A 10-bit analog-to-digital converter (ADC) has a sampling frequency of 1 MHz and a full scale voltage of 3.3 V.
For an input sinusoidal signal with frequency 500 kHz, the maximum SNR (in dB, rounded off to two decimal places) and the data rate (in Mbps) at the output of the ADC are _________, respectively.
Show Hint
- 61.96 and 10
- 61.96 and 5
- 33.36 and 10
- 33.36 and 5
The Correct Option is A
Solution and Explanation
Top Questions on Random Processes
- Consider a real-valued random process \[ f(t) = \sum_{n=1}^{N} a_n p(t - nT), \] where \( T > 0 \) and \( N \) is a positive integer. Here, \( p(t) = 1 \) for \( t \in [0, 0.5T] \) and 0 otherwise. The coefficients \( a_n \) are pairwise independent, zero-mean unit-variance random variables. Read the following statements about the random process and choose the correct option.
- (i) The mean of the process \( f(t) \) is independent of time \( t \).
- (ii) The autocorrelation function \( E[f(t)f(t + \tau)] \) is independent of time \( t \) for all \( \tau \).
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The identical MOSFETs \( M_1 \) and \( M_2 \) in the circuit given below are ideal and biased in the saturation region. \( M_1 \) and \( M_2 \) have a transconductance \( g_m \) of 5 mS. The input signals (in Volts) are: \[ V_1 = 2.5 + 0.01 \sin \omega t, \quad V_2 = 2.5 - 0.01 \sin \omega t. \] The output signal \( V_3 \) (in Volts) is _________.
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A positive-edge-triggered sequential circuit is shown below. There are no timing violations in the circuit. Input \( P_0 \) is set to logic ‘0’ and \( P_1 \) is set to logic ‘1’ at all times. The timing diagram of the inputs \( SEL \) and \( S \) are also shown below. The sequence of output \( Y \) from time \( T_0 \) to \( T_3 \) is _________.
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- A square metal sheet of 4 m \( \times \) 4 m is placed on the x-y plane as shown in the figure below. If the surface charge density (in \( \mu \)C/m\(^2\)) on the sheet is \( \rho_s(x, y) = 4|y| \), then the total charge (in \( \mu \)C, rounded off to the nearest integer) on the sheet is _________.
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In the circuit below, \( M_1 \) is an ideal AC voltmeter and \( M_2 \) is an ideal AC ammeter. The source voltage (in Volts) is \( v_s(t) = 100 \cos(200t) \). What should be the value of the variable capacitor \( C \) such that the RMS readings on \( M_1 \) and \( M_2 \) are 25 V and 5 A, respectively?
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In the circuit shown, the identical transistors Q1 and Q2 are biased in the active region with \( \beta = 120 \). The Zener diode is in the breakdown region with \( V_Z = 5 \, V \) and \( I_Z = 25 \, mA \). If \( I_L = 12 \, mA \) and \( V_{EB1} = V_{EB2} = 0.7 \, V \), then the values of \( R_1 \) and \( R_2 \) (in \( k\Omega \), rounded off to one decimal place) are _________, respectively.
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- Consider a continuous-time finite-energy signal \( f(t) \) whose Fourier transform vanishes outside the frequency interval \( [-\omega_c, \omega_c] \), where \( \omega_c \) is in rad/sec.
The signal \( f(t) \) is uniformly sampled to obtain \( y(t) = f(t) p(t) \). Here, \[ p(t) = \sum_{n=-\infty}^{\infty} \delta(t - \tau - nT_s), \] with \( \delta(t) \) being the Dirac impulse, \( T_s > 0 \), and \( \tau > 0 \). The sampled signal \( y(t) \) is passed through an ideal lowpass filter \( h(t) = \omega_c T_s \frac{\sin(\omega_c t)}{\pi \omega_c t} \) with cutoff frequency \( \omega_c \) and passband gain \( T_s \).
The output of the filter is given by _________.- GATE EC - 2025
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