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Early radio crackled. Lightning, motors and electrical machines all added noise that came through the loudspeaker. Edwin Armstrong spent years on this problem and solved it with frequency modulation, FM. This post covers his life, how FM differs from AM, a worked example on the numbers behind an FM channel, and what a student can learn from how he worked.
Who was Edwin Armstrong?
The National Inventors Hall of Fame gives the essentials. Armstrong was born in New York City on 18 December 1890 and died on 1 February 1954. He earned a degree in electrical engineering from Columbia University in 1913. While still a student he invented the regenerative circuit, the first amplifying receiver and the first reliable continuous-wave transmitter. In 1918 he invented the superheterodyne circuit, a selective way of receiving and amplifying very weak high-frequency signals. His crowning achievement, in 1933, was wide-band frequency modulation. He was a professor of electrical engineering at Columbia and was inducted into the Hall of Fame in 1980.
The IEEE History Center biography adds that he studied at Columbia under Michael Pupin, and that he received the Edison Medal of the American Institute of Electrical Engineers and the Medal of Honor of the Institute of Radio Engineers. His last years were taken up by patent lawsuits.
How is FM different from AM?
A radio station sends a carrier wave at a fixed frequency and changes it to carry sound. In amplitude modulation, AM, the strength of the carrier rises and falls with the sound. In frequency modulation, the sound shifts the carrier's frequency slightly up and down instead, as the IEEE biography explains.
Much of the noise from lightning and electrical machines shows up as random bursts in a wave's strength. An AM receiver cannot tell those bursts from the sound, because strength is where the sound is stored. An FM receiver reads the sound from the frequency, so changes in strength matter much less. Armstrong found he needed a much wider band than AM stations used, but the reward, the IEEE biography says, was relative freedom from static and much higher sound fidelity.
What did his patent and paper show?
His US patent 1,941,066, Radio Signaling System, was filed on 30 July 1930 and granted on 26 December 1933. In May 1936 he published A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation in the Proceedings of the IRE. Its abstract describes the transmitting and receiving arrangements, the theory of how the noise reduction works, and test transmissions over the previous year from the National Broadcasting Company's experimental station on the Empire State Building to Westhampton on Long Island and Haddonfield in New Jersey. It also reported methods of multiplexing, sending more than one signal on a channel.
Worked example: the numbers behind an FM channel
The US rules, in 47 CFR 73.201, define the FM broadcast band as 88 MHz to 108 MHz, divided into 100 channels of 200 kHz each.
Band width: 108 − 88 = 20 MHz = 20,000 kHz.
Number of channels: 20,000 kHz ÷ 200 kHz = 100. That matches the rule.
Wavelength of a station at 100 MHz: λ = c/f = (3.0 × 10^8 m/s) ÷ (1.0 × 10^8 Hz) = 3.0 m.
For comparison, take a sample AM station at 1 MHz: λ = 3.0 × 10^8 ÷ 1.0 × 10^6 = 300 m. FM waves are a hundred times shorter, which is one reason FM antennas are small.
The IEEE biography says an FM channel is twenty times as wide as an AM channel. So an AM channel is 200 ÷ 20 = 10 kHz. FM trades bandwidth for quality, exactly the bargain Armstrong made.
Common mistakes:
Mixing prefixes. 1 MHz = 1,000 kHz = 10^6 Hz. Convert before dividing.
Thinking FM waves are not electromagnetic. Both AM and FM are radio waves travelling at c; only the way the sound is stored differs. Our post on the electromagnetic spectrum shows where they sit.
Confusing modulation frequency with carrier frequency. A 100 MHz station carries sound frequencies of only thousands of hertz.
Modulation is no longer in the rationalised NCERT Class 12 physics book, which now ends at semiconductor electronics, but c = fλ and the spectrum are central to it.
Why was FM slow to spread?
The IEEE biography describes the struggle. RCA's engineers were impressed, but the company was committed to AM and to television, so Armstrong developed and field-tested FM largely on his own. Commercial FM was authorised in 1940. After the war the band was moved to 88 to 108 MHz, which made about 400,000 existing receivers obsolete, and growth was slow until the late 1950s. To see how radio began, read our posts on Heinrich Hertz and Guglielmo Marconi.
Ideas about waves are often easier to see than read, and Fermi's Simulation Lab has interactive simulations for exactly that kind of idea.
What can a student take from his way of working?
Attack the problem everyone accepts. Static was treated as part of radio; he treated it as a problem to solve.
Accept a cost if it buys what matters. Wider channels looked wasteful, and they gave the quality.
Test in the real world. His 1936 paper reported long-distance transmissions, not only theory.
Try it now: find a local FM station's frequency and work out its wavelength with c = fλ.
