TIDUEW8 Design guide

TIDUEW8 August 2022

2.3.3.3 Internal Average Power Dissipation of Driver Amplifier for RC Output Load

For a continuous sinusoidal output driving an RC load, the internal average power dissipation (P_OUT(AVG)) in the output transistors can be calculated as Equation 16 shows by subtracting the average power delivered to the load from the average power provided by the supply.

Equation 16.

P_{O U T (A V G)} (W) = P_{S u p p l y (A C)} - P_{L o a d (A C)}

where

P_SUPPLY(AVG) = Average input power from the supply while driving the RC load
P_LOAD(AVG) = Average output power delivered to the RC load

Figure 2-11 shows the output structure for an RC load, and Equation 17 gives the total reactive load (Z_L).

Equation 17.

Z_{L} = R_{S} + j X_{C}

where

Equation 18.

X_{C} = - j \frac{1}{2 π f C_{L}}

Figure 2-11 Output Structure for an RC Load (Source Phase)

Equation 19 shows the average power that the driver amplifier will draw from the power supplies when driving a continuous sinusoidal signal into an RC load referenced to ground. Similar to Equation 11, the power is integrated across the positive half-cycle and averaged.

Equation 19.

P_{S u p p l y (A V G)} (W) = \frac{1}{π} \int_{0}^{π} \frac{1}{|Z_{L}|} V c c \times V_{P} \times S i n (w t) \times d w t = \frac{2 V_{P} V_{S}}{π |Z_{L}|}

where

Equation 20.

|Z_{L}| = \sqrt{{|R_{S}|}^{2} + {|X_{C}|}^{2}}

Equation 21 shows the average output power delivered to the RC load. Cos(φ) is the power factor and gives the phase difference between the output voltage and output load current. The power factor corrects for the phase relationship between the voltage and current for the average output power calculation in an RC load. For a purely resistive load, the power factor equals 1 indicating no phase difference between the voltage and currents.

Equation 21.

P_{L o a d (A C)} (W) = \frac{1}{2 |Z_{L}|} {V_{P}}^{2} \times C o s (ϕ) = \frac{R_{S}}{2 {|Z_{L}|}^{2}} {V_{P}}^{2}

where

Equation 22.

C o s (ϕ) = \frac{R_{S}}{|Z_{L}|}

and represents the power factor of the circuit.

As a result, Equation 23 shows the internal average power dissipation in the output transistors for a single amplifier driving an RC load with a sinusoidal output.

Equation 23.

P_{O U T (A V G)} (W) = \frac{2 V_{P} V_{S}}{π |Z_{L}|} - \frac{R_{S}}{2 {|Z_{L}|}^{2}} {V_{P}}^{2}

By accounting for the quiescent power dissipation, Equation 24 shows the total internal average power dissipation for a single amplifier driving an RC load.

Equation 24.

P_{A M P (A V G)} (W) = V_{S} I_{Q} + \frac{2 V_{P} V_{S}}{π |Z_{L}|} - \frac{R_{S}}{2 {|Z_{L}|}^{2}} {V_{P}}^{2}