0195136047.pdf

672 COMMUNICATION SYSTEMS

(transverse) to the direction of propagation, which is along the axial line. That is to say, no

electromagnetic field component exists in the axial direction. In the case of single-conductor

hollow (pipelike) waveguides, either the TE (transverse electric) or the TM (transverse magnetic)

modecan be energized. In the TE configuration, the electric field is transverse to the direction of

propagation (which is along the axial line of the waveguide); that is to say, no electric field exists

in the direction of propagation, while an axial component of the magnetic field is present. On the

other hand, in the TM configuration, the magnetic field is transverse to the direction of propagation:

i.e., no magnetic field exists in the axial direction, whereas an axial component of the electric

field is present. Within either grouping, a number of configurations ormodescan exist, either

separately or simultaneously. However, we are generally concerned with the so-calleddominant

mode, which is defined as the lowest frequency mode that can exist in the waveguide. When

operating at a frequency abovefc, known as thecutoff frequency,a wave propagates down the

waveguide and the mode is calledpropagation mode. When operating below the cutoff frequency,

the field decays exponentially and there is no wave propagation.

Figure 15.1.3 represents a transmission line of lengthlconnecting a signal source to a distant

load. The line may be a two-wire line, a coaxial cable, or a hollow waveguide. The voltagev 1 (t)

between the source-side (input) terminals of the transmission line gives rise to an electric field,

while the currenti 1 (t) produces a magnetic field. Thecharacteristic impedanceZ ̄ 0 of the line is

given by

Z ̄ 0 =

V ̄ 1

I ̄ 1

(15.1.1)

which relates the voltage and current of the wave traveling along the line. AlthoughZ ̄ 0 in general

could be complex, for distortionless transmission,Z ̄ 0 (=R 0 ) must be constant and resistive over

the frequency range of the signal. The signal-source voltagevS(t) is related tov 1 (t)by

vS(t)=v 1 (t)+i 1 (t)RS (15.1.2)

whereRSis the signal-source internal resistance. From Equations (15.1.1) and (15.1.2), we get

v 1 (t)=

R 0

RS+R 0

vS(t) (15.1.3)

i 1 (t)=

1

RS+R 0

vS(t) (15.1.4)

As the electromagnetic fields associated withv 1 (t) andi 1 (t) propagate down the line, they carry

along the associated voltages and currents that are no different fromv 1 (t) andi 1 (t) except for a

delay in time, because the charges (and therefore current) move down the line at finite velocity

vg. Thus, at output terminalscanddin Figure 15.1.3, which are a distancelapart, the voltage

Transmission

line

Signal

source

Load

RS = Z 0

Z 0

ac

bd

vS(t) RL = Z 0

i 1 (t)

x(t) = v 1 (t)

Pin Pout

y(t) = v 2 (t)

i 2 (t)

Figure 15.1.3Transmission line (with

matched impedances).