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# Understanding Class-D amplifier power supply requirements

## 6/18/2008 2:30 PM EDT

Calculating the Power Supply Output Voltage and Current Requirements
Calculating the Power Supply Output Voltage and Current Requirements
In most cases, a designer starts with an output power requirement and then calculates the power supply voltage that is needed to meet that requirement. The voltage required to provide a given unclipped average output power for an amplifier with BTL outputs is:

VCC = √[(2 • PBTL(RMS)RT2) / RL] / MMAX        (equation 1)

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

VCC = √[(8 • PSE(RMS)RT2) / RL] / MMAX

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:

VCC(NOM) = VCC(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:

PPSU = PO(MAX) / ηAMP(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

ILIMIT(MIN) ≥ (VCC(MIN)MMAX) / RT        (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 PBTL(RMS) = 50W
Amplifier load impedance RL = 8Ω
Total output resistance RT = 8.3Ω
Power supply output voltage tolerance = ±5%
Maximum amplifier duty cycle MMAX = 88%
Maximum amplifier efficiency ηMAX = 93%

The minimum power supply voltage is

VCC(MIN) = √[(2 • PBTL(RMS)RT2) / RL] / MMAX

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

The nominal supply voltage is

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

= 33.34V / 0.95 = 35.1V

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

ILIMIT(MIN) ≥ (VCC(MIN)MMAX) / RT

= (33.34V • 88%) / 8.3Ω = 3.72A

The power supply must be able to deliver at least

PPSU = PO(MAX) / ηAMP(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.

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

WANMAN

11/18/2008 4:50 AM EST

Sorry, I really don't understand about how does digit "2" come in the first equation (PBTL(RMS) = [(VCC  MMAX)2 / (2  RT2)]  RLOAD ) ?

Thanks