explained in any greater extent than that
considered necessary for the understanding and appreciation of the
underlying concepts and in order not to obfuscate or distract from
the teachings of the present invention.
[0023] FIG. 2 illustrates one embodiment of noise shaping quantizer
200 in the DSP 110 shown in FIG. 1. Noise shaping quantizer 200
includes first and second comparators 202, 204, first and second
summers 208, 210, duty ratio quantizer 206, and integrating error
amplifier 220. Integrating error amplifier 220 contains saturation
function module 222, first, second, and third integrators 224, 228,
232, first and second multipliers 226, 230, and third summer
234.
[0024] Ramp r(t) and input signal x(t) are supplied to the inputs
of first comparator 202. Ramp r(t) provides double-sided sampling
of the input signal x(t). First comparator 202 compares ramp signal
r(t) to input signal x(t). Ramp r(t) is a periodic sawtooth signal
that repeats at half the desired sampling frequency. As above, the
sampling frequency is 10-20 times higher than the Nyquist rate. The
Nyquist rate is about twice the highest frequency of interest.
Thus, for audio signals the highest frequency of interest is about
20 KHz and the Nyquist rate is about 40 kilosamples/second. In this
case, the sampling frequency is about 600-800 kHz. By comparing the
ramp signal r(t) to the input signal x(t), a signal is provided
whose width is proportional to the amplitude of the input signal
x(t). The output from first comparator 202 is the ideal PWM signal
x.sub.PWM(t), which does not have quantization. Ideal PWM signal
x.sub.PWM(t) is supplied to first summer 208 and to saturation
function module 222 in integrating error amplifier 220.
[0025] Input signal x(t) is also supplied to the input of second
summer 210, along with summed integrated output v(t) from third
summer 234 in integrating error amplifier 220. The output from
second summer 210, noise shaped input signal z(t), and ramp r(t)
are supplied to the inputs of second comparator 204. Second
comparator 204 compares ramp signal r(t) to noise shaped input
signal z(t) and provides noise shaped PWM signal x.sub.NS(t).
[0026] Noise shaped PWM signal x.sub.NS(t) and counter clock c(t)
are supplied to the inputs of duty ratio quantizer 206. Counter
clock c(t) has a frequency that is much larger than the maximum
frequency of interest of input signal x(t). For audio signals, as
auditory range for the human ear extends nominally to 20 kHz, the
frequency of counter clock c(t) is about 96 kHz. The output of duty
ratio quantizer 206 is supplied to first summer 208 and is also
taken as the PWM output signal y(t) from noise shaping quantizer
200.
[0027] Saturation function module 222 supplies saturation function
SAT to first and second multipliers 226, 230. First summer 208
subtracts output signal y(t) from ideal PWM signal x.sub.PWM(t) and
supplies error signal e(t) to first integrator 224 of integrating
error amplifier 220. First integrator 224 integrates the error
signal e(t) to produce first integrator output signal
int.sub.1(t).
[0028] First integrator output signal int.sub.1(t) is supplied both
to first multiplier 226 and to third summer 234. First multiplier
226 combines the first integrator output signal int.sub.1(t) with
saturation function SAT from saturation function module 222 to
produce first multiplier output signal m.sub.1(t). First multiplier
output signal m.sub.1(t) is supplied to second integrator 228.
Second integrator 228 integrates first multiplier output signal
m.sub.1(t) to produce second integrator output signal
int.sub.2(t).
[0029] Second integrator output signal int.sub.2(t) is supplied
both to second multiplier 230 and to third summer 234. Second
multiplier 230 combines second integrator output signal
int.sub.2(t) with saturation function SAT from saturation function
module 222 to produce second multiplier output signal m.sub.2(t).
Second multiplier output signal m.sub.2(t) is supplied to third
integrator 232. Third integrator 232 integrates second multiplier
output signal m.sub.2(t) to produce third integrator output signal
int.sub.3(t), which is supplied to third summer 234. As above,
third summer 234 provides the feedback to second summer 210 that
provides noise shaping of the input signal x(t).
[0030] Saturation Function module 222 modifies the gain of the
feedback loop inside noise shaping quantizer 120. Saturation
function SAT may be either a linear or non-linear function. The
linear or non-linear function SAT can either be a continuous linear
or non-linear function or piecewise linear or non-linear function.
In addition, although saturation function module 222 is shown in
FIG. 2 as dependent on only the input signal, any combination of
the input signal x(t) and/or output signal y(t) may be used. The
modifications are such that the loop transitions from a higher
order feedback loop with multiple integrators 224, 228, 232, which
is not unconditionally stable, to a first order unconditionally
stable loop. This is shown in the example of FIG. 3, which
illustrates how the root locus (or poles) of the gain function move
with the onset of saturation.
[0031] As shown in FIG. 3, before any saturation, the system has
four poles (one due to each of the three integrators and one due to
the feedback loop). The location of the poles indicates stability
of the system; poles that are in the left half plane (to the left
of the y axis) and have a relatively small angle with respect to
the x axis result in a stable system. At full saturation, the poles
caused by second and third integrators 228, 232 become degenerate
and have no effect. Referring to FIG. 2, this is to say that
saturation function SAT becomes zero, and thus the input to second
and third integrators 228, 232 become zero. This, in turn, leads to
the output of second and third integrators 228, 232 becoming
constant, i.e. second and third integrators 228, 232 are
effectively removed from the feedback loop. The constant value is
the last value provided by second and third integrators 228, 232.
As can be seen in FIG. 3, since the angle from the x-axis in the
plot of the existing poles at saturation is not greater than when
no saturation is present, and the system is stable when no
saturation is present, the system is also stable at saturation.
[0032] FIG. 4 illustrates a quantized duty ratio when the input is
a sine wave having an amplitude (about 1.2) that is larger than the
switching amplifier can handle (1). Unlike arrangements that
artificially cap the duty ratio at less than 100% or greater than
0% (for example 10% and 90%), the duty ratio extends to 0% and
100%. That is, as the input signal x(t) saturates the system, the
pulse width becomes either high or low for the entire time period
of the PWM pulse. As illustrated in FIG. 4, one of the regions in
which this occurs is at about sample number 100 to about sample
number 275. In an example in which a battery is used as the power
supply for an audio system, at a 0% duty ratio, the entire negative
battery voltage is provided across the speaker and at a 100% duty
ratio, the entire positive battery voltage is provided across the
speaker.
[0033] Before saturation, the values from the integrators take any
value. However, when saturated, the values from the integrators
224, 228, 232 stop changing and maintain the last value before
saturation. An example of this is shown in FIG. 5, which shows
integrator values corresponding to the sample number between about
75 and 325. As illustrated, the signals from integrators 224, 228,
232 vary in the normal mode but when saturation is reached, the
signals stop changing. The operations in the feedback loop are
unchanged so that when the level of the input signal crosses the
transition point there is no transient or any associated artifact.
This is illustrated in FIG. 5, which clearly shows the lack of
ringing, overshoot or other transient at transitions between normal
operation and saturation.
[0034] The equations that define the integral noise shaping without
the saturation function are as follows: il 1 .function. ( n ) = I 1
.function. ( nT s ) = ir 1 .function. ( n - 1 ) + ( 1 - yr
.function. ( n - 1 ) ) - ( 1 - xr .function. ( n - 1 ) ) [ 1 ] il 2
.function. ( n ) = I 2 .function. ( nT s ) = ir 2 .function. ( n -
1 ) + ir 1 .function. ( n - 1 ) + ( 1 - yr .function. ( n - 1 ) ) 2
- ( 1 - xr .function. ( n - 1 ) ) 2 2 [ 2 ] il 3 .function. ( n ) =
I 3 .function. ( nT s ) = ir 3 .function. ( n - 1 ) + ir 2
.function. ( n - 1 ) + ir 1 .function. ( n - 1 ) 2 + ( 1 - yr
.function. ( n - 1 ) ) 3 - ( 1 - xr .function. ( n - 1 ) ) 3 6 [ 3
] zl .function. ( n ) = xl .function. ( n ) + k 1 .times. il 1
.function. ( n ) + k 2 .times. il 2 .function. ( n ) + k 3 .times.
il 3 .function. ( n ) [ 4 ] ir 1 .function. ( n ) = I 1 .function.
( ( n + 1 2 ) .times. T s ) = il 1 .function. ( n ) + ( ( xl
.function. ( n ) ) - ( yl .function. ( n ) ) ) [ 5 ] ir 2
.function. ( n ) = I 2 .function. ( ( n + 1 2 ) .times. T s ) = il
2 .function. ( n ) + il 1 .function. ( n ) + ( ( xl .function. ( n
) ) 2 - ( yl .function. ( n ) ) 2 ) 2 [ 6 ] ir 3 .function. ( n ) =
I 3 .function. ( ( n + 1 2 ) .times. T s ) = il 3 .function. ( n )
+ il 2 .function. ( n ) + il 1 .function. ( n ) 2 + ( ( xl
.function. ( n ) ) 3 - ( yl .function. ( n ) ) 3 ) 6 [ 7 ] zr
.function. ( n ) = xr .function. ( n ) + k 1 .times. ir 1
.function. ( n ) + k 2 .times. ir 2 .function. ( n ) + k 3 .times.
ir 3 .function. ( n ) [ 8 ] ##EQU1##
[0035] In eqns. 1-8, n is an integer, Ts is one switching period,
ir.sub.x and il.sub.x refer to the output from the integrator
number x (i.e. int.sub.x) during the falling and rising of the ramp
signal r(t), respectively, xl(n) and yl(n) are the input and output
duty ratio signals during the rising of the ramp signal r(t),
respectively, and xr(n) and yr(n) are the input and output duty
ratio signals during the falling of the ramp signal r(t),
respectively. Thus, eqns. 1-8 compute the first through third order
integrals of the error due to quantization for the right half of
the PWM signal y(t). For clarity of presentation, the order of the
integrals is from first to third. In practice, the third integral
is computed, then the second, and finally the first integral. These
integral equations, in closed form, allow the computation to be
performed at the sampling frequency. In equation 4, the k values
correspond to weighting factors of the integrators. Although the k
values shown in FIG. 2 are 1, the k values can take on any value
desired. For more information, see U.S. Pat. No. 6,414,613, herein
incorporated by reference.
[0036] The equations that define the integral noise shaping with
the saturation function SAT are as follows: il 1 .function. ( n ) =
I 1 .function. ( nT s ) = ir 1 .function. ( n - 1 ) + ( ( 1 - yr
.function. ( n - 1 ) ) - ( 1 - xr .function. ( n - 1 ) ) ) [ 9 ] il
2 .function. ( n ) = I 2 .function. ( nT s ) = ir 2 .function. ( n
- 1 ) + ( ir 1 .function. ( n - 1 ) + ( 1 - yr .function. ( n - 1 )
) 2 - ( 1 - xr .function. ( n - 1 ) ) 2 2 ) .times. SAT [ 10 ] il 3
.function. ( n ) = I 3 .function. ( nT s ) = ir 3 .function. ( n -
1 ) + ( ir 2 .function. ( n - 1 ) + ir 1 .function. ( n - 1 ) 2 + (
1 - yr .function. ( n - 1 ) ) 3 - ( 1 - xr .function. ( n - 1 ) ) 3
6 ) .times. SAT [ 11 ] zr .function. ( n ) = xr .function. ( n ) +
k 1 .times. ir 1 .function. ( n ) + k 2 .times. ir 2 .function. ( n
) + k 3 .times. ir 3 .function. ( n ) [ 12 ] ir 1 .function. ( n )
= I 1 .function. ( ( n + 1 2 ) .times. T s ) = il 1 .function. ( n
) + ( ( xl .function. ( n ) ) - ( yl .function. ( n ) ) ) [ 13 ]
##EQU2## ir 2 .function. ( n ) = I 2 .function. ( ( n + 1 2 )
.times. T s ) = il 2 .function. ( n ) + ( il 1 .function. ( n ) + (
( xl .function. ( n ) ) 2 - ( yl .function. ( n ) ) 2 ) 2 ) .times.
SAT [ 14 ] ir 3 .function. ( n ) = I 3 .function. ( ( n + 1 2 )
.times. T s ) = il 3 .function. ( n ) + ( il 2 .function. ( n ) +
il 1 .function. ( n ) 2 + ( ( xl .function. ( n ) ) 3 - ( yl
.function. ( n ) ) 3 ) 6 ) .times. SAT [ 15 ] zr .function. ( n ) =
xr .function. ( n ) + k 1 .times. ir 1 .function. ( n ) + k 2
.times. ir 2 .function. ( n ) + k 3 .times. ir 3 .function. ( n ) [
16 ] ##EQU3##
[0037] Thus, eqns. 9-16 are similar to eqns. 1-8, except that the
input and output signals at half the previous sampling period Ts
are multiplied by the saturation function SAT.
[0038] One example of a typical timing diagram for the input signal
x(t), the output signal y(t), and ramp r(t) is shown in FIG. 6. As
can be seen, ramp r(t) is periodic and has a period of Ts. If ramp
r(t) has a nadir at nTs, where n is an integer, the apex of ramp
r(t) occurs at (n-1/2)Ts. Between (n-1)Ts and nTs the input and
output signals on the left half of ramp r(t) are labeled xl(n-1)
and yl(n-1), respectively, and the input and output signals on the
right half of ramp r(t) are labeled xr(n-1) and yr(n-1),
respectively. Similarly, between nTs and (n+1)Ts the input and
output signals on the left half of ramp r(t) are labeled xl(n) and
yl(n), respectively, and the input and output signals on the right
half of ramp r(t) are labeled xr(n) and yr(n), respectively. The
rise and fall times, and thus the widths of the input and output
signals (xl(n-1), xr(n-1), yl(n-1), yr(n-1), xl(n), xr(n), yl(n),
and yr(n)) vary dependent on the quantization from the previous
period, as described in more detail in U.S. Pat No. 6,414,613.
[0039] The integral noise shaping and saturation function SAT can
be described by the following algorithms (where x and y here
indicate the duty ratio of the input and output signal,
respectively, 0=0% and 1=100%): SAT=0 for x=1 or x=0 (input
saturation) [17] SAT=1 for small signals (x=1/2) [18] SAT=0 for y=1
or y=0 (output saturation) [19]
[0040] These conditions can be filled by different continuous
nonlinear equations, for example: SAT=(1-(2x-1).sup.2n) [20]
SAT=(1-(2y-1).sup.2m)(1-(2x-1).sup.2n) [21] SAT=4x(1-x) [22]
SAT=8x(1-x){1-2x(1-x)} [23] SAT=1-(2x-1).sup.2.sup.n [24]
SAT={1-(2x-1).sup.2n}{1-(2y-1).sup.2m} [25]
[0041] Alternately, different nonlinear piecewise equations can be
used. For example: SAT=8(x-2x.sup.2) for 0.ltoreq.x<1/4, [26]
SAT=1 for 1/4.ltoreq.x<3/4, SAT=8(3x-2x.sup.2-1) for
3/4<x.ltoreq.1, SAT=16(x-4x.sup.2) for 0.ltoreq.x<1/8, [27]
SAT=1 for 1/8.ltoreq.x.ltoreq.7/8, SAT=16(7x-4x.sup.2-3) for
7/8<x.ltoreq.1, SAT=32(x-8x.sup.2) for 0.ltoreq.x< 1/16, [28]
SAT=1 for 1/16.ltoreq.x.ltoreq. 15/16, SAT=32(15x-8x.sup.2-7) for
15/16<x.ltoreq.1,
[0042] Continuous linear and piecewise linear equations can also be
used as saturation function SAT.
[0043] Depending on the algorithm used, there is little or no
branching for the integral noise shaping. As shown in FIG. 2,
integrating error amplifier 220 has a small module that supplies
the saturation algorithm (saturation function module 222), which
may have branching for piecewise linear saturation functions.
However, the feedback loop in the integral noise shaping is
performed (i.e. eqns. 9-16) are calculated with no branching--it
performs the same functions, merely using the saturation function
as a multiplicand. As there is no branching in the feedback loop,
this increases the efficiency of the processor, thereby saving
energy.
[0044] Turning to power consumption efficiency, the MOSFETs (not
shown) in power stage 124 dissipate very little power except during
the interval between their on and off states. The power wasted is
low because the instantaneous power dissipated in the MOSFETs is
the product of voltage and current, and one or the other is almost
always close to zero. The saturation function increases the peak
power out of switching amplifier 112 as power stage 124 is
relatively more efficient when operated with a 0% or 100% duty
ratio than when operated at a duty ratio close to 0% or 100%.
[0045] One cause of the inefficiency in the power stage 124 when
operating at a duty ratio close to 0% or 100%, however, is due to
the MOSFETs in the power stage being forced to transition fast
enough so that they are not able to reach steady state equilibrium.
A typical curve of efficiency vs. duty ratio is shown in FIG. 7. As
illustrated, the power conversion efficiency remains substantially
flat over a wide range of duty ratios, dropping rapidly at about
10% and 90% until the duty ratio reaches 0% or 100%. When the duty
ratio reaches 0% or 100%, however, the efficiency increases as no
switching of the MOSFETs occur.
[0046] Thus, the switching amplifier described can provide a PWM
signal with a duty ratio that extends between any arbitrary pair of
values, for example, as indicated from 0% to 100%. In different
embodiments, this may result in a peak power rating of the
switching amplifier being 30 to 40% greater (i.e. a higher output
power) compared to that of a switching amplifier whose duty ratio
is limited to about 10%-90% in order to maintain loop stability. A
higher power switching amplifier is not only louder but is often
perceived to be a higher audio quality than a lower power switching
amplifier. This may be desirable when the power supply of the
switching amplifier is a battery, as the battery voltage is not
changeable by design. Examples of using a battery voltage include
portable applications or automotive applications. In such examples,
it is impractical to use large, expensive, and/or high power
consuming components such as a boost power converter to increase
the power and limit the duty ratio between 10% and 90% of the
nominal duty ratio.
[0047] Note that although an embodiment with three integrators is
shown, the number of integrators can vary, and can be two, four,
five, or more, depending on how much performance or computation vs.
power consumed is desired. Similarly, only a single saturation
function can be used or a number of saturation functions can be
selectable as desired. For example, for automotive audio switching
amplifiers or stereo equipment that is plugged into a wall socket,
in which a substantial amount of power is available, a more
aggressive algorithm may be desired, whereas for a portable device
such as an MP3 player with a small amount of power is available, a
lower performance may be more desirable.
[0048] While the present disclosure has primarily described
applications such as digital audio amplification applications, it
is also applicable to other power applications, including motor
control, data conversion, power amplification, and radio frequency
(RF) synthesizers with or without amplification. In any system
where the output signal is quantized and noise is to be removed
from the output, the present invention provides a method of noise
shaping in which the quantization error and saturation function is
used in coordination with a noise shaping filter to remove the
noise from the desired baseband of the output.
[0049] In other embodiments, a feed forward arrangement rather than
a feedback arrangement may be provided. Although an embodiment
using a DSP is provided, in other embodiments software to achieve
the same results may be implemented as code stored in any adequate
computer readable medium and alternate hardware may be used. For
example, a hardware accelerator may be used to implement the noise
shaping function. The hardware accelerator may include a custom
logic board with processor, and may implement at least a portion of
the function in software. The entire operation may also be
implemented in an integrated circuit providing an embedded
solution.
[0050] Accordingly, the specification and figures are to be
regarded in an illustrative rather than a restrictive sense, and
all such modifications are intended to be included within the scope
of present invention. As used herein, the terms "comprises,"
"comprising," or any other variation thereof, are intended to cover
a non-exclusive inclusion, such that a process, method, article, or
apparatus that comprises a list of elements does not include only
those elements but may include other elements not expressly listed
or inherent to such process, method, article, or apparatus.
[0051] It is therefore intended that the foregoing detailed
description be regarded as illustrative rather than limiting, and
that it be understood that it is the following claims, including
all equivalents, that are intended to define the spirit and scope
of this invention. Nor is anything in the foregoing description
intended to disavow scope of the invention as claimed or any
equivalents thereof.
* * * * *