1
GATE ECE 2024
+2
-1.33

In the circuit shown below, the transistors $M_1$ and $M_2$ are biased in saturation. Their small signal transconductances are $g_{m1}$ and $g_{m2}$ respectively. Neglect body effect, channel length modulation and intrinsic device capacitances.

Assuming that capacitor $C_i$ is a short circuit for AC analysis, the exact magnitude of small signal voltage gain $\left| \frac{v_{out}}{v_{in}} \right|$ is ______.

A

$g_{m2}R_D$

B

$\frac{g_{m2} R_D \left( R_B + \frac{1}{g_{m1}} \right)}{R_B + \frac{1}{g_{m1}} + R_S}$

C

$\frac{g_{m2} R_D \left( R_B + \frac{1}{g_{m1}} + R_S \right)}{R_B + \frac{1}{g_{m1}}}$

D

$\frac{g_{m2} R_D \left( \frac{1}{g_{m1}} \right)}{\frac{1}{g_{m1}} + R_S}$

2
GATE ECE 2024
MCQ (More than One Correct Answer)
+2
-1.33

Which of the following statements is/are true for a BJT with respect to its DC current gain $\beta$?

A

Under high-level injection condition in forward active mode, $\beta$ will decrease with increase in the magnitude of collector current.

B

Under low-level injection condition in forward active mode, where the current at the emitter-base junction is dominated by recombination-generation process, $\beta$ will decrease with increase in the magnitude of collector current.

C

$\beta$ will be lower when the BJT is in saturation region compared to when it is in active region.

D

A higher value of $\beta$ will lead to a lower value of the collector-to-emitter breakdown voltage.

3
GATE ECE 2024
Numerical
+2
-1.33

An NMOS transistor operating in the linear region has $I_{D}$ of 5 $\mu$A at $V_{DS}$ of 0.1 V. Keeping $V_{GS}$ constant, the $V_{DS}$ is increased to 1.5 V.

Given that $\mu_{n}C_{ox} \frac{W}{L}$ = 50 $\mu$A/$V^2$, the transconductance at the new operating point (in $\mu$A/V, rounded off to two decimal places) is ______.

4
GATE ECE 2024
+1
-0.33

A digital communication system transmits through a noiseless bandlimited channel $[-W, W]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t) = \sum\limits_{n} b[n]x(t-nT)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol. The received signal is sampled at $t = mT$. The Fourier transform of $x(t)$ is $X(f)$. The Nyquist condition that $X(f)$ must satisfy for zero intersymbol interference at the receiver is ______.

A

$$\sum\limits_{m=-\infty}^{\infty} X \left( f + \frac{m}{T}\right) = T$$

B

$$\sum\limits_{m=-\infty}^{\infty} X \left( f + \frac{m}{T}\right) = \frac{1}{T}$$

C

$$\sum\limits_{m=-\infty}^{\infty} X (f + mT) = T$$

D

$$\sum\limits_{m=-\infty}^{\infty} X (f + mT) = \frac{1}{T}$$

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