The
Audio Pages

Elliott Sound Products

Class-D
Amplifiers

Class D Audio Amplifiers - Theory and Design
© June
2005, Sergio Sánchez Moreno (ColdAmp)
Edited & Additional Text by
Rod Elliott (ESP)
Page Created 04 June 2005

Articles Index
Main Index

Contents

1
-   Introduction

2
-   How Class-D Works

3
-   Topologies

4
-   Gate Driving

5
-   Level Shifting

6
-   Output Filter Design

7
-   Feedback

8
-   Other topologies

9
-   Some Final Notes

1 -   Introduction

A completely new technology for audio amplification has been evolving during
the last 15-20 years that has a clear benefit over current widespread Class-A,
and AB topologies. We are talking about the so-called “Class-D”. This benefit is
mainly its high power efficiency. Figure 1 shows typical efficiency curves vs.
Output power for Class-B and Class-D designs.

The theoretical maximum efficiency of Class-D designs is 100%, and over 90%
is attainable in practice. Note that this efficiency is high from very moderate
power levels up to clipping, whereas the 78% maximum in Class-B is obtained at
the onset of clipping. An efficiency of less than 50% is realised in practical
use with music signals. The PWM amp's high power efficiency translates into less
power consumption for a given output power but, more important, it reduces
heatsink requirements drastically. Anyone who has built or seen a high-powered
audio amplifier has noticed that big aluminium extrusions are needed to keep
the electronics relatively cool. The loading on the power transformer is also
reduced by a substantial amount, allowing the use of a smaller transformer for
the same power output.

Figure 1 - Efficiency Comparison for Class-D and
Class-AB

These heatsinks account for an important part of the weight, cost and size of
the equipment. As we go deeper in the details of this topology, we will notice
that a well behaving (low distortion, full range) Class-D amplifier must operate
at quite high frequencies, in the 100KHz to 1MHz range, needing very high speed
power and signal devices. This has historically relegated this class to uses
where full bandwidth is not required and higher distortion levels are tolerable
- that is, subwoofer and industrial uses.

However, this has changed and thanks to today's faster switches, knowledge
and the use of advanced feedback techniques it is possible to design very good
performance Class-D amplifiers covering the whole audio band. These feature high
power levels, small size and low distortion, comparable to that of good Class-AB
designs. (From now on, I will refer to Class-A and AB topologies as
“classical”).

Complete 400W Full-Range Class-D Amplifier Module
(Courtesy of ColdAmp)

From the DIY perspective, Class-D is rather unfortunate. Because of the
extremely high switching speeds, a compact layout is essential, and SMD (surface
mount devices) are a requirement to get the performance needed. The stray
capacitance and inductance of conventional through-hole components is such that
it is almost impossible to make a PWM amplifier using these parts. Indeed, the
vast majority of all ICs used for this application are available only in
surface mount, and a look at any PWM amplifier reveals that conventional
components are barely used anywhere on the board. Since SMD parts are so hard to
assemble by hand and the PCB design is so critical to final performance, DIY
versions of PWM amps are very rare indeed (I don't know of any).

2 -   How Class-D Works

In classical amplifiers, at least one of the output devices (let them be
bipolar transistors, MOSFETs or valves) is conducting at any given time. No
problem so far, but they are also carrying a given current where there is a
voltage drop between collector-emitter / drain-source etc. Since
P = V * I, they are dissipating power, and even if there is
no output a small quantity of current must pass through the transistors to avoid
crossover distortion, so some dissipation is present. As the output voltage
increases, for given supply rails the voltage drop across the transistors will
fall, but the current increases. At saturation (clipping), VCE or VDS will be
low, but current is quite high (Vout / Rspk). Conversely, at low power levels,
current is small but voltage drop is large. This leads to a power dissipation
curve that is not linear with output power. There is a non-zero minimum
dissipation (zero percent efficiency), and a point where maximum efficiency is
reached ... about 78% in pure Class-B designs, 25% or less with Class-A.

Class-D on the other hand, bases its operation in switching output devices
between 2 states, namely “on” and “off”. Before discussing the topology specific
details, we can say that in the “on” state, a given amount of current flows
through the device, while theoretically no voltage is present from drain to
source (yes, almost every Class-D will use MOSFETs), hence power dissipation is
theoretically zero. In the off state, voltage will be the total supply rails as
it behaves like an open-circuit, and no current will flow (that's very close to
reality).

But how can our beloved audio signal be represented by an awful square wave
with only two possible levels? Well, in fact it modulates some characteristics
of this square wave so the information is there. Now we “only” have to
understand the way the modulation is done and how to restore the amplified audio
signal from it. The most common modulation technique used in Class-D is called
PWM (Pulse Width Modulation) - a square wave is produced that has a fixed
frequency, but the time it is in the “high” and “low” states is not
always 50%, but it varies following the incoming signal. This way, when the
input signal increases, the “high” state will be present for longer than the
“low” state, and the opposite when the signal is “low”. If we do some maths, the
mean value of the signal in a single cycle is simply ...

Vmean = Vhigh * D + Vlow * (1-D), where D = Ton / T, (duty cycle)
T
being the period of the signal, that is, 1/Fsw (switching frequency).

For example, the mean value of a 50% duty cycle (both states are present for
exactly the same amount of time) signal going from +50V to –50V is: 50 * 0.5 +
(- 50) * 0.5 = 0V. In fact, the idle (no signal) output of a Class-D amplifier
is a 50% duty cycle square signal switching from the positive to the negative
rail.

If we modulate the input up to the maximum, we will have a near-100%
duty-cycle. Lets put 99%: Vmean = 50 * 0.99 + (-50) * 0.01 = 49V. Conversely,
if the signal is lowest, we need near 0% (lets use 1%), so Vmean = -49V.

PWM is usually generated by comparing the input signal with a triangle
waveform as shown in Figure 2. The triangle wave defines both the input
amplitude for full modulation and the switching frequency

Figure 2 - Basic PWM Generation

Figure 3 shows a typical PWM signal modulated by a sine wave. Notice that it
is designed so signals between –1 and 1V will produce 0% to 100% duty cycles,
50% corresponding to 0V input. The 'digital' output uses standard logic levels,
where 0V is a logic '0' and 5V is a logic '1'. Because of this digitisation of
the signal, PWM amps are sometimes erroneously referred to as digital amps. In
fact, the entire process is far more analogue than digital.

Figure 3 - Aspect of a PWM modulated
signal

Notice that for a correct representation of the signal, the frequency of the
PWM reference waveform must be much higher than that of the maximum input
frequency. Following Nyquist theorem, we need at least twice that frequency, but
low distortion designs use higher factors (typically 5 to 50). The PWM signal
must then drive power conversion circuitry so that a high-power PWM signal is
produced, switching from the +ve to –ve supply rails (assuming a half-bridge
topology).

The spectrum of a PWM signal has a low frequency component that is a copy of
the input signals spectrum, but also contains components at the switching
frequency (and its harmonics) that should be removed in order to reconstruct the
original modulating signal. A power low-pass filter is necessary to achieve
this. Usually, a passive LC filter is used, because it is (almost) lossless and
it has little or no dissipation. Although there must always be some losses, in
practice these are minimal.

3 -   Topologies

There are basically two Class-D topologies - half-bridge (2 output devices
are used) and full-bridge (4 output devices). Each one has its own advantages.
For example, half-bridge is obviously simpler and has more flexibility as a
half-bridge amplifier can be bridged as with classical topologies. If it is not
correctly designed and driven, can suffer from “bus pumping” phenomena (transfer
current to the power supply that can make it increase its voltage producing
situations dangerous to the amplifier, supply and speaker).

Full bridge requires output devices rated for half the voltage as an half
bridge amplifier of the same power, but it is more complicated. Figures 5a and
5b show both topologies conceptually. Obviously, many components such as
decoupling capacitors, etc are not shown.

Figure 4a - Half bridge Class-D
topology

Figure 4b - Full bridge Class-D
topology

Note that full bridge PWM amp needs only one supply rail - bipolar supplies
are not necessary, but can still be used. When a single supply is used, each
speaker lead will have ½ the Vdd voltage present. As it is connected
differentially, the loudspeaker doesn't see any DC if everything is well
balanced. However, this can (and does) cause problems if a speaker lead is
allowed to short to chassis!

The filter may be implemented by means of a single capacitor across the
loudspeaker, by a pair of caps to ground, or in some cases by both (as shown by
the dotted lines connecting the caps).

For the rest of the document, we will concentrate on half-bridge topologies,
although the vast majority of the ideas are also applicable to full-bridge
designs.

Half bridge design

The operation of the half bridge circuit depicted in Figure 4a is as follows
...

When Q1 is on (corresponding to the positive part of the PWM cycle), the
switching node (inductor input) is connected to Vdd, and current starts to
increase through it. The body diode of Q2 is reverse biased. When Q2 is on
(negative part of the PWM cycle), the body diode of Q1 is reverse biased and the
current through Lf starts to decrease. The current waveform in Lf is triangular
shaped.

Obviously, only one of the transistors must be on at any time. If for any
reason both devices are enhanced simultaneously, an effective short-circuit
between the rails will be produced, leading to a huge current and the
destruction of the MOSFETs. To prevent this, some “dead-time” (a small period
where both MOSFETs are off) has to be introduced.

Lf in conjunction with Cf and the speaker itself form the low pass filter
that reconstructs the audio signal by averaging the switching node voltage.

Timing is critical in all this process: any error as delays or rise-time of
the MOSFETs will ultimately affect efficiency and audio quality. So all the
involved components must be high-speed. Dead-time also affects performance, and
it must be minimised. At the same time, the dead-time must be sufficiently long
to ensure that under no circumstance both MOSFETs are on at the same time.
Typical values are 5 to 100ns.

The dead-time is a critical factor for distortion performance. For lowest
distortion, the dead-time must be as small as possible, but this risks
'shoot-through' currents, where both MOSFETs are on simultaneously. This not
only increases distortion and dissipation dramatically, but will quickly destroy
the output devices. If the dead-time is too great, the response of the output
stage no longer follows the true PWM signal generated in the modulator, so again
distortion is increased. In this case, dissipation is not affected.

4 -   Gate Driving

To ensure fast rise/fall times of the MOSFETs, the gate driver must provide
quite a high current to charge and discharge the gate capacitance during the
switching interval. Typically, 20 - 50ns rise/fall times are needed, requiring
more than 1A of gate current.

Note that the schematics shown use both N-channel MOSFETs. Although some
designs use N and P channel complementary devices, that is IMHO sub-optimal due
to the difficulty of obtaining suitable P devices and matched pairs. So lets
concentrate on N-channel only half-bridges. Note that, in order to drive a
MOSFET on, a voltage above Vth must be present between its gate and source. The
lower MOSFET has its source connected to –Vss, so its drive circuit has to be
referred to that node instead of GND.

However, the upper MOSFET is more difficult to drive, as its source is
continuously floating between +Vdd and –Vss (minus drops due to on resistance).
However, its driver must be also floating on the switching node and, what's
more, for the on-state, its voltage must be several volts above +Vdd so a
positive Vgs voltage is created when Q1 is on. This also implies a voltage
shifting so the modulator circuit can communicate correctly with the driver.

This is one of the major difficulties of Class-D design: gate drive. To solve
the issue, several approaches are taken ...

Transformer gate drive: useful in half-bridge power supplies where
duty-cycle doesn't vary widely. In audio amplifiers however, duty cycle ranges
from 0% to 100%, so this method creates a problem because the signal is AC
coupled. A DC restoration circuit (not shown) is needed.

Discrete gate driving: some designs use transistors to perform both the
level shifting and the MOSFET drive. Again, there is a problem: we need a
voltage that is higher than +Vdd.

Integrated drivers: there are a number of MOSFET drivers in the market,
optimised for high speed, that can be used. Again, a voltage higher than Vdd
is needed as well as level shifting.

Figure 5 (a, b & c) depict
some possibilities for 'High Side' gate driving ...

Figure 5a - Transformer Coupled

Figure 5b - Discrete BJT Driver

Figure 5c - IC Driver

Note that circuits in figures 5b and 5c have their PWM input referred to –Vss
so may require previous level shifting of the comparator output, that will
normally be referred to GND. Fig 5a will require level shifting of the inverted
PWM only, as the transformer input can be referenced to GND as shown. Many of
the driver ICs available now have inbuilt level shifters, and these are
optimised for speed. Remember that any delay introduced into the
switching waveform can cause distortion or simultaneous MOSFET conduction.

We have still one problem to solve ... obtaining 12V above VS (the switching
node). We can add another power supply, isolated from the main one, which (-) is
connected to VS. This solution can be impractical, so other techniques are
commonly used. The most widespread is a 'bootstrap' circuit. The bootstrap
technique uses a charge pump built with a high speed diode and a capacitor. The
output of the amplifier produces the switching pulses needed to charge the
capacitor.

Fig. 6 Bootstrap capacitor provides the high side
driver supply voltage

This way, the only auxiliary power supply needed is 12V referenced to –Vss
that is used for powering both the low side driver and the charge pump for the
high side driver. As the average current from this supply is low (although there
are high current charging peaks during the switching events, they last only
20-50ns, twice during a cycle, so the average is quite low, in the 50-80mA
range), this supply is easily obtained from the negative rail with a simple 12V
regulator (paying attention to its maximum input voltage rating, of course).

5 -   Level Shifting

As can be seen from the previous figures, in order to excite the MOSFET
driver, the PWM signal has to be referred to –Vss. So, as the modulator usually
works from +/-5 to +/-12V, typically, a level shifting function is needed. One
can choose to shift the level of the PWM signal and then generate the inverted
version, or generate both outputs and invert both of them. It depends, for
example, on the comparator type used (if complementary outputs are available,
the decision is made).

A basic level shifting function can be performed with a single or
two-transistor circuit similar to the one depicted in Figure 6 (before the high
side driver). While this may work at low frequencies, it is important to
simulate the behaviour of the comparator and level shifter, as they can
introduce considerable delays and timing errors if not properly designed.

It is fair to say that the level shifter is one of the most critical parts of
the circuit, and this is evidenced by the wide variety of competing ICs designed
for the job. Each will have advantages and disadvantages, but in all cases the
complexity is far greater than may be implied by the simplified diagrams.

6 -   Output Filter Design

The output filter is one of the most important parts of the circuit, as
the overall efficiency, reliability and audio performance depends on it. As
previously stated, a LC filter is the common approach, as it is (theoretically)
lossless and has a –40dB/decade slope, allowing for a reasonable rejection of
the carrier if the parameters of the filter and the switching frequency itself
are properly designed.

The first thing to do is to design the transfer function for the filter.
Usually, a Butterworth or similar frequency response is chosen, with a cutoff
frequency slightly above the audio band (30-60KHz). Have in mind that one of the
design parameters is the termination load, that is, the speaker impedance.
Usually, a typical 4 or 8 ohm resistor is assumed, but that would produce
variations in the measured frequency response in presence of different speakers.
That must be compensated for by means of proper feedback network design. Some
manufacturers simply leave it that way so the response is strongly dependent on
the load. Surely a non-desirable thing.

The design can be done mathematically or simply use one of the many software
programs available that aid in the design of LC filters. After that, a
simulation is always useful. Figure 7 shows a typical LC filter for Class-D
amplifiers and its typical frequency response.

Figure 7 - Frequency Response of a Typical Class-D LC
2nd Order Filter

This simple filter has a –3dB cutoff frequency of 39KHz (with 4 ohm load),
and suppresses the carrier as much as 31dB at 300KHz. For example, if our supply
rails are +/-50V (enough for about 275W at 4 ohms), the residual ripple will
have an amplitude of about 1Vrms.

This ripple is, obviously inaudible, and 1V RMS will dissipate only around
200mW in a typical tweeter (not likely a problem, especially since the tweeters
impedance will be a lot higher than 8 ohms at 300kHz). However, care must be
taken as the speaker wires can become an antenna and affect other equipment. In
fact, although a couple of volts RMS of ripple can seem low enough to run your
speakers safely, EMI can be a concern, so the less carrier level you have, the
better. For further rejection, higher order filters are used (with the potential
disadvantage of increased phase shift in the audio band), although there are
other clever ways to do it, as very selective bandstop or 'notch' filters tuned
to the carrier frequency (if it is fixed, and that only happens in synchronous
designs as the one described).

Well designed Class-D amplifiers have a higher order filter and/or special
carrier suppression sections in order to avoid problems with EMI. As can be seen
in Figure 8, the response is dependent on the load, and in fact the load is part
of the filter. This is one of the problems to solve in Class-D designs. It
doesn't help that a loudspeaker presents a completely different impedance to the
amplifier than a test load, and many PWM amps have filters that are (and never
can be) correct for all practical loudspeaker loads. Again, only a handful of
good Class-D amplifiers use feedback techniques that include the output filter
to compensate for impedance variations and have a nearly load independent
frequency response, as well as to reduce distortion produced by non-linearities
in the filter. Although passive components are thought to be distortion-free,
this does not apply to ferrite or powdered iron cores that are used for the
filters. These components most certainly do introduce distortion.

Now, The Filter Components ...
The output inductor has to withstand the
whole load current, and also have storage capability, as in any non-isolated
switching converter (Class-D half bridge design is in fact analogous to a buck
converter, its reference voltage being the audio signal).

The ideal inductor (in terms of linearity) is an air-core one, but the size
and number of turns required for typical Class-D operation usually makes it
impractical, so a core is normally used in order to reduce turns count and also
provide a confined magnetic field that reduces radiated EMI. Powder cores or
equivalent materials are the common choice. It can also be done with ferrite
cores, but they must have a “gap” where energy is stored. Wire size must also be
carefully chosen so DC losses are low (requiring thick wire) but also skin
effect is reduced (AC resistance must also be low).

Inductor core shape can be a drum core, gapped ferrite RM core, or toroidal
powder core, among others. Drum cores have the problem that their magnetic field
is not enclosed, hence producing more radiated EMI. RM cores solve this problem
but have most of the coil enclosed, so cooling problems may arise as no airflow
is possible. IMHO, toroids are preferred because they feature both closed
magnetic field that helps control radiated EMI, a physically open structure that
allows proper cooling, and easy and economical winding, as they don't need
bobbins.

Coil Shapes ... Drum, Toroid & RM Style Coils and
Cores (Wilco & Coilcraft)

Many core manufacturers such as Micrometals or Magnetics offer their own
software, very useful to design the output inductor as they help choosing the
right core, wire size and geometrical parameters. The capacitor usually falls in
the 200nF to 1uF range, has to be of good quality too, in order to ensure good
high frequency behaviour and low losses and of course has to be rated for the
whole output voltage. Usually, polypropylene capacitors are chosen. Needless to
say, you cannot use electrolytics!

7 -   Feedback

As I have stated previously, timing errors can lead to increased
distortion and noise. This cannot be skipped and the more precise it is kept,
the better the design will perform. Anyway, open loop Class-D amplifiers are not
likely to satisfy demanding specifications, so (negative) feedback is almost
mandatory. There are several approaches. The most simple and common is to take a
fraction of the switching signal, precondition it by means of a passive RC low
pass filter and feed it back to the error amplifier.

To put it simply, the error amplifier is an opamp placed in the signal path
(before the PWM comparator) that sums the input signal with the feedback signal
to generate a error signal that the amps automatically minimises (this is the
concept of every negative-feedback system, anyway).

Figure 8 - Typical Feedback Network
Connections

Although good results are obtained this way, there is still a problem: load
dependency, due to the speaker being an integral part of the filter, hence
affecting its frequency response as shown above.

Some more advanced amplifiers take the feedback signal from the very output,
trying to compensate this. This way, a constant frequency response is obtained,
with the further gain that the inductor resistance contributes much less to the
output impedance, so it is kept lower, hence damping factor is higher (higher
speaker control). However, taking feedback after the filter is not an easy task.
The LC introduces a pole and hence a phase shift that, if not properly
compensated, will make the amp become unstable and, ultimately, oscillate.
Feedback may be taken from both the switching node and the filter output.
Although this can give very good results, it is still difficult to maintain
stability because of the phase shift through the output filter.

8 -   Other topologies

Pure PWM (based on triangle generators, also called 'natural sampling
PWM') is not the only way to go in order to construct a Class-D amplifiers.
Some other topologies have arisen, many of them based on auto-oscillation, where
the hysteresis in the comparator and delays between the comparator and power
stage can be taken into account to design a system that oscillates by itself in
a somewhat controllable manner.

Although simpler, these designs have some disadvantages, IMHO. For example,
the switching frequency is not fixed, but depends on the signal amplitude. This
makes output notch filters ineffective, yielding higher ripple levels. Besides,
when several channels are put together, the difference in switching frequency
between them can produce audible beat tones that can become very annoying. This
can also happen of course with synchronous design as the one described here, but
there is a simple solution - use the same clock for all the channels.

Self oscillating designs in particular have some other difficulties like
start-up: special circuitry may be needed that forces the amplifier to start
oscillating. Conversely, if for any reason the oscillation stops, you could end
up with an 'always-on' MOSFET, and thus a large amount of DC at the output,
followed almost immediately by a dead loudspeaker. Of course, these issues can
be solved with proper design, but the added complexity can void the initial
simplicity, thus no gain is obtained.

Low distortion in a PWM amplifier requires a very linear triangle waveform,
along with a very fast and accurate comparator. At the high operating
frequencies needed for optimum overall performance, the opamps used need to have
a wide bandwidth, extremely high slew rate, and excellent linearity. This is
expensive to achieve, requiring premium devices. Some of these constraints are
relieved somewhat by self oscillating designs (therefore making them slightly
cheaper), but this is not an effective trade-off for the most part.

Clocked designs (fixed frequency) are not easier to make than
self-oscillating or modulated switching frequency designs, but are certainly
far more predictable and tend to have fewer problems overall. The ability to
synchronise multiple amplifiers ensures that mutual interference is minimised.
An 'advantage' claimed by the proponents of non-clocked and 'random switching'
designs is that the RF energy on the speaker leads is spread over a wide
frequency range, potentially making such amplifiers more likely (or perhaps less
unlikely) to pass EMI testing. From an overall perspective, this is more likely
to be a hinderance than a benefit, as it is no longer possible to optimise the
filter network for maximum switching frequency rejection.

There are also PWM amps that claim to be truly 'digital', using One-Bit™
technology, or generating the PWM signal directly from the PCM data stream.
Although the manufacturers of such amplifiers will naturally proclaim their
superiority over all others, such self-praise should generally be ignored.
Implementing feedback in a 'pure' digital design is at best difficult, and may
be impossible without using a DSP (digital signal processor) or resorting to an
outboard analogue feedback system. Including additional ADCs and DACs (analogue
to digital converters and vice versa) is unlikely to allow the amplifier to be
any 'better' than the direct analogue methods described in this article.

A relative newcomer to the scene is the Sigma-Delta modulator, however at the
time of writing this still has problems (challenges in corporate speak). The
main issue is that the transition rate is too high, and it must be reduced to
accommodate real-world components - particularly the power switching
MOSFETs.

The 'pure' digital solutions described above have another shortfall, and
that's the fact that the number of different pulse widths is finite, and
determined by the clock speed. A digital system can only switch on a clock
transition. Based on currently available information, only around 8 x
oversampling is possible if a digital noise shaping filter is added to the
system. An analogue modulation system has an effectively infinite number of
different pulse widths, but this is not possible with any true digital
implementation.

These latter comments cover a very complex area, one is outside the scope of
this article. However, even the scant information above will give most readers
far more information that is commonly available - especially from manufacturers
of digital Class-D amplifiers.

9 -   Some Final Notes

In conclusion, Class-D amplifiers have evolved a lot since they were
first invented, achieving levels of performance similar to conventional
amplifiers, and even better in some aspects, like an inherent low output
impedance that allows effortless bass. All this, with the great advantage of
high efficiency. Of course, only if they are properly designed.

However, although very attractive, Class-D designs are not very DIY friendly.
In order to achieve a properly working design in terms of efficiency,
performance and EMI, very careful PCB layout is mandatory, some component
selections are critical and of course proper instrumentation is absolutely
required.

This article has been written in order to throw some light about the
internals, advantages and difficulties of this not very well-known (and even
less well understood) technology. Everyone thinks that “Class-D” stands for
“Digital”. I hope that after reading this article, no-one thinks that any more

Articles Index
Main Index

Copyright
Notice. This article, including but not limited to all text and
diagrams, is the intellectual property of Sergio Sánchez Moreno and Rod
Elliott, and is Copyright © 2005. Reproduction or re-publication by any
means whatsoever, whether electronic, mechanical or electro- mechanical,
is strictly prohibited under International Copyright laws. The authors
grant the reader the right to use this information for personal use only,
and further allows that one (1) copy may be made for reference. Commercial
use is prohibited without express written authorisation from Sergio
Sánchez Moreno and Rod Elliott.

Page created and copyright © 04 Jun 2005