Lecture Notes for Analog Electronics - The Electronic Universe ...

f c
+
+
f m
V s
Figure 43: Schematic of modulation.
we can do a “poor man’s” Fourier transform of Vs:
Vs(t) =Acos ωct + 1
2 Am [cos ((ωc + ωm)t)+cos((ωc−ωm)t)] (46)
So we have a central carrier frequency plus two side-bands at fc ± fm.
One simple way to achieve an amplitude modulated signal is to use an amplifier for which
the input is the carrier signal and the amplifier power itself is modulated by the signal, e.g.
VCC − VEE = V0 + V1 cos ωmt, whereV0is the DC offset amd we identify m ∝ V1/V0.
8.3 Detection of AM
8.3.1 Heterodyne Detection
We first consider the simple, but subtle, radio receiver shown in Fig. 44. A real receiver
might include at the input an antenna followed by an LC bandpass filter, with tunable
capacitor. The filter is a resonant circuit with a sharp peak at the carrier frequency of the
broadcast ωc =1/ √ LC. The Q of the filter is set so that the width of the peak of the
transfer function matches the bandwidth ∆ω of the modulating signal, roughly from ωc −ωm
to ωc + ωm. With this addition, and without the amplified output, the passive “crystal”
radio receiver looks like this.
a R
IN G
OUT
Δω
r
Figure 44: Simple AM receiver.
The resistor R and capacitor clearly form a low-pass filter. The cutoff frequency would
be set between ωm and ωc in order to keep the information encoded by the low-frequency
modulations, and remove the carrier. However, without the diode, the effect would be to
throw away all of the information, too, since as we saw from Eqn. 46, all of the frequencies
49
C