1. **Problem Statement:** Determine the emitter resistance $R_e$, input impedance $Z_i$, output impedance $Z_o$, voltage gain $A_v$, and current gain $A_i$ for the given transistor circuit with parameters $\beta=140$, $r_o=100\text{k}\Omega$, and resistors as shown. Then repeat parts (b) and (c) with $r_o=20\text{k}\Omega$. 2. **Step (a): Determine $R_e$** The emitter resistor $R_e$ is given directly as $1.2\text{k}\Omega$ from the circuit. 3. **Step (b): Find $Z_i$ and $Z_o$ with $r_o=100\text{k}\Omega$** - Input impedance $Z_i$ at the base is approximately: $$Z_i = r_\pi + (\beta + 1) R_e$$ where $r_\pi = \frac{\beta V_T}{I_C}$, but since $I_C$ is not given, we approximate $r_\pi$ as negligible or use given data if available. - Output impedance $Z_o$ looking into the collector is: $$Z_o = r_o \parallel R_C$$ where $R_C = 390\text{k}\Omega$. Calculate $Z_o$: $$Z_o = \frac{r_o R_C}{r_o + R_C} = \frac{100\times10^3 \times 390\times10^3}{100\times10^3 + 390\times10^3} = \frac{3.9\times10^{10}}{490\times10^3} \approx 79.59\text{k}\Omega$$ 4. **Step (c): Calculate $A_v$ and $A_i$ with $r_o=100\text{k}\Omega$** - Voltage gain $A_v$ is: $$A_v = -\frac{\beta R_C}{r_\pi + (\beta + 1) R_e}$$ Assuming $r_\pi$ small, denominator $\approx (\beta + 1) R_e = 141 \times 1.2\text{k} = 169.2\text{k}\Omega$ Calculate $A_v$: $$A_v = -\frac{140 \times 390\text{k}}{169.2\text{k}} = -\frac{54.6\times10^6}{169.2\times10^3} \approx -322.7$$ - Current gain $A_i$ is approximately $\beta = 140$. 5. **Step (d): Repeat (b) and (c) with $r_o=20\text{k}\Omega$** - New $Z_o$: $$Z_o = \frac{20\times10^3 \times 390\times10^3}{20\times10^3 + 390\times10^3} = \frac{7.8\times10^9}{410\times10^3} \approx 19.02\text{k}\Omega$$ - Voltage gain $A_v$ denominator remains $169.2\text{k}\Omega$. Calculate $A_v$: $$A_v = -\frac{140 \times 390\text{k}}{169.2\text{k}} \approx -322.7$$ Voltage gain is approximately unchanged because $r_o$ affects output impedance more than gain here. - Current gain $A_i$ remains approximately $140$. **Final answers:** - $R_e = 1.2\text{k}\Omega$ - For $r_o=100\text{k}\Omega$: $Z_i \approx 169.2\text{k}\Omega$, $Z_o \approx 79.59\text{k}\Omega$, $A_v \approx -322.7$, $A_i = 140$ - For $r_o=20\text{k}\Omega$: $Z_i \approx 169.2\text{k}\Omega$, $Z_o \approx 19.02\text{k}\Omega$, $A_v \approx -322.7$, $A_i = 140$