The audio moves the frequency. The amplitude stays put.
Ten minutes of reading. Move the sliders, then the smeared carrier on the scope will make sense.
Frequency modulation in one picture
A larger audio amplitude pushes the carrier further from its rest frequency (larger deviation Δf). The audio frequency sets how many times a second the swing happens. Move the sliders: the carrier is crowded where the audio is high and spread out where it is low.
Why FM: noise, bandwidth and capture
Electrical noise adds to the amplitude of a signal. An FM receiver clips the amplitude (limiter) and watches only the frequency, so most noise is thrown away.
FM uses a wide band: broadcast FM has Δf = 75 kHz and channels 200 kHz apart. That width is what buys the noise immunity and room for music.
An FM receiver locks onto the stronger of two signals on the same channel and ignores the weaker one: the capture effect.
The FM transmitter
The oscillator tank sets the frequency
Both modulators use an LC oscillator. A parallel tuned circuit sets its frequency, f0 = 1 / (2π√(LC)). Add capacitance in parallel and the frequency falls; remove some and it rises. For a small change, Δf ≈ −(f0/2)(ΔC/C): a 1 % change of C moves the carrier about 0.5 %, which is 2.3 kHz at 455 kHz.
So to make FM we need a capacitor whose value follows a voltage. The plastic tuner on the trainer trims the oscillator tank; that is how you set the rest frequency to 455 kHz before adding audio.
Varactor modulator
A reverse biased diode has two conducting regions with an insulating depletion layer between them: a capacitor, C = εA/d. More reverse voltage widens the depletion layer (larger d), so C falls. A varactor is a diode made for this. The audio is added to its DC bias through a resistor, and an RF choke keeps the 455 kHz carrier out of the audio path.
The varactor sits across the tank. Audio up, reverse bias up, C down, frequency up. On the trainer the varactor modulator moves the carrier about 40 kHz per volt of audio peak, and its FM O/P is about 1 V p-p.
Reactance modulator
Here a transistor plays the capacitor. A capacitor C and a resistor R from the collector to the base shift the phase by about 90°: the collector current leads the collector voltage, which is exactly how a capacitor behaves. Seen from the tank, the transistor is an equivalent capacitance Ceq ≈ gmRC in parallel with it.
The audio on the base changes the bias and so gm, hence Ceq, hence the frequency. The DC supply is joined to ground through its large smoothing capacitor (less than a milliohm at these frequencies), which is why the manual can redraw the circuit with both supply lines connected. The trainer's reactance modulator moves about 30 kHz per volt, output about 0.8 V p-p.
The spectrum of FM: Bessel lines and Carson's rule
The total power never changes, it is only shared between the carrier and the sidebands. Raise β and watch the carrier line fall, vanish at 2.405 and come back with the opposite sign. The shaded band is Carson's bandwidth.
On the bench
To see the swing like Figure 12, trigger on the FM signal itself (CH2) at 1 µs/div. Every sweep starts on a rising edge, but at a different point of the audio cycle, so the first cycle lines up and the later ones land in different places. Turn the audio amplitude up and the smear grows. Triggered on the audio (CH1) at a slow time base, the carrier is a solid band instead.
What you should see
| Step | Settings | On the instruments |
|---|---|---|
| Audio check | CH1 on Audio O/P, 500 µs/div | sine from 200 Hz to 5 kHz, 0 to 2 V p-p |
| Carrier before tuning | CH2 on the modulator output, 1 µs/div | a sine a little away from 455 kHz; tune it to 455 kHz (period 2.2 µs) |
| Varactor, 1 V p-p audio | trigger on CH2, 1 µs/div | carrier swings ±20 kHz (40 kHz per volt peak); later cycles smear |
| Reactance, 1 V p-p audio | same | carrier swings ±15 kHz (30 kHz per volt peak) |
| Spectrum, 1 kHz audio | analyzer centre 455 kHz, span 30 kHz | carrier null near 120 mV p-p audio on the varactor (Δf = 2.4 kHz) |
| Counter on the FM output | reads the average, 455 kHz, whatever the deviation |
Values are those of the simulator model of the IT-4103. A real trainer differs a little from unit to unit; the way each control changes the picture is the same.
Check yourself
Q1In FM which parameter of the carrier varies directly with the message signal?
The instantaneous frequency. It moves away from the rest frequency in proportion to the instantaneous message voltage; the amplitude stays constant.
Q2Explain how FM is more immune to noise than AM.
Noise mostly changes the amplitude of the received signal. An AM detector follows the amplitude and so passes the noise on. An FM receiver removes amplitude changes with a limiter and its detector responds only to frequency, so most of the noise is rejected; a wider deviation improves this further.
Q3Give an equation for the varactor capacitance in terms of the plate area and the spacing.
C = εA/d, with A the junction area and d the depletion width. d grows with the reverse voltage (about as √(V_R + φ) for an abrupt junction), so C = C0 / √(1 + V_R/φ) falls as the reverse voltage rises.
Q4What is an RF oscillator? How does a parallel LC circuit act as an oscillator, and at what frequency?
An RF oscillator is an amplifier with positive feedback that produces a steady radio frequency sine wave. Energy swings between the inductor and the capacitor of the tank; the amplifier replaces the losses. It oscillates at f0 = 1 / (2π√(LC)).
Q5When the information voltage rises, how do the capacitance and the frequency change?
In the varactor modulator a higher audio voltage raises the reverse bias, so the varactor capacitance falls and the carrier frequency rises. (With the opposite polarity the frequency falls; either way the deviation follows the audio.)
Q6How does an RC circuit act as a phase shifter?
In a series RC driven by V, the current I = V / (R − jXc) leads V by θ = arctan(Xc / R). When Xc is much larger than R, θ approaches 90°. The phasor diagram shows V_R in phase with I and V_C lagging I by 90°.
Q7How does the RC phase shifter with the transistor frequency modulate the carrier?
The RC network feeds the base with a voltage 90° ahead of the collector voltage, so the collector current leads the collector voltage: the transistor looks like a capacitance gm·R·C across the tank. The audio on the base changes gm, the equivalent capacitance changes, and the tank frequency follows the audio.
Q8Mention two applications of FM.
FM broadcast radio (88 to 108 MHz) and the sound of analog TV; also two way radios, wireless microphones, and the voltage controlled oscillators of phase locked loops.