GATE Electronics and Communication Engineering (EC) Syllabus

Electronics and Communication Engineering (EC) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electronics and Communication Engineering (EC) in GATE, not a summary of it.

1. 1

   Networks, Signals and Systems

   4 topics

   • Network Analysis
     • Network theorems and transient analysis
     • Two-port networks
   • Continuous and Discrete Time Signals
     • LTI systems and convolution
   • Transforms
     • Laplace and Fourier transforms
     • Z-transform and DFT
   • Sampling Theorem
2. 2

   Electronic Devices and Analog Circuits

   4 topics

   • Semiconductor Devices
     • PN junction, BJT and MOSFET
     • Diodes and special devices
   • Amplifiers
     • Biasing and small-signal models
     • Frequency response and feedback
   • Operational Amplifiers
     • Ideal op-amp circuits
     • Oscillators and active filters
   • Power Supplies and Regulators
3. 3

   Digital Circuits

   4 topics

   • Combinational Logic
     • Boolean algebra and minimization
     • Multiplexers, decoders and adders
   • Sequential Logic
     • Flip-flops, counters and registers
   • Logic Families and Memories
     • TTL and CMOS
     • ROM, RAM and PLDs
   • Data Converters
     • ADC and DAC
4. 4

   Communications

   4 topics

   • Analog Modulation
     • Amplitude modulation
     • Angle modulation
   • Digital Communication
     • PCM and line coding
     • Digital modulation schemes
   • Random Processes and Noise
     • Autocorrelation and power spectral density
   • Information Theory Basics
     • Entropy and channel capacity
5. 5

   Electromagnetics

   4 topics

   • Electromagnetic Waves
     • Maxwell's equations
     • Wave propagation in media
   • Transmission Lines
     • Smith chart and impedance matching
   • Waveguides
     • Modes in rectangular waveguides
   • Antennas and Radiation Basics

Electronics and Communication Engineering (EC) flashcards for GATE

24 of 52 cards from the Electronics and Communication Engineering (EC) deck — real questions with worked answers.

1. State Ohm's law in phasor form for an impedance $Z$, and give the impedance of an ideal resistor, inductor, and capacitor.

   $\vec{V} = Z\,\vec{I}$. Resistor: $Z_R = R$; Inductor: $Z_L = j\omega L$; Capacitor: $Z_C = \dfrac{1}{j\omega C}$.

2. State Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL).

   KCL: the algebraic sum of currents entering any node is zero, $\sum i = 0$. KVL: the algebraic sum of voltages around any closed loop is zero, $\sum v = 0$.

3. State the Maximum Power Transfer theorem for an AC source with Thevenin impedance $Z_{th} = R_{th} + jX_{th}$.

   Maximum power is delivered when the load is the complex conjugate of the source impedance: $Z_L = Z_{th}^{*} = R_{th} - jX_{th}$. The maximum power is $P_{max} = \dfrac{V_{th}^{2}}{4R_{th}}$ (using RMS Thevenin voltage).

4. State Thevenin's theorem.

   Any linear two-terminal network can be replaced by a single voltage source $V_{th}$ (the open-circuit voltage) in series with an impedance $Z_{th}$ (the network impedance seen from the terminals with independent sources deactivated).

5. State the Superposition theorem and its key limitation.

   In a linear network, the response (current/voltage) due to multiple independent sources equals the sum of responses from each source acting alone (others deactivated: voltage sources shorted, current sources opened). Limitation: it applies to voltage and current but NOT to power, since power is nonlinear.

6. For a source-free series RLC circuit, write the condition for critical damping in terms of $R$, $L$, $C$.

   Critical damping occurs when the damping ratio $\zeta = 1$, i.e. $R = 2\sqrt{\dfrac{L}{C}}$. Equivalently $\alpha = \omega_0$, where $\alpha = \dfrac{R}{2L}$ and $\omega_0 = \dfrac{1}{\sqrt{LC}}$.

7. Define the time constant for a series RC and a series RL circuit, and state how many time constants are needed to reach about 99% of the final value.

   RC: $\tau = RC$. RL: $\tau = \dfrac{L}{R}$. The transient is essentially complete (about 99.3%) after $5\tau$.

8. Write the general natural-response expression for a first-order circuit and the step (forced + natural) response form.

   Natural response: $x(t) = x(0)\,e^{-t/\tau}$. Complete step response: $x(t) = x(\infty) + \left[x(0^{+}) - x(\infty)\right]e^{-t/\tau}$.

9. State the inductor and capacitor continuity (initial-condition) rules used in transient analysis.

   Inductor current cannot change instantaneously: $i_L(0^{+}) = i_L(0^{-})$. Capacitor voltage cannot change instantaneously: $v_C(0^{+}) = v_C(0^{-})$.

10. Define the Z-parameters (impedance parameters) of a two-port network.

    They relate port voltages to port currents: $V_1 = z_{11}I_1 + z_{12}I_2$ and $V_2 = z_{21}I_1 + z_{22}I_2$. Each parameter is found with one port open-circuited, e.g. $z_{11} = \dfrac{V_1}{I_1}\Big|_{I_2=0}$.

11. Define the Y-parameters (admittance parameters) of a two-port network and the condition for reciprocity.

    $I_1 = y_{11}V_1 + y_{12}V_2$, $I_2 = y_{21}V_1 + y_{22}V_2$, measured with ports short-circuited. The network is reciprocal if $y_{12} = y_{21}$ (equivalently $z_{12} = z_{21}$).

12. Write the ABCD (transmission) parameter equations and the condition for a reciprocal two-port.

    $V_1 = A V_2 - B I_2$, $I_1 = C V_2 - D I_2$. The network is reciprocal when $AD - BC = 1$.

13. For a two-port, state the symmetry condition in terms of Z-parameters and ABCD-parameters.

    A two-port is symmetrical if $z_{11} = z_{22}$ (equivalently $A = D$ in ABCD parameters).

14. Define hybrid h-parameters of a two-port network.

    $V_1 = h_{11}I_1 + h_{12}V_2$ and $I_2 = h_{21}I_1 + h_{22}V_2$. Here $h_{11}$ is input impedance (output shorted), $h_{12}$ reverse voltage gain (input open), $h_{21}$ forward current gain (output shorted), $h_{22}$ output admittance (input open).

15. Define an even signal and an odd signal, and give the even part of $x(t)$.

    Even: $x(-t) = x(t)$ (symmetric). Odd: $x(-t) = -x(t)$ (anti-symmetric). Even part: $x_e(t) = \dfrac{x(t) + x(-t)}{2}$; odd part: $x_o(t) = \dfrac{x(t) - x(-t)}{2}$.

16. State the condition for a continuous-time sinusoid $x(t) = \cos(\omega_0 t)$ to be periodic, and the condition for a discrete-time sinusoid $x[n] = \cos(\Omega_0 n)$ to be periodic.

    Continuous-time sinusoids are always periodic with $T = \dfrac{2\pi}{\omega_0}$. A discrete-time sinusoid is periodic only if $\dfrac{\Omega_0}{2\pi}$ is a rational number, i.e. $\dfrac{2\pi}{\Omega_0} = \dfrac{N}{k}$ for integers.

17. Define the energy and power of a signal, and classify energy vs power signals.

    Energy: $E = \int_{-\infty}^{\infty}|x(t)|^{2}\,dt$. Power: $P = \lim_{T\to\infty}\dfrac{1}{2T}\int_{-T}^{T}|x(t)|^{2}\,dt$. An energy signal has $0 < E < \infty$ (and $P=0$); a power signal has $0 < P < \infty$ (and $E=\infty$).

18. State the sifting (sampling) property of the continuous-time impulse function $\delta(t)$.

    $\int_{-\infty}^{\infty} x(t)\,\delta(t - t_0)\,dt = x(t_0)$. Also $x(t)\delta(t-t_0) = x(t_0)\delta(t-t_0)$.

19. List the four key properties that define an LTI system and which two define each part.

    Linearity = additivity + homogeneity (scaling), i.e. it obeys superposition. Time-invariance: a shift in input produces an identical shift in output. An LTI system is fully characterized by its impulse response $h(t)$.

20. Write the continuous-time and discrete-time convolution sum/integral for an LTI system.

    Continuous: $y(t) = x(t)*h(t) = \int_{-\infty}^{\infty} x(\tau)h(t-\tau)\,d\tau$. Discrete: $y[n] = x[n]*h[n] = \sum_{k=-\infty}^{\infty} x[k]h[n-k]$.

21. State the BIBO stability and causality conditions for an LTI system in terms of its impulse response $h(t)$.

    BIBO stable iff the impulse response is absolutely integrable: $\int_{-\infty}^{\infty}|h(t)|\,dt < \infty$ (discrete: $\sum|h[n]| < \infty$). Causal iff $h(t) = 0$ for $t < 0$.

22. List three key properties of convolution.

    Commutative: $x*h = h*x$. Associative: $(x*h_1)*h_2 = x*(h_1*h_2)$. Distributive: $x*(h_1 + h_2) = x*h_1 + x*h_2$. Also, convolution with $\delta(t)$ is identity: $x(t)*\delta(t) = x(t)$.

23. Define the bilateral Laplace transform and state its relationship to the Fourier transform.

    $X(s) = \int_{-\infty}^{\infty} x(t)\,e^{-st}\,dt$, with $s = \sigma + j\omega$. The Fourier transform is the Laplace transform evaluated on the imaginary axis, $X(j\omega) = X(s)\big|_{s=j\omega}$, valid when the ROC includes the $j\omega$-axis.

24. Give the Laplace transforms of $\delta(t)$, $u(t)$, $e^{-at}u(t)$, and $\cos(\omega_0 t)u(t)$.

    $\mathcal{L}\{\delta(t)\} = 1$; $\mathcal{L}\{u(t)\} = \dfrac{1}{s}$; $\mathcal{L}\{e^{-at}u(t)\} = \dfrac{1}{s+a}$; $\mathcal{L}\{\cos(\omega_0 t)u(t)\} = \dfrac{s}{s^{2}+\omega_0^{2}}$.

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