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Class D Power Amplifier

This article intends to cover basic concepts of switching mode power amplifier, and the design of class D power amplifier.

Simple Switching Amplifier

where we have

Vdc=12πππvsw(θ) dθ=παπVpkIdc=12πππisw(θ) dθ=απIpk

As for the fundamental components

V1=1πππvsw(θ)cosθ dθ=2sinαπVpkI1=1πππisw(θ)cosθ dθ=2sinαπIpk

Mathematica code for Fourier series

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f[x_] := Piecewise[{{0, -a <= x <= a}, {1, x < -a}, {1, x > a}}]
FourierCosCoefficient[f[x], x, 1]
Copy

Hence, we can calculate the efficiency as

η=PrfPdc=12V1I1VdcIdc=2sin2αα(πα)

To compare with the class A PA, we write the output power as

PUF=P1Plin=VdcIpk2sin2απ(πα)14VdcIpk=8sin2απ(πα)

We can plot the efficiency and PUF vs. conduction angle

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Eff[a_] := 2 Sin[a]^2/a/(Pi - a);
PUF[a_] := 8 Sin[a]^2/Pi/(Pi - a);
Plot[{Eff[a], PUF[a]}, {a, 0, Pi},
PlotLegends -> "Expressions"]
Copy

The peak power occurs at a conduction angle of around 113 degrees. Though the structure dissipate no heat, the peak efficiency is about 81%, as some of the power is wasted in harmonic components.

Switching Amplifier with Harmonic Short

To remove harmonic components, we can place a harmonic short across the load.

In this case, the voltage waveform must assume a sinusoidal form.

Repeat the analysis, we have

η=PrfPdc=sinααPUF=P1Plin=4sinαπ

It can be plotted as

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Eff[a_] := Sin[a]/a;
PUF[a_] := 4 Sin[a]/Pi;
Plot[{Eff[a], PUF[a]}, {a, 0, Pi},
PlotLegends -> "Expressions"]
Copy

The peak power occurs at a conduction angle of 90 degrees with an efficiency of 63 %.

Class D Power Amplifier

The key point is that the current in the LCR branch is constrained to remain sinusoidal. With a sufficiently large bypass capacitor, the voltage vsw would remain Vdc when the switch is turned to A, and remain zero when turned to B.

We have

V1=2πVdcI1=12IpkIpk=πIdcη=PrfPdc=VdcIpkπVdcIdc=1PUF=VdcIpkπ14VdcIpk=4π

It can achieve theoretically 100 % efficiency with 1 dB higher power than class A amplifier.

A realization

Reference

  1. S. C. Cripps. RF Power Amplifier for Wireless Communications. Artech House, 2014.
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