B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

230 ANGLE MODULATION AND DEMODULATION
Because only frequency doublers can be used, we have three equations:
M1 = 2 n ,
M2 = 2 n 2
n1 + n2 = 11
It is also clear that
and
To find/ LO
, there are three possible relationships:
and
Each should be tested to determine the one that will fall in
400, 000 :": / LO
:": 500, 000
(a)
First, we testf q
= fc 2 -fLO . This case leads to
97.3 X 10 6 = 2 n 2
(2 n1 fc 1 -/ LO )
_ 2
n1 +n2 + _ 2 n 2 1,
- J CJ LO
Thus, we have
fLO = r n z
( 4.096 X 10 7 - 9.73 X 10 7 ) < 0
This is outside the local oscillator frequency range.
(b) Next, we testf q
= fez + fLO . This case leads to
97.3 X 10 6 = 2 n 2
(2 n 'fci
+ / LO )
= 2 11 20 X 10 3 + 2 n2 / LO
Thus, we have
If n2 = 7, then/ LO
= 440 kHz, which is within the realizable range of the local oscillator.
(c) If we choose fc3 = Ko -fc 2 , then we have
97 3 X 10 6 - J, - 2 n 2 2 n1+
•
- LO
J CJ
= 2 n 2 fLO - 2 11 (20 X 10 3 )