Calculate the dc bias voltages and currents

Question

Problem 1: Calculate the DC bias voltages (V_{(c_1)}, V_{(c_2)}, V_{(E_2)}, V_{(B_1)}, V_{(CE_2)}) and currents (I_{(B_1), I(c_2), I(E_2 )}) for Darlington configuration in Figure 1. Given β₁ = 60, β₂ = 70.

Problem 2: An amplifier circuit is shown in Figure 2. The operational amplifier (op-amp) A1 can be assumed as ideal. The input impedance of this amplifier is 1MΩ. The gain of this amplifier is -100.

a. Show that I₂ = V₁/R₁.

b. Find the expression of the voltage gain, Av, in terms R1, R2, R3 and R4.

c. Due to practical reasons, the maximum value to be used for the resistors is set at 1MΩ. Based on the given design constraint, determine the values for R1, R2, R3 and R4.

Hint: V_out = - R₂/R₁ Vin(1 + R₄/R₂ + R₄/R₃).