Question

the parameters of the transistor in the circuit are: β = 80 and v_a = ∞. determinethe input resistance r_i
select one:
a. 124 ω
b. 3.12 kω
c. 13 ω
d. 23 ω

Explanation:

Step1: Calculate $r_{\pi}$

The formula for $r_{\pi}=\frac{\beta V_T}{I_C}$. Given $I_Q = I_C=2\mathrm{mA}=2\times 10^{- 3}\mathrm{A}$ and $V_T\approx26\mathrm{mV}=26\times 10^{-3}\mathrm{V}$, $\beta = 80$. Then $r_{\pi}=\frac{80\times26\times 10^{-3}}{2\times 10^{-3}}=1040\Omega$.

Step2: Determine input resistance formula

For a common - emitter amplifier with a current - source bias as in the given circuit, the input resistance $R_i = r_{\pi}/(1 + \beta)$.

Step3: Calculate $R_i$

Substitute $\beta = 80$ and $r_{\pi}=1040\Omega$ into the formula. $R_i=\frac{1040}{1 + 80}=\frac{1040}{81}\approx13\Omega$.

Answer:

C. 13 Ω