Question 1

If fixed positive charges are present in the gate oxide of an n-channel enhancement type MOSFET, it will lead to

Accepted Answer

a decrease in the threshold voltage. The presence of fixed positive charges in the gate oxide attracts more electrons to the channel, effectively lowering the voltage required to create a conductive channel, which results in a decrease in the threshold voltage.

Question 2

In the ac equivalent circuit shown in the figure, if i_in is the input current and R_F is very large, the type of feedback is

Accepted Answer

current-current feedback. When R_F is very large, the feedback mechanism primarily involves the output current being fed back to influence the input current, which characterizes it as current-current feedback.

Question 3

In the following circuit employing pass transistor logic, all NMOS transistors are identical with a threshold voltage of 1 V. Ignoring the body-effect, the output voltages at P, Q and R are

Accepted Answer

4 V, 3 V, 2 V. The correct option indicates that the output voltages at P, Q, and R are determined by the voltage drops across the NMOS transistors, which are influenced by their threshold voltage and the input levels. In this case, the outputs reflect the expected voltage levels after accounting for the threshold voltage of 1 V, resulting in the values of 4 V, 3 V, and 2 V respectively.

Question 4

In a code-division multiple access (CDMA) system with N = 8 chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is _______.

Accepted Answer

8. In a CDMA system, the maximum number of users that can be assigned mutually orthogonal signature sequences is equal to the number of chips available. Since there are 8 chips, up to 8 users can be accommodated with unique sequences that do not interfere with each other.

Question 5

The capacity of a Binary Symmetric Channel (BSC) with cross-over probability 0.5 is _______.

Accepted Answer

0. In a Binary Symmetric Channel with a cross-over probability of 0.5, the channel is essentially unreliable, as it flips the input bit with equal probability. This results in no information being transmitted effectively, leading to a capacity of 0.

Question 6

The force on a point charge +q kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity ε is

Accepted Answer

q²/(16π ε d²) towards the plate. The correct option is based on the principle of image charges, where the grounded metal plate creates an image charge that attracts the real charge towards it. The force is calculated using Coulomb's law, resulting in the specified magnitude and direction towards the plate.

Question 7

The doping concentrations on the p-side and n-side of a silicon diode are 1 × 10¹⁶ cm⁻³ and 1 × 10¹⁷ cm⁻³, respectively. A forward bias of 0.3 V is applied to the diode. At T = 300 K, the intrinsic carrier concentration of silicon n_i = 1.5 × 10¹⁰ cm⁻³ and kT/q = 26 mV. The electron concen

Accepted Answer

2.3 × 10¹⁰ cm⁻³. The electron concentration at the edge of the depletion region on the p-side can be calculated using the formula that accounts for the equilibrium condition and the applied forward bias. Given the doping concentrations and the intrinsic carrier concentration, the forward bias reduces the barrier, allowing more electrons to populate the edge of the depletion region, resulting in the calculated value of approximately 2.3 × 10¹⁰ cm⁻³.

Question 8

Consider the Boolean function, F(w,x,y,z) = wy + xy + w̅xyz + w̅x̅y + xz + x̅y̅z̅. Which one of the following is the complete set of essential prime implicants?

Accepted Answer

y, xz, z̅. The correct option includes essential prime implicants that cover all the minterms of the function without redundancy, ensuring that each minterm is accounted for by at least one of the implicants. In this case, 'y', 'xz', and 'z̅' are necessary to represent the function accurately.

Question 9

The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to input A of the XOR gate.
Suppose the XOR gate is replaced by an XNOR gate. Which one of the following options preserves the state diagram?

Accepted Answer

Input A is connected to Q1 and S is complemented. Connecting input A to Q1 and complementing S ensures that the output behavior of the XNOR gate matches the original state diagram, as the XNOR gate outputs true when both inputs are the same, which aligns with the intended logic when S is inverted.

Question 10

Let X be a real-valued random variable with E[X] and E[X²] denoting the mean values of X and X², respectively. The relation which always holds true is

Accepted Answer

E[X²] ≥ (E[X])². This inequality is a consequence of the Cauchy-Schwarz inequality, which states that the expected value of the square of a random variable is always greater than or equal to the square of its expected value, reflecting the concept of variance.

Question 11

Consider a random process X(t) = √2 sin(2πt + φ) where the random phase φ is uniformly distributed in the interval [0,2π]. The auto-correlation E[X(t1)X(t2)] is

Accepted Answer

cos(2π(t1 - t2)). The correct option is right because the auto-correlation function for a sinusoidal process with a uniformly distributed random phase results in a cosine function of the difference between the two time points, reflecting the periodic nature of the sine function and the properties of the expected value.

Question 12

Let Q(√γ) be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density N0/2. The parameter γ is a function of bit energy and noise power spectral density.

A system with two independent and identical AWGN channels with noise power spectral density N0/2 is sh

Accepted Answer

√2. The correct option is √2 because when two independent AWGN channels are combined, the effective signal-to-noise ratio (SNR) is increased by a factor of 2, leading to an improvement in the BER performance. This results in the argument of the Q-function being scaled by √2, hence the BER becomes Q(b√γ) with b equal to √2.

Question 13

A fair coin is tossed repeatedly until a 'Head' appears for the first time. Let L be the number of tosses to get this first 'Head'. The entropy H(L) in bits is _____.

Accepted Answer

2. L is geometric: P(L=k)=(1/2)^k for k>=1. H(L) = -sum (1/2)^k log2((1/2)^k) = sum k(1/2)^k = 2 bits.

Question 14

For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of 2 results in

(A) halving of v and no change in Z
(B) no changes in v and halving of Z
(C

Accepted Answer

(B). Reducing the spacing between the plates of a parallel plate transmission line decreases the capacitance, which in turn lowers the characteristic impedance Z, while the speed of propagation v remains unchanged because it is determined by the dielectric properties of the medium between the plates.

Question 15

Norton's theorem states that a complex network connected to a load can be replaced with an equivalent impedance

Accepted Answer

in parallel with a current source. Norton's theorem allows us to simplify a network by representing it as a current source in parallel with an equivalent impedance, which makes it easier to analyze the circuit's behavior when connected to a load.

Question 16

In CMOS technology, shallow P-well or N-well regions can be formed using

Accepted Answer

low energy ion-implantation. Low energy ion-implantation is the correct method because it allows for precise control over the doping concentration and depth of the P-well or N-well regions, which is essential for the performance of CMOS devices.

Question 17

The feedback topology in the amplifier circuit (the base bias circuit is not shown for simplicity) in the figure is

Accepted Answer

voltage series feedback. Voltage series feedback is used in this amplifier circuit because it takes a portion of the output voltage and feeds it back to the input in a series configuration, which helps stabilize the gain and improve linearity.

Question 18

In the differential amplifier shown in the figure, the magnitudes of the common-mode and differential-mode gains are A_cm and A_d, respectively. If the resistance R_E is increased, then

Accepted Answer

common-mode rejection ratio increases. Increasing the resistance R_E enhances the differential amplifier's ability to reject common-mode signals, thereby improving the common-mode rejection ratio (CMRR). This occurs because a higher R_E increases the gain for differential signals while reducing the gain for common-mode signals.

Question 19

A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The open-loop gain A_v0, input resistance R_in and output resistance Rₒ for A1 and A2 are as follows:
A1: A_v0 = 10, R_in = 10 kΩ, Rₒ = 1 kΩ.
A2: A_v0 = 5, R_in = 5 kΩ, Rₒ = 200 Ω.
The approximate overall volt

Accepted Answer

40. The overall voltage gain in a cascade connection is calculated by multiplying the gains of each amplifier while considering the loading effect. Here, the output resistance of A1 affects the input of A2, leading to an effective gain of 10 (from A1) multiplied by 4 (from A2 after accounting for the loading), resulting in an overall gain of approximately 40.

Question 20

For an n-variable Boolean function, the maximum number of prime implicants is

Accepted Answer

2^(n-1). The maximum number of prime implicants for an n-variable Boolean function is determined by the number of combinations of the variables that can form distinct groups, which is represented by 2^(n-1). This accounts for the various ways the variables can be combined while still maintaining the properties of prime implicants.

Question 21

The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is

Accepted Answer

4. In packed BCD each byte holds two decimal digits (4 bits each). The number 1856357 has 7 digits, so it needs ceil(7/2) = 4 bytes. The stored answer 5 is wrong; the correct answer is 4.

Question 22

In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by

Accepted Answer

M = X̅Y, N = X ⊕ Y. The correct option states that the Borrow (M) is determined by the condition where X is less than Y, which is represented by X̅Y, while the Difference (N) is calculated using the exclusive OR operation (X ⊕ Y), which accurately reflects the subtraction of Y from X.

Question 23

A FIR system is described by the system function
H(z) = 1 + 7/2 z⁻¹ + 3/2 z⁻²
The system is

Accepted Answer

mixed phase. H(z)=1+3.5z^-1+1.5z^-2 has zeros where z^2+3.5z+1.5=0, giving z=-0.5 and z=-3. One zero is inside the unit circle and one outside, so the FIR system is mixed phase, not minimum phase.

Question 24

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by C = W log2(1 + P/(σ² W)) bits per second (bps), where W is the channel bandwidth. P is the average power received and σ² is the one-sided power spectral density of the AWGN. For a fixed P/σ² = 1000, the

Accepted Answer

1.44. As the bandwidth approaches infinity, the capacity formula simplifies, and the term log2(1 + P/(σ² W)) approaches log2(1 + 1000) which is approximately 10. Therefore, the capacity becomes C = W * 10, and since W is infinite, the capacity approaches 1.44 kbps when considering the logarithmic scaling.

Question 25

Which one of the following field patterns represents a TEM wave travelling in the positive x direction?

Accepted Answer

E = −2ŷ, H = −3ẑ. A TEM wave's power flow S = E x H must be along +x. For E = -2y, H = -3z: (-2y)x(-3z) = +6(yxz) = +6x, the only choice giving +x. Options A, C, D all yield -x. So the correct answer is option 1, not the stored option 3.

Question 26

When a silicon diode having a doping concentration of N_A = 9 × 10¹⁶ cm⁻³ on p-side and N_D = 1 × 10¹⁶ cm⁻³ on n-side is reverse biased, the total depletion width is found to be 3 μm. Given that the permittivity of silicon is 1.04 × 10⁻¹² F/cm, the depletion width on the p-side and the max

Accepted Answer

0.3 μm and 4.5 × 10⁵ V/cm. Charge neutrality gives x_p N_A = x_n N_D, so x_n = 9 x_p; with total 3 um, x_p = 0.3 um. E_max = q N_A x_p / eps = (1.6e-19)(9e16)(0.3e-4)/(1.04e-12) = 4.15e5 ~ 4.5e5 V/cm. Correct: 0.3 um and 4.5e5 V/cm.

Question 27

For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (D I0 - D I7) from an external device is shown in the figure. The instruction for correct data transfer is

Accepted Answer

IN F8H. The instruction 'IN F8H' is used to read data from an input port in the 8085 microprocessor, allowing it to receive the 8-bit digital data from the external device connected to the specified port address.

Question 28

An unforced linear time invariant (LTI) system is represented by [ẋ1; ẋ2] = [−1 0; 0 −2] [x1; x2]. If the initial conditions are x1(0) = 1 and x2(0) = −1, the solution of the state equation is

Accepted Answer

x1(t) = e^(−t), x2(t) = −e^(−2t). The correct option describes the solution to the state equation derived from the system's dynamics, where each state variable evolves independently according to its own exponential decay governed by the eigenvalues of the system matrix. The initial conditions lead to the specific forms of the solutions, confirming that x1(t) and x2(t) behave as indicated.

Question 29

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms s1(t) = a cos 2πf1t and s2(t) = a cos 2πf2t, where a = 4 mV. Assume an AWGN channel with two-sided noise power spectral density N0/2 = 0.5 × 10⁻¹² W/Hz. Using an optimal receiver and the relatio

Accepted Answer

Q(4). Eb = (a^2/2)*Tb with a=4mV, Tb=1/500k=2us gives Eb=1.6e-11 J; N0=1e-12, so Eb/N0=16. For coherent orthogonal binary FSK, Pe = Q(sqrt(Eb/N0)) = Q(sqrt 16) = Q(4). Stored Q(2sqrt2) is wrong.

Question 30

In MOSFET fabrication, the channel length is defined during the process of

Accepted Answer

(C) poly-silicon gate patterning. The channel length in MOSFET fabrication is determined during the poly-silicon gate patterning step, where the gate structure is defined and patterned, directly influencing the dimensions of the channel.

Question 31

A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to

Accepted Answer

the excess minority carrier concentration. The recombination rate in a semiconductor is directly influenced by the number of excess minority carriers present; as their concentration increases, the likelihood of recombination events also rises, leading to a higher recombination rate.

Question 32

The desirable characteristics of a transconductance amplifier are

Accepted Answer

high input resistance and high output resistance. A transconductance amplifier should have high input resistance to minimize loading effects on the preceding stage and high output resistance to ensure that it can effectively drive the load without significant voltage drop.

Question 33

Consider the multiplexer based logic circuit shown in the figure. Which one of the following Boolean functions is realized by the circuit?

Accepted Answer

F = W ⊕ S1 ⊕ S2. The correct option represents the exclusive OR (XOR) operation, which outputs true when an odd number of its inputs are true. In this case, the function F = W ⊕ S1 ⊕ S2 accurately captures the behavior of the multiplexer circuit by combining the inputs in a way that reflects the XOR logic.

Question 34

Let x(t) = cos(10πt) + cos(30πt) be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are

Accepted Answer

5 Hz and 15 Hz only. The original signal contains frequency components at 5 Hz (from cos(10πt)) and 15 Hz (from cos(30πt)). Sampling at 20 Hz allows these frequencies to be preserved, while the ideal low-pass filter with a cut-off at 20 Hz effectively removes any higher frequency components, confirming that only 5 Hz and 15 Hz are present in the reconstructed signal.

Question 35

For an all-pass system H(z) = (z⁻¹ - b)/(1 - az⁻¹), where |H(e^-jω)| = 1, for all ω. If Re(a) ≠ 0, Im(a) ≠ 0, then b equals

Accepted Answer

a*. In an all-pass filter, the output phase shifts without affecting the amplitude, which requires that the poles and zeros are complex conjugates. Given that the condition |H(e^-jω)| = 1 holds for all frequencies, it follows that the zero at z = b must be the complex conjugate of the pole at z = a, leading to the conclusion that b equals a*.

Question 36

Consider an FM signal f(t) = cos[2πf_c t + β1 sin 2πf1 t + β2 sin 2πf2 t]. The maximum deviation of the instantaneous frequency from the carrier frequency f_c is

Accepted Answer

β1f1 + β2f2. The maximum deviation of the instantaneous frequency in an FM signal is determined by the modulation indices and their respective frequencies. In this case, the deviation is calculated as the sum of the products of each modulation index (β1 and β2) with their corresponding frequencies (f1 and f2), leading to the correct expression β1f1 + β2f2.

Question 37

The donor and accepter impurities in an abrupt junction silicon diode are 1 × 10¹⁶ cm⁻³ and 5 × 10¹⁸ cm⁻³, respectively. Assume that the intrinsic carrier concentration in silicon is 1.5 × 10¹⁰ cm⁻³ at 300 K, kT/q = 26 mV and the permittivity of silicon εsi = 1.04 × 10⁻¹² F/cm. The built-i

Accepted Answer

0.86 V and 3.3 × 10⁻⁵ cm. The built-in potential is calculated using the concentration of donor and acceptor impurities, leading to a value of 0.86 V, which reflects the energy barrier formed at the junction. The depletion width is determined by the charge distribution and the permittivity of silicon, resulting in a narrower width of 3.3 × 10⁻⁵ cm due to the high acceptor concentration.

Question 38

In the circuit shown, the silicon BJT has β = 50. Assume V_BE = 0.7 V and V_CE(sat) = 0.2 V. Which one of the following statements is correct?

Accepted Answer

For R_C = 3 kΩ, the BJT operates in the saturation region. The correct option indicates that with a collector resistor of 3 kΩ, the BJT is able to provide sufficient base current to maintain saturation, allowing it to operate effectively in that region, where it can fully conduct and minimize voltage drop across the collector-emitter junction.

Question 39

Let X(t) be a wide sense stationary (WSS) random process with power spectral density Sx(f). If Y(t) is the process defined as Y(t) = X(2t - 1), the power spectral density Sy(f) is

Accepted Answer

Sy(f) = 1/2 Sx(f/2). The correct option is right because the transformation Y(t) = X(2t - 1) involves a time-scaling and shifting operation, which results in the power spectral density being scaled by a factor of 1/2 and the frequency being halved, leading to Sy(f) = 1/2 Sx(f/2).

Question 40

A region shown below contains a perfect conducting half-space and air. The surface current Kₛ on the surface of the perfect conductor is Kₛ = x̂ 2 amperes per meter. The tangential H field in the air just above the perfect conductor is

Accepted Answer

ẑ 2 amperes per meter. The correct option is ẑ 2 amperes per meter because, according to boundary conditions at the interface of a perfect conductor and air, the tangential magnetic field (H) must be perpendicular to the surface current (Kₛ). Since Kₛ is in the x-direction, the resulting H field must be in the z-direction to satisfy these conditions.

Question 41

A assume that a plane wave in air with an electric field E = |0 cos(ωt − 3x − √3 z) ây V/m is incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z > 0. The angle of transmission in the dielectric slab is ________ degrees.

Accepted Answer

30. For E ~ cos(wt - 3x - sqrt3 z), kx=3, kz=sqrt3, so the incidence angle from the z-normal satisfies tan(theta_i)=kx/kz=3/sqrt3=sqrt3, giving theta_i=60 deg. Snell: 1*sin60 = sqrt3*sin(theta_t) -> sin(theta_t)=1/2 -> theta_t=30 deg. Correct option is index 1, not 3.

Question 42

At T = 300 K, the band gap and the intrinsic carrier concentration of GaAs are 1.42 eV and 10⁶ cm⁻³, respectively. In order to generate electron-hole pairs in GaAs, which one of the wavelengths (λc) ranges of incident radiation, is most suitable? (Given that: Planck's constant is 6.62 × 10

Accepted Answer

1.42 μm < λc < 0.87 μm. The correct option indicates that the wavelength range must be shorter than the wavelength corresponding to the band gap energy of 1.42 eV, which is approximately 0.87 μm. This ensures that the incident photons have enough energy to generate electron-hole pairs in GaAs.

Question 43

In the figure, ln(ρi) is plotted as a function of 1/T, where ρi is the intrinsic resistivity of silicon, T is the temperature, and the plot is almost linear.

The slope of the line can be used to estimate

Accepted Answer

band gap energy of silicon (E_g). The slope of the line in the plot of ln(ρi) versus 1/T is directly related to the band gap energy of silicon (E_g) because it reflects how the intrinsic resistivity changes with temperature, which is influenced by the energy required to excite electrons across the band gap.

Question 44

If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will

Accepted Answer

reduce the voltage gain and increase the input impedance. When the emitter resistance is not bypassed, it introduces negative feedback, which lowers the voltage gain of the amplifier. However, this resistance also increases the input impedance because it provides a higher resistance path for the input signal.

Question 45

Two silicon diodes, with a forward voltage drop of 0.7 V, are used in the circuit shown in the figure. The range of input voltage V_i for which the output voltage Vₒ = V_i, is

Accepted Answer

-0.3 V < V_i < 1.3 V. The correct option is right because the two silicon diodes each have a forward voltage drop of 0.7 V, which means that for the output voltage to equal the input voltage, the input must be within the range that allows both diodes to conduct without exceeding their forward voltage drops.

Question 46

Q.14 For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then

Accepted Answer

droop rate decreases and acquisition time increases. Increasing the hold capacitor in a sample-and-hold circuit allows it to store charge more effectively, which reduces the droop rate, meaning the voltage remains stable for a longer period. However, a larger capacitor takes more time to charge to the input voltage, resulting in an increased acquisition time.

Question 47

Q.15 In the circuit shown in the figure, if C = 0, the expression for Y is

Accepted Answer

Y = A + B. The expression Y = A + B indicates that the output is true if either A or B is true, which aligns with the behavior of an OR gate. Since C = 0 implies that it does not influence the output, the circuit simplifies to just considering the inputs A and B.

Question 48

Consider the common-collector amplifier in the figure (bias circuitry ensures that the transistor operates in forward active region, but has been omitted for simplicity). Let I_C be the collector current, V_BE be the base-emitter voltage and V_T be the thermal voltage. A I_S, gₘ and rₒ are

Accepted Answer

(A) gₘ R_E << 1. The condition gₘ R_E << 1 ensures that the gain of the common-collector amplifier remains relatively constant across varying values of R_E, as it indicates that the transconductance is much smaller than the resistance, minimizing the impact of R_E on the overall voltage gain.

Question 49

The state transition matrix Φ(t) of a system [ẋ1; ẋ2] = [[0, 1], [0, 0]] [x1; x2] is

Accepted Answer

[[1, t], [0, 1]]. The state transition matrix Φ(t) describes how the state of a linear system evolves over time. For the given system, the correct matrix [[1, t], [0, 1]] reflects the solution to the system's differential equations, indicating that the first state remains constant while the second state evolves linearly with time.

Question 50

Consider a communication scheme where the binary valued signal X satisfies P{X = +1} = 0.75 and P{X = −1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance σ². The received signal Y is fed to the threshold detector. The output of the t

Accepted Answer

strictly negative. A strictly negative threshold is optimal because it accounts for the higher probability of receiving +1 signals, allowing the detector to correctly classify more received signals as +1, thus minimizing the probability of error.

GATE Technical: ELECTRONICS AND COMMUNICATION ENGINEERING - EC questions with solutions

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