ECE Board Exam key terms

A number written in the form a + jb, where a is the real part, b is the imaginary part, and j is the square root of minus one. It can be plotted as a point or vector on the complex plane.

An integral transform that converts a time-domain function into a function of the complex variable s. It turns linear differential equations into algebra, simplifying circuit transient and control system analysis.

A representation of a periodic signal as a sum of sine and cosine waves at integer multiples of the fundamental frequency, each with its own amplitude and phase. It reveals a signal's harmonic content.

A single number computed from the entries of a square matrix. If it equals zero the matrix has no inverse and the related linear equations are dependent; it also appears in Cramer's rule solutions.

A scalar for which a square matrix times some nonzero vector equals that scalar times the same vector. It shows how the matrix scales a particular direction, useful in stability and vibration studies.

The derivative of a function of several variables taken with respect to one variable while the others are held constant. It is used to find slopes, gradients, and maxima or minima of multivariable functions.

An expansion of a smooth function as an infinite sum of terms built from its derivatives evaluated at one point. Truncating the series gives polynomial approximations used in calculators and numerical methods.

A function whose value at each point indicates the relative likelihood of a continuous random variable, with total area under its curve equal to one. Areas under the curve give probabilities of intervals.

An equation containing derivatives of an unknown function. Its order is the highest derivative present, and solving it yields the function describing circuit transients, motion, or heat flow.

The boundary formed where p-type and n-type semiconductor materials meet. It creates a depletion region and a built-in potential, giving a diode its one-way conduction and rectifying behavior.

A three-terminal semiconductor device containing two pn junctions, in which a small base current controls a much larger collector current. Its terminals are the emitter, base, and collector.

A field-effect transistor whose insulated gate controls current in a semiconductor channel through an electric field rather than gate current. It is widely used in digital logic and power switching circuits.

A high-gain differential voltage amplifier with very high input impedance and low output impedance. With external resistors and capacitors it performs amplification, summing, integration, and filtering functions.

Any linear two-terminal network can be replaced by one voltage source in series with one resistor. The source equals the open-circuit voltage, and the resistor is the resistance seen with sources killed.

Returning a fraction of an amplifier's output signal to its input with opposite polarity. It lowers gain but improves stability, bandwidth, linearity, and the input and output impedances of the circuit.

Setting the steady direct-current voltages and currents of a transistor so it rests at a chosen point on its characteristic curves, keeping the signal swing within the linear region.

The frequency at which a circuit's power gain falls to half its midband value, a drop of three decibels. It marks the edge of the passband of a filter or amplifier.

The ratio of a differential amplifier's gain for a difference signal to its gain for a signal common to both inputs, usually stated in decibels. Higher values mean better rejection of interference.

The current through a linear resistor equals the voltage across it divided by its resistance. It is the basic relationship linking voltage, current, and resistance in direct-current circuit analysis.

The internal force per unit area within a material, equal to the applied load divided by the cross-sectional area. Normal stress may be tensile or compressive and is always paired with strain.

The fractional deformation of a material, such as change in length divided by original length. It is dimensionless and, within the elastic limit, is directly proportional to the applied stress.

Within the elastic limit, the deformation of a material or spring is directly proportional to the applied force. The constant of proportionality is the stiffness or spring constant of the object.

Energy cannot be created or destroyed, only converted from one form to another. The total energy of an isolated system stays constant, a principle underlying the first law of thermodynamics.

The digits in a measured value that carry meaningful information about its precision. Rules for them govern how the results of calculations should be rounded and reported.

The internationally agreed metric system of measurement built on seven base units, including the meter, kilogram, second, ampere, kelvin, mole, and candela, from which all other units are derived.

Comparing an instrument's readings against a known reference standard and adjusting it so its output agrees with the true value within a stated tolerance. It establishes measurement accuracy and traceability.

The process of varying a property of a high-frequency carrier wave, such as its amplitude, frequency, or phase, in step with a lower-frequency information signal so it can be transmitted efficiently.

To reconstruct a band-limited signal without aliasing, it must be sampled at more than twice its highest frequency component. That minimum rate is called the Nyquist rate.

Converting a continuously varying sampled amplitude into one of a finite set of discrete levels. The step size sets resolution, and the resulting rounding error appears as quantization noise.

Combining several independent signals onto one shared channel by separating them in time, frequency, or code, so that a receiver can recover each one without interference from the others.

The ratio of wanted signal power to noise power at a given point in a system, often stated in decibels. Higher values indicate clearer, more reliable reception or measurement.

For a uniform transmission line, the ratio of voltage to current in a single traveling wave, set by the line's series inductance and shunt capacitance per unit length. Terminating a line in this value prevents reflections.

The fraction of transmitted bits that a receiver decides incorrectly, usually expressed as a probability. It measures digital link quality and depends on the signal-to-noise ratio and the coding scheme used.

A measure of how much more power an antenna radiates in its strongest direction than an ideal isotropic radiator would, usually expressed in dBi. It results from directivity, not added power.

A single integrated circuit containing a processor core, memory, and programmable input and output peripherals, intended to control devices and embedded systems rather than to serve as a general-purpose computer.

The number of discrete output codes an analog-to-digital converter can produce, normally stated in bits. An n-bit converter splits the input range into 2 to the n steps, setting the smallest detectable change.