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Week 9: Alternating Current Circuits 331

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Power in R

ω

Resonance of Parallel LRC Circuit

R = 10R = 2

R = 40

Figure 133: Parallel resonance power delivery in a greatly simplified resistive model.

In the next section we will see how to make practical use of the parallelLRCcircuit (and a
rectifier) in the design of acrystal radio, an inexpensive device capable of receiving, discriminating,
and decoding an AM-encoded signal.

The AM Radio and Bandwidth

The simplest way to transmit things like voice and music via electromagnetic (radio) waves is to use
Amplitude Modulation(AM) to encode the signal onto acarrierwave. Here’s how it works. First one
builds anoscillatorat the fixed frequency of the carrier (which is generally a much higher frequency
than any frequency in the signal). Without going into any details, theLCcircuits studied above
(combined with an amplifier) can be used to drivethemselvesto a stable, single frequency output
(especially when stabilized with and tuned to a “natural” electrical oscillator such as a piezoelectric
crystal). For our purposes this frequency doesn’t have to betooprecise – a bit of slow drift in phase
or frequency is OK, for example – but we’ll pretend that it is a single, pure harmonic wave at a
carrier frequencyωc.

Next, we need to collect the signal being encoded in electronic form.This is easily done with e.g.
a microphone, which creates a voltage proportional to the air pressure variations that it experiences
when we speak into it or play music into it. This sort of signal is called ananalogsignal (as opposed
to a digital signal) that can takeany valueand that varies over time.

Third, we combine the two. We use the varying voltage from the microphone as the relatively
slowly varyingamplitudeof carrier. The three signals (unmodulated carrier, modulating signal,
encoded/modulated carrier) are shown in figure 134. The final AM encoded voltage is used as
input to anamplifierthat drives the voltage supplied to thetransmission antenna, typically a tall
radio tower being driven at a power of tens to hundreds of kilowatts. The resultingradio signal–
electromagneticradiationof the sort we will study in the next chapter – propagates for long distances
at the speed of light and falls upon thereceiving antennaof your AM radio.

There it creates an alternating voltage with the same shape as the voltage applied to the transmit-
ting tower. However, this voltage is nowvery weak– the intensity of the radio wave diminishes with
roughly the square of the distance from the radio tower – and is mixed in with many otherequally
strong or even strongersignals from other radio sources (other radio stations, the sun, electrical