Radio Frequency (RF) & Wireless Design

There are many engineers who have been schooled and are educated but yet are not familiar with the Telegrapher's Equations .

So here is a Wikipedia reference to help you understand them :

https://en.wikipedia.org/wiki/Telegrapher's_equations

these were developed by Oliver Heavyside (which is given very little credit today) :

https://en.wikipedia.org/wiki/Oliver_Heaviside

[FYI ; he also simplified the Maxwell equations down from 22 to 4 equations ! ]

What is important to understand is that there are really *four* parts to an impedance equation : Resistance (R) , Inductive Reactance (XL) , Capacitive Reactance (XC) , and the rarely seen one - Conductance (G) .

In higher frequency circuits the resonance frequency is approximated by the familiar :

f = SQRT(XL/XC) = SQRT(L/C)

which happens to be a shortened version of the telegrapher's equation.

These form the more familiar Characteristic Impedance equations that are used in everything from understanding cables to transmission lines to signal integrity for PCBs.

https://en.wikipedia.org/wiki/Characteristic_impedance

In reviewing the characteristic impedance for CAT 5e cables, i came across this notation :

The characteristic impedance of a transmission line is given by Z 0 = R + j ω L G + j ω C {​​\displaystyle Z_{​​0}​​={​​\sqrt {​​\frac {​​R+j\omega L}​​{​​G+j\omega C}​​}​​}​​}​​ . There are two important transition frequencies related this equation: f R L = R 2 π L {​​\displaystyle f_{​​RL}​​={​​\frac {​​R}​​{​​2\pi L}​​}​​}​​ and f G C = G 2 π C {​​\displaystyle f_{​​GC}​​={​​\frac {​​G}​​{​​2\pi C}​​}​​}​​ . Typically we have f R L > f G C {​​\displaystyle f_{​​RL}​​>f_{​​GC}​​}​​ and the corner frequency (or break frequency) is defined as f R L {​​\displaystyle f_{​​RL}​​}​​ because at frequencies greater than f R L {​​\displaystyle f_{​​RL}​​}​​ the familiar "lossless" relation Z 0 = L C {​​\displaystyle Z_{​​0}​​={​​\sqrt {​​\frac {​​L}​​{​​C}​​}​​}​​}​​ for characteristic impedance holds true to excellent approximation. Unfortunately neither of the terms corner frequency nor break frequency are consistently used in the literature. Most often these frequencies are not given any special name, and the topic itself is glossed over in most modern texts.[

found at the bottom here for CAT 5 cables :

https://en.wikipedia.org/wiki/Category_5_cable

what is interesting to understand is that *most* transmission lines are lossy and that there does need to be considerations for losses, espeically when the cables are used for high data rates where dielectric material losses can be quite significant !

So next time you are doing any work with transmission lines remember that the are really four parts and don't forget the conductance variable !