Understanding Class-D amplifier power supply requirements

V_CC = √[(2 • P_BTL(RMS) • R_T²) / R_L] / M_MAX        (equation 1)

and the power supply voltage required for an amplifier with single-ended outputs is:

V_CC = √[(8 • P_SE(RMS) • R_T²) / R_L] / M_MAX

The power supply output voltage should be high enough to provide the amplifier's rated output power at the lower limit of the power supply's output voltage tolerance, so:

V_CC(NOM) = V_CC(MIN) / (1 - tolerance)        (equation 2)

The power efficiency of a digital Class-D amplifier is very high, more than 90%, but it still will have power losses. The power supply must be high enough to supply enough power for the maximum power output of the amplifier plus power losses in the amplifier as indicated in:

P_PSU = P_O(MAX) / η_AMP(MAX)        (equation 3)

In order to ensure that the power supply does not limit the output current during normal operation, its current limit must be set to a value greater than or equal to

I_LIMIT(MIN) ≥ (V_CC(MIN) • M_MAX) / R_T        (equation 4)

If the current limit threshold is lower than the maximum required output current then the amplifier output will be clipped, greatly increasing the amplifier's distortion. The same requirement also applies to the output protection for the amplifier.

Example:
The following is a sample calculation for a single-channel amplifier with BTL outputs and the following parameters:

        Maximum average (RMS) amplifier output power P_BTL(RMS) = 50W
        Amplifier load impedance R_L = 8Ω
        Total output resistance R_T = 8.3Ω
        Power supply output voltage tolerance = ±5%
        Maximum amplifier duty cycle M_MAX = 88%
        Maximum amplifier efficiency η_MAX = 93%

The minimum power supply voltage is

V_CC(MIN) = √[(2 • P_BTL(RMS) • R_T²) / R_L] / M_MAX

                 = √[(2 • 50W • 8.3Ω²) / 8Ω] / 88% = 33.34V

The nominal supply voltage is

V_CC(NOM) = V_CC(MIN) / (1 - tolerance)

                 = 33.34V / 0.95 = 35.1V

The power supply output current limit must be greater than or equal to

I_LIMIT(MIN) ≥ (V_CC(MIN) • M_MAX) / R_T

                 = (33.34V • 88%) / 8.3Ω = 3.72A

The power supply must be able to deliver at least

P_PSU = P_O(MAX) / η_AMP(MAX)

          = 50W / 93% = 53.8W

Figure 1 shows the load voltage, the load current the peak power (instantaneous power) and the RMS power.

Figure 1: Output voltage, load current, and instantaneous and RMS power

All the power delivered to the load comes from the power supply and from the decoupling capacitors.

Note that the frequency of the instantaneous power delivered to the load is twice the frequency of the audio input signal. The frequency of power supply output current is also twice that of the audio signal (see Figure 2).

Figure 2: Instantaneous Power and PSU current

Peak vs. Average Output Power
Regulatory agencies such as the U.S. Federal Trade Commission (FTC) require manufacturers of audio products to specify the average output power rather than the peak power for consumer audio products. The RMS voltage for an undistorted sinusoidal output is equal to the peak voltage divided by the square root of 2 so the maximum average output power for a Class-D amplifier with an undistorted sinusoidal output is equal to the peak power divided by 2.

Amplifier manufacturers will sometimes specify the output power at a higher level of THD in order to allow them to advertise a higher output power. A clipped sinusoidal output waveform with 10% THD has an average output power 28% higher than an undistorted sine wave output from the same amplifier.

P_O(RMS)(THD = 10%) = 1.28 • P_O(RMS)(THD = 1%)