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Notes > AMPLIFIER
AND COMPARATOR CIRCUITS   AUDIO
CIRCUITS

APP 624: Apr 01,
2002

KEYWORDS: Class D, audio
amplifiers, switching amplifer, output filter,
modulation noise, PWM, filterless, amplifers

Related Parts: MAX4295
MAX4297

Class D Audio Amplifier Output Filter
Optimization

This
application note examines the effect of the output filter
on audio Class D amplifier performance. Switch-mode
amplifiers such as the MAX4295 and MAX4297 offer
improved efficiency over their more traditional Class AB
counterparts. By understanding the operation of these
devices, the modulation noise spectrum and the loudspeaker
loads they are required to drive, it is possible to completely
eliminate the output filter while retaining the efficiency
benefits of Class D amplifiers.

This article examines the output filter often required with a
switch-mode (class D) audio power amplifier. Such filters not only
maintain efficiency, they also suppress RF interference produced by fast
output transitions. Each of the following circuits, based on Maxim's
MAX4295/MAX4297 amplifiers, can be optimized for a given application
if the designer is aware of the tradeoffs involved. The amplifiers
operate from a single supply in the range +2.7V to +5.5V, and they
drive bridge-tied 4
loads with continuous power as high as 2W, with efficiency exceeding
85%. That performance makes them attractive as speaker drivers for
portable equipment in which the battery life is limited.

The main advantage of class D amplifiers is their efficiency, which is
higher than that of class AB amplifiers. As a minimum condition for
achieving that efficiency, the load of a class D amplifier should
present a high impedance at the switching frequency. In typical
output waveforms (Figure 1) the duty cycle of the OUT+ terminal
varies but its pulse period is constant (the "ticks" shown between
the two waveforms denote equal time periods). A running average of
these pulses forms a slowly rising voltage (dashed line) over the
sequence shown. Because the OUT- signal is the inverse of OUT+, it
produces a slowly falling voltage. If the load is a speaker, in
which the load is connected between the + and - terminals, this
slow-moving component is audible but the high-frequency content is
not reproduced.

Figure 1. These
complementary PWM outputs are generated by a class D amplifier in the
bridge configuration (like the MAX4295). The average values of these
waveforms (the dashed lines) are produced by an output filter, whose loss
and distortion-producing artifacts should be held to a
minimum.

Whether to use an output filter or not depends on many factors.
Consider the following: the MAX4295/MAX4297 audio power amplifiers contain
complementary output MOSFETs that implement pulse-width modulation
(PWM). The duty cycles for the output waveforms from these devices
are approximately 50% with zero input signal applied, and to
maintain reasonable efficiency the MOSFETs should drive a high
impedance at the switching frequency. Otherwise, when a resistor is
connected directly across the outputs with no other components
present, the output stages conduct almost 100% of the time
regardless of changes in the duty cycle.

Now consider the impedance plot of a speaker such as an 8,
1.75" cone transducer, for which the MAX4295/MAX4297 amplifiers are
suitable drivers (Figure 2). The speaker impedance rises beyond the
audio band, but remains low below 20KHz. As implied earlier, the
MAX4295/MAX4297 output terminals are capable of driving this load
directly. Indeed, the series inductance of the loudspeaker voice coil
shown (approximately 10µH) allows efficient operation without a filter.
That mode of operation has limitations, however.

Figure 2. The impedance of
a small 8
speaker remains 8
for most of the audio band, rising above 10
at 400Hz due to self resonance. Skin effect and voice-coil
inductance yields higher resistance and reactance at higher frequencies,
causing the impedance to rise above 10KHz and approach 100
at 1MHz.
For a particular speaker to be driven, you
should verify the coil impedance at and above the switching frequency,
and remember that excessively long speaker leads can add a parallel
capacitive load that adversely affects the efficiency. The speaker leads
and voice coil carry signals whose high dv/dt can radiate high levels
of RF. Note that the switching action dissipates a small amount of
power in the voice coil. Though negligible at 500KHz and above, it
should be considered at lower frequencies when calculating the
maximum permissible speaker power.

Minimum
Implementation with Resistive Loads

If the load is mostly resistive, or looks capacitive at high
frequencies, then other components must be added to ensure reasonable
efficiency. A series inductor, for example, passes current to the load at
audio frequencies but provides increasing impedance at higher
frequencies.

As an example, consider an 8
resistive load driven by a MAX4295 amplifier from a 5V supply. In
calculating the series inductor value we could simply assume that the
3dB roll-off point due to the inductor should be placed just outside the
audio band, say at 30KHz:

L = 8 / (2f)
or 8 / 2
(30
103) = 42.4µH

If we set a 250KHz switching frequency for our class D amplifier, the
impedance seen by output devices at this point is due mostly to the
inductor:

XL = 2

250
103
42.4
10-6 = 66.7,

or more than 8X the load impedance, so no significant
power is lost at the switching frequency.

We can now look at the other parameters that affect
selection of the inductor. The data sheet tells us that the MAX4295
delivers 1.2W into 8
from a 5V supply. Thus, the inductor must handle about
387mArms (550mA peak) without saturation. Otherwise, the
penalty is distortion in the output waveform.

We can therefore choose a 47µH SM power inductor from J.W.
Miller Magnetics (model PM54-470L). Its rated current is 720mA
(which handles the required peak current), and its DC resistance of
0.37
(less than 5% of the load) does not cause much efficiency loss. The
inductor's physical dimensions are about 5.8mm x 5.2mm with a height
of 4.5mm. (In contrast, the MAX4295 in a QSOP package measures only 6 x
5mm x 1.5mm.) That height can be unacceptably large for portable
products, in which the space on and above the PCB is usually at a
premium.

One way to reduce the profile of the inductor is to mount
it in a hole or notch in the PCB. For a 1.6mm PCB, that approach
reduces the inductor's height above the PCB to 2.9mm. Another
approach is to increase the switching frequency of the class D
stage. The MAX4295/MAX4297 amplifiers allow the user to set this
frequency to one of four values, the highest of which is 1MHz.
Higher frequency allows lower inductance values, but the one-fourth
value obtained from a 4/X increase in frequency does not necessarily
result in one quarter the physical size. Moreover, the thinner wire
used in smaller-footprint inductors produces higher DC resistance,
but some improvement should be possible.

Increasing the switching frequency by a factor of four in
the previous example (from 250KHz to 1MHz) lets you reduce the
inductor value by a factor of four (42.4µH/4 = 10.6µH) while
maintaining a constant impedance at the switching frequency. The
required current handling and DC resistance are unchanged, however.
Choosing to switch at 1MHz has little effect on efficiency, but it
does degrade the THD+N performance slightly (see data sheet for
details). Does it save board space? At 1MHz we can now use a 10µH
inductor from Toko (model A914BYW-100M), with a current rating of
760mA and a DC resistance of 0.125.
X-Y dimensions are roughly the same, at 5mm x 5mm, but height above
the PCB is only 2mm, without special mounting techniques. Compared
with the 47µH inductor mentioned earlier, this component occupies only
half as much volume.

Output-Filter
Design

The above examples implement basic operation with a minimum of
complexity, but rapid switching in the output devices provides little or
no filtering of the RF spectrum. Radiated from speaker leads and PCB
traces, that energy can cause electro-magnetic interference (EMI).
Controlling such unwanted EMI effects can be important for two
reasons:

The amplifier operates in a portable device, where other RF
circuitry can be corrupted.

The amplifier operates in a product subject to RF emissions
standards testing (such as FCC/CE).

Most applications require RF-suppression filtering on the outputs. For
that purpose, the single inductor above can readily be turned into a
lowpass filter by adding a capacitor to the complementary output
(Figure 3). Radiation remains likely, however, because the speaker's
OUT lead still sees the full switching-voltage waveform. A balanced
2-pole filter is therefore more effective (Figure 4). EMI
performance is much improved because the 2-pole filter provides
low-pass filtering before the waveform reaches either speaker lead.
Next, we consider the effect of these extra filter components on the
PCB area.

Figure 3. A conceptually
simple, single-ended 2-pole LC filter is produced by adding
capacitance to the inductor value specified by the equation for
minimal implmentation. Because the "OUT-" terminal is not filtered
before the speaker, this filter does not reduce EMI sufficiently to
meet regulatory requirements.

Figure 4. At the cost of
additional components, a balanced 2-pole filter (the recommended
approach) is effective in reducing EMI emissions. Each inductor
value is half that of Figure 3. (See the text, and Figures 5 and
6.)

With two inductors now required, having a high impedance at the
switching frequency for load and LP filter is still a benefit. Because the
two inductors are effectively in series between the MOSFET outputs,
we can halve the 10µH inductor values and use two 5µH parts, while
retaining the MAX4295's 1MHz switching frequency. From the Coilcraft
catalog we can choose a 4.7µH inductor (model DT1608C-472) with a
current rating of 1.2A and a DC resistance of 0.085.
Both specs are more than adequate for this application. Note that
DC-resistance contributions are doubled because the inductors are in
series with the load, giving a total of 0.17.
This value is only ~2% of the load resistance, so it has little
effect on the efficiency.

The capacitance value can now be chosen to define the filter's
high-frequency rolloff. Considering only one half of the differential
output makes the math more straightforward, and allows us to realize a
2nd-order LCR filter in which R and L are known. Thus, we need only
define the value of C (Figure 5). A ~4% voltage overshoot in
response to a step input is acceptable, so the maximally flat
Butterworth filter is a reasonable choice. Using math that is
detailed elsewhere (see the Appendix and the MAX4295 data sheet),
the value of C is

C = L/(4R22)
= 4.7x10-6/(4
42
(0.707)2) = 0.146µF

where
equals 0.707 for Butterworth. This value can be realized with a
network (called an %alternate balanced 2-pole filter% in the data
sheet) of one capacitor across the inductors and one to ground from
each output. Using three 0.047µF caps simplifies the bill of
materials. Each + and Ð phase then sees a capacitance of 0.141µF (Figure
6). The filter's corner frequency is 192KHz. The inductors do not
self-resonate below 60MHz, so the filter attenuates switching noise over
a frequency span of two and a half decades (at that point the
switching energy is falling rapidly anyway). Rise and fall times for
the MAX4295 are about 30ns.

Figure 5. For analysis, a
single-ended circuit that models the output seen by each half-circuit
in Figure 4 can simplify the math somewhat.

Figure 6. This 2-pole,
differential-mode filter serves the example in the text. Inductor values
are 4.7µH, capacitor values are 0.047µF, and the speaker impedance
(RL) is 8.

To minimize radiation, the PCB layout should place the inductors as
close to the MAX4295 as possible. Tracking between the inductors and
capacitors should also be minimized. The physical size (and cost) of the
capacitors is much less of an issue than for the inductors. For the
required 0.047µF capacitor, a 16V surface-mount, 0402 ceramic with
X7R dielectric is available from AVX Corporation and others.

If filter optimization is important for the application, calculations
should account for the high-frequency load impedance. Further accuracy
can be gained by modelling the capacitor ESR, along with the
inductors' DC resistance and self-resonant behavior.

Results

The 2-pole filter of Figure 5 was tested with Coilcraft DT1608C-472
inductors, driving an 8
resistive load from one channel of a MAX4297 evaluation kit set with
a 1MHz switching frequency. Efficiency was calculated with a 2V sine
wave applied at four different frequencies:

Table 1. Measured
Efficiency

Input
Frequency (KHz)

Efficiency
(%)

1

74.9

5

84.3

10

86.3

15

86.7

These results show the high efficiency that class D devices can
achieve, which is much higher than that of traditional class AB
amplifiers. Figure 7 shows THD+N vs. frequency, measured over the
22Hz-22KHz bandwidth, with output power set to 0.7W at 1KHz. Distortion
(THD+N) was measured at three different frequencies (1KHz, 5KHz, and
10KHz) while varying the output power, using an Audio Precision System
One (Figure 8). The measurement bandwidth was 22Hz to 22KHz. The
results shown are in broad agreement with the data sheet, with
distortion dominating noise over most of the range. Distortion
remains below 1% for all frequencies up to the 0.7W output-power
level.

Figure 7. Operating at
1KHz with a power level of 0.7WRMS, a MAX4295 sensor with
filter of Figure 6 exhibits distortion vs. frequency as shown. At that
power level, the circuit delivers < or = 1% distortion over the
entire band.

Figure 8. Distortion vs.
output-power level for the MAX4295 sensor with filter of Figure 6
shows that distortion remains below 1% for power levels up to 0.7W,
and rises sharply at 1W. (The solid line represents operation at
1KHz, the dashed line at 5KHz, and the grayed line at
10KHz.)

Summary

Becoming familiar with the advantages and limitations of class D
amplifiers and their design concepts allows the user to optimize any
output filter for a given application. Informed design decisions can then
be reached by weighing these often-conflicting requirements against
one another:

Appendix: 2nd-Order Filter Calculations

The transfer function for the filter in Figure 5 can be
expressed as:

H(s) = (1/LC)/(s2 + s(1/CR) + (1/LC))

This H(s) expression can be equated to the generic
2nd-order system equation:

G(s) = n2/(s2
+ 2n

s + n2)

R and L are known, so we can solve for C:

C = L/(4R2
2)

The parameter n
is also useful:

n
= 1/(LC
) rads-1

___________________________

References
and Further Reading

1. MAX4295/MAX4297
data sheet
2. Principles of Active Network Synthesis and
Design, Gobind Daryanani (John Wiley & Sons, Inc.),
1976

Filter-Component
Manufacturers

1. Coilcraft
2. J.W.
Miller Magnetics
3. Toko
4.
AVX Corporation

A similar version of this article appeared in the
November 2001 issue of Electronik Industrie magazine.

A268, April 2002

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APP 624: Apr 01,
2002

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