The Class-D Amplifier(From the book Intr oduction to Electroacoustics and Audio A mplifier Design, SecondEdition - Revised Printing, by W. Marshall Leach, Jr., published by Kenda ll/Hunt,c° 2001.)A class-D amplifier is one in which the output transistors are operated as switches. When atransistor is off, the current through it is zero. When it is on, the voltage across it is small, ideallyzero. In each case, the power dissipation is very low. This increases the efficiency, thus requiringless pow er from the power supply and sm aller heat sinks for the amplifier. Thes e are importantadvantages in portable battery-powered equipment. The “D” in class-D is sometimes said to standfor “digital.” This is not correct because the operation of the class-D amplifier is based on analogprinciples. There is no digital coding of the signal. Before the advent of the class-D amplifier, thestandard classes were class-A , class-AB, class-B, and class-C. The “D” is simp ly the next letter inthe alphabet after “C.” Indeed, the earliest work on class-D amplifiers involved vacuum tubes andcan be traced to the early 1950s.Fig. 1 shows the basic simplified circuit of a class-D amplifier. We assume a bipolar power supplyso that V−= −V+. The amplifier consists of a comparator driving two MOSFET transistors whichoperate as switc hes. The comparator has t w o inputs. One is a triangle wa ve, the other is the audiosignal. The frequency of the triangle wave must be much higher than that of the audio input. Thevo ltage output of the comparator can be writtenvC= −V1for vS>vTvC=+V1for vS<vT(1)This vo ltage is applied to the input of a complementary common-source MOSFET output sta ge.Each transistor operates as a switch. For vC= −V1, M1is on and M2is off.Ifthevoltagedropacross M1is negligible, then v0O= V+. Similarly, for vC=+V1, M2is on, M1is off,andv0O= V−.In practice, there is a small voltage drop across the on MOSFET switch so that the peak outputvo ltage is less than the po wer supply v oltage. For the case vS=0, v0Ois a symmetrical squarewave. The lo w-pass filter consisting of L1and C1passes the average value of the square waveto the loudspeaker, whic h is zero. Thus vO=0for vS=0. The network consisting of R1andC2co mpensates for the inductive impedance of the loudspeaker v oice coil so that the filter sees aresistive load at high frequencies.Figure 1: Basic class-D amplifier.Fig. 2 shows the circuit waveforms for the case where vSis a sine wav e. For purposes ofillustration, the sine wave frequency is fS=1kHzandthetrianglewavefrequencyisfT=20kHz.Thesinewaveamplitudeis0.75VTP.ForvS> 0, the duty cycle of the square wave changes sothat v0Ospends more time at its positive level than at its negative level. This causes v0Oto have apositive average value. Similarly, for vS< 0, v0Ohas a negative average value. The waveform for v0O1is said to be pulse-width-modulated. The passive filter consisting of L1and C1passes the averageor low-frequency value of v0Oto the loudspeaker load and rejects the higher-frequency harmonics ofthe switching waveform .Figure 2: Amplifier voltage waveforms.The effective gain of the amplifier can be determined by applying a dc voltage at the input andcalculating the ratio of hv0Oi to vS,wherehv0Oi denotes the low-frequency time average of v0O.IfvSis increased, hv0Oi increases linearly until it reaches the level VOP, which corresponds to the positiveclipping voltage at the output. This occur s when vS= VTP. It follows that the effective gain k isgiven byk =hv0OivS=VOPVTP(2)Fig. 3 shows the waveforms of the output voltage vOfor two values of the cutoff frequency ofthe LC filter. The transfer function of the filter isVoV0o=1(s/ωc)2+(1/Qc)(s/ωc)+1(3)where ωc=2πfc=1/√L1C1is the resonance frequency and Qc=1/ (ωcRLC1) is the qualityfactor. The load resistance RLis the effective high-frequency resistance of the loudspea ker v oicecoil in parallel with the matching netw or k consisting of R1and C2. The quality factor is Qc=1/√2for the waveforms in Fig. 3 so that the gain is down by 3 dB at ωc. The signal frequency is fS=1kHz. The filter resonance frequency for the vO1waveform is fc=1kHz. For the vO2waveform, itis fc=8kHz. The harmonics of the pulse-width-modulated signal are clearly visible on the vO2waveform.For minimum distortion, the frequency of the triangle wave should be as high as possiblecompared to the cutoff frequency of the filter. Beca use the filter resonance frequency correspondsto the signal frequency for the vO1waveform in Fig. 3, the phase lag is 90o. The phase lag for thevO2wav eform is less because the resonance frequency is greater than the signal frequency. A higher-order filter can be used to more effectively remove the high-frequency switching harmonics. Forexample, a third-order LC filter or a fourth-order filter consisting of the cascade of two second-orderLC filters could be used.Fig. 4 shows the spectrum of the v0Owaveform. It contains a fundamental at fS.AbovefS,the significant switching harmonics are at fT, fT± 2fS, 2fT± fS, 2fT± 3fS,etc. Thelowestofthese is at the frequency fT− 2fS. The triangle wave f requency must be chosen high enough so2Fig ure 3: Output vo ltage wa veforms for two different LC filter cutoff frequencies.that the lowest significant harmonic is well above the highest signal frequency of interest. Thus wehave the r equiremen t fT− 2fSÀ fSor fTÀ 3fS. To minimize ripple on the output, the cutofffrequency of the LC filter should be much lower th an fT. For example, in a wideband amplifierwith a maximum signal frequency of 20 kHz, the switching frequency should ideally be 600 kHzor greater. Because of limita tions imposed by a high switching frequency, a more practical valuemight be 300 kHz. The −3 dB frequency of the LC filter should be much lower than the switchingfrequency. For example, it might be 30 kHz for a 300 kHz switching frequency. Note that theamplitude of the harmonic at fTis larger than that of the signal. At the signal clipping level, thesignal harmonic becomes 1.5 times as large as the harmonic at fT.Figure 4: Unfiltered spectrum of the output vo ltage.Negative feedback can be used around the basic amplifier circuit to improve its performance.Fig. 5 shows such a circuit. The input op amp acts as an integrator to set the bandwidth. Fora sin usoidal input signal w ith a frequency much lower than the switching frequency, the effectivetransfer function for the circuit and its pole