Impedance (Z)

Impedance is the total opposition to alternating current (AC) in an electrical circuit. Represented by the symbol Z and measured in ohms (Ω), it extends the concept of resistance by including both resistance (R) and reactance (X) as frequency-dependent components.

Mathematical Definition

Impedance is a complex quantity:

Z = R + jX

where:

• R: Resistance (Ω)

• X: Reactance (Ω)

• j: Imaginary unit (√−1)

The magnitude of the impedance is:

|Z| = √(R² + X²)

Reactance Components

Reactance varies with frequency and has two components:

• Inductive reactance:
  X_L = 2πfL
  Increases with frequency f and inductance L

• Capacitive reactance:
  X_C = 1 / (2πfC)
  Decreases with increasing frequency f and capacitance C

Practical Example

A loudspeaker rated at 8 Ω presents a frequency-dependent load to an amplifier. Its impedance results from the interaction of resistive, inductive, and capacitive elements, such as the voice coil and crossover network. Proper impedance matching ensures efficient power transfer and minimal distortion.

Applications

• RF and microwave engineering: Impedance matching prevents signal reflections and ensures efficient transmission in antennas and transmission lines

• Power systems: Used in AC load flow analysis and fault diagnostics

• High-speed digital circuits: Maintains signal integrity by controlling line impedance

• Audio engineering: Prevents mismatches between amplifiers and speakers to avoid signal loss and distortion