Signals & Wireless (RF)
How to filter a transmitter's harmonics with an LC low-pass
A transmitter's harmonics are copies of its signal at two, three and more times its frequency, made by the amplifier's imperfections. On the air they land on other people's channels, so they must be removed before the antenna. The usual fix is an LC low-pass filter: a coil in the signal's path and a capacitor from the antenna side to ground, with its corner just above the wanted frequency.
Where harmonics land
A perfect sine has one frequency. Bend it even slightly, as any real amplifier does, and you add components at whole multiples:
- A 10 MHz transmitter also sends some 20 and 30 MHz.
- One on 7 MHz leaks its second harmonic at 14 MHz.
Those may be someone else's band, which is why radio regulators set strict limits on them.
Coil blocks, capacitor shorts
The coil's reactance, 2π f L, rises with frequency, so it blocks the harmonics more than the signal. The capacitor's, 1 ÷ (2π f C), falls, so it shorts the harmonics to ground more than the signal. With 0.75 µH and 300 pF:
| Frequency | Coil in the path | Capacitor to ground |
|---|---|---|
| 10 MHz | 47 Ω | 53 Ω |
| 30 MHz | 141 Ω | 18 Ω |
At the signal both are mild; at the third harmonic the coil is a wall and the capacitor a near short.
Put the corner just above the signal
The 50 Ω antenna damps the peak there, so 10 MHz passes whole while 20 MHz comes out at about a third and 30 MHz at an eighth.
Live experiment
Clean up the wave
The transmitter sends 10 MHz with a second harmonic at 30 % and a third at 20 %. A 0.75 µH coil sits in the path and a capacitor runs from the antenna side to ground. 10 pF barely filters; 300 pF passes 10 MHz whole and cuts 20 MHz to about a third and 30 MHz to an eighth; 1 nF cuts the signal too.
“Clean the transmitter” is lesson 2 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the one before it first.
Get the corner wrong and it fails either way. With 10 pF it sits near 58 MHz and the harmonics sail through. With 1 nF it drops to about 6 MHz, and the 10 MHz signal itself comes out at under half.
Twelve decibels an octave
Well above the corner, every doubling of frequency cuts the output to a quarter: 12 dB per octave, two reactive parts, two slopes. Add another coil and capacitor and it falls at 24 dB per octave. Real transmitter filters often chain five or seven parts for a steep wall just above the band.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“Clean the transmitter” is lesson 2 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the one before it first.
Or start from the very first lesson, no account neededPractice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: Shorts the high frequencies to ground, where they go no further. A capacitor's reactance falls with frequency: at 30 MHz the 300 pF is 18 Ω to ground, a near short. The coil blocks; the capacitor shorts. Together they're a two-part wall.
- Why not “Nothing: it's the coil that filters”? The coil blocks the harmonics, and the capacitor shorts what gets past it to ground. Both do the filtering.
- Why not “Blocks the low frequencies”? A capacitor to ground passes more as frequency rises, so it takes away the high frequencies, not the low ones.
- Why not “Boosts the signal”? A capacitor can't add energy. It only diverts some of the signal to ground.
Show the answer
Answer: Its corner drops to about 6 MHz, so it cuts the 10 MHz signal too. More capacitance pulls the corner down: with 0.75 µH, 1 nF puts it near 6 MHz, and 10 MHz comes out at under half. The corner has to sit just above the signal: 300 pF puts it near 11 MHz.
- Why not “It makes the harmonics louder”? A bigger capacitor to ground cuts the harmonics harder. It's the wanted signal that suffers.
- Why not “The coil burns out”? Nothing here overloads the coil. The trouble is where the corner frequency lands.
- Why not “1 nF passes everything”? 1 nF is a low reactance at radio frequencies, so it diverts a lot to ground. It filters too much, not too little.
Show the answer
Answer: Sail through: a series capacitor blocks low frequencies, not high. In series, a capacitor's falling reactance lets the high frequencies through more easily. To stop them it must be a path to ground.
- Why not “Are cut the same”? Moved into the path, it stops shorting anything to ground, so it can't cut the harmonics the same way.
- Why not “Are cut harder”? In series, a capacitor's reactance falls as frequency rises, so it passes the harmonics more easily, not less.
- Why not “Are boosted”? A series capacitor can't add energy to any frequency. It just stops blocking the high ones.
“Clean the transmitter” is lesson 2 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the one before it first.
Questions people ask
What are harmonics in a radio transmitter?
Weaker copies of the signal at whole multiples of its frequency: a 10 MHz transmitter also puts out some 20 MHz, 30 MHz and so on. They come from the amplifier not being perfectly linear, which bends the sine wave slightly out of shape.
Why is an LC low-pass better than an RC one for a transmitter?
An RC filter turns signal into heat in its resistor, which a transmitter can't afford. A coil and a capacitor store and return energy instead of burning it, so the wanted signal passes almost without loss, and two reactive parts fall twice as steeply as one.
How many sections does a harmonic filter need?
Each coil-and-capacitor pair adds about 12 dB per octave above the corner. One pair cuts the second harmonic only modestly, so practical transmitter filters, like those in amateur radio kits, often use five or seven parts in a row to meet the limits on unwanted emissions.
Related topics
- Low-pass filter explainedA resistor and a capacitor that pass the bass and fade the treble, and where the cutoff sits.
- How an LC band-pass filter picks one stationA coil and a capacitor in the signal's path cancel at one frequency, and fight every other.
- Decibels explaineddB as a ratio on a log scale: 10 log for power, 20 log for voltage, and why gains just add.
- How to calculate antenna lengthWavelength is c ÷ f: a quarter of it makes a good antenna, and a loading coil tunes one that's too short.