Transmission Line Equations
The physics behind the derivation of transmission line filters is described with a well known set of transmission line equations, two of which are prominent. One prominent equation is useful in calculating the input impedance of a line. The other is useful in describing a voltage signal as it propagates down the line.
The input impedance, Zin, of a line may be described according to the following equations:
Lossy Transmission Line Input Impedance
If a line is lossless, meaning the resistance and conductance are both zero, then the equations reduce to a simpler form as seen below
Lossless Transmission Line Input Impedance
Striplines and Microstrips
Losses for striplines and microstrips are generally a function of frequency, and are calculated with attenuation using conductor resistivity dielectric loss tangents, frequency, and geometry rather than by resistance and conductance.