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Transmission and Reception of Radio Waves

Sound is a slow signal that cannot travel far on its own. A radio station puts it on a fast carrier wave by modulation: in amplitude modulation (AM) the carrier's height follows the sound. The wave leaves a transmitting antenna as a radio wave. At home, the antenna catches many stations at once; a tuned LC circuit with f = 1/(2π√LC) picks one. A diode and a filter then demodulate it, taking the sound back out of the carrier, and the speaker plays it.

🎬 Step-by-step story

  1. This orange wave is a sound signal. It wiggles slowly, only some thousands of times a second. On its own it is too slow and too weak to be sent far through the air.
  2. A radio station makes a second wave: the carrier (blue). It wiggles very fast, hundreds of thousands of times a second. This wave can travel far, but it carries no sound yet.
  3. Modulation. The station makes the carrier's height follow the sound. Where the sound is high, the carrier is tall. The yellow outline (the envelope) now has the shape of the sound.
  4. Transmission. Three stations send out their own carriers on different frequencies. The receiving antenna on the right catches all of them at once, all mixed.
  5. Tuning. A tuned LC circuit picks one station. Move the slider for the capacitor C: the circuit's own frequency f₀ changes, and only the station that matches f₀ comes out strong.
  6. Demodulation. A diode cuts the lower half of the wave. A filter smooths out the fast wiggles. What is left is the sound again, and the speaker plays it. Try the buttons to go back and forth.

Tip: drag the 3D scene to turn it. Use two fingers to zoom.

🤔 Common doubts, cleared

Why can we not just send the sound itself through the air as a radio wave?

Sound signals are slow, so the antenna would need to be kilometres long, they radiate poorly, and every station would be on the same frequencies. A fast carrier solves all three.

Is the carrier wave itself the sound?

No. The carrier alone is a steady wave with no message. The sound is only in the changes of its height.

Does the speed of the carrier change in AM?

No. Only the height (amplitude) changes. The frequency of the carrier stays the same.

Why do we not hear all stations at once?

All stations reach the antenna, but the tuned circuit responds strongly only to one frequency. Others are very weak.

Why does a bigger capacitor tune to a lower frequency?

f₀ = 1/(2π√(LC)). A bigger C makes the product LC bigger and the frequency smaller. Slide C to see it.

Why do we need a diode in the detector?

The modulated wave goes equally above and below zero, so its average is zero. The diode removes the lower half, so the filter can follow the top outline, which is the sound.

Radio waves and why we need a carrier

Radio waves are electromagnetic waves with frequencies from a few kilohertz up to several gigahertz. They are made when charges move to and fro in an antenna. They travel at the speed of light, c = 3 × 10⁸ m/s, and f × λ = c.

Sound from a voice or music has a low frequency, about 20 Hz to 5 kHz in radio. We do not send it directly, for three reasons:

  1. Antenna size. A good antenna is about λ/4 long. At 5 kHz, λ = 60 km, so the antenna would be 15 km long! At 1 MHz, λ = 300 m and the antenna is only 75 m.
  2. Weak radiation. Low-frequency waves are radiated very poorly.
  3. Mixing. If every station sent sound directly, all of them would arrive on the same frequencies and no one could separate them.

So the sound (the message signal) is put on a high-frequency carrier wave. Each station has its own carrier frequency.

Modulation: putting sound on the carrier

Modulation means changing one property of the carrier in step with the message. In amplitude modulation (AM) the amplitude of the carrier follows the signal; its frequency stays the same. In frequency modulation (FM) the frequency of the carrier follows the signal; the amplitude stays the same.

For AM, with carrier amplitude Ac and signal amplitude Am:

Modulation index μ = Am / Ac, and the modulated amplitude is Ac(1 + μ cos ωmt).

For good sound μ must be 1 or less. If μ is more than 1, the wave is over-modulated and the sound is distorted.

An AM wave with carrier fc and a signal of frequency fm contains three frequencies: fc − fm, fc and fc + fm. The two extra ones are the sidebands. The band of frequencies taken by one station (bandwidth) is 2fm. This is why stations are placed a few kHz apart (9 or 10 kHz in AM).

Transmission

A transmitter has an oscillator that makes the carrier, a modulator that mixes in the sound from the microphone, an amplifier to make the signal strong, and a transmitting antenna. The antenna sends the modulated wave out as an electromagnetic wave. Radio waves spread in all directions, and the signal gets weaker as it goes farther.

Medium-wave AM signals follow the ground and also reflect from the ionosphere at night, so they can be heard far away after sunset. FM and TV signals travel in nearly straight lines, so their towers are tall.

Reception and tuning

The receiving antenna catches the waves of every station as tiny, mixed voltages. We need to pick the one we want. This is done by tuning.

A tuning circuit is a coil L and a variable capacitor C joined together. It has its own frequency

f₀ = 1/(2π√(LC))

The circuit responds strongly to waves of frequency f₀ (resonance) and very weakly to others. By turning the knob, C changes, f₀ changes, and the circuit matches another station. Turn to a bigger C and f₀ becomes smaller.

The signal picked is very small. An amplifier makes it bigger before the next step.

Demodulation: taking the sound back out

Demodulation (also called detection) removes the carrier and recovers the message. In AM it takes two small parts:

  1. A diode lets current pass in one direction only. It cuts away the lower half of the wave (rectification).
  2. A filter (a capacitor with a resistor) smooths the fast wiggles of the carrier. It follows the outline of the wave, which is the sound.

The output is the low-frequency signal again. It is amplified and given to a loudspeaker, which turns it into sound.

Summary of a radio: antenna → tuner → amplifier → detector → audio amplifier → speaker.

Try it: a practical

Try it: In the 3D, press Waves. Drag the loudness (depth) slider to 1 and then down to 0.1. Does the carrier's outline still follow the sound? Next press Tune and move C. Find the value at which Station A is loudest. Predict first: does a larger C give a larger or smaller f₀? (Smaller.) At home: switch on an AM radio between stations and listen to the hiss. Then slowly turn the dial and notice how a station suddenly becomes clear, as the tuned circuit matches its frequency.

Key formulas and definitions

Worked examples

1. An AM station sends at 1000 kHz. Find the wavelength of its radio waves and a suitable antenna length (λ/4).

λ = c/f = 3 × 10⁸ / 1 × 10⁶ = 300 m. Antenna ≈ λ/4 = 75 m.

2. Why can speech at 4 kHz not be sent directly with a reasonable antenna?

λ = 3 × 10⁸ / 4000 = 75 000 m, so λ/4 ≈ 19 km. That is far too long. Modulating a high-frequency carrier needs a much shorter antenna.

3. A carrier of amplitude 10 V is modulated by a signal of amplitude 6 V. Find the modulation index.

μ = A_m / A_c = 6 / 10 = 0.6. This is less than 1, so there is no distortion.

4. A 1000 kHz carrier is modulated by a 2 kHz tone. Which frequencies are in the wave? Find the bandwidth.

f_c − f_m = 998 kHz, f_c = 1000 kHz, f_c + f_m = 1002 kHz. Bandwidth = 2 f_m = 4 kHz.

5. A tuning circuit has L = 250 µH and C = 100 pF. To what frequency is it tuned?

f₀ = 1/(2π√(LC)). LC = 2.5 × 10⁻⁴ × 1 × 10⁻¹⁰ = 2.5 × 10⁻¹⁴. √ = 1.58 × 10⁻⁷. f₀ = 1/(2π × 1.58 × 10⁻⁷) = 1.0 × 10⁶ Hz = 1.0 MHz.

6. With L = 200 µH, what value of C tunes the radio to 600 kHz?

C = 1/(4π²f²L) = 1/(4π² × (6 × 10⁵)² × 2 × 10⁻⁴) = 3.5 × 10⁻¹⁰ F, about 350 pF.

Common mistakes

Practice quiz

1. Putting a message signal on a carrier wave is called:
2. In AM, which property of the carrier follows the signal?
3. A radio is tuned to a station when:
4. In the detector, the diode:
5. A 6 V signal modulates a 12 V carrier. The modulation index is:

Practice: answer these yourself

Type or choose your answer, then press Check. Use a hint if you are stuck; the full solution appears after you answer.

Frequently asked questions

What is modulation in simple words?

It is a way to put a slow message (like speech) on a fast wave (the carrier), so that the message can travel far through the air.

How does a radio choose one station?

Its LC circuit has a frequency f₀ that you can change with a variable capacitor. When f₀ equals the carrier frequency of a station, the circuit resonates and that station comes out strongly.

What does demodulation do?

It removes the high-frequency carrier from the received wave and brings back the original sound signal, using a diode and a filter.

Where this is taught

China高二Selective 2 Ch.4 EM oscillations and waves

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