FIELD OF THE INVENTION
This invention relates to electronic amplifiers and more
particularly to a feedback amplifier in which a class D amplifier and a low-pass
filter connected in cascade thereto are fedback through two feedback loops of the
voltage signal supplied to a load.
BACKGROUND OF THE INVENTION
It is becoming even more difficult to realize high power
linear amplifiers of relatively small size with an ever increasing number of channels
to be amplified.
The so-called D amplifiers are widely used because they
are characterized by a relatively small power consumption and reduced size and weight.
One of the drawbacks due to the use of a class D audio amplifier is the need of
interposing between the power stage and the loudspeaker a filter for extracting
the low-frequency spectral content (from about 20Hz to about 20kHz) from the output
of the power stage.
The functioning principle of a class D amplifier consists
in modulating a carrier of a frequency ƒc
with a signal to be amplified of frequency ƒs
much smaller than ƒc, and in demodulating the output
signal generated by the power stage. A possible modulation appropriate for this
objective is the PWM modulation (Pulse Width Modulation), to which reference will
be made hereinafter. In this case, the modulated signal is a square wave with a
fixed frequency and duty-cycle adjusted in function of the signal to be amplified.
As shown in Figure 1, the information content relative
to the amplified signal may then be extracted from the PWM modulated signal by a
low-pass LC passive filter (called also demodulation filter).
Preferably, a snubber network SN is connected
in parallel to the load such to reduce the load voltage ripple.
The core of inductors for audio filtering applications
is of a material having a non negligible hysteresis, therefore the value of the
inductance L varies and depends on the current that flows through the winding.
This phenomenon is even more evident when the core is relatively small (low cost).
Therefore, the filtering operation introduces a nonlinearity
that directly influences the amplified signal. As a consequence, the THD (Total
Harmonic Distortion) of a class D amplifier is strongly influenced by the performances
of the demodulation filter, because the filter is one of the main sources of distortion
in switching amplifiers.
Moreover, the LC filter is connected in series to the load
and interferes with the direct control of the amplifier of the loudspeaker making
the frequency response depend from the load, as shown in the Bode diagrams of Figure
2. The frequency response becomes even less regular when the loads, such as loudspeakers,
are not purely resistive.
In order to prevent a modulation of the frequency response
in function of the load it is preferable to choose a cut-off frequency
of the cascade low-pass filter + load larger than 20kHz. In general the cut-off
is always chosen as a compromise between the need of dampening high frequency
components of the output signals generated by the power stage and the requisite
of the largest possible frequency response.
The possibility of introducing a filter inside a feedback
loop would allow a reduction of the output harmonic distortion by compensating eventual
nonlinearities introduced by the filter, or would allow a reduction of the costs
of the reactive elements of the filter (a cost that in practice may be close to
the cost of the whole amplifier), thus keeping unchanged the THD of the whole system.
Moreover, by introducing a feedback of the output of the filter an enhanced control
of the frequency response of the amplifier on the load could be expected, thus making
it less sensible to load variations.
However, feedbacking the system in a classic manner by
using the output of the filter, as shown in Figure 3, would be a hardly affordable
way because of the strong outphasing introduced by the LC pair that imposes a relevant
reduction of the loop gain of the circuit in order to stabilize the system. As a
consequence, this solution is not capable of reducing distortion nor of widening
the frequency response.
Several feedback amplifiers are described in literature.
discloses a switching amplifier that has a voltage and a current feedback
The presence of a feedback current complicates the circuit
structure and requires a current sensor that increases relevantly fabrication costs
of the system.
The article "
A Novel Audio Power Amplifier Topology with High Efficiency and State-of-the-Art
Perform", by T. Frederiksen, H. Bengtsson and K. Nielsen, 109th AES Convention,
2000 September 22-25, Los Angeles, California, USA
, discloses a switched power audio amplifier with at least two feedback
paths, one of which is connected directly to the output of the power stage according
to a COM (Controlled Oscillation Modulator) technique.
The presence of a feedback at the output of the power stage
generates aliasing that, generally speaking penalizes the linearity performances
of the system. Moreover, the functioning is based on a self-oscillating circuit
(the input signal modulates the duty-cycle of the square wave at the output of the
oscillator) with a variable oscillation frequency. This characteristic may penalize
the system from the point of view of the EMI (ElectroMagnetic Interference) and
makes difficult the synchronization of other signals with the oscillation frequency
of the circuit.
The article "
High Fidelity Pulse Width Modulation Amplifiers based on Novel Double Loop
Feedback Techniques", by N. Anderskouv, K. Nielsen, M. A. E. Denmark, 100th AES
Convention, 1996 May 11-14, Copenhag
en, discloses a power audio amplifier with a voltage feedback loop and
a current feedback loop.
Besides the drawbacks due to the presence of the previously
mentioned current feedback, the loop gain is unsatisfactory.
The article "
An Asynchronous switching high-end power amplifier", by P. van der Hulst,
A. Veltman e R. Groeneberg, 112th AES Convention, 2002 May 10-13, Munich, Germany
, discloses a switching power amplifier with current feedback that is affected
by the above mentioned drawbacks due to the current feedback.
SUMMARY OF THE INVENTION
A new architecture of a feedback amplifier easy to realize
that solves the above mentioned problems of distortion and worsening of the frequency
response, due to the presence of the demodulation low-pass filter has now been found.
This invention provides a new feedback architecture for
a PWM switching audio amplifier, capable of compensating the effects of the demodulation
filter through at least two feedback paths of the voltage applied to a load without
penalizing the overall loop gain of the device. Each of the feedback paths includes
a respective network (or filter) for compensating a respective frequency pole of
the cascade low-pass filter + load and establishing a certain band pass.
According to an embodiment of this invention, these networks
(or filters) are passive networks.
The feedback amplifier allows for a further reduction of
the distortion because the fedback signal is that output by the low-pass demodulation
filter, in cascade to the class D amplifier, differently from the prior art amplifiers
that feedback a signal that occupies an unlimited band generated from the power
stage (that is the class D amplifier), thus generating aliasing phenomena that degrade
the linearity performances of the circuit.
Moreover, the proposed architecture allows, with the same
pass band of known amplifiers, to reduce the high frequency voltage ripple on the
supplied load significantly lowering electromagnetic emissions.
The invention is defined in the annexed claims.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be described referring to the attached
DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION
Figure 1 illustrates schematically the functioning principle of a switching
Figure 2 shows the frequency response of the cascade low-pass filter + load
+ snubber network for different values of the purely resistive load Rload
(with L=50 µH, C=1 µF);
Figure 3 shows an example of a system fedback with a filter inside the feedback
Figure 4 is a block diagram of the proposed solution;
Figure 5a and 5b are respectively the linearized circuit of the internal
loop and the diagram of the module of the loop gain;
Figure 6 is a Bode diagram of the transfer function Vout
Figures 7a and 7b are respectively a block diagram of the external loop and
the relative Bode diagram of the loop gain;
Figure 8 is a block diagram of an embodiment of this invention;
Figure 9 is a block diagram of a second embodiment of this invention;
Figure 10 is a detailed view of the internal loop of the circuit of Figure
Figure 11 is a Bode diagram of the module of the gain of the internal loop
of the circuit of Figure 10;
Figure 12a is a detailed view of the internal loop of the circuit of Figure
9 with a generator of an input signal Vx
Figure 12b shows the Bode diagram of the transfer function VoutVx-
of the loop of Figure 12a;
Figure 13 shows schematically the outermost loop of the circuit of Figure
Figure 14 is a Bode diagram of the gain of the loop of Figure 13;
Figure 15 shows a classic voltage switching amplifier with feedback of the
output of the power stage;
Figure 16 is a diagram of the frequency response of the device of this invention
of Figure 9 for different values of the purely resistive load Rload
(with L=50 µH, C=1 µF).
Indeed, the demodulation filter introduces a phase shift
that may make the system unstable if a simple feedback is adopted. According to
this invention, this problem is effectively eliminated by realizing at least two
feedback paths with each loop comprising at least a filter for compensating the
poles of the low-pass demodulation filter and fixing (generally, widening) the pass
band of the amplifier.
Figure 4 depicts a preferred architecture of a device of
this invention, including:
- a plurality of feedback paths of the load voltage downstream the reconstruction
- a fixed frequency clock that defines the frequency of the output PWM waveform.
The stability of the distinct feedback loops, from the
innermost with a transfer function of the loop gain G
loop,1, to the outermost with a transfer function Gloop,n
, is analyzed herein below.
For better understanding how the device of this invention
works, that for simplicity of analysis is supposed linear, let us consider a circuit
with only two loops. Moreover, let us assume that the feedback loop includes a passive
network, described by the following transfer function:
with &tgr;2 << &tgr;1 and
that the transfer function of the cascade composed of the low-pass filter and the
load has two complex conjugated poles at a frequency ƒT
and that the presence of the snubber network may be neglected.
Considering only the innermost loop, shown in Figure 5a,
of the amplifier of this invention, one of the poles of Gloop,1
introduced by the LC low-pass filter is compensated by choosing the parameters
that define the network Rƒ
1 introduced in the feedback loop, the transfer function of
loop,1 as depicted in Figure 5b and the transfer function of
as shown in Figure 6 are obtained.
Compensation of the pole at a cut-off frequency
is achieved by positioning at the same frequency a zero of the network (filter)
introduced in the feedback path.
By substituting the inner loop with a block with a transfer
it is possible to obtain an equivalent system, depicted in Figure 7a with a loop
having the transfer function of Figure 7b, having supposed that
It is to be noticed that this transfer function is characterized by a single pole
at a frequency ƒin, that ensures the stability of the feedback
system. By choosing the parameters that define the block A2
and the network Rƒ2
(typically, but not necessarily independent from the frequency) of the second
loop the overall gain and also the cut-off frequency ƒex
of the transfer function
are determined and thus also the pass band of the feedback amplifier of this invention.
By optionally adding two further outer feedback paths (that
is paths around the previously illustrated two loops) of the load voltage
Vout, it is possible to vary (typically to increase) the cut-off frequency
of the system or the overall loop gain of the device. Increasing the overall loop
gain is desirable because it determines a reduction of the distortion introduced
by the system on the signal to be amplified.
Figure 8 depicts a prototype of an amplifier made according
to this invention, in which two control loops of the load voltage Vout, the
respective feedback paths of which include the networks Rƒ
1 and Rƒ
2, both fundamental for the stability of the system, while Figure 9 depicts
in a more detailed fashion the same circuit, with a current input (Iin
In general, the presence of only two feedback paths is
sufficient for satisfactorily compensating the negative effects of the LC filter
and obtaining a high loop gain.
Preferably, the reference carrier Irif
is a square wave at a fixed frequency ƒc, that may
be fixed in a broad frequency range. The frequency ƒc
should be chosen such to prevent possible interferences with devices operating
in the same electromagnetic environment. The output of the power stage, immediately
upstream the low-pass filter LC, is a PWM wave.
Using a square wave as a reference carrier instead of a
triangular wave, as typically done in PWM modulators at fixed frequency is advantageous
because a square waveform may be more easily generated than a triangular waveform.
According to a preferred embodiment of this invention,
the reference carrier is provided in the feedback loop and it is added to at least
a feedback signal provided by a respective feedback loop, that reduces sensitivity
of the device in respect to the characteristics of the square wave reference current,
thus the architecture is further simplified.
For studying the stability of the system let us refer to
Figure 10, that depicts the equivalent circuit of the linearized internal loop.
For linearizing the loop, a mathematical model involving the averages of the state
variables (available in literature, for example in:
R. D. Middlebrook - "Small-Signal Modelling of Pulse Width Modulation Switched-Mode
Power Converters", Proceedings of the IEEE, Vol. 76, pp.343-354, No. 4, April 1988
) is used, the square wave carrier being integrated and a corresponding
triangular wave being on the node Y. The equivalent gain of the cascade DRIVERS
+ POWER STAGE of Figure 9 is indicated with D.
The block with gain K
1 introduced in the feedback loop allows to attenuate the fedback signal
and may even be a simple resistive voltage divider. The pair R
1 introduces a zero at a frequency ƒT
in the transfer function of the loop gain Gloop,in
of the inner loop, that compensates one of the poles introduced in the cascade
of the low-pass filter + load (neglecting for sake of ease the effect of the snubber
network, as shown in Figure 12a). This condition makes the Bode diagram of the module
of the loop gain Gloop,in
cross the axis at 0dB with a slope not larger than - 40dB/dec. Tests demonstrated
that, by choosing properly the various parameters, a phase margin sufficient to
make stable the innermost loop can be obtained
Figure 11 depicts the Bode diagram of the module of the
loop gain Gloop,in
while the frequency diagram of the transfer function Vout
is depicted in Figure 12b.
Figure 13 schematically depicts the external loop of the
system, with a loop gain Gloop,ex. The inner loop has been substituted
with a block with a transfer function H=Vout
/Vx. Preferably, the blocks with gain K
2 and K
3 are attenuators, simply made of resistive voltage dividers.
The resistor R
2 and the capacitor C
2 allow to compensate a pole of the transfer function of the loop gain
of the outer loop by introducing a zero at a frequency ƒin,
as shown by the Bode diagram of Figure 14. Even in this case, the Bode diagram of
the module of the loop gain Gloop,ex
crosses the axis at 0dB with a slope not larger than -40dB/dec, thus it is
possible to obtain a phase margin sufficient for making stable the outermost loop
by properly designing the parameters of the circuit.
The values of K
3 and R define the gain of the circuit and contribute to determine
the band (equal to ƒex) of the feedback amplifier of this
invention. The block K
2 allows to shift up or down the characteristic of the module of the
loop gain Gloop,ex
thus allowing an optimization of the phase margin.
Moreover, by diminishing the gain K
2, it is possible to maintain the same loop gain Gloop,ex
by diminishing the capacitance C
2, thus reducing the silicon area occupation. This is highly desirable
for integrating the device. Similarly, the gain K
3 allows to limit the value of R, thus to reduce the relative
silicon area occupation.
Among the advantages that the amplifier of this invention
offers compared to known amplifiers are:
- a) Compensation of nonlinearity introduced by the LC filter:
tests carried out on prototypes realized by the applicant confirm that the device
of this invention sensibly reduces nonlinearity of the low-pass demodulation filter,
even by two orders of magnitude with only two feedback loops. This allows to reduce
the total harmonic distortion THD of the amplifier or alternatively for the same
linearity performances, to use low cost reactive components.
- b) Possibility of reducing the radiated emission:
from the previous considerations emerges that the band B of the amplifier
may be made independent from the cut-off frequency ƒT
of the cascade low-pass filter + load. It is possible to obtain B≈k20H
z , even if ƒT
<k 20H z, thus, in respect to a traditional circuit architecture
(that is with a demodulating filter external to the feedback loop), the proposed
architecture allows to attenuate more strongly the spectral components at high frequency
of the amplified signal (that are inevitably present even after having filtered
a PWM modulation signal).
Indeed, in the classical architecture of switching amplifier of Figure 15 with feedback
at the output of the power stage, it is necessary to impose ƒT
≈ B for having a band-pass of B≈k20H z. By
supposing that the frequency of the reference carrier is ƒc
= 10B, the main harmonic frequency of the carrier is attenuated on the
load by about 40dB in respect to the amplitude of the carrier output by the power
By contrast, with the novel architecture of this invention it is possible to obtain
B ≈k20H z even imposing
This implies an attenuation of 80dB of the amplitude of the first harmonic of the
carrier (that could be obtained with a traditional solution only by employing a
It should be noticed that the Power Bandwidth (PB) of the amplifier (that is the
bandwidth inside which it is possible to have an amplified output signal with the
largest amplitude allowed by the supply voltage of the power stage) is in both cases
limited by the frequency ƒT. Therefore, by referring to
the previous example, for the amplifier of this invention there is a PB of about
even if it is B ≈k20H z. This, in general, is not a
problem because the energy content of an audio signal is concentrated at the low
frequencies of the audible band.
- c) Control of the frequency response:
the fact that the low-pass filter LC is inside the feedback loop ensures that the
amplifier has a direct control of the amplified signal applied to the loudspeaker,
without interposing elements connected in series or in parallel that may modify
the frequency response. Figure 16 shows a sample frequency response on purely resistive
loads, obtained with the amplifier of this invention depicted in Figure 9 by using
the same filtering components used for the simulation of Figure 2.
By comparing the Bode's diagrams of Figure 16 and Figure 2 it is immediately recognized
that the amplifier of this invention has a pass band much larger than that of the
classic amplifier of Figure 1 and has a practically flat frequency response in the
audible band because the frequency poles of the amplifier are positioned outside
the audible band. The amplifier of this invention is characterized by a frequency
response in the audible band that is substantially independent from the supplied
load and it is the more regular the larger the overall loop gain in this frequency