Physics · Electricity and magnetism · Grade 11

Radio communication and radar

How does sound “ride” on a radio wave, and how does radar see an aeroplane?

The situation

The Tashkent TV Tower (375 m high) spreads radio and television signals across the whole city. Dozens of stations' waves are in the air at the same time, yet when you turn the knob of a car radio only one of them is heard. And the radar at the airport “sees” an aircraft tens of kilometres away with invisible pulses. In 1928 it was in Tashkent that a moving picture was transmitted electronically. How are sound and pictures “loaded” onto a radio wave, how are they picked out in the receiver, and how does radar measure distance?

Topic

Radio communication and television. Radio station, modulation, radar and the television demonstrated in Tashkent in 1928

Key ideas

Modulation and detection
The simplest radio receiver
Radar

Formulas

u = U_{0} (1 + m \cos Ω t) \cos ω_{0} t

Amplitude modulation: lines at $f_{0}$ and $f_{0} \pm F$ in the spectrum, bandwidth $2 F$ .

u = U_{0} \cos (ω_{0} t + β \sin Ω t), β = \frac{Δ f}{F}, B \approx 2 (Δ f + F)

Frequency modulation and Carson's rule.

f_{0} = \frac{1}{2 π \sqrt{L C}}

The resonant frequency of the circuit: a station is chosen by turning the capacitor.

\frac{1}{f_{0}} ≪ R C \leq \frac{\sqrt{1 - m^{2}}}{2 π F m}

The detector filter: it smooths out the carrier, but does not “cut off” the sound.

R = \frac{c t}{2}, f_{D} = \frac{2 v_{r} f_{0}}{c}

Radiolocation: distance from the pulse's round-trip time, radial velocity from the Doppler shift.

Theory

What radio communication is based on

Oscillating charges radiate an electromagnetic wave, but for an antenna to radiate efficiently its size must be comparable with the wavelength: the wavelength of a 1 kHz electromagnetic wave is 300 km! That is why sound is “loaded” onto a high-frequency carrier wave — modulation. Each station works on its own frequency, and the receiver selects the one it needs. Transmitter: generator (carrier) → modulator (microphone signal) → amplifier → antenna. In 1895 A. S. Popov demonstrated a receiver consisting of a coherer with metal filings, an antenna and a bell; G. Marconi also developed the radiotelegraph in those years. Radiotelephone communication (the mobile phone): each device is both a transmitter and a receiver at the same time — for two-way (duplex) communication two different frequencies or alternating time slots are used.

Modulation: AM, FM and digital

In AM the amplitude of the carrier varies with the sound; if the depth is $m > 1$ the envelope is distorted (overmodulation). The spectrum has the carrier and two side lines $f_{0} \pm F$ : bandwidth $2 F$ . On medium waves the spacing between stations is 9 kHz. In FM the frequency of the carrier deviates by $Δ f$ and the amplitude does not change — it is more resistant to noise, but the bandwidth is wider: in FM radio $Δ f = 75$ kHz, which is why it works at 87.5–108 MHz. The FM spectrum is given by Bessel functions $J_{n} (β)$ : at $β \approx 2.4$ the carrier line almost disappears — try it. In digital communication 0 and 1 are transmitted: the simplest is frequency-shift keying (FSK), and modern systems change phase and amplitude together (QAM).

The simplest radio receiver and detection

The antenna carries the currents of all the stations. An oscillating circuit ( $L$ , $C$ ) responds strongly only to a signal at its resonant frequency: $f_{0} = 1 / (2 π \sqrt{L C})$ is changed by turning the plates of a variable capacitor; the greater the quality factor $Q$ of the circuit, the sharper the selection. But the average value of a modulated signal is zero — the diaphragm of an earphone does not “feel” millions of oscillations. The detector (a diode) passes only the half-waves in one direction, and the capacitor $C_{f}$ and the earphone resistance $R$ smooth out the carrier and pick out the envelope — the sound: detection (demodulation). If $R C$ is too small, the carrier ripple remains; if it is too large, the capacitor cannot follow the envelope and the sound is distorted (“diagonal clipping”). This is how a battery-free “crystal set” works.

Radiolocation and GPS

Radar sends a short radio pulse and waits for the echo reflected from the target: the distance is $R = c t / 2$ (the path is covered twice). A 1 µs delay corresponds to 150 m. The time between pulses limits the unambiguous range: $R_{m a x} = c / (2 f_{p u l s e})$ . The direction is found from the angle of the rotating antenna (the circular display). The wave reflected from a moving target has a Doppler shift in frequency: $f_{D} = 2 v_{r} f_{0} / c$ — traffic police radar and weather radar are based on this. The echo power falls as $1 / R^{4}$ . GPS (USA) and GLONASS (Russia) work on the reverse principle: from the arrival times of the signals of at least four satellites at a height of ~20 000 km, the receiver finds three coordinates and the error of its own clock. A 1 µs timing error equals a 300 m distance error — even corrections from the theory of relativity are applied to the satellite clocks.

Television: scanning the picture

A picture can be transmitted not all at once but line by line: the camera tube divides the picture into lines and turns the brightness of each point into an electrical signal; in the receiving cathode-ray tube an electron beam lights up the screen in the same order (scanning). Because of the persistence of vision, 25 frames per second look like continuous motion. With 625 lines × 25 frames: the line frequency is $f_{H} = 15 625$ Hz, the line period 64 µs. For fine detail the bandwidth of the video signal is measured in megahertz ( $\sim 6$ MHz) — that is why television works on metre and decimetre waves; these travel in straight lines, so tall television towers are built. For a colour picture three colour signals are added.

Tashkent — one of the birthplaces of television

According to many sources, on 26 July 1928 in Tashkent Boris Grabovsky and Ivan Belyansky, using the “Telefot” device, transmitted a moving picture (Belyansky's face on the screen) entirely electronically — without mechanical discs; this is considered one of the world's first electronic television transmissions. In those years other countries mainly tried mechanical television with a rotating disc with holes (a few dozen lines). In “TV” mode compare the mechanical 30-line picture with the 625-line picture. Modern radio communication: a cellular network divides an area into “cells”, each with a base station; frequencies are reused in cells that are not neighbours. Wi‑Fi, mobile internet and satellite communication use digital modulation, error-correcting codes and several antennas.

Did you know?

On 7 May 1895 in St Petersburg, at a meeting of the Russian Physical-Chemical Society, A. S. Popov demonstrated a radio receiver he had built. Its detector was a tube with metal filings — a coherer; later Popov used this as the basis of a “storm recorder” that registered lightning discharges. In some countries 7 May is celebrated as “Radio Day”.
According to many sources, on 26 July 1928 in Tashkent B. Grabovsky and I. Belyansky transmitted a moving picture electronically with the “Telefot” device — Belyansky's face was seen on the screen.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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