Lossless Lines

In electrical engineering, a lossless transmission line is characterized by a purely imaginary propagation constant and a resistive characteristic impedance. The ABCD parameters, which describe the relationship between the input and output voltages and currents, indicate an equivalent π circuit with an imaginary series impedance and a shunt admittance. This results in a transmission line that, when the product of the phase constant (beta) and the length of the line is less than pi, exhibits inductive series impedance and capacitive shunt admittance, ensuring that it remains lossless.

Wavelength and Propagation

The wavelength is the physical length over which the voltage or current phase changes by 2π. This is determined using the signal's propagation velocity. For a lossless line, the wavelength is crucial in determining the electrical length of the line and its phase characteristics.

Surge Impedance Loading

Surge impedance loading (SIL) is a concept used to describe the power that can be delivered to a load resistance equal to the surge impedance of the transmission line. For a transmission line with a resistive characteristic impedance, the SIL is calculated using the rated voltage and the surge impedance:

In this condition, the voltage remains constant along the line, and there is a constant flow of real power from the sending end to the receiving end, with zero reactive power flow.

Voltage Profiles and Loading Conditions

In practical scenarios, transmission lines are rarely terminated with their surge impedance, leading to non-uniform voltage profiles along the line. Under no-load conditions, the voltage increases from the sending end to the receiving end due to the Ferranti effect. Conversely, in a short-circuit condition, the voltage drops to zero at the receiving end. At full load, the voltage profile lies between these two extremes, generally higher than the short-circuit profile but lower than the no-load profile.

These characteristics of lossless transmission lines are vital for the design and analysis of power systems, ensuring efficient and reliable power delivery with minimal losses and stable voltage profiles under varying load conditions.