0195136047.pdf

736 COMMUNICATION SYSTEMS

identical paraboloidal antennas with pencil beam-
width of 1°, aperture efficiency of 0.8, and radi-
ation efficiency of 0.85. The transmitting station
hasPt=60 W andLt=2 at 8 GHz. WithLr=1.5
andLch= 2.5, find the diameter of the antennas and
the signal power available at the receiver input.
15.1.37Two stations (using identical antennas, with di-
ameters of 50λand aperture efficiencies of 0.6 at
35 GHz) are separated by 30 km. With negligible
antenna losses, antenna connection-path losses are
Lt=Lr=1.33 at a physical temperature of 285
K, while the antenna temperature is 85 K. The re-
ceiver at either station hasGa(f 0 )= 107 ,T ̄R= 250
K, andBN=12 MHz. The rain attenuation and
clear-air attenuation are given to be 3.9 dB/km
and 0.072 dB/km, respectively. Determine:
(a) The required output power to guarantee a sys-
tem signal-to-noise power ratio of 45 dB when
heavy rain falls over a distance of 6 km.
(b) The available noise power occurring at the
receiver output.
(c) The output signal power occurring with and
without rain, when the transmitted power
found in part (a) is used.
15.1.38If an antenna has an available noise power of

1. 6 × 10 −^15 W in a 1-MHz bandwidth, find the
   antenna temperature.
   15.1.39Determine the effective input noise temperature
   of a long piece of waveguide (that connects an
   antenna to a receiver) with a loss of 3.4 dB at 12
   GHz and a physical temperature of 280 K.
   *15.1.40An antenna with an effective noise temperature of
   130 K couples through a waveguide that has a loss
   of 0.8 dB to a receiver. Find the effective noise
   temperature presented by the waveguide output to
   the receiver if the waveguide’s physical tempera-
   ture is 280 K.
   15.1.41If the antenna and waveguide of Problem 15.1.40
   feed a receiver for whichBN=10 MHz,Ga(f 0 )=

1012 , andT ̄R=300 K, determine the system noise

temperature andNaoat the receiver output.

15.1.42(a) An amplifier withF 0 =3 or 4.77 dB,f 0 =

4 GHz, andBN=14 MHz is used with an

antenna for whichTa=200 K. The connecting

path loss is 1.45, or 1.61 dB at a physical tem-

perature of 250 K. Find the available system

noise power.

(b) If the antennas of Example 15.1.5 are used

with the receiver of part (a), compute the

signal-to-noise ratio.

*15.2.1Find the number of possible station frequencies in

the AM broadcast system in the United States.

15.2.2Leta(t)=[ 1 +mAx(t)]andx(t)=cos 2πfmt,

fm<< fc, andxc(t)=A(t)cos 2πfct.

(a) WithmA=1, sketch one full period of the AM

wave and draw the envelope by connecting the

positive peaks ofxc(t).

(b) Repeat part (a) withmA=2, and notice that

the carrier is overmodulated and the envelope

does not have the same shape asx(t).

15.2.3Figure P15.2.3 illustrates a way to generate an

AM wave of the form of Equation (15.2.2), using

a nonlinear device and an appropriate bandpass

filter. Comment on the nature of the BPF to be

used.

15.2.4If the nonlinear device in Problem 15.2.3 pro-

ducesz=ay^2 , determine how the system must

be augmented to obtain an AM wave in the form

of Equation (15.2.2).

15.2.5If the message has a spectrum

F(ω)=

{

Kcos 2 πωWf, −Wf≤ω≤Wf

0 , elsewhere

whereKandWfare positive constants, sketch the

spectrum of a standard AM signal that uses the

message. Comment on the physical significance

ofKandWfin the modulation process.

Ac cos 2πfct

Nonlinear

device BPF

x(t) = Am cos 2πfmtzy = y + ay^2 xout(t)

+

Figure P15.2.3