User:Prayerfortheworld/EE137A

Lossless line
The analysis of lossless lines provides an accurate approximation for real transmission lines that simplifies the mathematics considered in modeling transmission lines. A lossless line is defined as a transmission line that has no line resistance. This would imply that the line has infinite conductivity and acts like a perfect conductor. For a lossless line, R and G are both zero, so the equation for characteristic impedance derived above reduces to:


 * $$Z_0 = \sqrt{\frac{L}{C}}$$

The above expression is wholly real, since the imaginary term j has canceled out, implying that Z0 is purely resistive. For a lossless line terminated in Z0, there is no loss of current across the line, and so the voltage remains the same along the line. The lossless line model is a useful approximation for many practical cases, such as low-loss transmission lines and transmission lines with high frequency. For both of these cases, R and G are much smaller than ωL and ωC, respectively, and can thus be ignored.