PROBLEMS 737*15.2.6In a standard AM system, represented by Equation
(15.2.3),Ac=200 V,∣∣∣f (^2) (t)
∣
∣∣^1 /^2 =50 V, and
Z ̄ 0 =R 0 = 50 . CalculateηAM,Pc,Pf, and
PAM.
15.2.7If a standard AM waveform [Equation (15.2.3)]
of 1-kW average power is transmitted by an an-
tenna with an input resistance of 75, evaluate
f^2 (t), carrier power, and sideband power, given
the efficiency to be 0.1.
15.2.8In the envelope detector [Figure 15.2.8(a)] of a
standard AM receiver, the productRCis chosen
to satisfyπ/ωIF << RC < 1 /ωm,max, where
ωm,max/ 2 π=5 kHz in standard AM andωIF=
455 kHz. IfR= 5000 , find the value of its
capacitor (by applying a factor of 10 to represent
<<).
15.2.9In an AM transmitter that transmits a total power
of 1 kW, the unmodulated carrier power is 850
W. Compute the required value of(Si/Ni)AMat a
receiver, if(S 0 /N 0 )AM= 2 ηAM(Si/Ni)AMmust
be 10^3 for good performance.
15.2.10At the transmitter in a standard AM system,Pf=
50 W. In the receiver(S 0 /N 0 )AM =250 when
(Si/Ni)AM =3000. Find the transmitter’s un-
modulated carrier power and the total transmitted
power if(S 0 /N 0 )AM= 2 ηAM(Si/Ni)AM.
15.2.11Determine the image frequency if an AM radio
receiver is tuned to a station at 1030 kHz and has
a high-side local oscillator.
15.2.12Although the low side is not as good a choice as
the high-side local oscillator frequency, let an AM
broadcast receiver be designed with a low-side
local oscillator. Asfcis varied from 540 to 1600
kHz, find the valuesfLOandfimage.
15.2.13For a DSB system for whichf(t)=Amcosωmt,
ωc= 5 ωm, andφc=0, sketch the transmitted
signal.
15.2.14One of the many types of product device to pro-
duce suppressed-carrier AM is shown in Figure
P15.2.14. Explain briefly how the device operates.
15.2.15If the output signal from an AM modulator is given
byu(t)=5 cos 1800πt+20 cos 2000πt+
5 cos 2200πt, determine:
(a) The modulating signalm(t) and carrierc(t).
(b) The modulation index.
(c) The ratio of the power in sidebands to the
power in the carrier.
15.2.16The signalm(t), whose frequency spectrumM(f)
is shown in Figure P15.2.16, is to be transmitted
from one station to another. Let the signal be nor-
malized, i.e.,− 1 ≤m(t)≤1. Find the bandwidth
of the modulated signal:
(a) If USSB (upper single sideband) is employed.
(b) If DSB (double sideband) is employed.
(c) If an AM modulation scheme with a modula-
tion index of 0.8 is used.
(d) If an FM signal with the frequency deviation
constantkf=60 kHz is used.
15.2.17An FM signal, for whichf(t)=2 cosωmt, is given
by
sFM(t)=50 cos
{
185 π( 106 )t+
π
3
+6 sin
[
π( 104 )t
]}
Determine:Ac,ωc,φc,ωm,kFM, and the modulation
indexβFM= ω/ωm.
15.2.18A commercial FM station broadcasts a signal with
180-kHz bandwidth when|f(t)|max=2 V. Find
kFMfor the modulator if the spectral extent off(t)
is 30 kHz, by using Carson’s rule.
T 1 T 2
Q 1
Q 3
Q 4
Q 2
b
d
a
c
f(t) Output
cos ωct
- Figure P15.2.14