GATE E&C Engineering Networks, Signals and Systems Syllabus

Networks, Signals and Systems syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Networks, Signals and Systems in GATE E&C Engineering, not a summary of it.

1. 1

   Circuit analysis

   5 topics

   • Node and mesh analysis
   • Superposition
   • Thevenin's theorem
   • Norton’s theorem
   • Reciprocity
2. 2

   Sinusoidal steady state analysis

   3 topics

   • Phasors
   • Complex power
   • Maximum power transfer
3. 3

   Time and frequency domain analysis of linear circuits

   2 topics

   • RL, RC and RLC circuits
   • Solution of network equations using Laplace transform
4. 4

   Linear 2-port network parameters

   1 topic

   • Wye-delta transformation
5. 5

   Continuous-time signals

   1 topic

   • Fourier series and Fourier transform
6. 6

   Discrete-time signals

   4 topics

   • DTFT
   • DFT
   • Z-transform
   • Discrete-time processing of continuous-time signals
7. 7

   LTI systems

   9 topics

   • Definition and properties
   • Causality
   • Stability
   • Impulse response
   • Convolution
   • Poles and zeroes
   • Frequency response
   • Group delay
   • Phase delay

Networks, Signals and Systems flashcards for GATE E&C Engineering

23 of 51 cards from the Networks, Signals and Systems deck — real questions with worked answers.

1. In nodal analysis, what physical law is applied at each node, and what is the unknown variable being solved for?

   Kirchhoff's Current Law (KCL) is applied at each node: the algebraic sum of currents leaving a node is zero. The unknowns are the node voltages measured with respect to a chosen reference (ground) node.

2. In mesh analysis, what law is written for each loop, and how many independent equations are needed for a planar circuit with $b$ branches and $n$ nodes?

   Kirchhoff's Voltage Law (KVL) is written around each mesh. The number of independent mesh equations is $b - n + 1$ (the number of independent loops).

3. What is a supernode, and when is it used in nodal analysis?

   A supernode is formed by enclosing a voltage source (and its two nodes) that connects two non-reference nodes. KCL is applied to the entire supernode, and a constraint equation relates the two node voltages via the source voltage.

4. State the Superposition Theorem for linear circuits.

   In a linear circuit with multiple independent sources, the response (voltage or current) in any branch equals the algebraic sum of the responses caused by each independent source acting alone, with all other independent sources deactivated.

5. When applying superposition, how do you deactivate independent voltage and current sources?

   Deactivate an independent voltage source by replacing it with a short circuit ($V=0$), and an independent current source by replacing it with an open circuit ($I=0$). Dependent sources remain unchanged.

6. Why can superposition not be used directly to compute power dissipated in a resistor?

   Because power is a nonlinear function of current/voltage ($P = I^{2}R$). Superposition only applies to linear quantities; the squared terms produce cross-products, so individual-source powers do not add.

7. State Thevenin's Theorem.

   Any linear two-terminal network can be replaced by an equivalent circuit consisting of a single voltage source $V_{Th}$ in series with a single resistance (impedance) $R_{Th}$, where $V_{Th}$ is the open-circuit voltage at the terminals.

8. How do you find the Thevenin resistance $R_{Th}$ when the network contains dependent sources?

   Deactivate all independent sources, apply a test source $V_{test}$ at the terminals, and compute $R_{Th} = \frac{V_{test}}{I_{test}}$. Equivalently, $R_{Th} = \frac{V_{oc}}{I_{sc}}$ using open-circuit voltage and short-circuit current.

9. State Norton's Theorem.

   Any linear two-terminal network can be replaced by an equivalent of a single current source $I_{N}$ in parallel with a resistance (impedance) $R_{N}$, where $I_{N}$ is the short-circuit current at the terminals and $R_{N} = R_{Th}$.

10. How are the Thevenin and Norton equivalents related by a source transformation?

    $V_{Th} = I_{N} R_{N}$ and $R_{Th} = R_{N}$, so $I_{N} = \dfrac{V_{Th}}{R_{Th}}$. The open-circuit voltage, short-circuit current, and equivalent resistance interconnect the two forms.

11. State the Reciprocity Theorem for a linear, passive, bilateral network.

    In a single-source linear bilateral network, the ratio of an excitation in one branch to the resulting response in another branch is unchanged if the excitation and response are interchanged. Reciprocity fails if the network contains dependent sources or non-bilateral elements.

12. What is a phasor representation of the sinusoid $v(t) = V_{m}\cos(\omega t + \phi)$?

    The phasor is $\mathbf{V} = V_{m}\angle\phi = V_{m}e^{j\phi}$, a complex number encoding amplitude and phase. The time signal is recovered via $v(t) = \operatorname{Re}\{\mathbf{V}e^{j\omega t}\}$.

13. Give the impedances of a resistor, inductor, and capacitor in phasor (frequency) domain.

    $Z_{R} = R$, $\quad Z_{L} = j\omega L$, $\quad Z_{C} = \dfrac{1}{j\omega C} = -\dfrac{j}{\omega C}$.

14. For an inductor and a capacitor, what is the phase relationship between voltage and current?

    In an inductor, voltage leads current by $90^{\circ}$. In a capacitor, current leads voltage by $90^{\circ}$ (voltage lags current by $90^{\circ}$).

15. Define complex power $S$ in terms of phasor voltage and current.

    $S = \mathbf{V}\,\mathbf{I}^{*} = P + jQ$, where $\mathbf{I}^{*}$ is the complex conjugate of the current phasor, $P$ is average (real) power in watts, and $Q$ is reactive power in VAR.

16. Write the formulas for real power $P$, reactive power $Q$, and apparent power $|S|$ using RMS values and phase angle $\theta$.

    $P = V_{rms}I_{rms}\cos\theta$, $\quad Q = V_{rms}I_{rms}\sin\theta$, $\quad |S| = V_{rms}I_{rms} = \sqrt{P^{2}+Q^{2}}$, where $\theta$ is the angle by which voltage leads current.

17. What is the power factor, and how does it differ for inductive vs capacitive loads?

    Power factor $= \cos\theta = \dfrac{P}{|S|}$. For an inductive (lagging) load the current lags voltage so PF is lagging; for a capacitive (leading) load the current leads voltage so PF is leading.

18. State the Maximum Power Transfer Theorem for a DC resistive network.

    Maximum power is delivered to a load $R_{L}$ when $R_{L} = R_{Th}$. The maximum power delivered is $P_{max} = \dfrac{V_{Th}^{2}}{4R_{Th}}$.

19. For an AC source with Thevenin impedance $Z_{Th} = R_{Th} + jX_{Th}$, what load impedance gives maximum power transfer?

    The load must be the complex conjugate: $Z_{L} = Z_{Th}^{*} = R_{Th} - jX_{Th}$. Maximum power delivered is $P_{max} = \dfrac{|V_{Th}|^{2}}{8R_{Th}}$ using amplitude phasors.

20. What is the efficiency of power transfer at the maximum-power-transfer condition $R_L = R_{Th}$?

    Efficiency is exactly $50\%$, because equal power is dissipated in $R_{Th}$ and $R_{L}$. Maximum power transfer is therefore not the same as maximum efficiency.

21. Write the time constant and natural response form of a source-free RL circuit.

    Time constant $\tau = \dfrac{L}{R}$. The current decays as $i(t) = i(0)\,e^{-t/\tau} = i(0)\,e^{-Rt/L}$.

22. Write the time constant and natural response form of a source-free RC circuit.

    Time constant $\tau = RC$. The capacitor voltage decays as $v(t) = v(0)\,e^{-t/\tau} = v(0)\,e^{-t/RC}$.

23. For a series RLC circuit, define the resonant frequency $\omega_{0}$ and the quality factor $Q$.

    $\omega_{0} = \dfrac{1}{\sqrt{LC}}$ and $Q = \dfrac{\omega_{0}L}{R} = \dfrac{1}{R}\sqrt{\dfrac{L}{C}}$.

See more Networks, Signals and Systems flashcards →

Planning Networks, Signals and Systems for GATE E&C Engineering

Networks, Signals and Systems (GATE E&C Engineering) FAQ