Voltage and Current Gain-Input and Output Resistance For the circuit shown in Figure 8.56 find Av, Ai, Ri, and Ro.

Question

Voltage and Current Gain-Input and Output Resistance

For the circuit shown in Figure 8.56 find [latex]A_v, A_i, R_i,[/latex] and [latex]R_o[/latex].

Accepted Answer

DC analysis

The DC equivalent circuits are shown in Figure 8.57.

The Thévenin voltage, [latex]V_{BB},[/latex] corresponds to:

[latex]V_{BB}=21 imes \frac{45}{45+90}=7 V[/latex]

Also, the Thévenin resistance corresponds to:

[latex]R_{B}=\frac{45 imes 90}{45+90}=30 k \Omega[/latex]

Referring to Figure 8.57(b), and assuming the active region, the base current corresponds to:

[latex]\begin{aligned}I_{B} &=\frac{V_{BB}-0.7}{R_{B}+(1+\beta) R_{E}} \&=\frac{7-0.7}{30+101 imes 2} \&=0.0272 mA\end{aligned}[/latex]

The collector current is given by:

[latex]I_{C}=\beta I_{B}=100 imes 0.0272=2.72 mA[/latex]

The collector-emitter voltage corresponds to:

[latex]\begin{aligned}V_{CE} &=V_{CC}-I_{C} R_{C}-I_{E} R_{E} \&=21-2.72 imes 3-(2.72+0.0272) imes 2 \&=7.37 V\end{aligned}[/latex]

Because [latex]V_{CE}>0.2 V[/latex], the transistor does operate in the active region; therefore, the assumption was correct.

AC analysis

The AC equivalent circuits are shown in Figure 8.58. The base-emitter resistance corresponds to:

[latex]r_{be}=\frac{0.259}{0.0272 imes 10^{-3}}=953.78 \Omega[/latex]

Following the same procedure as in the previous examples:

[latex]\begin{aligned}&A_{v}=\frac{-100 imes 3000 imes 10,000}{(3000+10,000) imes 953.78}=-241.95 \&A_{i}=-241.95 imes \frac{90,000\parallel45,000\parallel953.78}{10,000}=-22.37 \&R_{i}=90,000\parallel45,000\parallel 953.78=924.39 \Omega \&R_{o}=R_{C}=3 k \Omega\end{aligned}[/latex]

Question 8.18: Voltage and Current Gain-Input and Output Resistance For the...

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