Transmission Line Length Calculator

Transmission line theory applies when the physical length of a conductor is a significant fraction of the signal wavelength - typically more than about one-tenth of a wavelength. Below this threshold, the conductor can be treated as a lumped element (a resistor, inductor, or capacitor) without significant error. At 100 MHz, one-tenth wavelength in free space is about 30 cm; in coax with VF = 0.66, it is 20 cm. Any circuit board trace, cable, or conductor shorter than this can be treated as a lumped element. Above this length, you must account for the distributed nature of the fields and use transmission line analysis. For high-speed digital circuits, the same rule applies with the rise time substituted for the period: a trace longer than the signal rise time multiplied by the propagation velocity divided by 10 needs transmission line treatment.

Standing waves appear whenever there is an impedance mismatch at the load end of the transmission line. When the load impedance does not equal the line's characteristic impedance Zo, part of the forward-traveling wave is reflected back toward the source. The incident and reflected waves of the same frequency traveling in opposite directions superimpose to form a standing wave pattern. At certain points along the line, the waves add constructively (voltage maximum, current minimum) and at other points they cancel (voltage minimum, current maximum). The ratio of maximum to minimum voltage is the VSWR. A perfectly matched load (Zload = Zo) produces no reflection and no standing wave; a short circuit (Zload = 0) or open circuit (Zload = infinity) produces total reflection and a VSWR of infinity. Practical antenna and load impedances fall between these extremes, producing partial reflection and finite VSWR.