New approaches to switched-mode audio power amplifiers Tom Lawson-March 06, 2013

The Class D amplifier has been the usual switched-mode answer to linear amplifiers for three decades. Class D amps have a clear efficiency advantage over their linear alternatives, which, over the years, has led to much effort being invested in improving the linearity of switched-mode designs.Even so, the harmonic distortion of switched-mode amps remains inferior to that of linear power amplifiers. A new approach promises better efficiency than Class D amplifiers and better performance than linear amplifiers.The Basic Class D AmplifierThe basic Class D audio amplifier is shown in Figure 1. Either the upper or lower switch in the totem pole is ON at any time, except for a brief transitional period which prevents both switches conducting at the same time. The two switches operate alternately to produce an average output that remains between the Power Input voltage and ground. The time ratio of the ON time of the two switches determines the average output voltage.For example, a 50% duty cycle will produce an output of half the Power Input voltage. The series capacitor removes the DC component. The series inductor and shunt capacitor form an LC low pass filter. The switches operate at a frequency at least least ten times higher than the maximum output frequency to allow the filter to remove the chopping frequency from the desired output signal.

Figure 1: The basic Class D switched mode audio amplifier shown here in block formA simple amplifier of this sort is entirely adequate for voice applications, but there are implementation details that need careful attention for more demanding uses. A cell phone audio amplifier is typically a Class D amp. These amplifiers were originally thought of as needing only to meet the standards for voice communication. Increasingly, phones and handheld devices are being called on to produce high fidelity audio. With care to minimize distortion, Class D amplifiers can still meet that need, though their limitations are too often plainly audible.There are three main sources of distortion in Class D Amps. First, the best FET switches, driven optimally, still spend a significant time in the linear region when switching. That means dead time must be inserted to avoid upper and lower FETs conducting at the same time (shoot-through). Dead time causes non-linearity in the output which is difficult to correct for. The brief period of linear switch operation is a source of asymmetry which contributes to distortion, as well as reducing efficiency.Second, Class D amplifiers do not provide power supply rejection. Audio frequency noise on the supplies will appear only slightly attenuated at the output. That requires extra care in regulating and filtering the power supply. The task is further complicated by the way Class D amps return inductive energy to the rails, sometimes called bus pumping. Bus pumping can cause a power rail to rise above its regulation point, leading to distortion.Third, the switched inductor in a Class D amp interacts with the speaker's inductance (or capacitance) in non-linear fashion. Care must be taken to avoid resonances and beat frequencies that can be heard in the audio range.Faster clocking decreases the size of filter elements and extends the upper range of the bandwidth, but it also increases switching losses. As the clock rate increases, dead time becomes a higher percentage of the cycle time, which increases non-linearity. This effect can quickly become the largest source of distortion.Take the example of a Class D amplifier running at 1 MHz with 25 ns of dead time. At a 50% duty cycle, after subtracting for the dead time, the upper switch is on for 475 ns and the lower switch is on for the same 475 ns. The theoretic output is then exactly where it should be, at 50% of full scale. The situation is different at 25% of full scale. On time is now 175 ns and OFF time is 775 ns instead of 200 ns and 800 ns. That puts the theoretic output at 175 / 775, or 22.58%. There is almost 2.5% distortion before the non-idealities of the power switching are taken into account.While it is possible to reduce dead time below 25 ns, extreme care must be exercised. Temperature and aging effects can shorten dead time, causing shoot-through. Even a little shoot-through disturbs the power rails and generates distortion. A little more shoot-through can be destructive.A related issue is the difficulty in producing extremes of duty cycle that still exhibit symmetrical positive and negative edges, and that do not dwell too long in the linear switching region. The problem stems largely from the limitations of switch drivers.One answer is to use Sigma-Delta modulation instead of Pulse Width Modulation. With Sigma-Delta modulation, periods of ON or OFF are integer multiples of the clock period. Linearity can then be improved, but at the expense of a higher clock rate. Sigma-Delta systems generally need to run at least 64 times the maximum signal frequency. There are significant efficiency penalties associated with clocking that much faster.

Even after taking careful measures to minimize the error sources cited above, negative feedback is required to obtain good performance. Negative feedback is problematic in a Class D amplifier because the output filter necessarily inserts a delay, which tends to destabilize any feedback loop.The Class D amp is essentially a buck converter. Buck converters need compensation to remain stable for the same reasons. In order for feedback from the output to be applied without inducing a tendency toward oscillation, the feedback must be processed. That processing must be done with care to avoid causing frequency-dependent delays appearing as distortion. Otherwise, the feedback must be taken before the filtration, which means the non-linearity of the filter, and the interaction of filter and load reactance, is outside the loop.The conflicting aims of faster correction of errors and limiting the tendency toward unwanted oscillation are all too familiar to those who work with this topology. Ultimately, it is this compromise which defines the limits of performance for Class D amplifiers.Another limitation of the Class D amplifier of Figure 1 is easier to address, i.e., the limited output voltage swing. In a cell phone, the power input is apt to be 4 volts, and a 4-volt output swing is often not enough for audio. The solution is the Bridge Tied Load (BTL) topology. In Figure 2, below, a Class D BTL amplifier is shown driving a piezo speaker, which is essentially capacitive. Piezo, or ceramic, speakers are desirable in cell phones because of their thinness and efficiency, but they require higher voltages to drive them properly.The Bridge Tied Load Variation on Class D amplifiers

Figure 2: Here, a Class D BTL amplifier drives a piezo speaker.The differential voltage across the speaker can now be twice the Power Input voltage. In operation, both totem poles need one, and only one, switch to be ON at any time.The efficiency of the BTL amp can be very good, but it is reduced by the need for a second switching element in series with the power path. The BTL form is more flexible, and it exhibits less bus pumping. In the piezo speaker case, a larger efficiency issue appears. Series resistance needs to be added to prevent oscillations caused by the capacitive loading. That resistance can easily become the largest single source of inefficiency in the system. On balance, the compromises work out to favor the BTL configuration for handheld devices.

Filterless VariationsIn some cases, the reactance of the speaker itself is relied on to filter out the chopping frequency. That can be satisfactory, but it requires the speaker to dissipate extra power due to the high-frequency ripple current. Not all dynamic speakers are sufficiently inductive at those frequencies to be efficient as a filter. Equivalent Series Resistance, ESR, causes analogous losses in piezo speakers.In either case, efficiency suffers, the speaker heats, and the sound quality is compromised. Also, if the speaker is at any distance from the amplifier, the wiring is required to carry square waves. The edges are attenuated by stray inductance, degrading the sound, and those edges are a source of electromagnetic interference.Care must be taken to avoid damage to dynamic speakers in the filterless case. Above the audible range, voice coil movement is proportional to 1 / frequency2. If the modulation frequency is high enough, the movement is small, so the voice coil won't hit the limit of travel and cause damage. As long as the speaker is sized to dissipate the extra energy, the filterless variation can be satisfactory. An additional efficiency implication is concealed here. You cannot simply reduce the modulation frequency to save power, without putting the speaker at risk.Filterless amplifiers for piezo speakers do not need to take voice coil damage into account. These amplifier/speaker combinations are the most efficient option now available. One manufacturer documents power consumption approaching half the power of Class D driving a dynamic speaker. That comparison includes a 10 ohm series resistor for stability in the piezo case. The largest single source of inefficiency is that resistor, so there is still room here for improvement.The awkward overall conclusion is that the efficiency advantages of Class D amplifiers stem from the digital nature of their output, while the performance disadvantages of Class D amplifiers stem from that same digital nature. What is really called for is a digital amplifier with an analog output. There is now an option in that category, enabled by improved FET switches and a control strategy called Predictive Energy Balancing (PEB).

Principles of Predictive Energy BalancingPredictive Energy Balancing, (PEB), allows immediate, direct feedback in a switched-mode power converter by effectively removing the filter pole from the feedback loop. Predictive Energy Balancing makes switching decisions based on the eventual outcome of those decisions, which can be calculated in advance using the fundamental energy equations. In the process, the unavoidable delay of the output filter is removed from the feedback loop. PEB allows the maximization of both agility and stability.The mathematics for energy balancing in any type of power converter can be derived from a few fundamental formulas. The kinetic energy held in an inductor, L, is:KEL = (I2x L) / 2where KEL is inductive energy in joules, I is current in amps, and L is switched inductance in henries.The kinetic energy held in a capacitor, C, is:KEC = (V2x C) / 2where KEC is capacitive energy in joules, V is voltage in volts, and C is filter capacitance in farads.In general, the inductive energy term represents the Supply and the capacitive energy term represents the Demand. The Demand is the difference between the instantaneous capacitive energy and the desired capacitive energy. At the regulation voltage, Reg, the energy held in the output filter capacitor would be:KEReg = (Reg2x C) / 2where KEReg is desired capacitive energy in joules, Reg is Reference point in volts, and C is filter capacitance in farads.The capacitive energy deficit is then KEReg - KEC.For a simple, discontinuous flyback converter, the energy balance point is the moment in time when the inductive energy is equal to the capacitive energy deficit:KEL = KEReg - KECIn an energy balancing power converter, during a control cycle, the supply term, KEL, rises exponentially while the demand term, KEReg - KEC, rises in piecewise linear fashion. The balance point is reached when the Supply equals the Demand. Then, inductive energizing stops, and the inductive energy is transferred from the switched inductor to the output filter capacitor. With the balance properly scaled, after the inductive energy has been transferred, the voltage on the filter capacitor will equal the regulation voltage.

Figure 3: Simulation showing the operation of PEB controls for a switched mode amplifierThe figure above illustrates a PEB amplifier in operation. A simulation is used here for clarity, though the waveforms on the bench are substantially the same. Each control cycle here is 5 s long. Demand has been rising since the end of the previous Transfer period. The Energize period begins with the Supply term at zero. Supply rises exponentially until the balance point is reached, which causes switching to begin the Transfer period. Transfer continues until the inductive energy has been moved to the output. At this point, both Supply and Demand are near zero, and the Output closely matches the Reference voltage. An Idle period follows, waiting for the next control cycle to begin.Notice that the Idle period can be short or long. The PEB calculation is not affected by the conversion rate. Also note that each control cycle is self-contained. There is no averaging or history involved. That property allows instantaneous feedback without inducing a tendency toward sub-harmonic behavior.

The Predictive Energy Balancing AmplifierBecause PEB allows an output to be regulated precisely on a cycle-by-cycle basis, instead of on the average, PEB enables an entirely new form of switched-mode amplifier. The following block diagram shows one version of this new class of amplifier. At first glance it appears similar to the H-bridge configuration of a Class D amplifier, but with some of the components rearranged, and with different controls. In operation, it is quite different, being essentially a bidirectional flyback converter. Figure 4 shows one form of PEB amplifier driving a piezo speaker, though the same amplifier will drive a dynamic speaker, as well.

Figure 4: A Block Diagram of One Form of PEB AmplifierThe PEB calculations are done in real time by the circuitry on the left side of the block diagram. These calculations can be done in analog or digital fashion. We have chosen simple, low power analog circuitry for the demonstration systems. The squaring circuits respond in a few nanoseconds and consume only micro amps of current. A reasonably fast differential amp and comparators will suffice. Synchronous rectification is used for efficiency in the demonstration system, but is not essential.There are no requirements here that stretch the limits of conventional practice. Eventually, these calculations should be integrated for cost and size advantages. The circuitry on the right in Figure 4 consists of two ordinary totem poles forming an H-bridge. BTL Class D audio amplifiers would have the speaker in place of L1. Here, the speaker is placed between the output and the power supply. Depending on the process and power level, the power circuitry can be incorporated into the same integrated circuit.In operation, the amplifier uses flyback energy transfers to push the output away from zero. It uses reverse flyback transfers to draw energy back from the speaker to pull the output towards zero. The inductor in a PEB amplifier is active at the switching frequency, so a much smaller inductor filters the digital power switching to produce an analog output, when compared to the inductors needed to filter Class D amplifiers. PEB amplifiers can be fully bipolar, or can be offset to drive the output above and below the power supply voltage, as shown here. The speaker could just as well be connected between the output and ground with a coupling capacitor to remove the DC bias voltage.

Figure 5: Screen shot of a PEB amplifier producing a 10 kHz sine wave 8 volts peak to peak driving a piezo speakerThe 200-kHz modulation frequency can be plainly seen in the output trace. A minimal low pass filter will remove the remnants of the modulation, if desired. The reference trace represents the ideal output. The narrow peaks in the output trace, every 5 s, indicate the regulation points. Those peaks are caused by the ESR of the speaker's capacitance.The inductor current flows out of the battery when the voltage at the output increases, and flows back into the battery when the output voltage decreases. At lower frequencies, or lower amplitudes, less energy needs to be moved to keep the loop in balance. Because feedback acts to control regulation on a cycle by cycle basis, the difficulties of Class D feedback are avoided. Any changes related to power supply voltage, dead time, or the impedance of the load are corrected inside the loop in the course of each control cycle.

CautionsBecause of their differences from Class D amplifiers, there are a few cautions to observe when applying PEB amplifiers. The gain of an amplifier refers to the amplitude of the output signal relative to the input signal, but there is second gain term in a PEB amplifier that governs its dynamic behavior.Because the energy balance scaling is in proportion to the ratio of the switched inductance and the load capacitance, the PEB gain needs to be matched to the capacitance of the load. One consequence is that inductors showing large changes of inductance at different currents should not be used for PEB applications to avoid causing non-linearity.In the case of a dynamic speaker, which is inductive, not capacitive, a capacitor is added at the amplifier output to set the PEB scaling and the output ripple. Then, the resistance or inductance of the speaker has little effect on the dynamic performance. For piezo speakers, the PEB scaling must be set to match the chosen speaker's capacitance.That limitation is not inconvenient in the case of a handheld device with built-in speakers, or in the case of a powered speaker, but it could be an issue for a general purpose amplifier. If the ability to dynamically adjust for varying capacitance at the load is needed, an additional circuit must be added. Conventional negative feedback, heavily filtered to have only a DC effect, can be added to set the PEB scaling.

Efficiency comparison of PEB and Class D amplifiersThe theoretic maximum efficiency of Class D and PEB amplifiers is 100%. As a practical matter, both types of amplifiers can be expected to run in the region of 90% efficiency. There are five factors which can give the PEB amplifier an incremental efficiency advantage over Class D amplifiers:1. First, Class D amps need to be clocked faster because of the digital nature of their outputs. A PEB amplifier can run at half, or one-fourth, the clock frequency and still offer superior fidelity.2. Second, the clock frequency does not enter into the PEB equations, so the dynamics remain intact as the clock frequency changes. That enables dynamic clocking to be used to save power with little effect on fidelity.3. Third, the greatly improved power supply rejection of PEB amplifiers eliminates the losses associated with decoupling and re-regulating power supplies.4. Fourth, almost all the losses due to ripple current in the speaker are eliminated in the PEB amplifier.5. The last factor applies only to piezo speakers. Class D amplifiers need series resistance added to remain stable when driving capacitive loads. A typical minimum value for that resistance is 8 ohms. The resistor is dissipative, and can account for the majority of power losses in a Class D amp, greatly reducing the efficiency advantage of piezo speakers. PEB amplifiers do not need such series resistance.

ConclusionsBy rearranging the same circuit elements now employed in BTL Class D amplifiers and by adding predictive controls, real improvements in fidelity and efficiency of power amplifiers have been achieved. Since changing the control intelligence does not add to the cost of an integrated circuit, these benefits can be realized without an increase in cost. In fact, system costs can be reduced by eliminating filter inductors and by generating less waste heat. PEB amplifiers are particularly well suited for driving piezo loads.The same audio amplifier technology can be scaled for hearing aids, or consumer electronics, all the way up to theater-sized systems. Related versions of this technology can be adapted to motor drives and other power amplifier applications, as well as to power converters, in general. The PEB amplifiers shown here are covered by four issued US patents. Other patents are pending.

About the authorTom Lawson began working in instrumentation in 1968. He formed Lawson Labs in 1981, and CogniPower in 2009. His patents span five decades.