Page 83 - Circuit Analysis II with MATLAB Applications

Radio and Television Receivers

Then,

I = I + I C = > Re I^` + Im I^` V + > Re I^` + Im I^` V
@
@
L
L
L
T
C
C
= > Re I ^` + Re I^` + Im I^` + Im I^` V (2.36)
@
L
L
C
C
= > Re I ^` + Im I^` V
@
T
T
Now, at resonance, the imaginary component of I T must be zero, that is,
§ Z L ·
Im I^` = Im I^` + Im I^` = ¨ Z C – -----------------------------¸ 0 V = 0
L
C
T
2
© 0 R + Z L ¹ 0 2
and solving for Z 0 we get
2
1 R
Z = ------- – ------ 2 (2.37)
0
LC
L
or
1 1 R 2
f = ------ ------- – ------ 2 (2.38)
0
2S LC
L
1
We observe that for R = 0 , (2.37) reduces to Z = ----------- as before.
0
LC
2.9 Radio and Television Receivers

When a radio or TV receiver is tuned to a particular station or channel, it is set to operate at the res-
onant frequency of that station or channel. As we have seen, a parallel circuit has high impedance
(low admittance) at its resonant frequency. Therefore, it attenuates signals at all frequencies except
the resonant frequency.
We have also seen that one particular inductor and one particular capacitor will resonate to one fre-
quency only. Varying either the inductance or the capacitance of the tuned circuit, will change the
resonant frequency. Generally, the inductance is kept constant and the capacitor value is changed as
we select different stations or channels.

The block diagram of Figure 2.16 is a typical AM (Amplitude Modulation) radio receiver.

Circuit Analysis II with MATLAB Applications 2-17
Orchard Publications