Class D Audio Amplifier Output Filter Optimization

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App=20 Notes > AMPLIFIER=20 AND COMPARATOR CIRCUITS = AUDIO=20 CIRCUITS	APP 624: = Apr 01, =20 2002
KEYWORDS: Class D, = audio=20 amplifiers, switching amplifer, output filter,=20 modulation noise, PWM, filterless, = amplifers
Related Parts: MAX4295= =20 MAX4297= =20	=

Class D Audio Amplifier Output Filter =20 Optimization

This =20 application note examines the effect of the output = filter=20 on audio Class D amplifier performance. = Switch-mode=20 amplifiers such as the MAX4295 and MAX4297 offer = improved efficiency over their more traditional = Class AB=20 counterparts. By understanding the operation of = these=20 devices, the modulation noise spectrum and the loudspeaker = =20 loads they are required to drive, it is possible to = completely =20 eliminate the output filter while retaining the = efficiency=20 benefits of Class D amplifiers.

This article examines the output filter often required with a = =20 switch-mode (class D) audio power amplifier. Such filters not only = =20 maintain efficiency, they also suppress RF interference produced = by fast =20 output transitions. Each of the following circuits, based on = Maxim's =20 MAX4295/MAX4297 amplifiers, can be optimized for a given = application=20 if the designer is aware of the tradeoffs involved. The = amplifiers=20 operate from a single supply in the range +2.7V to +5.5V, = and they=20 drive bridge-tied 4=20 loads with continuous power as high as 2W, with efficiency = exceeding=20 85%. That performance makes them attractive as speaker drivers = for=20 portable equipment in which the battery life is limited.

The main advantage of class D amplifiers is their efficiency, = which is =20 higher than that of class AB amplifiers. As a minimum = condition for =20 achieving that efficiency, the load of a class D amplifier = should=20 present a high impedance at the switching frequency. In = typical=20 output waveforms (Figure 1) the duty cycle of the OUT+ = terminal=20 varies but its pulse period is constant (the "ticks" shown = between=20 the two waveforms denote equal time periods). A running = average of=20 these pulses forms a slowly rising voltage (dashed line) = over the=20 sequence shown. Because the OUT- signal is the inverse of = OUT+, it=20 produces a slowly falling voltage. If the load is a speaker, = in=20 which the load is connected between the + and - terminals, = this=20 slow-moving component is audible but the high-frequency content is = =20 not reproduced.

Figure 1. These = =20 complementary PWM outputs are generated by a class D amplifier in = the =20 bridge configuration (like the MAX4295). The average values of = these =20 waveforms (the dashed lines) are produced by an output filter, = whose loss=20 and distortion-producing artifacts should be held to a = minimum.

Whether to use an output filter or not depends on many factors. = =20 Consider the following: the MAX4295/MAX4297 audio power amplifiers = contain=20 complementary output MOSFETs that implement pulse-width = modulation=20 (PWM). The duty cycles for the output waveforms from these = devices=20 are approximately 50% with zero input signal applied, and to = maintain reasonable efficiency the MOSFETs should drive a = high=20 impedance at the switching frequency. Otherwise, when a = resistor is=20 connected directly across the outputs with no other = components=20 present, the output stages conduct almost 100% of the time=20 regardless of changes in the duty cycle.

Now consider the impedance plot of a speaker such as an 8,=20 1.75" cone transducer, for which the MAX4295/MAX4297 amplifiers = are=20 suitable drivers (Figure 2). The speaker impedance rises beyond = the =20 audio band, but remains low below 20KHz. As implied earlier, the = =20 MAX4295/MAX4297 output terminals are capable of driving this load = =20 directly. Indeed, the series inductance of the loudspeaker voice = coil =20 shown (approximately 10=B5H) allows efficient operation without a = filter. =20 That mode of operation has limitations, however.

=20

Figure 2. The = impedance of=20 a small 8=20 speaker remains 8=20 for most of the audio band, rising above 10=20 at 400Hz due to self resonance. Skin effect and voice-coil =20 inductance yields higher resistance and reactance at higher = frequencies, =20 causing the impedance to rise above 10KHz and approach 100=20 at 1MHz.

For a particular speaker to be driven, = you=20 should verify the coil impedance at and above the switching = frequency, =20 and remember that excessively long speaker leads can add a = parallel =20 capacitive load that adversely affects the efficiency. The = speaker leads =20 and voice coil carry signals whose high dv/dt can radiate = high levels=20 of RF. Note that the switching action dissipates a small = amount of=20 power in the voice coil. Though negligible at 500KHz and = above, it=20 should be considered at lower frequencies when calculating = the=20 maximum permissible speaker power. =20

Minimum =20 Implementation with Resistive Loads

If the load is mostly resistive, or looks capacitive at high = =20 frequencies, then other components must be added to ensure = reasonable =20 efficiency. A series inductor, for example, passes current to the = load at=20 audio frequencies but provides increasing impedance at = higher =20 frequencies.

As an example, consider an 8=20 resistive load driven by a MAX4295 amplifier from a 5V supply. = In=20 calculating the series inductor value we could simply assume that = the =20 3dB roll-off point due to the inductor should be placed just = outside the =20 audio band, say at 30KHz:

L =3D 8 / (2f)=20 or 8 / 2=20 (30 =20 10³) =3D 42.4=B5H

If we set a 250KHz switching frequency for our class D = amplifier, the =20 impedance seen by output devices at this point is due mostly = to the =20 inductor:

X_L =3D 2=20 =20 250 =20 10³=20 42.4 =20 10^-6 =3D 66.7,

or more than 8X the load impedance, so no = significant=20 power is lost at the switching frequency.

We can now look at the other parameters that = affect =20 selection of the inductor. The data sheet tells us that the = MAX4295 =20 delivers 1.2W into 8=20 from a 5V supply. Thus, the inductor must handle about =20 387mA_rms (550mA peak) without saturation. Otherwise, = the =20 penalty is distortion in the output waveform.

We can therefore choose a 47=B5H SM power = inductor from J.W.=20 Miller Magnetics (model PM54-470L). Its rated current is = 720mA=20 (which handles the required peak current), and its DC = resistance of=20 0.37=20 (less than 5% of the load) does not cause much efficiency loss. = The=20 inductor's physical dimensions are about 5.8mm x 5.2mm with a = height =20 of 4.5mm. (In contrast, the MAX4295 in a QSOP package measures = only 6 x =20 5mm x 1.5mm.) That height can be unacceptably large for = portable=20 products, in which the space on and above the PCB is usually = at a=20 premium.

One way to reduce the profile of the inductor is = to mount=20 it in a hole or notch in the PCB. For a 1.6mm PCB, that = approach=20 reduces the inductor's height above the PCB to 2.9mm. = Another=20 approach is to increase the switching frequency of the class = D=20 stage. The MAX4295/MAX4297 amplifiers allow the user to set = this=20 frequency to one of four values, the highest of which is = 1MHz.=20 Higher frequency allows lower inductance values, but the = one-fourth=20 value obtained from a 4/X increase in frequency does not = necessarily=20 result in one quarter the physical size. Moreover, the = thinner wire=20 used in smaller-footprint inductors produces higher DC = resistance,=20 but some improvement should be possible.

Increasing the switching frequency by a factor = of four in =20 the previous example (from 250KHz to 1MHz) lets you reduce = the=20 inductor value by a factor of four (42.4=B5H/4 =3D 10.6=B5H) = while=20 maintaining a constant impedance at the switching frequency. = The=20 required current handling and DC resistance are unchanged, = however.=20 Choosing to switch at 1MHz has little effect on efficiency, = but it=20 does degrade the THD+N performance slightly (see data sheet = for=20 details). Does it save board space? At 1MHz we can now use a = 10=B5H=20 inductor from Toko (model A914BYW-100M), with a current rating = of=20 760mA and a DC resistance of 0.125.=20 X-Y dimensions are roughly the same, at 5mm x 5mm, but height = above=20 the PCB is only 2mm, without special mounting techniques. Compared = =20 with the 47=B5H inductor mentioned earlier, this component = occupies only =20 half as much volume.

Output-Filter =20 Design

The above examples implement basic operation with a minimum of = =20 complexity, but rapid switching in the output devices provides = little or =20 no filtering of the RF spectrum. Radiated from speaker leads = and PCB =20 traces, that energy can cause electro-magnetic interference = (EMI). =20 Controlling such unwanted EMI effects can be important for two=20 reasons:

The amplifier operates in a portable device, where other RF = =20 circuitry can be corrupted. =20
The amplifier operates in a product subject to RF emissions = =20 standards testing (such as FCC/CE).

Most applications require RF-suppression filtering on the = outputs. For =20 that purpose, the single inductor above can readily be turned = into a =20 lowpass filter by adding a capacitor to the complementary = output=20 (Figure 3). Radiation remains likely, however, because the = speaker's=20 OUT lead still sees the full switching-voltage waveform. A = balanced=20 2-pole filter is therefore more effective (Figure 4). EMI=20 performance is much improved because the 2-pole filter = provides=20 low-pass filtering before the waveform reaches either = speaker lead.=20 Next, we consider the effect of these extra filter = components on the=20 PCB area.

Figure 3. A = conceptually =20 simple, single-ended 2-pole LC filter is produced by adding=20 capacitance to the inductor value specified by the equation = for=20 minimal implmentation. Because the "OUT-" terminal is not = filtered=20 before the speaker, this filter does not reduce EMI = sufficiently to=20 meet regulatory requirements.

Figure 4. At the = cost of =20 additional components, a balanced 2-pole filter (the = recommended=20 approach) is effective in reducing EMI emissions. Each = inductor=20 value is half that of Figure 3. (See the text, and Figures 5 = and=20 6.)

With two inductors now required, having a high impedance at the = =20 switching frequency for load and LP filter is still a benefit. = Because the=20 two inductors are effectively in series between the MOSFET = outputs,=20 we can halve the 10=B5H inductor values and use two 5=B5H = parts, while=20 retaining the MAX4295's 1MHz switching frequency. From the = Coilcraft=20 catalog we can choose a 4.7=B5H inductor (model DT1608C-472) = with a=20 current rating of 1.2A and a DC resistance of 0.085.=20 Both specs are more than adequate for this application. Note = that=20 DC-resistance contributions are doubled because the inductors are = in =20 series with the load, giving a total of 0.17.=20 This value is only ~2% of the load resistance, so it has little = =20 effect on the efficiency.

The capacitance value can now be chosen to define the filter's = =20 high-frequency rolloff. Considering only one half of the = differential =20 output makes the math more straightforward, and allows us to = realize a =20 2nd-order LCR filter in which R and L are known. Thus, we need = only=20 define the value of C (Figure 5). A ~4% voltage overshoot in = response to a step input is acceptable, so the maximally = flat=20 Butterworth filter is a reasonable choice. Using math that = is=20 detailed elsewhere (see the Appendix and the MAX4295 data = sheet),=20 the value of C is

C =3D L/(4R²²)=20 =3D 4.7x10^-6/(4 =20 4²=20 (0.707)²) =3D 0.146=B5F

where =20 equals 0.707 for Butterworth. This value can be realized = with a=20 network (called an %alternate balanced 2-pole filter% in the = data=20 sheet) of one capacitor across the inductors and one to ground = from=20 each output. Using three 0.047=B5F caps simplifies the bill of = =20 materials. Each + and =D0 phase then sees a capacitance of = 0.141=B5F (Figure =20 6). The filter's corner frequency is 192KHz. The inductors do = not =20 self-resonate below 60MHz, so the filter attenuates switching = noise over=20 a frequency span of two and a half decades (at that point = the=20 switching energy is falling rapidly anyway). Rise and fall = times for=20 the MAX4295 are about 30ns.

Figure 5. For = analysis, a =20 single-ended circuit that models the output seen by each = half-circuit=20 in Figure 4 can simplify the math somewhat.

Figure 6. This = 2-pole, =20 differential-mode filter serves the example in the text. = Inductor values=20 are 4.7=B5H, capacitor values are 0.047=B5F, and the speaker = impedance =20 (R_L) is 8.

To minimize radiation, the PCB layout should place the = inductors as =20 close to the MAX4295 as possible. Tracking between the inductors = and =20 capacitors should also be minimized. The physical size (and = cost) of the=20 capacitors is much less of an issue than for the inductors. = For the =20 required 0.047=B5F capacitor, a 16V surface-mount, 0402 = ceramic with=20 X7R dielectric is available from AVX Corporation and = others.

If filter optimization is important for the application, = calculations =20 should account for the high-frequency load impedance. Further = accuracy=20 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 =20 inductors, driving an 8=20 resistive load from one channel of a MAX4297 evaluation kit = set with=20 a 1MHz switching frequency. Efficiency was calculated with a = 2V sine=20 wave applied at four different frequencies:

Table 1. = Measured =20 Efficiency

Input Frequency = (KHz)=20	Efficiency (%)=20
1	74.9
5	84.3
10	86.3
15	86.7

These results show the high efficiency that class D devices can = =20 achieve, which is much higher than that of traditional class AB = =20 amplifiers. Figure 7 shows THD+N vs. frequency, measured over the = =20 22Hz-22KHz bandwidth, with output power set to 0.7W at 1KHz. = Distortion =20 (THD+N) was measured at three different frequencies (1KHz, = 5KHz, and =20 10KHz) while varying the output power, using an Audio Precision = System=20 One (Figure 8). The measurement bandwidth was 22Hz to 22KHz. = The=20 results shown are in broad agreement with the data sheet, = with=20 distortion dominating noise over most of the range. = Distortion=20 remains below 1% for all frequencies up to the 0.7W = output-power=20 level.

Figure 7. = Operating at =20 1KHz with a power level of 0.7W_RMS, a MAX4295 sensor = with =20 filter of Figure 6 exhibits distortion vs. frequency as shown. = At that =20 power level, the circuit delivers < or =3D 1% distortion = over the=20 entire band.

Figure 8. = Distortion vs. =20 output-power level for the MAX4295 sensor with filter of = Figure 6=20 shows that distortion remains below 1% for power levels up = to 0.7W,=20 and rises sharply at 1W. (The solid line represents = operation at=20 1KHz, the dashed line at 5KHz, and the grayed line at=20 10KHz.)

Summary

Becoming familiar with the advantages and limitations of class = D =20 amplifiers and their design concepts allows the user to optimize = any =20 output filter for a given application. Informed design decisions = can then =20 be reached by weighing these often-conflicting requirements = against=20 one another:

Appendix: 2nd-Order Filter Calculations =

The transfer function for the filter in Figure 5 = can be =20 expressed as:

H(s) =3D (1/LC)/(s² + s(1/CR) + = (1/LC))

This H(s) expression can be equated to the = generic=20 2nd-order system equation:

G(s) =3D _n²/(s^{2=20
+ 2_n=20
=20
s + _n²)}

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

C =3D L/(4R²^{=20
2})

The parameter _n=20 is also useful:

_n=20 =3D 1/(LC=20 ) rads^-1

___________________________

References=20 and Further Reading

1. MAX4295/MAX= 4297=20 data sheet
2. Principles of Active Network = Synthesis and =20 Design, Gobind Daryanani (John Wiley & Sons, Inc.),=20 1976

Filter-Component =20 Manufacturers

1. Coilcraft
2. J.W.=20 Miller Magnetics
3. Toko
4.=20 AVX Corporation

A similar version of this article appeared in = the =20 November 2001 issue of Electronik Industrie = magazine.

A268, April 2002

MORE INFORMATION APP 624: = Apr 01, =20 2002

MAX4295: QuickVi= ew -- Full=20 (PDF) Data Sheet (728k) -- Free=20 Sample

MAX4297: QuickVi= ew -- Full=20 (PDF) Data Sheet (728k) -- Free=20 =20 = Sample

=20

CORPORATE

Copyright =A9 2003 Maxim Integrated Products =95 = Legal=20 Notices
Maxim Integrated Products, 120 San Gabriel = Dr.,=20 Sunnyvale, CA 94086 USA
408-737-7600; http://www.maxim-ic.com/=20

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