Sinusoidal Steady-State Analysis

These flashcards cover the key vocabulary and concepts related to Sinusoidal Steady-State Analysis in electric circuit analysis.

Phasor transform

A method that converts time-domain sinusoidal signals into a frequency-domain representation using complex numbers.

Impedance (Z)

The complex ratio of the voltage to the current in a circuit element, measured in ohms (Ω).

Rectangular form

A way to express complex numbers as a + jb, where a is the real part and b is the imaginary part.

Polar form

A way to express complex numbers as r∠θ, where r is the magnitude and θ is the phase angle.

Transient response

The temporary behavior of a circuit immediately after a change in an input value before reaching a steady state.

Steady-state response

The long-term behavior of a circuit after all transients have decayed, often analyzed under sinusoidal excitation.

Euler's Formula

The mathematical relationship e^(jθ) = cos(θ) + jsin(θ) that relates complex exponentials to sinusoidal functions.

Frequency (f)

The number of cycles per second of a periodic signal, measured in hertz (Hz), related to angular frequency by f = ω/2π.

Phase angle (φ)

The angle that represents the position of a sinusoidal waveform, indicating how far the waveform is shifted from a reference point.

Fourier transform

A mathematical transform that expresses a function in terms of the frequencies it is composed of, used for analyzing non-sinusoidal signals.

Conjugate of a complex number

For a complex number C = a + jb, the conjugate is denoted C* = a - jb.

Addition of complex numbers

Combining complex numbers by adding their real parts and their imaginary parts independently.

Multiplication of complex numbers

Combining complex numbers using distributive property, resulting in a new complex number.

Division of complex numbers

Dividing complex numbers using the complex conjugate to simplify.

AC Steady-State (ACSS) response

The response of a circuit to a sinusoidal input after the transient response has decayed to zero.

Sinusoidal source

An alternating current (AC) source that produces sinusoidal voltage or current waveforms described by v(t) = Vm*cos(ωt + φ).

Phasor domain equations

Equations that relate voltage and current in circuits using phasors instead of time-domain representations.

KVL (Kirchhoff's Voltage Law)

The sum of all voltages around a closed loop in a circuit is equal to zero.

KCL (Kirchhoff's Current Law)

The sum of currents entering a junction must equal the sum of currents leaving the junction.

Complex plane

A two-dimensional plane where the x-axis represents the real part of a complex number and the y-axis represents the imaginary part.

Magnitude of a complex number

The distance from the origin to the point in the complex plane representing the number, calculated as r = √(a² + b²).

Inductor’s Impedance

Z = jwL

Capacitor’s Impedance

Z = -j/(wC)

Resistor’s Impedance

Z = R

Is this angle positive or negative? vs = 100cos(50t + 30)

Positive 30 degrees, 100<30

What is the conversion equation for vs to phasor?

vs = magnitude