Heaviside condition
The Heaviside condition, named for Oliver Heaviside (1850–1925), is the condition an electrical transmission line must meet in order for there to be no distortion of a transmitted signal. Also known as the distortionless condition, it can be used to improve the performance of a transmission line by adding loading to the cable.
A transmission line can be represented as a distributed element model of its primary line constants as shown in the figure. The primary constants are the electrical properties of the cable per unit length and are: capacitance C (in farads per meter), inductance L (in henries per meter), series resistance R (in ohms per meter), and shunt conductance G (in siemens per meter). The series resistance and shunt conductivity cause losses in the line; for an ideal transmission line, .
The Heaviside condition is satisfied when
This condition is for no distortion, but not for no loss.
A signal on a transmission line can become distorted even if the line constants, and the resulting transmission function, are all perfectly linear. There are two mechanism: firstly, the attenuation of the line can vary with frequency which results in a change to the shape of a pulse transmitted down the line. Secondly, and usually more problematically, distortion is caused by a frequency dependence on phase velocity of the transmitted signal frequency components. If different frequency components of the signal are transmitted at different velocities the signal becomes "smeared out" in space and time, a form of distortion called dispersion.
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