Exercise 8.6 A bipolar output stage

The circuit below shows an output stage of a voltage amplifier. It is given that $v_G(t)=V_G\cdot \mathit{sin}(\mathit{\omega t})$, $R_L=100\mathrm{\Omega }$ and $V_{\mathit{CC}}=10V$.

In this exercise, the characteristics of $T_1$ and $T_2$ are strongly idealized and shown below. Note that, except for the signs, the characteristics of the NPN and PNP are equal. For both transistors $\mathit{\beta fe}\gg 100$. The power delivered to $R_L$ by the source $v_G$ can be ignored. Furthermore, the transistors are never conducting simultaneously. Yep, this is really over-simplified behavior.

a)

Sketch, as a function of time, for $V_G=10V$ and for at least one period of the input signal ${}_g(t)$, the currents delivered by the power supply sources $V_{\mathit{CC}}$ and $-V_{\mathit{CC}}$.

b)

Derive an expression for the power delivered by the two power supply sources.

c)

Derive an expression for the power dissipated in $R_L$.

d)

Calculate for $V_G=10V$:

• the numerical value of the total power delivered by the sources
• the numerical value of the total power dissipated in $R_L$
• the ratio between the two

e)

What happened to the difference in power delivered by the sources and he power dissipated in $R_L$?

f)

Derive an expression for the power efficiency as a function of $V_G$ and draw a plot of this relation.