GATE Technical: GATE 2022 Electronics and Communications Engineering (EC) questions with solutions

Q1. Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 10¹⁷ cm⁻³ and the intrinsic carrier concentration is 10¹⁰ cm⁻³. Electron and hole diffusion lengths are 2 μm and 1 μm, respectively. The left side of the bar (x = 0) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at x = 0 because of the laser. The steady state electron density at x = 0 is 0.15 × 10¹⁴ cm⁻³ due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at x = 2 μm, is _________.

1. 0.37 × 10¹⁴ cm⁻³
2. 0.63 × 10¹³ cm⁻³
3. 3.7 × 10¹⁴ cm⁻³
4. 10³ cm⁻³

Answer: 0.63 × 10¹³ cm⁻³

The steady state electron density at a distance from the generation point can be approximated using the diffusion equation, which accounts for the initial excess electron density and the diffusion length. Given the diffusion length of electrons is 2 μm and the initial density at x = 0 is 0.15 × 10¹⁴ cm⁻³, the density decreases exponentially with distance, leading to a calculated value of approximately 0.63 × 10¹³ cm⁻³ at x = 2 μm.

Q2. Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for A0, A1, A2, and A3 are ____________.

1. A0 = 0, A1 = 0, A2 = 1, A3 = 1
2. A0 = 1, A1 = 0, A2 = 1, A3 = 0
3. A0 = 0, A1 = 1, A2 = 1, A3 = 0
4. A0 = 1, A1 = 1, A2 = 0, A3 = 0

Answer: A0 = 0, A1 = 1, A2 = 1, A3 = 0

The correct option sets the multiplexer inputs such that the output reflects the XOR operation between inputs C and D, which requires specific combinations of the select lines to enable the correct input paths for the desired output.

Q3. The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and −1 V, respectively. The MOSFET substrates are connected to their respective sources. Ignore leakage currents and assume that the capacitors are initially discharged. For the applied voltages as shown, the steady state voltages are _____________.

1. V1 = 5 V, V2 = 5 V
2. V1 = 5 V, V2 = 4 V
3. V1 = 4 V, V2 = 5 V
4. V1 = 4 V, V2 = −5 V

Answer: V1 = 4 V, V2 = 5 V

An nMOS pass transistor passes a degraded high of Vdd - Vtn = 5 - 1 = 4 V (V1 = 4 V), while a pMOS passes a strong high of 5 V (V2 = 5 V). Correct is V1 = 4 V, V2 = 5 V, not the stored V1 = 5, V2 = 4.

Q4. In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is 2sin(t + π/2). The displacement current (in Amperes) through the capacitor is ________.

1. 2sin(t)
2. 2sin(t + π)
3. 2sin(t + π/2)
4. 0

Answer: 2sin(t + π/2)

In a series circuit, the conduction current through the resistor and the displacement current through the capacitor are equal. Since the conduction current is given as 2sin(t + π/2), the displacement current must also be 2sin(t + π/2) to maintain continuity in the circuit.

Q5. Select the CORRECT statement(s) regarding semiconductor devices.

1. Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.
2. Collector region is generally more heavily doped than Base region in a BJT.
3. Total current is spatially constant in a two terminal electronic device in dark under steady state condition.
4. Mobility of electrons always increases with temperature in Silicon beyond 300 K.

Answer: Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.

In an intrinsic semiconductor, the number of electrons generated in the conduction band is equal to the number of holes created in the valence band, resulting in equal density of both charge carriers at thermal equilibrium.

Q6. Consider an FM broadcast that employs the pre-emphasis filter with frequency response H_pe(ω) = 1 + jω/ω₀, where ω₀ = 10⁴ rad/sec. For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of (R, C) values is/are _______.

1. R = 1 kΩ, C = 0.1 μF
2. R = 2 kΩ, C = 1 μF
3. R = 1 kΩ, C = 2 μF
4. R = 2 kΩ, C = 0.5 μF

Answer: R = 1 kΩ, C = 0.1 μF

The correct option provides values for R and C that create a time constant that matches the de-emphasis requirements of the FM broadcast system, effectively counteracting the pre-emphasis filter's frequency response to restore the original signal's characteristics.