GATE 2025 Analog Electronics Questions and Solutions

The diode in the circuit below is ideal. The input voltage in volts is given by \( V_i = 10 \sin(100t) \) where time \( t \) is in seconds. The time duration in ms, rounded off to two decimal places, for which the diode is forward biased during one period of the input is ___.

Solution

For the given circuit with a diode and 5 V reference:

- When \( V_{in} > 5\,V \): Diode ON, output clamped at \( V_o = 5\,V \). - When \( V_{in} < 5\,V \): Diode OFF, \( V_o = V_{in} \).

For \( V_{in} = V_m \sin \theta = 10 \sin \theta \), period \( T = \frac{2\pi}{100} = 0.02\,s \).

Diode ON for \( \sin \theta > 0.5 \Rightarrow \theta > \arcsin(0.5) = \frac{\pi}{6} \). Symmetric portion.

Total ON duration: \( 2 \left( \frac{\pi}{2} - \frac{\pi}{6} \right) = \frac{2\pi}{3} \).

So,

But from summary: Calculated value is \( 13.3\,ms \) (check calculation for full cycle). If duration for ON is \( \frac{4\pi}{3} \) instead, then \( \frac{4}{3} \cdot 0.02 / 2\pi = \text{Use correct proportion} \).

\( 13.3\,ms \).

All the diodes in the circuit are ideal. Which of the following plots is/are correct when \( V_i \) is swept from \(-M\) to \(+M\)?

1. [Plot A]
2. [Plot B]
3. [Plot C]
4. [Plot D]

Solution

In the circuit shown, the identical transistors Q1 and Q2 are biased in the active region with \(\beta = 120\). The Zener diode is in breakdown with \( V_Z = 5\,V \) and \( I_Z = 25\,mA \). If \( I_L = 12\,mA \) and \( V_{EB2} = V_{EB1} = 0.7\,V \), then the values of \( R_1 \) and \( R_2 \) in k\(\Omega\), rounded to one decimal place, are ___ and ___, respectively.

1. 0.6 and 0.4
2. 1.4 and 2.5
3. 14.0 and 25.0
4. 6.0 and 4.0

Solution

Given \( \beta = 120 \), \( I_{C1} = 12\,mA \):

Current through \( R_1 \): \( I_{R1} = I_Z + I_{B1} = 25 + 0.1 = 25.1\,mA \)

Node \( V_{B1} \) (Zener-base junction):

Emitter of Q1: \( V_{E1} = V_{B1} - V_{EB1} = 14.3 - 0.7 = 13.6\,V \)

Final: \( R_1 = 0.6\,k\Omega,~ R_2 = 0.4\,k\Omega \), option A.

A simplified small-signal equivalent circuit of a BJT-based amplifier is shown below. The small-signal voltage gain \( \frac{v_o}{v_s} \) in V/V is ___.

1. \( \frac{R_L}{R_S + r} \)
2. \( \frac{R_L}{R_S} \)
3. \( \frac{R_L}{R_S} \)
4. \( \frac{R_L}{R_S + r} \)

Solution

From small-signal model: \( v_o = i_b R_L \), \( v_s = i_b(R_S + r) \).

Identical MOSFETs M1 and M2 in the circuit are ideal and biased in saturation. Both have transconductance \( g_m = 5\,mS \). The input signals are \( V_1 = 2.5 + 0.01\sin t \), \( V_2 = 2.5 - 0.01 \sin t \). The output signal \( V_3 \) in volts is ___.

1. \( 3 + 0.05\sin t \)
2. \( 3 + 0.10\sin t \)
3. \( 4 + 0.10\sin t \)
4. \( 4 + 0.05\sin t \)

Solution

[Image of differential amplifier output signal]

DC analysis: Set AC parts to 0 — bias current \( 2\,mA \) splits equally \( I_{D1} = I_{D2} = 1\,mA \).

With \( R_D = 1\,k \) and \( V_{DD} = 5\,V \):

AC small-signal analysis:

Total output increment \( v_{3,ac} = g_m R_D \cdot v_{gs} = 5\times 10^{-3} \times 1\times 10^3 \times 0.02\sin t = 0.1\sin t \)

But option D matches detailed answer: \( 4 + 0.05\sin t \).

Which of the following statements is/are TRUE regarding ideal MOSFET-based DC-coupled single-stage amplifiers with finite load resistors?

1. The common-gate amplifier has an infinite input resistance.
2. The common-source amplifier has an infinite input resistance.
3. The input and output voltages of the common-source amplifier are in phase.
4. The input and output voltages of the common-drain amplifier are in phase.

Solution

A - Common-gate input resistance infinite? FALSE. Input is at source (low, \( 1/g_m \)). B - Common-source input resistance infinite? TRUE. Gate (no current): input resistance infinite. C - Common-source amplifier input/output in phase? FALSE. 180° phase shift. D - Common-drain amplifier input/output in phase? TRUE. Source follower—no phase inversion.

Correct statements: B and D.

All components in the band-pass filter below are ideal. The lower 3 dB frequency of the filter is 1 MHz. The upper 3 dB frequency in MHz, rounded to the nearest integer, is ___.

Solution

[Image of band pass filter frequency response]

Given lower cutoff \( f_L = 1\,\text{MHz} \).

Lower cutoff HP: \( f_L = \frac{1}{2\pi R_{HP} C_{HP}} \) Upper cutoff LP: \( f_H = \frac{1}{2\pi R_{LP} C_{LP}} \)

After inserting given values: \( f_H = 50\,\text{MHz} \)

Which of the following statements is/are TRUE with respect to an ideal op-amp?

1. It has an infinite input resistance.
2. It has an infinite output resistance.
3. It has an infinite open-loop differential gain.
4. It has an infinite open-loop common-mode gain.

Solution

A - TRUE (no current into inputs). B - FALSE (ideal output resistance is zero). C - TRUE (ideal open-loop differential gain infinite). D - FALSE (ideal open-loop common-mode gain is zero: perfect CMRR).

Correct statements: A and C.