Radio-frequency basics
A radio link is a transmitter, an antenna and a receiver. Watch a 2.4 GHz wave leave a quarter-wave antenna, see how frequency sets the wavelength (λ = c ÷ f, about 12.5 cm), how AM, FM and QAM carry information, and how a receiver moving away loses 6 dB for every doubling of distance, measured in dBm. Finish with bandwidth: how wide a slice of frequencies a signal uses.
5 quick questions
Pick an answer to see why. Your score saves with your progress.
01What is the wavelength of a 2.4 GHz radio wave (c ≈ 300,000,000 m/s)?
λ = c ÷ f = 299,792,458 ÷ 2,400,000,000 ≈ 0.125 m, which is 12.5 cm.
02A quarter-wave antenna for 2.4 GHz should be roughly how long?
A quarter of the 12.5 cm wavelength is about 3.1 cm. Real antennas are trimmed a few per cent shorter.
03What does FM change in the wave?
FM keeps the height steady and makes the waves slightly tighter or looser. AM is the one that changes the height; QAM changes height and phase together.
04A transmitter sends 20 dBm. How many milliwatts is that?
dBm = 10·log10(P ÷ 1 mW). Every 10 dB is ten times the power, so 20 dBm is 10 × 10 = 100 mW.
05In free space, the receiver moves from 2 m to 4 m away. Roughly how does the received power change?
Free-space path loss grows by 20·log10(2) ≈ 6 dB each time the distance doubles, so a quarter of the power arrives.
Glossary
- Frequency
- How many times a wave repeats each second, measured in hertz (Hz). 1 GHz is a billion times a second.
- Wavelength (λ)
- The distance from one crest of a wave to the next: the speed of light divided by the frequency.
- Antenna
- A conductor sized to the wave that turns a radio-frequency current into a radio wave, and back.
- Quarter-wave monopole
- An antenna made of one rod a quarter of a wavelength long, standing on a metal ground plane.
- Modulation
- Changing a steady carrier wave (its height, frequency or phase) so that it carries information.
- QAM
- Quadrature amplitude modulation: each symbol has one of many height-and-phase shapes; 16 shapes carry 4 bits.
- dBm
- Power on a decibel scale counted from 1 milliwatt: 0 dBm = 1 mW, 20 dBm = 100 mW, -30 dBm = 1 µW.
- Bandwidth
- The width of the range of frequencies a signal uses, such as a 20 MHz Wi-Fi channel.
Notes and sources
- The 20 dBm (100 mW) transmitter and the simple 0 dBi antennas are a teaching model with round numbers, not one product's datasheet. A real quarter-wave monopole has some gain (a few dBi), which would raise every meter reading by the same amount.
- Wavelength λ = c / f with c = 299,792,458 m/s (exact): 12.5 cm at 2.4 GHz, so a quarter-wave rod is about 3.1 cm. The waves on the screen and on the table are slowed down billions of times; the rings are not drawn to scale.
- Path loss uses the free-space formula (Friis 1946; ITU-R P.525): 40.1 dB at 1 m and 2.4 GHz, plus 6.02 dB for every doubling of distance. Walls, furniture and people add more. The distance marks on the table are spaced by doubling, not to scale.
- AM 535–1705 kHz and FM 88–108 MHz are the ITU Region 2 (Americas) broadcast bands; Europe's FM band starts at 87.5 MHz. The QAM bit labels on the screen are one example mapping.
- NIST CODATA: speed of light in vacuum (exact)
- ITU-R P.525: Calculation of free-space attenuation
- Friis (1946): A Note on a Simple Transmission Formula, Proc. IRE
- MIT OCW 6.013: Electromagnetics and Applications (antennas)
- NIST SP 811: Guide for the Use of the SI (logarithmic quantities, decibel)
- ITU Radio Regulations (frequency allocations, Article 5)
- IEEE 802.11 (Wi-Fi) standard
- IEEE 802.11be (Wi-Fi 7): 4096-QAM, 320 MHz channels
- Python docs: math.log10
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