Impedance & Admittance

Impedance (Z)

Here:

• : Resistance
• : Reactance

Admittance (Y)

Inverse of impedance.

Here:

• : Conductance
• : Susceptance

From the definitions:

For simple circuit elements

Resistor

Let is applied across a resistor with resistance . From Ohm’s law:

No changes in frequency, phase angle. is in phase with . doesn’t have reactance.

Inductor

Let is applied across an inductor with inductance .

Reactance of the inductor is .

Note

leads by . No changes in frequency.

Capacitor

Let is applied across an capacitor with capacitance .

Reactance of the capacitor (capacitive reactance) is .

Note

lags by . No changes in frequency.

Note

If :

• lags - circuit is capacitive
• leads - circuit is inductive

For complex circuit elements

Real Inductor

Take as the reference. We get:

From here can be written (in cartesian or polar form):

RLC series circuit

Complex impedances are added up to find the total impedance of a series circuit.

For a series circuit

Total impedance is the sum of each component’s impedance.

For a parallel circuit

Total admittance is the sum of each component’s admittance.