GATE 2025 Analog Electronics Questions and Solutions

The diode in the circuit below is ideal. The input voltage in volts is given by \( V_i = 10 \sin(100\pi t) \) 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

While the diode is off no current flows, so there is no drop across \( R \) and the anode sits at \( V_i \). The 5 V source is connected with its positive terminal at the bottom rail, so the cathode is held at \( -5\,V \). The diode is therefore forward biased whenever

The period of the input is

Writing \( \theta = 100\pi t \), the condition \( \sin\theta > -\frac{1}{2} \) holds over \( -\frac{\pi}{6} < \theta < \frac{7\pi}{6} \), an interval of \( \frac{4\pi}{3} \) out of every \( 2\pi \). Hence

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):

Q1 is a PNP transistor, so its emitter sits one \( V_{EB} \) above its base: \( V_{E1} = V_{B1} + V_{EB1} = 14.3 + 0.7 = 15.0\,V \)

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. \( \frac{-\beta R_L}{R_S + r_\pi} \)
2. \( \frac{+\beta R_L}{R_S} \)
3. \( \frac{-\beta R_L}{R_S} \)
4. \( \frac{+\beta R_L}{R_S + r_\pi} \)

Solution

The input loop is \( R_S \) in series with \( r_\pi \), so

The controlled source \( \beta i_b \) draws its current downward out of the output node, so that same current flows up through \( R_L \) from ground into the node:

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

DC analysis: set the signal components to zero. The 2 mA tail current splits equally, so \( I_{D1} = I_{D2} = 1\,mA \). With \( R_D = 1\,k\Omega \) and \( V_{DD} = 5\,V \):

AC analysis: the drive is purely differential, so the common source node is an AC ground and each half-circuit sees half of the differential input:

\( V_3 \) is the drain of \( M_1 \), so it is inverted with respect to \( V_1 \):

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

The input branch, \( R \) in series with \( 10C \), sets the lower (high-pass) corner; the feedback network, \( 2R \) in parallel with \( 0.1C \), sets the upper (low-pass) corner:

The unknown product \( RC \) cancels in the ratio:

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.