GATE EC key terms

An integral operation that rewrites a time-domain signal as a continuous spectrum of complex exponentials, revealing the amplitude and phase present at each frequency. It is the main tool for analyzing linear time-invariant systems in the frequency domain.

A generalization of the Fourier transform using the complex variable s that converts differential equations into algebraic ones and handles signals that grow or start at a defined instant. It is used for circuit and control analysis.

The set of complex values of s for which a Laplace transform integral converges. Its boundary and extent determine stability and causality, so two transforms with identical algebraic form can describe different signals.

The discrete-time counterpart of the Laplace transform, mapping a sequence into a function of complex variable z. It solves difference equations and characterizes digital filters through pole locations and convergence region.

An operation combining two signals by multiplying one with a reversed, shifted copy of the other and summing or integrating over all shifts. In linear systems, the output equals the input convolved with the impulse response.

The output a system produces when driven by a unit impulse with zero initial conditions. It completely characterizes a linear time-invariant system and its Fourier or Laplace transform gives the transfer function.

A system obeying superposition and time-shift invariance, so scaling and adding inputs scales and adds outputs and a delayed input yields the same delayed output. Such systems are fully described by their impulse response.

A statement that the energy of a signal computed in the time domain equals the energy computed from its Fourier transform. It links signal power or energy to spectral content and is useful for checking transform calculations.

The rule that a bandlimited signal must be sampled at more than twice its highest frequency to allow exact reconstruction. Violating it causes aliasing, where high frequencies masquerade as lower ones.

The distortion occurring when a signal is sampled too slowly, causing frequency components above half the sampling rate to appear at incorrect lower frequencies. It cannot be removed after sampling, so anti-alias filtering precedes conversion.

The ratio of a system's Laplace or Z transform output to its input under zero initial conditions. Its poles and zeros reveal stability, frequency response and transient behavior without solving the full differential equation.

A pair of graphs plotting a system's magnitude in decibels and phase in degrees against logarithmic frequency. Straight-line asymptotes make it a fast hand method for assessing gain margin and phase margin.

The amount by which open-loop gain can be increased before a closed-loop feedback system becomes unstable, read as the negative decibel value at the phase crossover frequency. A positive value indicates a stable design.

The additional phase lag, measured at the gain crossover frequency, that would drive a feedback system to the stability boundary. It quantifies damping and overshoot in the closed-loop response.

An algebraic test that counts right-half-plane roots of a polynomial from its coefficients using an array, without factoring it. It determines closed-loop stability from the characteristic equation directly.

A property whereby every bounded input produces a bounded output. For linear time-invariant systems it holds exactly when the impulse response is absolutely integrable or summable.

A two-terminal semiconductor device conducting appreciably in one direction only. Its exponential current-voltage relation underlies rectification, clipping, clamping and small-signal resistance calculations in analog circuits.

A heavily doped diode designed to operate in reverse breakdown, holding an almost constant voltage across a range of currents. It serves as a shunt voltage reference and regulator in biased circuits.

The bipolar junction transistor, a three-terminal current-controlled device whose collector current is roughly the base current multiplied by beta in forward-active mode. It is central to amplifier and biasing analysis.

The metal-oxide-semiconductor field-effect transistor, a voltage-controlled device whose drain current depends on gate-source overdrive above threshold. It dominates digital and analog integrated circuit design.

A linearized equivalent circuit replacing a nonlinear device by resistors and controlled sources valid for tiny variations about a bias point. Transconductance, input resistance and output resistance parameterize it for gain calculations.

The slight dependence of a bipolar transistor's collector current on collector-emitter voltage, seen as sloping output characteristics. It is modeled by a finite output resistance in parallel with the controlled current source.

The increase of MOSFET drain current with drain-source voltage caused by effective channel shortening near saturation. It appears as a finite output resistance that limits intrinsic gain.

A high-gain differential voltage amplifier used with feedback to realize precise gain, filtering and arithmetic functions. Ideal analysis assumes infinite gain and input impedance with zero output impedance.

The condition in a negative-feedback op-amp circuit where the inverting input sits at nearly the same potential as the non-inverting input without being physically grounded. It simplifies node equations for gain derivations.

The maximum rate at which an amplifier's output voltage can change, usually quoted in volts per microsecond. It limits large-signal high-frequency performance and causes distortion when exceeded.

The nearly constant product of closed-loop gain and bandwidth for an op-amp with dominant-pole compensation. It lets designers trade amplification for speed when selecting an operating point.

Returning a fraction of a system's output to its input to modify behavior. Negative feedback stabilizes gain, widens bandwidth and reduces distortion at the cost of potential instability.

The algebra of binary variables using AND, OR and NOT, with identities such as De Morgan's laws and absorption. It is the mathematical basis for simplifying logic expressions before implementation.

A grid arrangement of truth-table cells where adjacent entries differ in one variable, allowing visual grouping into minimal product terms. It yields simplified two-level logic expressions by hand.

A unique standardized representation of a logic function, either as a sum of minterms or a product of maxterms. It provides an unambiguous starting point for simplification and comparison.

An input combination whose output is unspecified because it never occurs or its value is irrelevant. Treating such cells as either zero or one during mapping can produce a simpler circuit.

A bistable storage element retaining one bit until clocked or triggered. Types such as SR, JK, D and T differ in excitation behavior and are the building blocks of registers and counters.

The minimum interval a synchronous input must remain stable before the active clock edge for reliable capture. Violating it risks metastability in the storage element.

The minimum interval a synchronous input must stay stable after the active clock edge. It constrains how early the next logic level may change and is checked in static timing analysis.

An unstable condition in which a bistable element lingers between logic levels after a timing violation. It resolves unpredictably and is mitigated by synchronizers and adequate timing margins.

A sequential model with a finite set of states, transitions triggered by inputs and outputs determined by state or transition. It is implemented as combinational logic plus state registers.