1. **Problem statement:** Given a transistor circuit with parameters \( \beta = 140 \), \( r_o = 100\text{k}\Omega \) (and later \( 20\text{k}\Omega \)), and resistors \( R_B = 390\text{k}\Omega + 2.2\text{k}\Omega \), \( R_E = 1.2\text{k}\Omega \), find: (a) the intrinsic emitter resistance \( r_e \), (b) input impedance \( Z_i \) and output impedance \( Z_o \), (c) voltage gain \( A_v \) and current gain \( A_i \), then repeat (b) and (c) with \( r_o = 20\text{k}\Omega \). 2. **Step (a): Determine \( r_e \)** The intrinsic emitter resistance is given by: $$ r_e = \frac{26\text{mV}}{I_E} $$ Assuming room temperature, 26mV is the thermal voltage \( V_T \). Since \( I_E \) is not given explicitly, we approximate \( r_e \) using \( r_e = \frac{26\text{mV}}{I_C} \) and \( I_C \approx \frac{V_{BE}}{R_E} \) if \( V_{BE} \approx 0.7V \). Calculate \( I_E \): $$ I_E \approx I_C = \frac{0.7}{1.2\times10^3} = 5.83 \times 10^{-4} A $$ Then: $$ r_e = \frac{0.026}{5.83 \times 10^{-4}} \approx 44.6 \Omega $$ 3. **Step (b): Find \( Z_i \) and \( Z_o \) with \( r_o = 100\text{k}\Omega \)** Input impedance \( Z_i \) at the base is: $$ Z_i = Z_B || (\beta + 1)(r_e + R_E) $$ where \( Z_B = 390\text{k}\Omega + 2.2\text{k}\Omega = 392.2\text{k}\Omega \). Calculate \( (\beta + 1)(r_e + R_E) \): $$ (140 + 1)(44.6 + 1200) = 141 \times 1244.6 = 175,438 \Omega $$ Then: $$ Z_i = \frac{392,200 \times 175,438}{392,200 + 175,438} \approx \frac{68.8 \times 10^9}{567,638} \approx 121,200 \Omega = 121.2\text{k}\Omega $$ Output impedance \( Z_o \) looking into emitter is: $$ Z_o = R_E || r_o = \frac{1.2\text{k} \times 100\text{k}}{1.2\text{k} + 100\text{k}} \approx \frac{120,000}{101,200} \approx 1.185\text{k}\Omega $$ 4. **Step (c): Calculate voltage gain \( A_v \) and current gain \( A_i \)** Voltage gain: $$ A_v = -\frac{\beta R_C}{Z_i} $$ Here, \( R_C = 2.2\text{k}\Omega \) (collector resistor). Calculate: $$ A_v = -\frac{140 \times 2200}{121,200} = -\frac{308,000}{121,200} \approx -2.54 $$ Current gain: $$ A_i = \beta \times \frac{Z_o}{Z_i} = 140 \times \frac{1,185}{121,200} \approx 140 \times 0.00978 = 1.37 $$ 5. **Step (d): Repeat (b) and (c) with \( r_o = 20\text{k}\Omega \)** Output impedance: $$ Z_o = R_E || r_o = \frac{1.2\text{k} \times 20\text{k}}{1.2\text{k} + 20\text{k}} = \frac{24,000}{21,200} \approx 1.132\text{k}\Omega $$ Input impedance \( Z_i \) remains the same as it depends on \( r_e \) and \( R_E \), not \( r_o \): $$ Z_i = 121.2\text{k}\Omega $$ Voltage gain: $$ A_v = -\frac{140 \times 2200}{121,200} = -2.54 $$ (unchanged) Current gain: $$ A_i = 140 \times \frac{1,132}{121,200} = 140 \times 0.00934 = 1.31 $$ **Final answers:** - (a) \( r_e \approx 44.6 \Omega \) - (b) \( Z_i \approx 121.2\text{k}\Omega, Z_o \approx 1.185\text{k}\Omega \) with \( r_o=100\text{k}\Omega \) - (c) \( A_v \approx -2.54, A_i \approx 1.37 \) with \( r_o=100\text{k}\Omega \) - (d) \( Z_o \approx 1.132\text{k}\Omega, A_v \approx -2.54, A_i \approx 1.31 \) with \( r_o=20\text{k}\Omega \)