Consider the bipolar diff-amp with an active load and a pair of offset-null terminals as shown in Figure 14.22 in the text. Let \(R_{1}=R_{2}=500 \Omega\) and let \(R_{x}\) be a \(50 \mathrm{k} \Omega\) potentiometer.

(a) If the wiper arm of the potentiometer is exactly in the center, determine the effective resistances \(R_{1}^{\prime}\) and \(R_{2}^{\prime}\).

(b) Assume \(I_{Q}=250 \mu \mathrm{A}\) meaning that \(i_{C 1}=i_{C 2}=125 \mu \mathrm{A}\). Let \(I_{S 3}=\) \(2 \times 10^{-14} \mathrm{~A}\) and \(I_{S 4}=2.2 \times 10^{-14} \mathrm{~A}\). Determine the required values of \(x\) and \((1-x)\) of the potentiometer to compensate for the transistor mismatches.

ici (3) lo icz Q2 24 Q3 + + VBE3 UBE4 Offset- null terminal ww R RI ww x 1-x ww Rx Offset- null terminal Figure 14.22 Basic bipolar input diff-amp stage, including a pair of offset-null terminals connected to a potentiometer