ESE ECE Prelims key terms

The minimum sampling frequency equal to twice the highest frequency present in a bandlimited signal; sampling below this rate causes aliasing, where high-frequency components fold onto lower frequencies and cannot be separated afterwards.

The distortion that occurs when a signal is sampled below its Nyquist rate, causing distinct frequency components to overlap and become indistinguishable; prevented by anti-aliasing filters placed before the sampler.

A low-pass filter placed ahead of a sampler to remove frequency content above half the sampling rate, ensuring the sampled signal remains bandlimited and free of fold-over distortion after reconstruction.

A system satisfying both superposition (linearity) and time-shift invariance, fully characterised by its impulse response; its output equals the convolution of input with impulse response, and sinusoids pass through unchanged in shape.

A mathematical operation combining two signals to produce a third, computed as the integral (or sum) of one signal multiplied by a reversed, shifted copy of the other; it gives the LTI system output from input and impulse response.

The output of a system when its input is a unit impulse; for LTI systems it completely determines behaviour, and its Fourier transform is the system's frequency response including magnitude and phase.

The complex function describing how a system scales and phase-shifts each sinusoidal input frequency; its magnitude gives gain and its argument gives phase shift, usually plotted against frequency on logarithmic axes.

A pair of asymptotic plots showing a system's magnitude in decibels and phase in degrees against logarithmic frequency; straight-line approximations between corner frequencies make stability margins and bandwidth easy to read.

The amount by which open-loop gain must be increased, at the frequency where phase shift reaches 180 degrees, to bring a feedback system to the verge of instability; a positive margin indicates a stable closed loop.

The difference between the actual open-loop phase and minus 180 degrees at the frequency where open-loop gain equals unity; it measures relative stability and damping of the closed-loop response.

An algebraic test that determines the number of closed-loop poles in the right half of the s-plane from the coefficients of the characteristic polynomial, using an array of rows without solving for roots.

The polynomial equation obtained by setting one plus the open-loop transfer function to zero; its roots are the closed-loop poles, and their locations in the s-plane determine system stability and transient behaviour.

The property that a system's response remains bounded for bounded inputs and its natural response decays to zero; for continuous systems all poles must lie strictly in the left half of the s-plane.

Any linear two-terminal network can be replaced at a pair of terminals by a single voltage source in series with a single resistance, where the source equals the open-circuit voltage and the resistance the terminal impedance with sources killed.

Any linear two-terminal network can be replaced by a single current source in parallel with a resistance; the current equals the short-circuit current and the resistance equals the Thevenin resistance.

In a linear network with multiple independent sources, the total response in any branch equals the algebraic sum of responses produced by each source acting alone with all others deactivated, voltage sources shorted and current sources opened.

A source delivers maximum power to a load when the load resistance equals the source's internal (Thevenin) resistance; under this condition efficiency is only fifty percent, the rest dissipated internally.

The frequency at which a series or parallel RLC circuit's inductive and capacitive reactances cancel, making the impedance purely resistive; at this point current is maximum in series resonance and minimum in parallel resonance.

A dimensionless measure of a resonant circuit's sharpness, equal to resonant frequency divided by the half-power bandwidth; high values indicate a narrow, selective resonance with slow energy decay.

The range of frequencies between the half-power (minus three decibel) points of a system's magnitude response; it indicates how fast a system can respond and how much noise it admits.

The frequency at which a filter's output power falls to half its passband value, that is, magnitude drops by three decibels; it marks the boundary between passband and stopband of the response.

The ratio of output to input quantity (voltage, current, or power) of an amplifier; voltage gain is often expressed in decibels as twenty times the logarithm of the ratio.

Returning a fraction of the output to the input in antiphase, which reduces gain but improves bandwidth, input and output impedance, linearity, and reduces distortion and noise sensitivity in amplifiers.

The maximum rate of change of an operational amplifier's output voltage, usually quoted in volts per microsecond; it limits full-power bandwidth and causes distortion for large, fast signals.

A high-gain differential voltage amplifier with very high input impedance and low output impedance; with external feedback it implements adders, integrators, filters, and comparators in analog circuits.

A heavily doped diode designed to operate in reverse breakdown, where voltage stays nearly constant over a wide current range; commonly used as a shunt voltage reference or regulator.

A two-terminal semiconductor device with a p-n junction that conducts readily in forward bias and blocks in reverse bias; it rectifies, clamps, and protects circuits.

Setting the quiescent operating point (drain or collector current and voltage) so an active device stays in its linear region over the full signal swing, preventing clipping and thermal runaway.

The algebra of binary variables using AND, OR, and NOT operations, with identities such as De Morgan's laws; it allows logic expressions to be simplified before implementation in gates.

A graphical grid that arranges truth-table minterms so adjacent cells differ by one variable, enabling manual minimisation of Boolean expressions into simplified sum-of-products form.

A bistable sequential logic element storing one bit, whose output changes on clock edges; types include SR, D, JK, and T, and they form registers, counters, and memory.

The intervals before and after a clock edge during which a flip-flop's data input must remain stable for reliable capture; violations cause metastability, where output settles unpredictably.

A modulation scheme in which the amplitude of a high-frequency carrier varies linearly with the message signal; it produces upper and lower sidebands around the carrier and needs envelope detection.

For amplitude modulation, the ratio of message amplitude to carrier amplitude, ranging from zero to one for undistorted envelope detection; higher values give greater sideband power but risk overmodulation.

A modulation scheme in which the instantaneous carrier frequency deviates in proportion to the message amplitude; it offers better noise immunity than amplitude modulation at the cost of wider bandwidth.

The maximum error-free data rate of a channel with bandwidth B and signal-to-noise ratio S/N, given by C equals B log base two of (1 plus S/N); it bounds all practical coding schemes.

The ratio of signal power to accompanying noise power at a point in a system, usually expressed in decibels; it sets the fidelity limit for detection and demodulation.

The ratio of voltage to current for a wave travelling in one direction along a transmission line, determined by line inductance and capacitance; matching it at the load prevents reflections.

The ratio of maximum to minimum voltage magnitude along a mismatched transmission line, ranging from one for a matched load upward; it quantifies reflected power and mismatch loss.

The ratio of radiated power density in the strongest direction to that of an isotropic radiator fed the same power, usually in dBi; it reflects directivity modified by radiation efficiency.

An integral transform mapping a time-domain signal to a complex frequency-domain spectrum, revealing the amplitude and phase of each frequency component; it underlies filter and modulation analysis.