Q10Electromagnetics Waves

The characteristic impedance Z0 = √[(R+jωL)/(G+jωC)] of a transmission line is the ratio of voltage to current for a single travelling wave moving in one direction along an infinitely long (or matched) line; it is a property of the line's geometry and materials, not of any load connected to it. Its effect is decisive whenever a finite line is terminated in a load ZL ≠ Z0: the mismatch produces a reflected wave with reflection coefficient Γ = (ZL−Z0)/(ZL+Z0), which combines with the incident wave to form a standing-wave pattern (VSWR > 1), reduces the net power delivered to the load (maximum power transfer occurring only when ZL = Z0*, matched conjugate for maximum power, or ZL = Z0 for a lossless line and zero reflection), and can cause the line's own input impedance (seen by the source) to vary strongly with line length and frequency rather than remaining fixed at Z0. Correctly matching ZL to Z0 (using techniques such as the quarter-wave transformer or stub matching discussed elsewhere in this paper) is therefore essential to achieving efficient power transfer, minimizing standing-wave voltage stress on the line, and ensuring stable, frequency-independent input impedance for the source.