Circuit Theory/Impedance

From Wikibooks, open books for an open world
Jump to: navigation, search

The impedance concept has to be formally introduced in order to solve node and mesh problems.

the impedance symbol is .. a box

Symbols & Definition[edit]

Impedance is a concept within the phasor domain / complex frequency domain.

Impedance is not a phasor although it is a complex number.

Impedance = Resistance + Reactance:

Z = R + X
Impedance = Z
Resistance = R
Reactance = X

Reactance[edit]

Reactance comes from either inductors or capacitors:

X_L
X_C

Reactance comes from solving the terminal relations in the phasor domain/complex frequency domain as ratios of V/I:

\frac{V}{I} = R
\frac{V}{I} = X_L = j\omega L or X_L = sL
\frac{V}{I} = X_C = \frac{1}{j\omega C} or X_C = \frac{1}{sC}

Because of Euler's equation and the assumption of exponential or sinusoidal driving functions, the operator \frac{d}{dt} can be decoupled from the voltage and current and re-attached to the inductance or capacitance. At this point the inductive reactance and the capacitive reactance are conceptually imaginary resistance (not a phasor).

Reactance is measured in ohms like resistance.

Characteristics[edit]

Impedance has magnitude and angle like a phasor and is measured in ohms.

Impedance only exists in the phasor or complex frequency domain.

Impedance's angle indicates whether the inductor or capacitor is dominating. A positive angle means that inductive reactance is dominating. A negative angle means that capacitive reactance is dominating. An angle of zero means that the impedance is purely resistive.

Impedance has no meaning in the time domain.