Download Presented at AUDI the 100th Convention 1996 May 11

High Fidelity PWM based Amplifier Concept for Active Speaker
Systems with a very Low Energy Consumption
Karsten Nielsen
Bang & Olufsen, Denmark
and Technical University of Denmark,
Presented at
the 100th Convention
1996 May 11-14
Copenhagen
Preprint 4259 (Q-4)
Lyngby, Denmark
AUDI
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AN AUDIO ENGINEERING SOCIETY PREPRINT
High
Fidelity PWM based Amplifier
Concept for Active
Systems with a very Low Energy Consumption
Speaker
Karsten Nielsen
Bang & ()lufsen, Denmark
and
Institute of Automation, Technical University of Denmark
E-mall: kn@iau:dtu.dk
Abstract
This paper addresses various aspects on dedicated Pulse Width Modulation
(PWM) based amplifiers for active speaker systems. An new amplifier concept,
dedicated to woofer/midrange (0-4KHz) loads, has been developed to provide a
high fidelity solution with minimal energy consumption in both analogue and
digital active speaker systems. The concept is based on a novel feedback
topology, a modulation strategy which is dependent of bandwidth, and the use of
a switching frequency as low as 44.1KHz without compromising the sound
quality. Detailed measurements on two 200W example implementations (700Hz
and 4KHz bandwidths) are given, showing THD+N < 0.1% and an unweighted
dynamic around 110dB. A new efficiency measure termed the energy efficiency is
defined, based on consumer behaviour investigations. The amplifier examples are
shown to provide reductions in energy consumption by more than 90% compared
to conventional principles, mainly due to a total idle power consumption of only
1.5W, and power stage efficiencies approaching 96% at higher ot_tput powers.
1.
Introduction
Conventional very inefficient and bulky class A or AB amplifiers are still almost exclusively
used to drive loudspeakers. Relatively little research activity is directed towards the (in theory,
at least) much more efficient digital amplifiers based on Pulse Width Modulation (PWM),
despite numerous obvious advantages of this amplifier technology:
· Considerable reductions in volume and weight.
· Potential reductions in amplifier cost, especially for high power amplifiers.
· A theoretical higher level of basic linearity.
· Reductions in power supply transformer and decoupling.
· Temperature stability and reliability.
· A higher level of design freedom.
Several problems have prevented the use of the basic PWM amplifier concept such as
complexity, distortion and noise problems, Electromagnetic Interference (EMI), and finally a
power consumption that was not far from analogue counterparts due to e.g. high switching
losses. This paper addresses various aspects on high fidelity PWM amplifier design, with
active speaker systems as application. The design decisions have been driven by the following
basic design philosophy and overall design goals:
· The total amplifier energy consumption has been given high priority.
· The sound quality has to be comparable with the best analogue class AB counterparts. Very
low distortion and noise is desirable.
· The concept should cover 400Hz (woofer) - 4KHz (woofer and midrange) bandwidths and
an continuos output power range of 40W - 200W without changes in the topology.
· The use of advanced (expensive) techniques requiring tuning in production etc. should be
avoided. A very low resulting complexity is desirable.
Power amplifier energy consumption in a given period of time, is a factor that has not been
given much interest, although it is well known that in common audio products nearly all the
supplied power is dissipated as heat. The major consumers are in general the audio amplifier
and power supply (and the speaker obviously). The energy consumption is adressed here by
definition of a new efficiency measure - the energy efficiency, on the basis of simple consumer
behaviour investigations, in terms of an average distribution of volume control positions. The
energy efficiency makes it possible to optimise the amplifier in respect to energy consumption
(what the consumer will see on the bill). The novel amplifier concept can reduce the energy
consumption ia a given speaker system considerably, without compromising the sound
quality. All energy efficiency considerations and optimisation guidelines can be easily
generalised to general purpose amplifiers, as e.g. the novel topology that is presented in [1].
2. Definition
of energy efficiency
The traditional efficiency measure is given by:
n(x) = P o(x)
pc,(X)
( 1)
where Po(x) and Poe(x) are the output power and supplied power, respectively. (1) does not
provide any information on the energy consumption of the amplifier, due to its inherent
dependence on the relative output level x. Fig. 1 illustrates both ideal and typical efficiency
curves for representative examples of the three amplifier classes: AB, G and AB with switch
mode supply's (following the audio signal). A description of the models use to estimate the
efficiency of theses alternative amplifier principles, is beyond the scope of this paper. Below 20dB the typical efficiency of all amplifiers principles gets very low, primarily due to the
quiescent power losses. The traditional efficiency measure is usually specified at the level
with maximal power dissipation or at the maximal output level (heat sink design
considerations), and there is in general no correlation between (1) and the amplifier energy
consumption.
A definition of the average consumer behaviour, will inevitably have to be based on
assumptions. The average distribution of volume control positions will thus vary, due to
variable loudspeaker sensitivity, room size, user age and numerous other parameters. Still it is
possible to generalise, and define four subjective listening levels as given in the table below:
Distribution
0%
1%
1.0,%
89 %
Output level (dB re max.)
0dB
-9 dB
-24 dB
-40 dB
Subjectivelevel
Clipping
Party
Listening
Back_round.
,,,
The distributi9n should be interpreted as: In 89% of the time, the average user listens to
background music with an average relative output level at -40dB etc. The given categories
represent a good average in consumer applications. The dissipation for a given output power
on the contrary, will vary a lot dependent on amplifier size and construction. A new measure,
the energy efficiency neff, is defined on the basis of the distribution given in the table above.
By use of the the energy efficiency measure, concepts can be categorised on the basis of '
simple power loss measurements. More important, the simple measure can be used as an
optimisation parameter to minimise the energy consumption.
To generalise, given a set of data on the following form:
(nl,Po,l,Pv,1),(n2,Po,2,Pv,2)
....
(nn. Po.n,PD,t_)
(2 )
where (nj,Po.j, Po.j) refers to that the output power in average is Po.j in nj percent of the
time, and Pt,.j refers to the losses at the given output power. The effective output power and
the effective power dissipation are:
N
Po,el=Y_ni·Po,i
( 3)
i=l
and
N
PD.eff = Z ni ' PD,i
i=1
(4 )
The energy efficiency is now defined as:
N
Z
?o,eff =
Po.eff
neff= Pcc,eff PO,el + POef
'
ni 'PO.i
i=_
(5)
N
N
i=1
i=l
y_n_.PD,i+Y_n_.PO.,
rleffrepresents the real amplifier energy efficiency, i.e. r/effis directly indicates how much of
the supplied energy, that is utilised in the speakers. Fig. 2 illustrates the typical energy
efficiency for class AB, G and class AB with switching supplies, as a function of the quiescent
power loss factor (5, defined as:
= Pcc,idle
Po....
(6 )
Again, the analysis has been based on realistic models of the amplifiers, including amongst
others estimated quiescent power losses and the finite headroom. The different classes can not
be compared directly, since typical values of t5will vary. For a class AB amplifier, t5is thus in
the area 0.1-0.2, while the typical values for the other classes are lower.
Some rather interesting conclusions can be drawn by the use of the energy efficiency measure:
· The typical energy efficiency for a typical class AB amplifier is in the area 0.5%-2% !
(adding supply losses, the number is even lower).
· The energy efficiency for an ideal class B amplifier is only 7.1% (se Fig. 2) independent on
output power capability. This is due to the inherent losses bound to the principle.
· THe traditional efficiency measure reveals close to nothing about the energy consumption,
since it is usually specified at a level far from the normal user situation (i.e. it should only
be used in heat sink design considerations).
· Idle power losses and the losses at low output levels are crucial for the overall energy
consumption.
Given these results one can ask, why use of the class AB principle is so dominant today, There
are several answers to this question: First of all, until recently no audio company have had a
declared green policy. Second, amplifier weight has by many actually been considered an
important parameter, i.e. the more weight the better amplifier. Third, construction of reliable
low distortion class AB power amplifiers up to 200-300W is relatively simple and well
known. Despite this it is the authors belief, that the 'green wave' will also soon hit
audio/video products, making a high energy efficiency an attractive parameter, especially
since labelling or standardisation in consumer electronics in general seems to be on its way
[5].
3. Pulse Width Modulation
Fig. 3 illustrates the very basic principle behind a Pulse Width Modulated (PWM) amplifier,
also known as a digital power amplifier [17-18] due to digital operation of the power stage
transistors, or a class D amplifier. An audio signal is modulated by a carrier signal. The carrier
is a sawtooth or a triangle signal, corresponding to single sided modulation (leading or trailing
edge) and double sided modulation, respectively. The resulting PWM signal is converted to
power levels by a power switch. The power switch used in this work is a bridge configuration,
which is illustrated in Fig. 5. The secret of the theoretical very high efficiency of the PWM
amplifier at all output levels, is that the power transistors are operating either fully 'on'
(shorted) or 'off'. The power transistors are thus kept out of the power consuming active
region, whereby the theoretical efficiency (and energy efficiency) is 100%.
3.1 Bandwidth limited digital amplification in active speaker systems
The amplifier concept is targeted for an active speaker system with separate amplifiers for
each band, as illustrated by the 3. way example in Fig. 4. The specific use of digital amplifier
technology in active speaker systems have some very important advantages:
· The load and amplifier can be matched perfectly. In general purpose amplifier systems one
has to consider nominal load variations (typically 2, 4 and 8 ohms). Furthermore, the
loudspeaker cable length is not known.
· It is possible to optimise the load impedance to obtain minimal power consumption in any
given application.
· Bandwidth limited amplification can be utilised to its full extent. While the power
dissipation of a class B amplifier is independent on amplifier bandwidth, a reduced
bandwidth can be used to reduce the carrier frequency and thereby the switching losses.
· Connection wires from amplifier to speaker can be made very short. The simplifies post
filter Radio Frequency Interference (RFI) relations.
As introduced above, this work concentrates on the woofer/midrange area only. This is no
limitation in respect to the total energy consumption, since almost all acoustic energy, and
thereby amplifier power consumption is concentrated in this band. The spectral amplitude
distribution varies with music material of course, but it is possible to generalise [2-4] and
determine an a/verage distribution. Fig. 6 illustrates a more specific analysis carried out in [2].
Almost independent of music material, the average acoustic power in the tweeter band 4KHz 20KHz. is much lower than in the other bands. This will be reflected in the necessary power
amplifier size and thereby the average power consumption. Even with conservative tweeter
amplifier design in regard to the high transients, the necessary power handling capability is
only around 10-15% of the total power.
The tweeter could be driven by a full bandwidth PWM amplifier of course (full bandwidth
versions prototypes of the amplifier concept has been developed with very satisfying
performance), but still this will not lead to the same remarkable change in either volume,
weight or energy consumption in most applications due to the lower tweeter amplifier size.
3.2 Pulse width modulation
schemes
Pulse width modulation results in a sampling of the signal. There are two main sampling
forms, termed natural sampling (NPWM) and uniform sampling (UPWM). Natural sampling
refers to that it is the instantaneous intersections of the carrier and signal, which is used to
determine the switching instants of the width modulated pulses. The natural sampling thus
implies an intrinsic natural selection of the sampling points. The other major category of
modulation is Uniform sampling. 'Uniform' refers to, that the signal remains uniform
(constant) over one period of the reference triangle wave or sawtooth signal. It is thus the
sampled signal, which is compared with the reference. The 'uniform sampling' is a natural
consequence in digital systems, where the modulator input is already sampled.
Further modulation subclasses are defined by the switching method, which can be either class
AD or class BD (three level). They will be termed AD PWM and BD PWM in the following.
The differences of these modulation schemes are illustrated in Fig. 8, and the two modulators
are illustrated in Fig. 7, with bridge connections indicated left. AD PWM takes two values,
whereas unipolar switching takes three values, since a zero level is included in the modulation
Jrocess. A summary of the possible modulation schemes is given in the table below:
Natural sampling (NPWM)
Singlesided
Leading
Trailing
AD BD AD BD
Uniform sampling (UPWM)
Doublesided
AD
BD
Singlesided
Leading
Trailing
Doublesided
Leading
Trailing
AD BD AD BD AD BD AD BD
A through analysis of the advantages/disadvantages of the different modulation strategies in
PWM amplifier systems is beyond the scope of this paper. This paper is concentrated on
double sided NPWM, class AD and BD. Natural sampling has the clear advantage over
uniform sampling that it only generates intermodulation components and no forward harmonic
distortion. By using reasonable carrier to audio frequency ratios, the audio signal can thus be
perfectly regenerated, as it will be illustrated in the following.
Pulse width modulation of a sine wave has amongst others, been analysed by Bennett [6]
followed by Black [7] and Bowes [8]. Using a double fourier series, a sine wave modulated by
double sided AD PWM and BD PWM, can be expressed as:
XAD (t) =
M. U. cos(tO,t) + 4. U. _
JO(M'
m'ir m.2 ) sin(ne.2 ). cos(re,tOc't)
m=l
(7)
+4.U. m=ln=+l
_n=_ Jn(M'm'2)ne.lr
sin((m+n)'2)'c°s(ne'C°c .t+n.tO.t)
and
xBo(t) = M. U. cos(tO,t)
+_
-4.U.
_
_
m=ln=+l
Jn(m'M. 2)
ne.Jr
sin((m+n)'_)'sin(n'2)'sin((m'tOc
(8)
+n't°)'t-n'2)
Where:
M
U
co
COc
Jn
n
m
Modulation index. M_ [0;1].
The bridge power supply level (DC).
Audio signal angle frequency.
Carrier signal angle frequency.
Bessel function of nth order.
Index to the harmonics of the audio signal.
Index to the harmonics of the carrier signal.
A double fourier series expansion is necessary since, in the general case no relationship exists
between the signal and the carrier. The PWM waveform will thus not be periodic, and a single
fourier series is not adequate. From the series, the individual components of the modulated
signal are easily determined. Fig. 9 illustrates the spectral content of an AD and BD pulse
width modulated sine wave. The spectrum is shown for modulation indexes varying over a
60dB input signal range, with a switching frequency of 44. IKHz and a 4KHz input (the upper
bandwidth limit). Clearly, the modulation is a non linear process, but the modulation does not
directly distort the audio signal, i.e. no forward harmonic distortion is present in the
modulation spectrum.
From ( 7 ), ( 8 ) and Fig. 9, several important differences between double sided BD PWM and
double sided AD PWM are observed:
· The effective sampling frequency of the audio signal is doubled when using BD, while the
switching losses are retained. Alternatively, BD offers the theoretical possibility of halving
the switching frequency.
· In BD PWM; neither the carrier or its harmonics are present in the modulated signal. The
IM components with the lowest frequencies are located around 2.fc.
· In BD PWM, the intermodulation components components amplitude decrease linearly
with the audio signal. The residual is thus in theory totally 'noiseless'.
· The maximum output voltage step is halved in BD, i.e. less differential noise has to be
eliminated by a post filter.
· In BD PWM, the PWM bridge output terminals contains high level common mode
components with a peak to peak amplitude of U, while AD only generates a DC common
mode component of U/2. This is illustrated in the bottom of Fig. 8.
· The BD PWM modulator is somewhat more complex. (Fig. 7).
Both modulation strategies are used by the concept to obtain an optimal configuration at any
given amplifier bandwidth. The background for using both modulation strategies, will be
discussed in section 5 and 6.
4. Main PWM amplifier
topologies
In recent years, there has been a considerable interest in PWM amplifiers based on digital
PWM, where the modulation is performed in the digital domain by a enhanced sampling
process based on precompensation techniques, which approaches natural sampling in terms of
modulation spectra [13-15]. A PWM amplifier based on digital PWM is interesting, since all
signal processing in the system is either digital or time discrete. A good solution to the coarse
UPWM distortion by precompensation was introduced in [12-13]. Recently addressed
problems has been the intermodulation between noise shaper generated wide band noise
components in the non linear PWM process [16]. In general, the work performed has
concentrated on the small signal PWM performance, and very good small signal (PWM DAC)
performance is achievable today. But to the best of the authors knowledge, no fully specified
PWM power amplifier based on digital PWM with satisfying distortion and noise
performance exists to date.
To illustrate the reason for this problem, and to argue for analogue PWM as an alternative also
in digital input amplifier systems, Fig. 10 shows two equivalent digital amplifier systems
based on digital and analogue PWM, where the precompensation is performed by linear
interpolation [15] in the XPU unit. Performing the modulation in the digital domain saves
three functional blocks:
· The DAC analogue Iow pass filter. Since a PWM DAC is based on fine requanitsation, the
necessary order of the small signal demodulation filter is small.
· The analogue PWM modulator, consisting of a comparator (AD) and a precision triangle
wave generator (basically a few opamps and a comparator).
· The feedback block.
All these elements can be realised in very high quality at a low cost with general purpose
active devices. These differences should therefore not determine the choice of topology.
4.1 The powerstage problem
The fundamental problem of the digital PWM based topology (top of Fig. 10), is that the
power stage can not easily be encompassed by general feedback. Although the natural linearity
of a PWM output stage can be designed more linear than e.g. a class AB output stage, it will
still be not reach high end performance, in terms of distortion and noise. It is well known, that
a system only performs as good as it weakest part, at this is what troubles the digital PWM
based power amplifier. The inherent non-ideal elements, that causes the problems are mainly:
· A cross-over type of distortion, caused by blanking.
· Finite (and especially unequal) rise- and fall times of the PWM signal.
· Power supply induced distortion. Since the power supply level directly 'generates' the
PWM signal, any power supply variations will be reflected as distortion in the audio
waveform. In other words the power supply rejection ratio PSRR is OdB with a power stage
operating open loop.
· Temperature dependence and component tolerances leads to rather large deviations in
transistor parameters.
· The output stage will introduce some audio band noise, which is not reduced by regulation.
The use of an A/D converter to provide the digital feedback is not considered rational, due to
its inherent failings and cost. Efficient digital precompensation is difficult, due to the complex
dynamic operation of the power stage non-ideal elements. It is the authors belief that a high
end, cost efficient, reliable and robust commercial digital amplifier can not be realised without
the positive features of general feedback. Similar conclusions have been drawn by
Vanderkooy [11 ].
4,2 Analouge PWM and digital input
Referring to Fig. 10 (bottom), the digital amplifier based on analogue PWM with a PWM
DAC front, if correctly implemented, offers the possibility of general feedback with the
following very important advantages over the other topology:
· Considerable lower distortion and intermodulation at all output powers and frequencies.
· Considerably lower residual noise level, i.e. a higher dynamic range.
· The power design can be relaxed. An unregulated supply will be sufficient in most
applications.
· A more robust construction, with a natural correction of variations due to ageing, spread in
production etc.
· New possibilities, e.g. supply variation to lower the quiescent and low level power
consumption. With sufficient regulation, the power supply level could be changed while
retaining the amplifier gain. The is a very interesting new possibility, when the scope is to
design amplifiers with the highest energy efficiency possible.
The bottom topology in Fig. 10 offers the possibility of combining digital PWM with power
stage feedback, whereby the DAC as an individual block can be saved. This is a very
important where DSP circuitry is already present, as in digital speaker systems. Referring to
Fig. 10 (bottom) the first three modules can therefore be realised by the DSP. Due to the
limited bandwidths in woofer/midrange amplifiers the complexity of the DSP algorithms is
considerably lower than in full bandwidth versions, e.g. the interpolation module can be
eliminated or reduced considerably in complexity, and the remaining instructions are
performed at a lower sampling frequency. Simulations has shown, that very high quality
woofer/midrange PWM DAC performance can be achieved by only around 5-10% (dependent
on quality) of processor time in the general purpose floating point DSP processors of today. In
a three way digital speaker system, the total amount of DSP processor time would thus be
maximal 20% for the woofer and midrange amplifier, which is a minimal loss considering that
two high quality general purpose DAC's can be saved.
5, The concept
A block diagram of the basie amplifier topology is shown in Fig. 11. As discussed above, the
possibility of digital input is provided, either by implementing the DSP of the digital PWM
modulator in a' general purpose digital signal processor, or by the use of a general purpose
DAC. The 2. order crossover filter (active/digital) also limits to input slew rate and noise,
besides realising the crossover function:
5.1 The feedback topology
Although the research activity in this field has been very limited over the past 30 years, some
feedback topologies have been presented. The dominating technique has been feedback after
the post filter [9-101, combined with phase compensation for the post filter phase shift.
Reasonable amount of feedback can only be realised by rather high switching frequencies
degrading the overall efficiency, which is not desirable. A novel topology is presented in the
parallel paper [1]. This approach could be generalised to lower bandwidths, but current
measurement adds complexity and power dissipation, and the loop optimisation is bound by
more restrictions typically leading to a higher switching frequency for a given amplifier
bandwidth. These factors are of course not desirable, when the task is to develop amplifiers
with the highest energy efficiency possible.
The essential overall feedback is taken before the output filter to avoid the phase shift of the
post filter. The basic advantage of this approach is a higher level of freedom to shape both
forward and feedback paths for optimal performance. The loop is shaped by considering the
following important parameters/trade-offs:
· A consistent loop gain of 30-40dB at all audio frequencies, with the highest gain at lower
fi'equencies where the non-linear and linear errors dominate.
· Wide open loop bandwidth, to obtain a good transient response and avoid Transient
Intermodulation Distortion (TIM).
· High PSRR especially at lower frequencies, to lower the demands of supply regulation.
Ideally, the use of a simple and cost efficient unregulated power supply is desirable.
· Avoidance of missed pulses at the modu!ator, which can produce undesirable sub harmonic
components.
The concept is based on a switching frequency of only 44.1KHz, independent of bandwidth.
The exact choice of 44.1KHz is based on a desire to synchronise the amplifier switching
frequency to the remaining system, especially in event of a digital speaker system. To
minimise the possibility of interference problems, this synchronisation is necessary.
The modulation strategy is determined primarily by amplifier bandwidth. At bandwidths
lower than 2KHz, AD has shown most advantages in terms of complexity of modulator and
post filter (the basic post filter topology varies with modulation method). BD is used in the
remaining bandwidth area 2KHz - 4KHz. The characteristics of BD (se Fig. 9) is used at these
higher bandwidths to provide a higher loop bandwidth without introducing noise. In this way,
a satisfying control loop response can be realised without increasing the switching frequency.
Loop synthesis software has been developed with MATLAB. The software will synthesise an
optimal loop configuration for any given bandwidth, output power, load impedance etc.
5.2 Modulator, driver and power stage
The modulator, driver and power stage are important elements in the system. Careful design
and layout are essential to obtain optimal performance. Open loop distortion rising from
0.01% to 0.5-1% at maximal power can be achieved at all frequencies, even in high power
amplifiers. Such open loop figures are necessary to obtain a satisfactory closed loop
performance.
There has been a considerable development in Power MOSFET transistors and driver
technology in the recent years. The amplifier concept is based on a integrated H-bridge driver,
capable of sourceing and sinking the high peak currents at the necessary speeds for the above
mentioned open loop performance. The basic power stage topology is the bridge
configuration, shown in Fig. 5. The single supply operation is a very important advantage,
which simplifies the power supply design compared to conventional amplifier topologies,
especially class G.
5.3 The reconstruction
filter
As previously mentioned, a very important advantage of dedication is the possibility of
matching the post filter and load perfectly. The 2. order reconstruction filter of the PWM
amplifier se}'ves a double function. Besides the reconstruction, it also realises half of the 4.
order crossover filter, which can be designed arbitrary. An advantage of this precise 2. order
passive cut-off at the bandwidth limit, is a lower audio band noise level. The broad band
noise, that inevitably is introduced in the modulation process, is thus limited at the bandwidth
limit.
The post filter / cross-over filter topology vary
encountered with PWM amplifiers for reduced
get bulky in high power applications if high
primary parameters influencing the post filter
bandwidth and the maximal output power.
with modulation strategy. One of the problems
bandwidth, is that post filter inductors tend to
post filter linearity is to be maintained. The
inductor size is the load impedance, amplifier
One of the solutions is to use a low loudspeaker impedance (2-4 ohms) at the very low woofer
bandwidths in high power applications. Another solution for further reductions in filter
volume is possible when using AD PWM. The total filter vblume (and cost) can be redaced by
more than 50%. Si-ice there is no common mode components (Fig. 8) when using AD PWM,
ground referenced capacitors are not necessary. This reduces the filter complexity, since the
filter capacitance is reduced by a factor of 4. Further reductions are possible by realising the
two filter inductors on the same core. Besides halving the number for cores in the filter to only
one, the use of coupled inductors reduces the total amount of copper. Due to the high level of
common mode components with BD PWM, common mode filtering is essential. Since the
lower bandwidth limit for BD is specified to 2KHz, filter volume will not be serious with the
given limitation on amplifier power capability of up to 200W.
6. PWM amplifier examples
Two high power examples have been developed to demonstrate the performance of the
concept. The specifications are summarised in the table below. The specifications will now be
documented in detail with a series of practical measurements and observations.
10
Rated continuos output power.
(THD+N_0.1%)
Clipping
level(THD+N-1%)
Bandwidth
Switching frequency
Equivalent crossover filter
Nominalloadimpedance
Modulation strategy
Supply voltage (single)
THD+N
(20Hz-_f,_,_, 100mW--)Po,_)
Residualnoise20Hz-22KHz
Example1
200W
Example2
200W
300W
700Hz (Wf)
44.1KHz
4. order Bessel
4 ohms
AD
50V
0.01%-0.08 %
300W
4KHz (Wf/Mid)
44.1KHz
4. order Bessel
4 ohms
BD
50V
0.003%-0.1%
60_V RMS
120_tVRMS
(unw)
Dynamic
range(unw)
Idleconsumption
-Total
Max.powerstageefficiency
Typ.totalmax.efficiency
Powerstageefficiencyat 1W
Energy
efficiency
Estimated
energysavings
compared with 200W class AB
amplifier.
115dB
1.5W
96%
92%
60%
=20%
>90%
108dB
1.SW
96%
94%
60%
=20%
>90%
6.1 Theoretical and measured power dissipation and efficiency
Fig. 12 illustrates the theoretical calculations on the power stage dissipation and efficiency
with the given parameters. The calculations are based on realistic switching characteristics of
the bridge transistors. Also shown is the power stage dissipation / efficiency with higher
carrier frequencies (full bandwidth frequencies). The analysis clearly illustrates the effect of a
reduced switching frequency in woofer/midrange applications, especially in regard to
quiescent power losses. It should be mentioned, that an increase in switching frequency, e.g.
to 88.2KHz, especially at higher bandwidths is a possible alternative, which can give better
results in terms of distortion and noise. The price is an increase in power dissipation, but as
Fig. 12 illustrates this price is modest. Still, the concept is based on 44.1KHz to illustrate that
it is possible to obtain satisfying performance with maximal efficiency, and a carrier
frequency very close to the audio band.
Fig. 13 shows the measured power consumption and efficiency for Example 1, and the main
results are summarised in the table. Measurements on Example 2 gave similar results. The
power losses are divided into power stage losses (determining the heat sink), filter and
analogue losses (primarily the driver). The measured power stage power losses should be
compared the theoretical figures given in Fig. 12. Whereas the power stage losses are
determined by the amplifier parameters (power, switching frequency... ), the post filter losses
could be optimised further by reducing the filter inductor DC resistance, which would also
reduce the amplifier output impedance. This is a theoretical way of increasing the efficiency
further than the 92% at higher output powers. From the measured power losses, the energy
efficiency is easily determined as defined in (5). The result is an energy efficiency around 20%
11
for both amplifiers, which should be compared with the maximal 2% obtainable with an
equivalent class AB amplifier. The reduction in energy consumption is thus by more than
90%.
6.2 Distortion and noise
Fig. 14 and Fig. 15 shows the measured THD+N for both amplifiers at selected output levels.
All measurements are performed with Audio Precision System One. For Example 1, the
distortion remains at a low 0.01%-0.03% level at all practical output levels up to -6dB. A
higher output powers the distortion rises to 0.08%. Example 2 showed a larger spread in
distortion (Fig. 15), with THD+N varying from the very low 0.003% level at low frequencies
to approximately 0.1% at maximum continuos power. Again, the overall distortion is low
(THD+N<0.04%) at output levels below -6dB.
The continuous power is specified at 200W for both examples, although very good distortion
figures (determined by the post filter mainly) were obtained up to the clipping level at
approximately 300W where distortion rapidly rises to 1%. The amplifiers thus have a good
power reserve. In general, the maximal power level can simply be changed by changing the
supply level. On of the advantages of PWM amplifiers, is this tremendous flexibility to
change in the output power capability without changes in the construction other the power
supply level.
An FFT analysis of the residual noise is illustrated in Fig. 16. The residual is sampled at
44.1KHz and an 16K FFT with 16x averaging has been performed. From the resulting FFT,
the unweighted audio band noise level has been calculated, and it is given in the table above
as RMS unweighted noise level and dynamic range. A wide band FFT analysis of the residual
of Example 1 is shown in Fig. 18. The only component of importance is the well damped first
harmonic of the carrier at -70dB, corresponding to about 15mV.
As a supplement to the THD+N curves, an FFT analysis at two lower output powers (100mW
and 1W) are shown in Fig. 17. These analysis reveal the dominating distortion to be uneven
harmonic distortion. The harmonic roll-off is satisfying. All harmonics above the 5. harmonic
are thus well damped.
7. Electromagnetic
compatibility (EMC)
A problem of considerable interest in digital power amplifier systems is Electromagnetic
Compatibility (EMC). With discrete power stage components, optimal connections between
power FET die's and power bus decoupling capacitors is impossible, and the very high power
stage di/dt and dv/dt necessary to secure the high overall efficiency and acoustic performance,
is the source of conducted and radiated EMI. A further side effect is that the EMI can couple
(by common impedance paths or by radiation) to the modulator section, degrading the audio
performance by increasing the audio band noise or causing spurious tones to be present in the
audio band. Layout is of paramount importance to reduce the problems at the source (where it
should be attacked). The examples prototypes have been implemented using surface mount
technology (SMT) on a 12x12 cm 4. layer PCB, with high density layout of the driver and
power stage in an area of only 3x4 cm.
To illustrate the sources of the EMI problems, and to obtain an extra angle on the comparison
of the two modulation schemes, Fig. 19 - 20 shows an idealised analysis of some of the
important power stage currents in both time and frequency domain. The differential output
12
current (Fig. 19) has a relative low HF-content due to the inductive load, and these
connections are less critical. The primary current components are around multiple of the
carrier frequency 44.1KHz for AD and around multiples of the double carrier frequency when
using BD modulation. Fig. 20 illustrates the high frequency content of the currents in the
bridge transistors in each half bridge, concentrated around multiples of the carrier frequency
with both modulation schemes. The power transistors should ideally be connected by single
point connections. The supply current'has a large amount of high frequency content as the
current in the bridge transistors, and tight deeoupling of each half bridge is therefore
necessary. When using BD modulation, the supply current components will concentrate
around multiples of the double carrier frequency. (similar to the differential load current).
Of primary importance when discussing EMC in digital amplifier systems is disturbance of
the AC mains in the area 10KHz-30MHz, and the high frequency radiated emissions measured
at a 3m distance. The standards therefore are given in [19]. Example 1 has been tested in
regard to AC mains disturbance with a simple unregulated supply. Measurement equipment
and recommendations were as specified in [191. A peak measurement of the AC mains
disturbance is shown in Fig. 21. The peak measurement method can be interpreted as a
conservative quasi-peak (CISPR) measurement [19], and the quasi peak standards can
therefore be used. Clearly, the disturbance is well below the standards at all frequencies. The
dominating peaks are caused by resonances between power bus decoupling capacitors and
output stage resonances.
8, Conclusions
Various aspects on dedicated Pulse Width Modulation (PWM) based amplifiers for analogue
and digital active speaker systems have been addressed. The energy consumption of various
amplifier principles has been investigated by definition of a new energy efficiency measure.
The investigations show, that traditional amplifiers principles have a very poor energy
efficiency around 1%. The novel amplifier concept has been shown to provide high fidelity
solution with minimal energy consumption in both analogue and digital active speaker
systems, by the use of a novel feedback topology, varying modulation strategies with
bandwidth and a very low 44.1KHz switching frequency.
Detailed measurements were given on two high power 200W prototypes. Despite the carrier
frequency very close to the audio band and the high power capability, the prototypes
demonstrate a low residual audio band noise level of 70gV-120gV RMS. Furthermore,
THD+N was below 0.1% (in the area 0.003%-0.1%) at all frequencies and output powers.
Measurements have shown reductions in amplifier energy consumption by more than 90%,
due to energy efficiencies around 20%. The major reasons were pointed out to be a low total
idle power consumption of only 1.5W, and a high efficiency at lower output levels.
Furthermore, the high power stage efficiencies approaching 96% at higher output levels,
virtually eliminates the need for a heat sink, despite the high power handling capability.
The disadvantages of bandwidth limited, digital power amplification in active speakers were
pointed out to be the filter volume in low bandwidth, high power applications, and the issue of
Electromagnetic Compatibility. A solution was given to reduce the filter volume by around
50%, and the EMC problems was shown to be solvable. To conclude on the
advantages/disadvantages in these applications, PWM amplifiers seems to be an ideal solution
which will open up for a range of new possibilities.
13
9. Acknowledgements
The author want to thank Michael A.E. Andersen for being a valuable reference in the field of
power electronics. Thanks also to the Electroacoustics Research & Development department
at Bang & Olufsen, for being open minded and very helpful.
10. References
[1]
Niels Anderskouv, Karsten Nielsen and M. A. E. Andersen. "High fidelity PWM
switching amplifiers based on a novel double loop feedback technique"
To be presented at the 100th AES Convention, Copenhagen. May 11-14.
[2]
P.J. Chapman. "Programme material analysis"
To be presented at the 100th Convention of the AES. Copenhagen. May 11-14.
[3]
R.A Greiner et al. "The spectral Amplitude Distribution of selected compact Discs".
Journal of the AES, April 1989. p. 246-275.
[4]
IEC Publication note IEC268-5.
[5]
Karsten Nielsen and Michael A. E. Andersen.
"Possible technical solutions to reduce energy consumption in Audio Products.".
EU Workshop on Energy savings in Consumer Electronics. Copenhagen May 1995.
[6]
Bennet. W.R. "New results in the calculation of modulation products". Bell. Syst.
Tech. Journal. 1933, 12, p, 228-243.
[7]
H.S. Black. "Modulation Theory".
Van Nostrand. 1953.
[8]
S. Bowes et al. "Novel approach to the analysis and synthesis of modulation
processes in power converters."
Proc. IEE. May. 1975. p. 507-513
[9]
B. Attwood ' Design Parameters Important for the Optimisation of Very-High-Fidelity
PWM (Class D) Audio Amplifiers
Journal of the AES, Nov. 1983. p. 842-853.
[10]
J, Hancook. "A class D Amplifier Using MOSFET's with Reduced Minority Carrier
Lifetime"
89th Convention of the AES. Los Angeles. CA. September 21-25.
[11]
J. Vanderkooy. "New Concepts in Pulse-Width Modulation".
97th Convention of the AES. San Francisco. November 10-13.
[12]
Leigh, S.P et al. "Distortion minimisation in Pulse Width Modulated systems using a
digital sampling process"
Electronic Letters. Aug. 1990. Vol. 26. No. 16. p. 1310-1311.
14
[13]
P.H. Melior et al. "Reduction of the spectral distortion in class D amplifiers by an
enhanced pulse width modulation sampling process ".
IEE Proceedings-G. Vol. 138. Aug. 1991. p. 441-448.
[14]
R.E Hiorns et al. "Power Digital to analogue conversion using pulse width modulation
and digital signal processing.".
IEE Proceedings-G. No-5, October 1993. p. 329-338.
[15]
M. Shajaan et al. "All digital Power Amplifier Based on Pulse Width Modulation"
96th Convention of the AES. Amsterdam. 26/2 - 1/3. Preprint 3809.
[16]
P. Craven "Towards the 24-bit DAC: Novel Noise-Shaping Topologies Incorporating
Correction for the Nonlinearity in a PWM Output Stage"
JAES. Vol. 41. No. 5. May 1993.
[17]
Taylor, W.E. "Digital Audio Amplifier". U.S Patent. No. 4724396.
[18]
B.S.King. "Switched-On Amps: Power with a pulse".
Audio, Feb. 1995. p. 42-45.
[19]
European Standard EN55013 on Electromagnetic
15
Compatibility.
Ideal efficiency vs. rel output level
]
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Typical efficiency vs. rel. output level
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Fig. 1 Ideal (left) and typical (right) efficiency vs. relative output level for class AB, class G and
class AB with switch mode supply (following the audio signal).
Energy efficiencyvs. quies, lossfactor
1
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' Fig.
Class G (lower supply level at 50%)
Class AB with sw. supply.
2 Energy
efficiency
and class AB with
switch
vs. the quiescent
mode
supply
loss factor
(following
16
for models
the audio
signal)
of typical
amplifiers.
class
AB,
G
x_put
Reference
t_
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'Power Switch
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Fig. 3 Basic elements of a Pulse Width Modulated amplifier.
v_
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Fig. 5 The power stage is based on a bridge configuration, providing
single supply operation, and both two- and three-level PWM control.
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Fig, 4 An active speaker system (here 3 way) based on separate amplifiers for each band.
Also shown is the typical necessary relative power handling capability of the power amplifiers
of each band.
17
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Fig. 6 An example of the distribution of signal levels on a CD in four
bands [2]. The bands are divided at 650hz, 1500hz and 4.5KHz. The
programme material is "The Division Bell" by Pink Floyd.
Audi°/_'/
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Fig. 7 Double sided AD and BD PWM modulators.
18
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Fig. 8 Central waveforms of the considered modulation schemes. On top is shown the signal and
carrier for reference. The middle figures show the signals in each half-bridge, and the lower
curves show the resulting differential and common mode signals at the bridge terminals. The
differential signal is demodulated by the passive post filter.
19
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AD. f=4 KHz, fc=44.1 KHz
BD. f=4 KHz, fc=44.1KHz
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amplitude range. The audio signal frequency is 4 KHz (the bandwidth limit).
20
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Theoretical power stage efficiency
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Fig. 12 Theoretical calculations of power stage power dissipation and power stage efficiency vs. switching
frequency and output power. The switching frequencies are fc=44.1KHz, 2'fc, 4lc, 8fo The upper
efficiency curve and lower power dissipation curve correspond tofc=44.1KHz.
22
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curve (lower dissipation curve) is for the power stageon]y, and the lower efficiency curve (upper
dissipation curve) is for the total amplifier.
Z
HZ
Fig. 14 Measured THD+N for Example 1. THD+N vs. frequency is measured
at IW, 10W, 50W, 100W and 200W (the top curve).
23
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lW, 10W, 50W, 100W and at the maximal 200W output power (the top
curve),
-60
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Fig. 16 A 16K, 16x averaged FFT of the output residual noise for the two amplifier examples
(44.1KHz sampling frequency). Also indicated are the resulting unweighted RMS levels, relative
to full scale.
24
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Fig. 17 FFT analysis of both amplifier outputs at 100mW and 1W output power. (16K, 16x av.,
44.1KHz). Left shows the results for Ex. I with a 250Hz input, and right shows the results for Ex.
:2 with a IKHz input. The rise in noise floor level compared to Fig. 16 to is due 'to Audio
Precision One resolution.
25
0
,
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-40
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40
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50
Frequency
(KHz)
'-i '''''' _'''''_ , ....
60
70
':
80
Fig. 18 Wide band noise FF-Tanalysis of Ex. 1 (16K FFT, 176,4KHz, 16x av.). The
higher residual noise level is due to the higher sampling frequency used in the FFT.
The only noticeable component is the damped -70dB (15mV) 44,1KHz carrier.
AD
.......................................................................................................... i
BD
"T..............................................................................................................
Fig. 19 Differential load current in both types of modulation in both time and frequency
domain (0-1MHz). The parameters are M=0.9 and f=2KHz. Remark the very low high
frequency current content in the load due to its inductive nature.
26
AD
BD
:' ''''''''
_
t
"i
i
1" I
Fig. 20 The current though a single bridge FET illustrated in time and frequency domain
(0-1MHz). The parameters are M=0.9 and3_--2KHz.The high frequency content (high dj/dr)
is the cause of oscillations and radiation.
Bang & Olufsen]
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Fig. 21 AC mains measurement according to EN55013. The illustrated peak
measurements (limits as CISPR) shows that the mains disturbance is well below
the standards.
27