GATE EE key terms

A pair of first-order partial differential equations that a complex function must satisfy for its derivative to exist; they link the real and imaginary parts of an analytic function.

A result stating that the contour integral of a function around a closed curve equals 2πi times the sum of the residues of its poles enclosed by the curve.

An integral transform that converts a time-domain function into a complex-frequency function, widely used to solve linear differential equations and analyse circuits and control systems.

A scalar λ for which a nonzero vector v satisfies Av = λv for a square matrix A; it indicates a direction in which the matrix acts as a simple scaling.

The maximum number of linearly independent rows or columns of a matrix, equal to the dimension of its column space and used to judge consistency of linear systems.

Kirchhoff's current law states that currents entering a node sum to zero; Kirchhoff's voltage law states that voltages around any closed loop sum to zero. Both underpin all circuit analysis.

A two-terminal linear network can be replaced by a single voltage source in series with a resistance; the source is the open-circuit voltage and the resistance is the network's equivalent resistance.

A dual of the Thevenin form in which a linear two-terminal network is represented by a current source in parallel with a resistance, with the source equal to the short-circuit current.

In a linear circuit with multiple independent sources, the response in any branch equals the algebraic sum of responses produced by each source acting alone with the others deactivated.

The frequency at which a circuit's inductive and capacitive reactances cancel, making the impedance purely resistive; for a series RLC circuit it equals 1/(2π√(LC)).

A dimensionless measure of a resonant circuit's sharpness, defined as the ratio of stored energy to energy lost per radian, or as resonant frequency divided by bandwidth.

Four coupled equations describing how electric and magnetic fields arise from charges and currents and how they interrelate; they are the foundation of classical electromagnetics.

The cross product of electric and magnetic field intensities, giving the instantaneous power flux density of an electromagnetic wave; its time average indicates average power flow.

The distance into a conductor at which a propagating electromagnetic field decays to 1/e of its surface value; it decreases as frequency, permeability, or conductivity increase.

An integral transform that decomposes a signal into its frequency components, mapping a time-domain function to a continuous spectrum of complex amplitudes.

A bandlimited signal can be reconstructed exactly if sampled at a rate greater than twice its highest frequency; otherwise aliasing occurs and information is lost.

The discrete-time counterpart of the Laplace transform, converting a sequence into a function of a complex variable z; used to analyse difference equations and discrete systems.

The ratio of the Laplace transform of a system's output to that of its input under zero initial conditions; it characterises the system's input-output behaviour.

A pair of logarithmic plots showing a system's magnitude and phase response versus frequency, used to assess stability margins and bandwidth of linear time-invariant systems.

An algebraic test applied to the coefficients of a characteristic polynomial to determine the number of closed-loop poles in the right half-plane without solving for the roots.

Stability margins read from frequency response: gain margin is the dB gain change at the phase crossover needed for instability, and phase margin is the phase change at the gain crossover.

The fractional difference between synchronous speed and actual rotor speed of an induction machine, expressed as a per-unit or percentage value; it determines rotor frequency and torque.

The rotational speed of the rotating magnetic field in an AC machine, equal to 120 times frequency divided by the number of poles, in revolutions per minute.

A model representing a transformer as ideal windings with series leakage reactances and resistances plus a shunt magnetising branch, often referred to one side for analysis.

A method of expressing voltages, currents, impedances, and powers as fractions of chosen base values, simplifying analysis of interconnected machines and power networks.

A technique decomposing an unbalanced three-phase set into positive, negative, and zero sequence components, enabling analysis of faults and unbalanced operation in power systems.

The maximum short-circuit current or apparent power a power system location can deliver under fault conditions, used to select switchgear and protective device ratings.

A graphical method for assessing transient stability of a synchronous generator by comparing accelerating and decelerating areas on a power-angle curve.

A two-stage configuration in which a common-source stage drives a common-gate stage, giving high output resistance, reduced Miller effect, and wide bandwidth.

The multiplication of feedback capacitance between input and output nodes by the amplifier gain, which lowers input impedance and reduces high-frequency bandwidth.

A linearised representation of a nonlinear device around a DC operating point, using parameters such as transconductance and output resistance to analyse incremental behaviour.

Timing constraints for a flip-flop: data must be stable for a minimum interval before the clock edge (setup) and after it (hold) for reliable capture.

A graphical arrangement of truth-table cells in Gray-code order used to simplify Boolean expressions by visually grouping adjacent minterms into minimal product terms.

The fraction of a switching period during which a power semiconductor device conducts or the output is high; it controls average output voltage in switching converters.

A technique varying the on-time of switching devices at fixed frequency to control average voltage or current, widely used in inverters and DC-DC converters.

The process of transferring current from one conducting device or phase to another in power converters or machines, often requiring stored energy to be managed.

An instrument that reconstructs fast repetitive waveforms by capturing samples at different delays over many cycles, extending bandwidth beyond real-time acquisition limits.

The error introduced when an instrument's finite input impedance draws current from or alters the circuit under test, changing the very quantity being measured.

The ratio of absolute measurement error to the true or indicated value, often expressed as a percentage; it quantifies measurement accuracy independent of magnitude.