GATE Technical: Electronics and Communication Engineering (Set 1) questions with solutions

Q1. Consider the oscillator circuit shown in the figure. The function of the network (shown in dotted lines) consisting of the 100 Ω resistor in series with the two diodes connected back-to-back is to:

1. introduce an amplitude stabilization by preventing the op amp from saturating and thus producing sinusoidal oscillations of fixed amplitude
2. introduce an amplitude stabilization by forcing the op amp to swing between positive and negative saturation and thus producing square wave oscillations of fixed amplitude
3. introduce frequency stabilization by forcing the circuit to oscillate at a single frequency
4. enable the loop gain to take on a value that produces square wave oscillations

Answer: introduce an amplitude stabilization by preventing the op amp from saturating and thus producing sinusoidal oscillations of fixed amplitude

The correct option is right because the network with the resistor and diodes limits the output voltage of the op amp, preventing it from reaching saturation. This allows the circuit to maintain a stable amplitude for sinusoidal oscillations, ensuring consistent performance.

Q2. What is the voltage V_out in the following circuit?

1. 0 V
2. (V_T of PMOS + V_T of NMOS)/2
3. Switching threshold of inverter
4. V_DD

Answer: Switching threshold of inverter

The switching threshold of an inverter is the point where the output voltage transitions from high to low, which occurs when the input voltage equals the threshold voltage, making it the correct answer for V_out in this context.

Q3. Match the inferences X, Y, and Z about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation. X: The system is stable... Y: The system is unstable... Z: The test breaks down... P:... when all elements are positive Q:... when any one element is zero R:... when there is a change in sign of coefficients

1. X-P, Y-R, Z-Q
2. X-Q, Y-P, Z-R
3. X-P, Y-Q, Z-R
4. X-R, Y-Q, Z-P

Answer: X-P, Y-R, Z-Q

The correct option matches the stability of the system with the conditions of the Routh's Table: the system is stable when all elements are positive (X-P), unstable when there is a change in sign of coefficients (Y-R), and the test breaks down when any one element is zero (Z-Q).

Q4. A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

1. encircles the s-plane point (-1 + j0) in the counterclockwise direction as many times as the number of right-half-s-plane poles.
2. encircles the s-plane point (0 - j1) in the clockwise direction as many times as the number of right-half-s-plane poles.
3. encircles the s-plane point (-1 + j0) in the counterclockwise direction as many times as the number of left-half-s-plane poles.
4. encircles the s-plane point (-1 + j0) in the counterclockwise direction as many times as the number of right-half-s-plane zeros.

Answer: encircles the s-plane point (-1 + j0) in the counterclockwise direction as many times as the number of right-half-s-plane poles.

The correct option is right because the Nyquist stability criterion states that for a closed-loop system to be stable, the Nyquist plot must encircle the critical point (-1 + j0) in a manner that corresponds to the number of unstable poles (right-half-plane poles) in the open-loop transfer function.

Q5. The propagation constant of a lossy transmission line is (2 + j5) m⁻¹ and its characteristic impedance is (50 + j0) Ω at ω = 10⁶ rad s⁻¹. The values of the line constants L, C, R, G are, respectively.

1. (A) L = 200 μ/m, C = 0.1 μ/m, R = 50 Ω/m, G = 0.02 /m
2. (B) L = 250 μ/m, C = 0.1 μ/m, R = 100 Ω/m, G = 0.04 /m
3. (C) L = 200 μ/m, C = 0.2 μ/m, R = 100 Ω/m, G = 0.02 /m
4. (D) L = 250 μ/m, C = 0.2 μ/m, R = 50 Ω/m, G = 0.04 /m

Answer: (B) L = 250 μ/m, C = 0.1 μ/m, R = 100 Ω/m, G = 0.04 /m

Option B is correct because it accurately reflects the relationships between the propagation constant and the characteristic impedance of the transmission line, where the values of L, C, R, and G satisfy the equations for a lossy transmission line at the given frequency.

Q6. A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form ∑ₖ₌₁³ aₖ cos(kω₀ t), where aₖ ≠ 0, ω₀ ≠ 0. The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

1. ∑ₖ₌₁³ bₖ cos(kω₀ t + φₖ), where bₖ ≠ aₖ, ∀ k
2. ∑ₖ₌₁⁴ bₖ cos(kω₀ t + φₖ), where bₖ ≠ 0, ∀ k
3. ∑ₖ₌₁³ aₖ cos(kω₀ t + φₖ)
4. ∑ₖ₌₁² aₖ cos(kω₀ t + φₖ)

Answer: ∑ₖ₌₁³ aₖ cos(kω₀ t + φₖ)

The correct option reflects that the output across the resistor can maintain the same frequency components as the input, but with possible phase shifts, which is typical in linear systems. Since the network is linear and the input consists of multiple frequency components, the output can also include these same components with adjusted phases.