Honors Physics Labs

Lab 4 - Transmission Lines
Overview

The purpose of this lab is to understand the characteristics of coaxial transmission lines (coax cables). Please see the notes on transmission lines - go to the March calendar.

Consider the following schematic of a coax cable that has a battery at one end (with a switch) between the inner and outer conductors and a resistor at the other end between the inner and outer conductors. At t=0 the switch is closed but the voltage which appears at end A between the inner and outer conductors does not instantaneously appear between the inner and outer conductors at the other end (B). The voltage (and current) propagate down the cable with a certain characteristic speed equal to the speed of light if the space between the inner and outer conductors is a vaccum and less than the speed of light if the space is filled with material. Because the the voltage across and current through the resistor at end B must be always related by Ohm's Law, there may or may not be a reflection that occurs at end B.

Characteristic Length (in nanoseconds !)

Since pulses propogate down cables with a speed characteristic of a cable (between 0.5 and 1.0 times c - speed of light) and a given cable has a specific physical length, cable lengths are often specified in units of time - nanoseconds - where the time is the physical length divided by the propsagation speed. Thus a "1 ns" cable would have a physical length of about 1 ft if the characteristic speed were c.

Characteristic Impedance

Another quantity characterizing a cable is the characteristic impedance (Z_o) which relates the voltage in the coax to the current:

The relation between voltage and current for a pulse propagating in the positive x direction

The relation between voltage and current for a pulse propagating in the negative x direction - note the minus sign

Reflections

If the characteristic impedance is the same as the terminating resistor R, there is no reflection since V=IR is automatically satisfied at end B. However if the cable impedance is not the same as the terminating resistor that will be a reflection. If the incident pulse is along the positive x-direction, the reflected pulse is along the negative x direction and we have these relations:

Where capital Greek gamma is the reflection coefficient and unsubscripted V and I are the voltage across and current through the terminating resistor where V=IR. It is not difficult to show that:

Consider the following:

cable properly terminated
There is no reflection

The reflected voltage pulse has the same polarity as the incident pulse but is reduced in amplitude.

The reflected voltage pulse has the opposite polarity as the incident pulse but is reduced in amplitude.

short circuit
The voltage between the inner and outer conductors at end B is zero - the reflected voltage pulse has the opposite polarity as the incident pulse.

open circuit
The current between the inner and outer conductors at end B is zero - the reflected voltage pulse has the same polarity as the incident pulse.

Procedure

An RG58 cable

BNC connectors: (left) a T adaptor, (middle) union, (right) 50 ohm terminator

Images above from http://www.oscaroscar.com

You will be given several transmission lines, a function generator, and an oscilloscope to study the reflections in various cables of unknown impedances and length. You will be looking at the input and reflected signals at point A (see the above circuit).

Procedure

You will be given a 60-ft RG58 coax (impedance = 50 ohm). Verify that the reflected signal occurs at the right delay time and has the right polarity using no terminator, a 50 ohm terminator and a short between inner and outer conductor. Also use a potentiometer (to be supplied to you) to verify that the amplitude of the reflected signal agrees with expectations when the terminating resistor is above and below the cable impedance.

You will be given three 'mystery boxes' containing a transmission line of unknown length and impedance. Find the impedance and the propation delay through each.

The writeup should report the answers for each box and a brief statement of procedure.

60-ft 50-ohm cable

Two terminators: left: 50-ohm; right: short

Mystery Box

	The relation between voltage and current for a pulse propagating in the positive x direction
	The relation between voltage and current for a pulse propagating in the negative x direction - note the minus sign

cable properly terminated		There is no reflection
		The reflected voltage pulse has the same polarity as the incident pulse but is reduced in amplitude.
		The reflected voltage pulse has the opposite polarity as the incident pulse but is reduced in amplitude.
short circuit		The voltage between the inner and outer conductors at end B is zero - the reflected voltage pulse has the opposite polarity as the incident pulse.
open circuit		The current between the inner and outer conductors at end B is zero - the reflected voltage pulse has the same polarity as the incident pulse.