Page 85 - Circuit Analysis II with MATLAB Applications

Radio and Television Receivers

Example 2.4

A radio receiver with a parallel GLC circuit whose inductance is L = 0.5 mH is tuned to a radio
station transmitting at 810 KHz frequency.

a. What is the value of the capacitor of this circuit at this resonant frequency?

b. What is the value of conductance if Q 0P = 75 ?
G
c. If a nearby radio station transmits at 740 KHz and both signals picked up by the antenna have the
same current amplitude (PA ), what is the ratio of the voltage at 810 KHz to the voltage at
I
740 KHz ?
Solution:

a.
1
2
Z = -------
0 LC
or
1
f 0 2 = ----------------
2
4S LC
Then,
1
C = ----------------------------------------------------------------------- = 77.2 pF
3 2
2
4S 0.5 u 10 – 3 u 810 u 10
b.
Z C
0
Q = ----------
0P G
or
5
2Sf C 2S u 8.1 u 10 u 77.2 u 10 – 12 –
0
G = --------------- = ---------------------------------------------------------------------- = 5.4 P: 1
Q 0P 75
c.
I
I
I
I
V 810 KHz = ----------------------- = ----- = ---- = --------------------------- 6 (2.39)
Y
–
Y
G
10
5.24 u
0
810 KHz
Also,
I
V 740 KHz = -----------------------
Y
where 740 KHz
2
1 ·
Y 740 KHz = G + § © ZC – ------- ¹ 2
ZL
Circuit Analysis II with MATLAB Applications 2-19
Orchard Publications