GATE Technical: Electronics and Communication Engineering questions with solutions

Q1. Two identical nMOS transistors M1 and M2 are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. Vbias and VD are adjusted so that both transistors are in saturation. The transconductance of this combination is defined as gm = ∂iD/∂vGS, while the output resistance is ro = ∂vDS/∂iD, where iD is the current flowing into the drain of M2. Let gm1, gm2 be the transconductances and ro1, ro2 be the output resistances of transistors M1 and M2, respectively. Which of the following statements about estimates for gm and ro is correct?

1. gm ≈ gm1 + gm2·ro2 and ro ≈ ro1 + ro2.
2. gm ≈ gm1 + gm2 and ro ≈ ro1 + ro2.
3. gm ≈ gm1 and ro ≈ ro1·gm2·ro2.
4. gm ≈ gm1 and ro ≈ ro2.

Answer: gm ≈ gm1 and ro ≈ ro1·gm2·ro2.

The correct option indicates that the transconductance gm is primarily determined by the first transistor M1, while the output resistance ro is influenced by both transistors, specifically the output resistance of M1 combined with the effect of M2's transconductance and output resistance, reflecting the interaction in the amplifier configuration.

Q2. A good transimpedance amplifier has

1. low input impedance and high output impedance.
2. high input impedance and high output impedance.
3. high input impedance and low output impedance.
4. low input impedance and low output impedance.

Answer: low input impedance and low output impedance.

A good transimpedance amplifier is designed to convert current to voltage efficiently, which requires low input impedance to allow for better current sensing and low output impedance to drive the load effectively.

Q3. The points P, Q, and R shown on the Smith chart (normalized impedance chart) in the following figure represent:

1. P: Open Circuit, Q: Short Circuit, R: Matched Load
2. P: Open Circuit, Q: Matched Load, R: Short Circuit
3. P: Short Circuit, Q: Matched Load, R: Open Circuit
4. P: Short Circuit, Q: Open Circuit, R: Matched Load

Answer: P: Short Circuit, Q: Matched Load, R: Open Circuit

The correct option identifies P as a short circuit, which is represented at the center of the Smith chart, Q as a matched load located on the 1.0 normalized impedance circle, and R as an open circuit, positioned at the edge of the chart. This arrangement accurately reflects the characteristics of each impedance type on the Smith chart.

Q4. Let M be a real 4 × 4 matrix. Consider the following statements: S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M is non-singular (invertible). Which one among the following is TRUE?

1. S1 implies S2
2. S1 implies S3
3. S2 implies S1
4. S3 implies S2

Answer: S2 implies S1

If a matrix has 4 distinct eigenvalues, it guarantees that there are 4 linearly independent eigenvectors corresponding to those eigenvalues, as distinct eigenvalues lead to independent eigenvectors.

Q5. A discrete-time all-pass system has two of its poles at 0.25∠0° and 2∠30°. Which one of the following statements about the system is TRUE?

1. It has two more poles at 0.5∠30° and 4∠0°.
2. It is stable only when the impulse response is two-sided.
3. It has constant phase response over all frequencies.
4. It has constant phase response over the entire z-plane.

Answer: It is stable only when the impulse response is two-sided.

The correct option is true because a discrete-time all-pass system can be stable only if its impulse response is two-sided, ensuring that the system's output remains bounded for all inputs, particularly in the case of poles located outside the unit circle.

Q6. Let c(t) = A_c cos(2π f_c t) and m(t) = cos(2π fₘ t). It is given that f_c >> 5 fₘ. The signal c(t)+m(t) is applied to the input of a non-linear device, whose output vₒ(t) is related to the input v_i(t) as vₒ(t) = a v_i(t) + b v_i²(t), where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency f_c and bandwidth 5 fₘ to produce an amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then a/b is

1. 0.25
2. 0.5
3. 1
4. 2

Answer: 2

The ratio a/b equals 2 because, in amplitude modulation, the sideband power is proportional to the square of the modulation index, which is determined by the ratio of the amplitudes of the modulating signal and the carrier. To achieve sideband power equal to half of the carrier power, the modulation index must be set such that the relationship a/b = 2 holds true, ensuring the desired power distribution in the AM wave.

Q7. Consider a white Gaussian noise process N(t) with two-sided power spectral density S_N(f) = 0.5 W/Hz as input to a filter with impulse response 0.5e^(-t²/2) (where t is in seconds) resulting in output Y(t). The power in Y(t) in watts is

1. 0.11
2. 0.22
3. 0.33
4. 0.44

Answer: 0.22

The power in the output Y(t) can be calculated using the formula that relates the power spectral density of the input noise and the filter's impulse response. The filter's impulse response has a corresponding frequency response that modifies the input noise's power spectral density, resulting in an output power of 0.22 watts.

Q8. Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having different band-gaps. The built-in voltages of red, green and blue diodes are V_R, V_G and V_B, respectively. A same donor and acceptor doping to be the same (N_A and N_D, respectively) in the p and n sides of all the three diodes. Which one of the following relationships about the built-in voltages is TRUE?

1. V_R > V_G > V_B
2. V_R < V_G < V_B
3. V_R = V_G = V_B
4. V_R > V_G < V_B

Answer: V_R < V_G < V_B

The built-in voltage of a diode is inversely related to the band-gap energy of the semiconductor material used; since blue light has the highest energy and red light the lowest, the built-in voltage for red LEDs is less than that for green, which in turn is less than that for blue.

Q9. The distance (in meters) a wave has to propagate in a medium having a skin depth of 0.1 m so that the amplitude of the wave attenuates by 20 dB, is

1. 0.12
2. 0.23
3. 0.46
4. 2.3

Answer: 0.23

The amplitude of a wave attenuates by 20 dB when it travels a distance equal to approximately 0.23 times the skin depth, which is derived from the relationship between attenuation in decibels and distance in a medium.