Electrical Impedance Lecture Notes

Overview of Electrical Impedance

• Definition: A measure of opposition to a sinusoidal alternating current (AC).
• Extends the concept of resistance to AC circuits by describing both relative amplitudes of voltage and current and their phases.
• Direct Current (DC): No distinction between impedance and resistance in DC.
• Symbol: Usually represented in complex form; coined by Oliver Heaviside in 1886.
• SI Unit: Ohm; reciprocal is admittance.

Complex Impedance

• Complex Quantity: Impedance is often represented as a complex quantity, capturing magnitude and phase.
• Polar Form: Magnitude is the ratio of voltage amplitude to current amplitude; argument gives phase difference.
• Cartesian Form: Real part is resistance; imaginary part is reactance.
• Conversion: Necessary between polar and Cartesian forms during calculations.

Ohm's Law and Impedance

• Impedance can be incorporated into Ohm's law for AC circuits.
• Phase factor indicates that current lags voltage by a phase.
• DC circuit analysis results (voltage division, Thevenin’s theorem, etc.) can be extended to AC by replacing resistance with impedance.

Complex Voltage and Current

• Sinusoidal voltage and current represented as complex-valued functions of time.
• Validity: Justified using Euler's formula.
• Phasors: Represent complex amplitude (magnitude and phase) of sinusoidal functions. Simplifies computations involving sinusoids.

Device Impedance Examples

• Resistor: Impedance is purely resistive.
• Capacitor: Impedance is purely reactive; voltage leads current by -90 degrees.
• Inductor: Impedance is purely reactive; voltage leads current by 90 degrees.

Resistance vs. Reactance

• Resistance: Real part of impedance; no phase shift between voltage and current.
• Reactance: Imaginary part; induces phase shift.
  • Capacitive Reactance: Inversely proportional to signal frequency.
  • Inductive Reactance: Proportional to signal frequency.

Combining Impedances

• Series Combination: Current through each element is the same.
• Parallel Combination: Voltage across each element is the same.
• Impedances combined like resistances, using complex numbers.

Measuring Impedance

• Can be calculated using Ohm's law by complex division of voltage and current.
• Impulse Impedance Spectroscopy: Uses impulse response and FFT for measurement; compares well to other methodologies.

Additional Resources

• External links and references to further explore the topic of electrical impedance.