Question 13.8: Common-Emitter Amplifier Find Av, Avoc, Zin, Ai , G, and Zo ...

First, we need to know I_CQ to be able to find the value of r_π. Hence, we start by analyzing the dc conditions in the circuit. Only the dc supply, the transistor, and the resistors R₁,R₂,R_C, and R_E need to be considered in the bias-point analysis. The capacitors, the signal source, and the load resistance have no effect on the Q point (because the capacitors behave as open circuits for dc currents).

The dc circuit was shown earlier in Figure 13.23 and was analyzed in Example 13.7. For β = 100, the resulting Q point was found to be I_CQ = 4.12 mA and V_CE = 6.72V. Substituting values into Equation 13.35, we have

r_{\pi}=\frac{\beta V_T}{I_{CQ}}=631~\Omega

Using Equations 13.39 and 13.40, we find that

R_B=R_1\|R_2=\frac{1}{1/R_1+1/R_2}=3.33\mathrm{~k}\Omega

R^′_L=R_L\|R_C=\frac{1}{1/R_L+1/R_C}=667~\Omega

Equations 13.43 through 13.48 yield

A_v=\frac{v_{\mathrm{o}}}{v_{\mathrm{in}}}=-\frac{R^′_L \beta }{r_{\pi}}=-106

A_{v\mathrm{oc}}=\frac{v_{\mathrm{o}}}{v_{\mathrm{in}}} =-\frac{R_C \beta}{r_{\pi}}=-158

Z_{\mathrm{in}}=\frac{v_{\mathrm{in}}}{i_{\mathrm{in}}}=\frac{1}{1/R_B+1/r_{\pi}}=531~\Omega

A_i=\frac{i_{\mathrm{o}}}{i_{\mathrm{in}}}=A_v\frac{Z_{\mathrm{in}}}{R_L}=-28.1

G=A_iA_v=2980

Z_{\mathrm{o}}=R_C=1\mathrm{~k}\Omega

Notice that A_v is somewhat smaller in magnitude than A_voc. This is due to loading of the amplifier by R_L as discussed in Chapter 11. Power gain is quite large for the common-emitter amplifier, and primarily for this reason, it is a commonly used configuration.

The source voltage divides between the internal source resistance and the input impedance of the amplifier. Thus, we can write

v_{\mathrm{in}}=v_s\frac{Z_{\mathrm{in}}}{Z_{\mathrm{in}}+R_s}=0.515v_s

Now, with the load connected, we have

v_\mathrm{o}=A_vv_{\mathrm{in}}=-54.6v_s

But, we are given that v_s(t) = sin(ωt) mV, so we have

v_{\mathrm{o}}(t)=-54.6\sin{(\omega t)}~\mathrm{mV}

The source voltage v_s(t) and the output voltage are shown in Figure 13.29. Notice the phase inversion.