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GATE 2017 EE – Question 62

Analog and Digital Electronics · Amplifiers: biasing, equivalent circuit and frequency response · 2 marks · Numerical answer

The circuit shown in the figure uses matched transistors with a thermal voltage $V_T = 25$ mV. The base currents of the transistors are negligible. The value of the resistance R in $k\Omega$ that is required to provide 1 $\mu$A bias current for the differential amplifier block shown is ________. (Give the answer up to one decimal place.)

Two matched transistors whose bases are tied together form a current mirror between $\pm 12$ V. The left transistor is diode connected and carries 1 mA. The right transistor has a resistor R in its emitter and supplies 1 $\mu$A to the differential amplifier block.

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Correct answer: 170 to 174

Explanation

The two base-emitter voltages differ by the voltage across R, so $V_T\ln\frac{I_{ref}}{I_{out}} = I_{out}R$. This gives $0.025 \times \ln\frac{1\ \text{mA}}{1\ \mu\text{A}} = 0.025 \times 6.908 = 0.1727$ V. Then $R = \frac{0.1727}{1\ \mu\text{A}} = 172.7\ \text{k}\Omega$.