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May 9, 2007

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Feature

Class D audio-power amplifiers: Interactive simulations assess device and
filter performance

Class D amplifiers are much more efficient than other classical amplifiers,
but their high efficiency comes at the expense of increased noise and
distortion. You can assess the frequency- and time-domain characteristics of a
Class D amplifier, including the output filter, using online simulations.

Duncan McDonald, Transim Technology Corp -- EDN, 1/4/2001

Unless you've been stuck on Survivor Island, you know growth in
battery-operated electronic devices has exploded in the last few years. And, of
course, one of the prime requirements for any battery-operated device is low
power consumption. Every device in a signal chain must be as power efficient as
possible to achieve a long battery life. This requirement applies to such
ubiquitous components as amplifiers. For high efficiency, a Class D amplifier is
the best type to use. A Class D type is much more efficient than other classical
amplifiers but tends to achieve increased efficiency at the expense of increased
noise and distortion.

With the advent of IC versions of Class D amplifiers, you can easily design
an efficient amplifier suitable for battery-operated devices. The key to using
an IC version of a Class D amplifier is designing an appropriate output filter.
You can use any of the classic filters depending on your needs: Bessel for flat
phase at the expense of stopband attenuation, Chebyshev for high-stopband
attenuation at the expense of passband ripple, and Butterworth for no ripple.
However, Butterworth is not a good choice for flat phase or for achieving the
best stopband attenuation. The advent of online tools, such as WebSim, makes it
easy to simulate various filter scenarios and examine frequency- and time-domain
trade-offs. Just make sure you know what the performance objectives of the
output filter need to be to optimize your design so you won't be voted off the
island.

Traditionally, power amplifiers rely on a constantly biased output stage to
produce low distortion. Low distortion results when you bias a transistor or
MOSFET within its linear range so that signal excursions do not drive the
output device near the saturation or cutoff condition. Power amplifiers must
also be able to source and sink current so that the output can swing positive
and negative with respect to ground.

Designers have developed several types of power-amplifier output stages,
which have convenient labels, including Class A, Class B, and Class C. Class A,
B, AB, and D are common in low-frequency audio designs and have some application
in other areas, such as servo-motor drives and RF amplification. You see Class
C, E, and F types only in RF designs. The lowest distortion power amplifier is
the Class A (Figure
1). In this scheme, at least half of the output stage conducts the
full-rated load current. However, one disadvantage of the Class A is its
inefficiency; so much current flows in the output stage during low signal
conditions or when these conditions are not occurring. In a Class B scheme,
there are two series transistors in the output stage, and only one of them is
turned on at a time (Figure
2). This type of output stage is much more efficient than Class A but gains
its efficiency at the expense of distortion. The reason for the increased
distortion is that as one transistor turns off, or becomes nonlinear, before the
other transistor turns on, or becomes linear, the amplifier inevitably has
substantial nonlinearity and corresponding distortion for a period of time
around the crossover point.

The definition of efficiency is:

Because the typical input impedance is fairly high in an audio application,
internal amplifier losses, which stem primarily from output-stage losses,
dominate efficiency. Class B power dissipation is for the same circuit
conditions as Class A (Figure
2b). Class B turns on the upper transistor only for the positive half-cycle
and the lower transistor only for the lower half-cycle, which makes Class B
more efficient.

Figure
3 shows a Class AB output stage and the power dissipation for the same
conditions as a Class A output stage. You can notice the slight increase in
average power due to the bias current. The Class AB is almost as efficient as
the Class B but is more linear because of the constant bias current.

Class D amplifiers improve efficiency

The development of Class D amplifiers represents an effort to improve
amplifier efficiency. Similar in scheme to a switching regulator, a Class D
amplifier pulse-width-modulates the audio-input signal with a higher frequency
square wave so that audio-signal information becomes the variations in pulse
width of the modulated signal (Figure
4). This modulation signal feeds a set of half-bridge switches, usually
called H-bridges, and each H-bridge consists of two power MOSFETs. Unlike with
Class A or B structures, you place the amplifier load, or the loudspeaker,
across the legs of the bridge instead of from the output to ground. This
configuration allows the amplifier to reproduce low-frequency signals as slow as
20 Hz without requiring bipolar power supplies or without introducing a dc
offset in the output. The scheme then requires filtering the modulated output to
remove high-frequency signals and recover the amplified audio-input signal.
Using this modulation approach, you can achieve efficiencies of 90% because the
output stage is either cut off or saturated and doesn't spend any appreciable
time in the inefficient linear region. Strictly speaking, H-bridges are not part
of the definition of a Class D amplifier. However, H-bridges allow output to
swing positive and negative while a unipolar supply powers the amplifier. This
design doubles the output voltage and increases the output power by a factor of
four compared with the output swing of a Class A or B amplifier with the same
unipolar supply. For this reason, Class D amplifiers almost always use
H-bridges; they piggyback elegantly onto the switching topology of a Class D
amplifier.

Figure
5a shows the schematic of a Class D amplifier IC (see sidebar
"Simulating a Class D amplifier circuit"). The input drives one input of a
comparator, and the other comparator input connects to a 300-kHz sawtooth
generator. (This IC comes in both 300-kHz and more efficient 600-kHz versions).
The output of the comparator connects to gate-drive circuitry that drives the
complementary H-bridge output stage. The comparator pulse-width-modulates the
ramp frequency with the audio signal. In another sense, the comparator is also
sampling the audio signal and performing a 1-bit quantization. As a sampled-data
system, the Class D amplifier produces aliasing of the input signal according to
the Nyquist theorem. You can easily prevent aliasing by limiting the bandwidth
of the audio signal going into the Class D amplifier to less than one-half of
the switching frequency. In this case, the input bandwidth should be less than
150 kHz. Output filtering is necessary to remove the switching artifacts, which
include the high-frequency-switching fundamental and harmonics as well as
intermodulation products of the switching and input-signal waveforms. Figure
5b shows the amplifier-output spectrum after passing through an 85-kHz
lowpass filter, and you can see the intermodulation products around 300 kHz.
More filtering is necessary to reduce undesirable harmonics. Typically, you
filter a Class D audio amplifier to a much lower frequency than a switching
frequency, such as 15 to 20 kHz.

As for distortion, this Class D amplifier IC has the same level of THD as an
equivalent IC-type Class AB amplifier, typically about 0.5%. However, a Class D
amplifier does not always have higher distortion than a Class AB amplifier. The
quality of the filter, the amount of negative feedback (loop gain), and the
quality of the board layout affect final THD numbers.

Filtering has a large impact

Filter design has a big impact on the performance of the overall amplifier
circuit. Besides impacting the amplifier design, the filter can also have a
significant effect on production cost. A Class D amplifier may be more expensive
than other amplifiers due to the cost of the required output-filter components.
Because you place the filter, like the loudspeaker, across the two H-bridges,
the resultant design requires a minimum of two inductors and two capacitors that
need to carry the output current of the amplifier. On the other hand, because a
Class D amplifier is more efficient, it requires less, if any, heat-sinking.
However, you must resolve problems that EMI presents. Because Class D
amplifiers are switching high-frequency pulses, the resulting EMI-generating
fast edges may require you to reduce the Class D amplifiers's conducted and
radiated EMI. You can use ground and power planes as well as decoupling
capacitors close to the power pins. You must keep the trace lengths short
between the IC output pins and the output-filter inductors. The layout should
keep the output traces and components away from the input circuitry.

The sources of efficiency and inefficiency in Class D amplifiers are
substantially the same as for a switch-mode power supply. A Class D amplifier
improves efficiency by switching at the highest possible frequency while keeping
losses as low as possible. Losses stem from the RDS(ON) of the
MOSFETs as well as switching losses due to the nonlinear gate capacitance of the
MOSFETs. Switching losses increase as switching frequency increases, so there is
a natural limit to the maximum switching frequency that is practical for a given
level of MOSFET technology and performance. This limit is the point at which any
efficiency that you gain by increasing the switching frequency is balanced by
an increase in losses.

The output filter is an integral part of the Class D amplifier (Figure
4). Because the filter typically has inductors and capacitors and is
separate from the IC, you must add an external filter. To obtain the best
signal fidelity, you need to carefully design the output filter to achieve the
highest level of rejection of the switching modulation signal and artifacts
while trying to maintain as much signal bandwidth as possible. For audio
applications, you should also keep the passband amplitude and phase responses as
flat as possible to keep fidelity as high as possible.

Designing the output filter

Because the IC in Figure
5 primarily acts as an audio amplifier, you can design for a passband of 15
kHz and examine the performance of Butterworth, Chebyshev, and Bessel filters.
Figure
6 shows the transfer-function response of the Chebyshev filter, and Table
A shows a summary of their performance (see sidebar
"Trying an interactive amp+filter simulation").

You can design filters for Class D amplifiers using a design program that
handles passive filters, such as Filter Free (www.nuhertz.com/filter/),
which is an excellent, free filter-design program. Usually, filter-design
software assumes that you are designing a single-ended filter, but Class D
amplifiers require a balanced filter. To convert the design, you have to design
one-half of the filter using a load that is one-half of the actual load. Then,
you use the inductor and capacitor values, L1 and C1, that
you calculated in the half-filter design on both legs of the balanced full
filter. Thus, L1 of the half-filter equals L1 and
L2 of the full filter, and C1 of the half-filter equals
C1and C2 of the full filter (Figure
7).

Which filter is the best one to use? The Chebyshev filter has the best
stopband characteristics, but the high stopband attenuation comes at the
expense of 3-dB passband ripple (the amplitude ripple below the cutoff
frequency), which reduces signal fidelity. The Butterworth and Bessel filters do
not suffer from passband ripple, and so these filters are a better choice. The
Bessel topology has the advantage of more linear phase characteristics with
approximately the same stopband attenuation (the attenuation of the amplitude
above the filter cutoff frequency).

You should choose a filter based on your application. In a car stereo, for
instance, you can trade off some stopband attenuation for better phase linearity
by picking the Bessel filter. The filter-circuit topology changes only for the
component values, not for each of the filter types. For the Bessel filter, the
output inductor should equal 36.8 µH, and the capacitor should equal 3.1
µF.

Simulating a Class D-amplifier circuit

You can see the operation
of the CM8686 Class D power amplifier online at Transim's Web site
by using WebSim (Figure Aa). Try
the program at www.transim.com/champion/ by
clicking "CM8686 amplifier with a two-pole filter operates at: 300
kHz." Select the efficiency test and click "Go." After the
simulation completes, click the link toward the bottom of the page
marked V_L1-V_L2. You should see the same waveform as in Figure
Ab, which is the unfiltered modulation waveform that shows the
pulse modulation of the input sine wave. Change the input frequency
and run the simulation again to see how the modulation changes. Zoom
in on the waveform by clicking and dragging it from the upper left
side to the lower right side of the screen. Notice how the output is
always switching and spends little time in the linear region, which
is how Class D amplifiers gain their efficiency. Also click the
voltage probe on the schematic marked V_OUT1. You should see a
waveform similar to that in Figure
Ac that shows the filtered output waveform, which is the
amplified input without the switching
artifacts.

Trying an interactive amp+filter simulation

You can try an interactive
simulation of the CM8686 Class D amplifier IC with the three types
of filters by clicking on the links below. You can run simulations
of the Class D amplifier with the default filter configurations
listed in Table
A, or you can modify the circuit to try your own
values.

Two-pole
Butterworth:

www.transim.com/cgi-bin/init_webench.cgi?Device=CM8686&Flavor=300&Circuit=2pole&web_id=champion&C1=3.75u&C2=3.75u&L1=30u&L2=30u&source=edn_demo

Two-pole
Chebyshev:

www.transim.com/cgi-bin/init_webench.cgi?Device=CM8686&Flavor=300&Circuit=2pole&web_id=champion&C1=8.2u&C2=8.2u&L1=19.3u&L2=19.3u&source=edn_demo

Two-pole
Bessel:

www.transim.com/cgi-bin/init_webench.cgi?Device=CM8686&Flavor=300&Circuit=2pole&web_id=champion&C1=3.1u&C2=3.1u&L1=36.8u&L2=36.8u&source=edn_demo

When you start the
analysis, you should see a plot similar to Figure
A, which is the frequency-domain response of the CM8686
amplifier with the appropriate
filter.

Author info
Duncan McDonald is director of marketing at Transim
Technology Corp (http://www.transim.com/).
He holds a BSEE from the University of California (Berkeley) and an MBA from
the University of Santa Clara (CA). In his spare time, he enjoys building and
flying high-power amateur rockets.

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