0195136047.pdf

PROBLEMS 733

15.1.16A transmitter is connected to an antenna by a

transmission line for whichZ ̄ 0 =R 0 = 50 .

The transmitter source impedance is matched to

the line, but the antenna is known to be unmatched

and has areflection coefficient

L=

RL−R 0

RL+R 0

= 0. 3

whereRL(=Z ̄L)is the load impedance. The

transmitter produces a power of 15 kW in the inci-

dent wave to the antenna and will be destroyed due

to overheat if the reflected wave’s power exceeds

2 kW. Determine the antenna’s radiated power in

this case and comment on whether the transmitter

will survive.

*15.1.17A source of impedanceZ ̄S=RS= 100 has
an open-circuit voltagevS(t)=12.5 cosωotand
drives a 75-transmission line terminated with
a 75-load. Find the current and voltage at the
input terminals of the line.
15.1.18The model of an elemental length of a lossy trans-
mission line is shown in Figure P15.1.18(a),

along with its parameters, whereRis series re-

sistance per unit length,Lis series inductance

per unit length,Gis shunt conductance per unit

length, andCis shunt capacitance per unit length.

Thecharacteristic impedanceZ ̄ 0 of the line is

given by

Z ̄ 0 =

√

Z ̄

Y ̄=

√

R+jωL

G+jωC

Thepropagation constant Vis given by

V ̄=

√

Z ̄Y ̄=

√

(R+j ωL)(G+jωC)

=α+jβ

whereαis the attenuation constant (nepers per

unit length) andβis the phase constant (radi-

ans per unit length). The ac steady-state solu-

tion for the uniform line reveals the voltage on a

matched line(Z ̄L=Z ̄ 0 )to beE(x) ̄ =E ̄Se− ̄γx=

E ̄Se−αxe−jβx, whereE ̄Sis the sending-end volt-

age andxis distance along the line from the send-

ing end.

∆x

= 100 mi

ES ER

L∆x

G ∆x

(a)

C ∆x

I− R∆x I− + ∆I−

E E + ∆E−

−

+

−

+

− −

600 Ω

Eg = 10 ∠ 0 ° v RMS

(b)

ZR = Z 0

I−S I−R

− −

+

−

−

−

+

+

−

−

−

Figure P15.1.18