# How do you derive the class D Power Amplifiers Efficiency?

## Efficiency of a Class D Power Amplifier

The efficiency of a Class D power amplifier can be calculated by looking at its working principle & the probable waveforms involved. Class D amplifiers function as switching amplifiers, with the output transistors acting as switches that are either entirely on (or) totally off, avoiding the linear zone where power dissipation occurs.

## Efficiency Calculation

To calculate efficiency, imagine an ideal Class D amplifier &based on the following assumptions:

• The output transistors are perfect switches, with no switching time and no on resistance.
• The output filter is optimal and lossless.
• The input signal is a full-swing square wave that ranges from 0 to Vdd (supply voltage).

Using these presumptions, the analysis may be conducted as follows:

• The output voltage waveform is a pulse width modulated (PWM) square wave that alternates between zero and Vdd.
• The output current waveform is a filtered variant of the PWM waveform, which produces a reconstructed sine wave (considering a sinusoidal input signal).
• The output voltage and current waveforms combine to create the instantaneous power delivered to the load.
• The average power provided to the load (Pout) is calculated by taking the integral of instantaneous power during one cycle and dividing by the duration.

The average power output to the load can be stated mathematically as:

Pout = (Vdd^2 / π) X (1 / Rload)

Where,

The input power (Pin) is calculated by multiplying the supply voltage (Vdd) by the average input current, which is equal to Vdd / (π X Rload) for a full-swing square wave input.

Therefore, the input power is:

Pin = Vdd^2 / (π X Rload)

Efficiency (η) - Ratio of output to input power

η = Pout / Pin

η = (Vdd^2 / π) X (1/Rload) / (Vdd^2 / (π X Rload)).

η = 1 / π

η ≈ 0.318 (or) 31.8%

An ideal Class D amplifier has a theoretical efficiency of 31.8%, which is better than the efficiency of linear amplifier classes (such as Class A, B, or AB) but lower than other switching amplifier classes.

## Practical Considerations

In application, the efficiency of real Class D amplifiers is lower than the theoretical number due to a variety of non-idealities, including switching losses, transistor on-resistance, output filter losses, and non-ideal driving signals.

However, well-constructed Class D amplifiers can attain efficiencies of 80-90%, which are much greater than linear amplifiers.