Impedance
From Wikiham, the ham radio free encyclopedia
Impedance describes the relationship between voltage and current in a sinusoidal steady-state circuit, including their phase difference. It generalises resistance and is central to antennas, filters and transmission lines.
Complex representation
Z = R + jX V = Z I (phasors) |Z| = sqrt(R² + X²) φ = atan2(X, R)
Z is impedance in ohms, R is resistance and X is reactance. j is the imaginary unit, with j² = -1. V and I in the second expression are phasors, not instantaneous waveform values. Positive reactance is inductive; negative reactance is capacitive.
For a series combination of ideal resistance, inductance and capacitance:
X = 2 π f L - 1 / (2 π f C)
f is in hertz, L in henries and C in farads. At resonance, the two reactive terms cancel; resistance and losses remain.
Worked example
A load of 50 + j50 Ω has a magnitude of about 70.7 Ω and a phase angle of +45 degrees. A 10 V RMS source across it produces approximately 0.141 A RMS, with current lagging the voltage. Real power in its 50 Ω resistive part is 1 W.
Using 70.7 Ω as though it were a pure resistance would give the wrong real power. The phase relationship is part of the answer.
In a radio station
A nominal 50 Ω antenna system is intended to present approximately 50 + j0 Ω at the relevant reference plane and frequency. A feed line can transform the impedance seen at its input. A matching network can improve the transmitter's match without removing losses elsewhere in the system.
The characteristic impedance of coax is not its resistance measured with a DC ohmmeter. Standing wave ratio describes mismatch relative to a line's characteristic impedance.