Give the Fourier transform pair for a rectangular pulse of width $T$ and the corresponding duality result.

A rectangular pulse $\text{rect}(t/T)$ transforms to a sinc: $T\,\text{sinc}\!\left(\dfrac{\omega T}{2}\right)$. By duality, a sinc in time gives a rectangle (ideal low-pass) in frequency.

Define the bilateral Z-transform and the unit-circle relationship to the DTFT.

$X(z) = \sum_{n=-\infty}^{\infty} x[n]z^{-n}$. The DTFT is the Z-transform on the unit circle: $X(e^{j\Omega}) = X(z)\big|_{z=e^{j\Omega}}$, valid when the ROC includes $|z| = 1$.

Give the Z-transforms of $\delta[n]$, $u[n]$, and $a^{n}u[n]$, including ROC.

$\mathcal{Z}\{\delta[n]\} = 1$ (all $z$); $\mathcal{Z}\{u[n]\} = \dfrac{1}{1-z^{-1}}$, $|z|>1$; $\mathcal{Z}\{a^{n}u[n]\} = \dfrac{1}{1-az^{-1}}$, $|z|>|a|$.

State the ROC-based stability and causality conditions for a discrete-time LTI system in the Z-domain.

Causal: ROC is the exterior of the outermost pole and includes $z=\infty$. Stable: ROC includes the unit circle $|z|=1$. A causal and stable system has all poles strictly inside the unit circle.

Define the N-point Discrete Fourier Transform (DFT) and its inverse.

$X[k] = \sum_{n=0}^{N-1} x[n]e^{-j2\pi kn/N}$, $k=0,\dots,N-1$. Inverse: $x[n] = \dfrac{1}{N}\sum_{k=0}^{N-1} X[k]e^{j2\pi kn/N}$.

How many complex multiplications does a direct $N$-point DFT need versus the radix-2 FFT?

Direct DFT: $N^{2}$ complex multiplications. Radix-2 FFT: about $\dfrac{N}{2}\log_2 N$ complex multiplications — a major reduction for large $N$.

State the Nyquist sampling theorem.

A band-limited signal with maximum frequency $f_m$ can be perfectly reconstructed from its samples if the sampling rate satisfies $f_s > 2f_m$. The minimum rate $f_{s,min} = 2f_m$ is the Nyquist rate, and $2f_m$ is the Nyquist frequency.

Define aliasing and how it is avoided.

Aliasing is the overlap/folding of spectral replicas when $f_s < 2f_m$, causing high frequencies to masquerade as lower ones. It is prevented by band-limiting the signal with an anti-aliasing (low-pass) filter before sampling and/or increasing $f_s$.

Write the intrinsic carrier concentration relation and the mass-action law for a semiconductor.

Mass-action law: $np = n_i^{2}$ in thermal equilibrium. Intrinsic concentration $n_i = \sqrt{N_C N_V}\,e^{-E_g/2kT}$, so $n_i$ increases strongly with temperature and decreases with band gap $E_g$.

Write the built-in potential of a PN junction and the diode (Shockley) equation.

Built-in potential: $V_{bi} = \dfrac{kT}{q}\ln\!\left(\dfrac{N_A N_D}{n_i^{2}}\right)$. Diode current: $I = I_S\left(e^{V/\eta V_T} - 1\right)$, where thermal voltage $V_T = \dfrac{kT}{q} \approx 26\text{ mV}$ at 300 K.

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GATE Electronics and Communication Engineering (EC) Flashcards

52 question-and-answer cards covering Electronics and Communication Engineering (EC) as it is examined in GATE. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.

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24 sample cards from the Electronics and Communication Engineering (EC) deck

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Give the Fourier transform pair for a rectangular pulse of width $T$ and the corresponding duality result.
A rectangular pulse $\text{rect}(t/T)$ transforms to a sinc: $T\,\text{sinc}\!\left(\dfrac{\omega T}{2}\right)$. By duality, a sinc in time gives a rectangle (ideal low-pass) in frequency.
Define the bilateral Z-transform and the unit-circle relationship to the DTFT.
$X(z) = \sum_{n=-\infty}^{\infty} x[n]z^{-n}$. The DTFT is the Z-transform on the unit circle: $X(e^{j\Omega}) = X(z)\big|_{z=e^{j\Omega}}$, valid when the ROC includes $|z| = 1$.
Give the Z-transforms of $\delta[n]$, $u[n]$, and $a^{n}u[n]$, including ROC.
$\mathcal{Z}\{\delta[n]\} = 1$ (all $z$); $\mathcal{Z}\{u[n]\} = \dfrac{1}{1-z^{-1}}$, $|z|>1$; $\mathcal{Z}\{a^{n}u[n]\} = \dfrac{1}{1-az^{-1}}$, $|z|>|a|$.
State the ROC-based stability and causality conditions for a discrete-time LTI system in the Z-domain.
Causal: ROC is the exterior of the outermost pole and includes $z=\infty$. Stable: ROC includes the unit circle $|z|=1$. A causal and stable system has all poles strictly inside the unit circle.
Define the N-point Discrete Fourier Transform (DFT) and its inverse.
$X[k] = \sum_{n=0}^{N-1} x[n]e^{-j2\pi kn/N}$, $k=0,\dots,N-1$. Inverse: $x[n] = \dfrac{1}{N}\sum_{k=0}^{N-1} X[k]e^{j2\pi kn/N}$.
How many complex multiplications does a direct $N$-point DFT need versus the radix-2 FFT?
Direct DFT: $N^{2}$ complex multiplications. Radix-2 FFT: about $\dfrac{N}{2}\log_2 N$ complex multiplications — a major reduction for large $N$.
State the Nyquist sampling theorem.
A band-limited signal with maximum frequency $f_m$ can be perfectly reconstructed from its samples if the sampling rate satisfies $f_s > 2f_m$. The minimum rate $f_{s,min} = 2f_m$ is the Nyquist rate, and $2f_m$ is the Nyquist frequency.
Define aliasing and how it is avoided.
Aliasing is the overlap/folding of spectral replicas when $f_s < 2f_m$, causing high frequencies to masquerade as lower ones. It is prevented by band-limiting the signal with an anti-aliasing (low-pass) filter before sampling and/or increasing $f_s$.
Write the intrinsic carrier concentration relation and the mass-action law for a semiconductor.
Mass-action law: $np = n_i^{2}$ in thermal equilibrium. Intrinsic concentration $n_i = \sqrt{N_C N_V}\,e^{-E_g/2kT}$, so $n_i$ increases strongly with temperature and decreases with band gap $E_g$.
Write the built-in potential of a PN junction and the diode (Shockley) equation.
Built-in potential: $V_{bi} = \dfrac{kT}{q}\ln\!\left(\dfrac{N_A N_D}{n_i^{2}}\right)$. Diode current: $I = I_S\left(e^{V/\eta V_T} - 1\right)$, where thermal voltage $V_T = \dfrac{kT}{q} \approx 26\text{ mV}$ at 300 K.
Distinguish avalanche breakdown from Zener breakdown in a reverse-biased PN junction.
Avalanche: occurs in lightly doped (wide depletion) junctions at higher voltages via impact ionization; breakdown voltage increases with temperature (positive temperature coefficient). Zener: occurs in heavily doped (narrow depletion) junctions at low voltages via quantum tunneling; breakdown voltage decreases with temperature (negative coefficient).
Name the four regions of BJT operation and the junction bias conditions for each.
Active: emitter-base forward, collector-base reverse (amplification). Saturation: both junctions forward. Cutoff: both junctions reverse. Reverse-active: emitter-base reverse, collector-base forward.
Relate the BJT current gains $\alpha$ and $\beta$.
$\beta = \dfrac{\alpha}{1-\alpha}$ and $\alpha = \dfrac{\beta}{1+\beta}$. Also $I_C = \beta I_B$ and $I_E = I_C + I_B = (\beta+1)I_B$. Here $\alpha$ is common-base gain (<1) and $\beta$ is common-emitter gain.
Write the drain-current equations for an n-channel MOSFET in the triode and saturation regions.
Triode ($V_{DS} < V_{GS}-V_{th}$): $I_D = \mu_n C_{ox}\dfrac{W}{L}\left[(V_{GS}-V_{th})V_{DS} - \dfrac{V_{DS}^{2}}{2}\right]$. Saturation ($V_{DS} \geq V_{GS}-V_{th}$): $I_D = \dfrac{1}{2}\mu_n C_{ox}\dfrac{W}{L}(V_{GS}-V_{th})^{2}(1+\lambda V_{DS})$.
Give the small-signal transconductance $g_m$ of a BJT and of a MOSFET in saturation.
BJT: $g_m = \dfrac{I_C}{V_T}$. MOSFET: $g_m = \mu_n C_{ox}\dfrac{W}{L}(V_{GS}-V_{th}) = \sqrt{2\mu_n C_{ox}\dfrac{W}{L}I_D} = \dfrac{2I_D}{V_{GS}-V_{th}}$.
Why is the voltage-divider (self-bias) configuration preferred for BJT biasing?
It gives the most stable Q-point against variations in $\beta$ and temperature because the base voltage is set by the divider and the emitter resistor $R_E$ provides negative feedback (stabilization factor is low). The collector current is nearly independent of $\beta$.
State the four feedback topologies and the effect of negative feedback on gain and bandwidth.
Topologies: voltage-series (series-shunt), voltage-shunt (shunt-shunt), current-series (series-series), current-shunt (shunt-series). Negative feedback reduces gain by factor $(1+A\beta)$ but increases bandwidth by the same factor, so the gain-bandwidth product is roughly constant; it also reduces distortion and stabilizes gain.
What causes the low-frequency and high-frequency roll-off in an amplifier's frequency response?
Low-frequency roll-off: coupling and bypass capacitors (their reactance rises as $f$ falls). High-frequency roll-off: internal device junction/parasitic capacitances and the Miller effect. Mid-band gain is flat between these.
State the Miller effect for a capacitance $C$ bridging input and output of an inverting amplifier with gain $-A_v$.
The effective input capacitance is multiplied: $C_{in} = C(1 + A_v)$, and the effective output capacitance is $C\!\left(1 + \dfrac{1}{A_v}\right) \approx C$. This Miller multiplication dominates the high-frequency response of CE/CS stages.
List the ideal op-amp assumptions and the closed-loop gains of inverting and non-inverting configurations.
Ideal op-amp: infinite open-loop gain, infinite input impedance ($I_{in}=0$), zero output impedance, infinite bandwidth, and a virtual short ($V_+ = V_-$). Inverting gain: $A_v = -\dfrac{R_f}{R_1}$. Non-inverting gain: $A_v = 1 + \dfrac{R_f}{R_1}$.
Give the output expressions for an op-amp integrator and differentiator.
Integrator (R at input, C feedback): $V_{out} = -\dfrac{1}{RC}\int V_{in}\,dt$. Differentiator (C at input, R feedback): $V_{out} = -RC\dfrac{dV_{in}}{dt}$.
State the Barkhausen criterion for sustained oscillations.
For sustained sinusoidal oscillation the loop gain magnitude must be unity, $|A\beta| = 1$, and the total loop phase shift must be $0^{\circ}$ (or a multiple of $360^{\circ}$). For start-up, $|A\beta| > 1$ initially.
Compare the frequency-determining elements of Wien-bridge, RC phase-shift, Hartley, and Colpitts oscillators.
Wien-bridge: RC network, $f = \dfrac{1}{2\pi RC}$. RC phase-shift: three RC sections giving $180^{\circ}$. Hartley: LC tank with tapped inductors ($L_1, L_2$). Colpitts: LC tank with tapped capacitors ($C_1, C_2$), $f = \dfrac{1}{2\pi\sqrt{L\,C_{eq}}}$ with $C_{eq} = \dfrac{C_1 C_2}{C_1+C_2}$.
Define the quality factor $Q$ of a second-order active filter and give the cutoff/center frequency for a basic Sallen-Key filter.
$Q$ measures selectivity: $Q = \dfrac{f_0}{BW}$, where $BW$ is the $-3\text{ dB}$ bandwidth. For a Sallen-Key (or similar RC active filter) the characteristic frequency is $f_0 = \dfrac{1}{2\pi\sqrt{R_1 R_2 C_1 C_2}}$.

What this deck covers

The Electronics and Communication Engineering (EC) deck follows the GATE Electronics and Communication Engineering (EC) syllabus — 5 chapters and 20 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.4 cards per chapter.

Answers are written to be recallable, not just readable — averaging about 219 characters, which is long enough to carry the reasoning and short enough to say out loud.

A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.

Electronics and Communication Engineering (EC) flashcards FAQ

How many Electronics and Communication Engineering (EC) flashcards are in this GATE deck?

52 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.

Are these GATE flashcards free?

Yes. The preview here is free to read with no signup, and the full 52-card deck is free inside the Examius app.

What do the Electronics and Communication Engineering (EC) cards cover?

They follow the GATE Electronics and Communication Engineering (EC) syllabus — 5 chapters and 20 topics — so the questions track what is actually examinable.

How should I use these flashcards?

Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.