Maxim > Design=20 support > App = notes=20 > Audio=20 Circuits > APP 3977
Maxim > Design = support >=20 App = notes=20 > Automotive=20 > APP 3977

Jan 31, = 2007

Keywords: Audio, Amplifier, Audio = Amplifier,=20 Stereo, Stereo Class D, Mono, Mono Class D, High = Efficiency,=20 Class D, PWM, Spread Spectrum, EMI, Low EMI, Notebook, = Notebook Audio, Microsoft Vista Audio, Vista Audio, = TV, FPTV,=20 FPD, Cellphone, MP3, PMP
Related=20 parts

Download,=20 PDF format (150kB)

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APPLICATION NOTE 3977

Class D Amplifiers: Fundamentals of = Operation and=20 Recent Developments

Abstract: A=20 Class D amplifier's high efficiency makes it ideal for = portable and compact high-power applications. = Traditional=20 Class D amplifiers require an external lowpass filter = to=20 extract the audio signal from the = pulse-width-modulated (PWM)=20 output waveform. Many modern Class D amplifiers, = however,=20 utilize advanced modulation techniques that, in = various=20 applications, both eliminate the need for external = filtering=20 and reduce electromagnetic interference (EMI). = Eliminating=20 external filters not only reduces board-space = requirements,=20 but can also significantly reduce the cost of many=20 portable/compact systems.

Attend=20 this brief webcast by Maxim on=20 = TechOnline

Introduction

Most audio system design = engineers are=20 well aware of the power-efficiency advantages of Class = D=20 amplifiers over linear=20 audio-amplifier classes such as Class A, B, and AB. In = linear=20 amplifiers such as Class=20 AB, significant amounts of power are lost due to = biasing=20 elements and the linear operation of the output = transistors.=20 Because the transistors of a Class D amplifier are = simply used=20 as switches to steer current through the load, minimal = power=20 is lost due to the output stage. Any power losses = associated=20 with a Class D amplifier are primarily attributed to = output transistor=20 on-resistances, switching losses, and quiescent=20 current overhead. Most power lost in an amplifier is=20 dissipated as heat. Because heatsink=20 requirements can be greatly reduced or eliminated in = Class D=20 amplifiers, they are ideal for compact high-power=20 applications.

In the past, the power-efficiency = advantage of classical PWM-based Class D amplifiers = has been=20 overshadowed by external filter component cost, = EMI/EMC=20 compliance, and poor THD+N performance when compared = to linear=20 amplifiers. However, most current-generation Class D=20 amplifiers utilize advanced modulation and feedback = techniques=20 to mitigate these issues.

The Basics of Class D Amplifiers

While there = are a=20 variety of modulator topologies used in modern Class D = amplifiers, the most basic topology utilizes = pulse-width=20 modulation (PWM) with a triangle-wave (or sawtooth)=20 oscillator. Figure 1 shows a simplified block = diagram=20 of a PWM-based, half-bridge Class D amplifier. It = consists of=20 a pulse-width modulator, two output MOSFETs, and an = external=20 lowpass filter (L_F and C_F) to = recover=20 the amplified audio signal. As shown in the figure, = the p-channel=20 and n-channel=20 MOSFETs operate as current-steering switches by = alternately=20 connecting the output node to V_DD and = ground.=20 Because the output transistors switch the output to = either=20 V_DD or ground, the resulting output of a = Class D=20 amplifier is a high-frequency square wave. The = switching=20 frequency (f_SW) for most Class D amplifiers = is=20 typically between 250kHz to 1.5MHz. The output square = wave is=20 pulse-width modulated by the input audio signal. PWM = is=20 accomplished by comparing the input audio signal to an = internally generated triangle-wave (or sawtooth) = oscillator.=20 This type of modulation is also often referred to as = "natural=20 sampling" where the triangle-wave oscillator acts as = the=20 sampling clock. The resulting duty cycle of the square = wave is=20 proportional to the level of the input signal. When no = input=20 signal is present, the duty cycle of the output = waveform is=20 equal to 50%. Figure 2 illustrates the = resulting PWM=20 output waveform due to the varying input-signal=20 level.

Figure=20 1. This simplified functional block diagram = illustrates a=20 basic half-bridge Class D amplifier.

Figure=20 2. The output-signal pulse widths vary proportionally = with the=20 input-signal magnitude.

In order to extract = the=20 amplified audio signal from this PWM waveform, the = output of=20 the Class D amplifier is fed to a lowpass filter. The = LC=20 lowpass filter shown in Figure 1 acts as a passive = integrator=20 (assuming the cutoff frequency of the filter is at = least an=20 order of magnitude lower than the switching frequency = of the=20 output stage) whose output is equal to the average = value of=20 the square wave. Additionally, the lowpass filter = prevents=20 high-frequency switching energy from being dissipated = in the=20 resistive load. Assume that the filtered output = voltage=20 (V_{O_AVG}) and current (I_AVG) = remain=20 constant during a single switching period. This = assumption is=20 fairly accurate because f_SW is much greater = than=20 the highest input audio frequency. Therefore, the = relationship=20 between the duty cycle and resulting filtered output = voltage=20 can be derived using a simple time-domain analysis of = the=20 inductor voltage and current.

The instantaneous = current=20 flowing through the inductor is:

3D"Equation

where=20 V_L(t) is the instantaneous voltage across = the=20 inductor using the sign convention shown in Figure=20 1.

Because the average current = (I_AVG)=20 flowing into the load is assumed constant over one = switching=20 period, the inductor current at the beginning of the = switching=20 period (T_SW) must be equal to the inductor = current=20 at the end of the switching period, as shown in = Figure=20 3.

In mathematical terms, this means=20 that:

3D"Equation

Figure=20 3. Filter inductor current and voltage waveforms are = shown for=20 a basic half-bridge Class D = amplifier.

Equation 2=20 shows that the integral of the inductor voltage over = one=20 switching period must be equal to 0. Using equation 2 = and=20 examining the V_L(t) waveform shown in = Figure 3, it=20 is clear that the absolute values of the areas = (A_ON=20 and A_OFF) must be equal to each other in = order for=20 equation 2 to be true. With this information, we can = now=20 derive an expression for the filtered output voltage = in terms=20 of the duty ratio of the switching = waveform:

Substituting=20 equations 4 and 5 into equation 3 gives the new=20 equation:

3D"Equation

Finally,=20 solving for V_O gives:

3D"Equation

where=20 D is the duty ratio of the output-switching = waveform.

Using Feedback to Improve Performance

Many = Class D=20 amplifiers utilize negative feedback from the PWM = output back=20 to the input of the device. A closed-loop approach not = only=20 improves the linearity of the device, but also allows = the=20 device to have power-supply rejection. This contrasts = with an=20 open-loop amplifier, which inherently has minimal (if = any)=20 supply rejection. Because the output waveform is = sensed and=20 fed back to the input of the amplifier in a = closed-loop=20 topology, deviations in the supply rail are detected = at the=20 output and corrected by the control loop. The = advantages of a=20 closed-loop design come at the price of possible = stability=20 issues, as is the case with all systems utilizing = feedback.=20 Therefore, the control loop must be carefully designed = and=20 compensated to ensure stability under all operating=20 conditions.

Typical Class D amplifiers operate = with a=20 noise-shaping type of feedback loop, which greatly = reduces=20 in-band noise due to the nonlinearities of the = pulse-width=20 modulator, output stage, and supply-voltage = deviations. This=20 topology is similar to the noise shaping used in sigma-delta=20 modulators. To illustrate this noise-shaping function, = Figure 4 shows a simplified block diagram of a=20 1st-order noise shaper. The feedback network typically = consists of a resistive-divider network but, for = simplicity,=20 the example shown in Figure 4 uses a feedback ratio of = 1.=20 Also, the transfer=20 function for the integrator has been simplified to = equal 1/s=20 because the gain of an ideal integrator is inversely=20 proportional to frequency. It is also assumed that the = PWM=20 block has a unity-gain and zero-phase-shift = contribution to=20 the control loop. Using basic control-block analysis, = the=20 following expression can be derived for the=20 output:

3D"Equation

Figure=20 4. A control loop with 1st-order noise shaping for a = Class D=20 amplifier pushes most noise out of = band.

Equation 8=20 shows that the noise term, E_n(s), is = multiplied by=20 a highpass filter function (noise-transfer function) = while the=20 input term, V_IN(s), is multiplied by a = lowpass=20 filter function (signal-transfer function). The = noise-transfer=20 function's highpass filter response shapes the noise = of the=20 Class D amplifier. If the cutoff frequency of the = output=20 filter is selected properly, most of the noise is = pushed out=20 of band (Figure 4). While the preceding example dealt = with a=20 1st-order noise shaper, many modern Class D amplifiers = utilize=20 multi-order noise-shaping topologies to further = optimize=20 linearity and power-supply rejection.

Class-D Topologies=E2=80=94Half Bridge vs. Full = Bridge

Many=20 Class D amplifiers are also implemented using a = full-bridge=20 output stage. A full bridge uses two half-bridge = stages to=20 drive the load differentially. This type of load = connection is=20 often referred to as a bridge-tied=20 load (BTL).=20 As shown in Figure 5, the full-bridge = configuration=20 operates by alternating the conduction path through = the load.=20 This allows bidirectional=20 current to flow through the load without the need of a = negative supply or a DC-blocking = capacitor.

Figure=20 5. A traditional full-bridge Class D output stage uses = two=20 half-bridge stages to drive the load=20 differentially.

Figure 6 illustrates = the=20 output waveforms of traditional BTL, PWM-based, Class = D=20 amplifiers. In Figure 6, the output waveforms are = complements=20 of each other, which produce a differential PWM signal = across=20 the load. As with the half-bridge topology, an = external LC=20 filter is needed at the output to extract the = low-frequency=20 audio signals and prevent high-frequency energy from = being=20 dissipated in the load.

Figure=20 6. Traditional full-bridge Class D output waveforms = complement=20 each other, thus creating a differential PWM signal = across the=20 load.

A full-bridge Class D amplifier = shares the=20 same advantages of a Class AB BTL amplifier, but adds = high=20 power efficiency. The first advantage of BTL = amplifiers is=20 that they do not require DC-blocking capacitors on the = outputs=20 when operating from a single supply. The same is not = true for=20 a half-bridge amplifier as its output swings between=20 V_DD and ground and idles at 50% duty cycle. = This=20 means that its output has a DC offset equal to=20 V_DD/2. With a full-bridge amplifier, this = offset=20 appears on each side of the load, which means that = zero DC=20 current flows at the output. The second advantage they = share=20 is that they can achieve twice the output signal swing = when=20 compared to a half-bridge amplifier with the same = supply=20 voltage because the load is driven differentially. = This=20 results in a theoretical 4x increase in maximum output = power=20 over a half-bridge amplifier operating from the same=20 supply.

A full-bridge Class D amplifier, = however,=20 requires twice as many MOSFET=20 switches as a half-bridge topology. Some consider this = to be a=20 disadvantage, because more switches typically mean = more=20 conduction and switching losses. However, this = generally is=20 only true with high-output power amplifiers (> 10W) = due to=20 the higher output currents and supply voltages = involved. For=20 this reason, half-bridge amplifiers are typically used = for=20 high-power applications for their slight efficiency = advantage.=20 Most high-power full-bridge amplifiers exhibit power=20 efficiencies in the range of 80% to 88% with 8=CE=A9 = loads.=20 However, half-bridge amplifiers like the MAX9742 = achieve power=20 efficiencies greater than 90% while delivering more = than 14W=20 per channel into 8=CE=A9.

Eliminating the Output Filter=E2=80=94Filterless=20 Modulation

One of the major drawbacks of = traditional Class=20 D amplifiers has been the need for an external LC = filter. This=20 need not only increases a solution's cost and board = space=20 requirements, but also introduces the possibility of=20 additional distortion=20 due to filter component nonlinearities. Fortunately, = many=20 modern Class D amplifiers utilize advanced = "filterless"=20 modulation schemes to eliminate, or at least minimize, = external filter requirements.

Figure 7 = shows a=20 simplified functional diagram of the MAX9700 = filterless=20 modulator topology. Unlike the traditional PWM BTL = amplifier,=20 each half bridge has its own dedicated comparator,=20 which allows each output to be controlled = independently. The=20 modulator is driven with a differential audio signal = and a=20 high-frequency sawtooth waveform. When both comparator = outputs=20 are low, each output of the Class D amplifier is high. = At the=20 same time, the output of the NOR gate goes high, but = is=20 delayed by the RC circuit formed by R_ON and = C_ON. Once the delayed output of the NOR = gate=20 exceeds a specified threshold, switches SW1 and SW2 = close.=20 This causes OUT+ and OUT- to go low and remain as such = until=20 the next sampling period begins. This scheme causes = both=20 outputs to be on for a minimum amount of time=20 (t_ON(MIN)), which is set by the values of=20 R_ON and C_ON. As shown in = Figure=20 8, with zero input, the outputs are in phase with = pulse=20 widths equal to t_ON(MIN). As the audio = input=20 signals increase or decrease, one comparator trips = before the=20 other. This behavior, along with the minimum on-time=20 circuitry, causes one output to vary its pulse width = while the=20 other output pulse width remains at = t_ON(MIN)=20 (Figure 8). This means that the average value of each = output=20 contains a half-wave rectified version of the output = audio=20 signal. Taking the difference of the average values of = the=20 outputs yields the complete output audio = waveform.

Figure=20 7. This simplified functional diagram shows the = MAX9700's=20 filterless Class D modulator = topography.

Figure=20 8. The input and output waveforms are shown for the = MAX9700's=20 filterless modulator topography.

Because = the=20 MAX9700's outputs idle with in-phase signals, there is = no=20 differential voltage applied across the load, thereby=20 minimizing quiescent power consumption without the = need for an=20 external filter. Rather than depend on an external LC = filter=20 to extract the audio signal from the output, Maxim's=20 filterless Class D amplifiers rely on the inherent = inductance=20 of the speaker load and the human ear to recover the = audio=20 signal. The speaker resistance=20 (R_E) and inductance (L_E) form a=20 1st-order lowpass filter which has a cutoff frequency = equal=20 to:

3D"Equation

With=20 most speakers, this 1st-order rolloff is enough to = recover the=20 audio signal and prevent excessive amounts of = high-frequency=20 switching energy from being dissipated in the speaker=20 resistance. Even if residual switching energy results = in=20 speaker movement, these frequencies are inaudible to = the human=20 ear and will not adversely affect the listening = experience.=20 When using filterless Class D amplifiers, the speaker = load=20 should remain inductive at the amplifier's switching = frequency=20 to achieve maximum output-power capabilities.

Minimizing EMI=20 with Spread-Spectrum Modulation

One disadvantage = of=20 filterless operation is the possibility of radiated = EMI from=20 the speaker cables. Because the Class D amplifier = output=20 waveforms are high-frequency square waves with = fast-moving=20 transition edges, the output spectrum contains a large = amount=20 of spectral energy at the switching frequency and = integer=20 multiples of the switching frequency. Without an = external=20 output filter located within close proximity of the = device,=20 this high-frequency energy can be radiated by the = speaker=20 cables. Maxim's filterless Class D amplifiers help = mitigate=20 possible EMI problems through a modulation scheme = known as=20 spread-spectrum modulation.

Spread-spectrum = modulation=20 is accomplished by dithering=20 or randomizing the switching frequency of the Class D=20 amplifier. The switching frequency is typically varied = up to=20 =C2=B110% of the nominal switching frequency. While = the period of=20 the switching waveform is varied randomly = cycle-to-cycle, the=20 duty cycle is not affected, thereby preserving the = audio=20 content of the switching waveform. Figures 9a = and=20 9b show the wideband output spectrum of the = MAX9700 to=20 illustrate the effects of spread-spectrum modulation. = Rather=20 than having the spectral energy concentrated at the = switching=20 frequency and its harmonics, spread-spectrum = modulation=20 effectively spreads out the spectral energy of the = output=20 signal. In other words, the total amount of energy = present in=20 the output spectrum remains the same, but the total = energy is=20 redistributed over a wider bandwidth. This reduces the = high-frequency energy peaks at the outputs, therefore=20 minimizing the chances of EMI being radiated from the = speaker=20 cables. While it is possible that some spectral noise = may=20 redistribute into the audio band with spread-spectrum=20 modulation, this noise is suppressed by the = noise-shaping=20 function of the feedback loop.

<= I>Figure=20 9a. The wideband output spectrum is shown for the = MAX9700=20 using a fixed switching frequency.

<= I>Figure=20 9b. Spread-spectrum modulation redistributes the = spectral=20 energy of the MAX9700 over a wider = bandwidth.

Many=20 of Maxim's filterless Class D amplifiers also allow = the=20 switching frequency to be synchronized to an external = clock=20 signal. This allows the user to manually set the = switching=20 frequency of the amplifier to a less-sensitive = frequency=20 range.

While spread-spectrum modulation = significantly=20 improves EMI performance of filterless Class D = amplifiers,=20 there is typically a practical limit on the length of = the=20 speaker cables that can be used before the device = begins to=20 fail FCC or CE radiated-emissions regulations. If a = device=20 fails radiated-emissions tests due to long speaker = cables, an=20 external output filter may be needed to provide = additional=20 attenuation of the high-frequency components of the = output=20 waveform. In many applications with moderate speaker = cable=20 lengths, ferrite bead/capacitor filters on the outputs = will=20 suffice. EMI performance is also very layout = sensitive, so=20 proper PCB-layout guidelines should be strictly = followed to=20 guarantee compliance with applicable FCC and CE=20 regulations.

Conclusion

Recent advancements in Class D = modulation=20 techniques have allowed Class D amplifiers to flourish = in=20 applications where linear amplifiers once dominated. = Modern=20 Class D amplifiers include all of the advantages of = Class AB=20 amplifiers (i.e., good linearity and minimal = board-space=20 requirements) with the added bonus of high power = efficiency.=20 Currently, there are a wide variety of Class D = amplifiers=20 available, thus making them suitable for numerous=20 applications. These applications range from low-power = portable=20 applications (e.g., cell phones, notebooks) in which = battery=20 life, board-space requirements, and EMI compliance are = of=20 utmost importance, to high-power applications (e.g.,=20 automotive sound systems or flat-panel displays) where = minimizing heatsinking requirements and heat = generation is=20 vital. Having a fundamental understanding of Class D=20 amplifiers and their recent technological advances = will aid=20 designers in selecting the correct amplifier for their = application and allow them to successfully weigh the=20 advantages and disadvantages of specific features. =

Related parts =

MAX9700<= /TD>	1.2W, = Low-EMI,=20 Filterless, Class D Audio Amplifier	Free=20 samples
MAX9701<= /TD>	1.3W, = Filterless,=20 Stereo Class D Audio Power Amplifier	Free=20 samples
MAX9703<= /TD>	10W = Stereo/15W Mono,=20 Filterless, Spread-Spectrum, Class D = Amplifiers	Free=20 samples
MAX9704<= /TD>	10W = Stereo/15W Mono,=20 Filterless, Spread-Spectrum, Class D = Amplifiers	Free=20 samples
MAX9705<= /TD>	2.3W, = Ultra-Low-EMI,=20 Filterless, Class D Audio Amplifier	Free=20 samples
MAX9708<= /TD>	20W/40W, = Filterless,=20 Spread-Spectrum, Mono/Stereo, Class D = Amplifier	Free=20 samples
MAX9709<= /TD>	25W/50W, = Filterless,=20 Spread-Spectrum, Stereo/Mono, Class D = Amplifier	Free=20 samples
MAX9713<= /TD>	6W, = Filterless,=20 Spread-Spectrum Mono/Stereo Class D = Amplifiers	Free=20 samples
MAX9714<= /TD>	6W, = Filterless,=20 Spread-Spectrum Mono/Stereo Class D = Amplifiers	Free=20 samples
MAX9715<= /TD>	2.8W, = Low-EMI, Stereo,=20 Filterless Class D Audio Amplifier	Free=20 samples
MAX9741<= /TD>	12W+12W, = Low-EMI,=20 Spread-Spectrum, Stereo, Class D = Amplifier	Free=20 samples
MAX9742<= /TD>	Single-/Dual-Supply,=20 Stereo 16W, Class D Amplifier with = Differential=20 Inputs	Free=20 samples
MAX9744<= /TD>	20W Stereo = Class D=20 Speaker Amplifier with Volume Control	Free=20 samples
MAX9752<= /TD>	2.2W, = Low-EMI, Stereo,=20 Class D Power Amplifiers with DirectDrive=20 Headphone Amplifiers
MAX9753<= /TD>	2.2W, = Low-EMI, Stereo,=20 Class D Power Amplifiers with DirectDrive=20 Headphone Amplifiers
MAX9755<= /TD>	2.6W Stereo = Audio Power=20 Amplifiers and DirectDrive=C2=AE Headphone = Amplifiers
MAX9770<= /TD>	1.2W, = Low-EMI,=20 Filterless, Mono Class D Amplifier with = Stereo=20 DirectDrive Headphone Amplifiers	Free=20 samples
MAX9773<= /TD>	1.8W, = Filterless,=20 Ultra-Low EMI, Stereo Class D Audio Power=20 Amplifier
MAX9775<= /TD>	2 x 1.5W, = Stereo Class=20 D Audio Subsystem with DirectDrive = Headphone=20 Amplifier
MAX9776<= /TD>	2 x 1.5W, = Stereo Class=20 D Audio Subsystem with DirectDrive = Headphone=20 Amplifier	Free=20 samples
MAX9789<= /TD>	Windows=20 Vista-Compliant, Stereo Class AB Speaker=20 Amplifiers and DirectDrive Headphone = Amplifiers

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Download,=20 PDF format (150kB)
APP 3977: Jan = 31, 2007=20
AN3977, AN 3977, = APP3977,=20 Appnote3977, Appnote 3977=20 =