Signals & Wireless (RF)
How an LC notch filter removes one frequency
A notch filter removes one narrow band of frequencies and passes the rest. The simplest RF notch is a trap: a coil and a capacitor in series, hung from the signal line to ground. At their resonant frequency the coil's and capacitor's reactances cancel, the trap becomes nearly a short, and that frequency goes to ground instead of to the receiver. Away from resonance the trap is just a reactance, a load on the line but not a short.
Resonance
A coil's reactance rises with frequency and a capacitor's falls. At one frequency they're equal and opposite, and the series pair adds up to almost nothing: only the coil's own wire resistance is left.
Calculate the capacitor
Rearrange for C:
A loud station at 1.5 MHz is drowning out the 1 MHz one you want. With a 10 µH coil, C = 1 ÷ (4π² × (1.5 × 10⁶)² × 10⁻⁵) ≈ 1.13 nF.
What happens to the station you want
At 1 MHz the coil is 63 Ω and the capacitor −141 Ω, leaving about 78 Ω of capacitive reactance from the line to ground. With a 50 Ω source and a 50 Ω receiver, about 48 % of the 1 MHz signal arrives: hardly less than the 50 % the source's own resistance leaves with no trap at all. The interferer at 1.5 MHz drops to 0.7 %.
| Capacitor | Trap tuned to | Effect |
|---|---|---|
| 10 nF | 500 kHz | Traps a frequency nobody uses |
| 2.53 nF | 1 MHz | Swallows the station you want |
| 1.13 nF | 1.5 MHz | Removes the interferer, keeps yours |
Live experiment
Trap the loud station
Your station is at 1 MHz and a loud interferer at 1.5 MHz. A 10 µH coil and a capacitor hang from the line to ground. Pick the capacitor: 10 nF traps 500 kHz where nobody is, 2.53 nF swallows your own station, 1.13 nF leaves 0.7 % of the interferer. Then move the LC into the line.
“Trap the interferer” is lesson 1 of 6 in Oscillator Outcrop, Signals & Wireless (RF) World 2. Free with an account. Lessons unlock in order, so you’ll do the 7 before it first.
Same parts, opposite job
How narrow is the notch?
Stations close to the notch get dimmed too, more the closer they are. How sharp the notch is depends on the coil's own resistance and on the impedance of the line it shorts: the lower the coil's resistance, the deeper and narrower the trap. Here the trap leaves 0.7 % of the interferer; a better coil leaves less still.
Where traps are used
Old TV aerials carried traps to cut a strong local transmitter that swamped the rest. Receivers trap their own intermediate frequency out of the antenna input, and transmitters trap a harmonic that would land on someone else's band. At audio frequencies the same idea removes mains hum, usually with an active or digital notch rather than a coil.
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.
“Trap the interferer” is lesson 1 of 6 in Oscillator Outcrop, Signals & Wireless (RF) World 2. Free with an account. Lessons unlock in order, so you’ll do the 7 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: About 1.5 MHz. 1 ÷ (2π√(10 µH × 1.13 nF)) ≈ 1.5 MHz. There the coil and capacitor cancel and the line is shorted to ground.
- Why not “DC”? At DC the capacitor is an open circuit, so the trap passes nothing to ground.
- Why not “About 500 kHz”? 500 kHz is where the trap sits with 10 nF. Less capacitance moves the resonance up.
- Why not “About 1 MHz”? 1 MHz with a 10 µH coil needs about 2.53 nF. With only 1.13 nF the resonance is higher.
Show the answer
Answer: A reactance of about 78 Ω to ground: the station loses some, not all. Off resonance the two reactances don't cancel: −j78 Ω left over, a load on the line but not a short. About half the station arrives.
- Why not “A resistor”? What's left off resonance is reactance, not resistance: it stores energy instead of turning it into heat.
- Why not “Still a short”? The coil and capacitor only cancel at resonance, 1.5 MHz. At 1 MHz about 78 Ω is left over.
- Why not “An open circuit”? A series LC is open only at DC. At 1 MHz it's about 78 Ω of capacitive reactance.
Show the answer
Answer: It's a short in the line: the interferer passes perfectly. In the line, resonance is a clear path: that's the band-pass. To remove a frequency the short has to go to ground.
- Why not “The receiver is shorted”? Nothing connects to ground now. The LC in series is a near-zero impedance in the signal path.
- Why not “It's blocked”? In the line, resonance is the easiest path, so 1.5 MHz is the frequency that passes best.
- Why not “Nothing changes”? Moving the LC from the line-to-ground position into the line swaps its job from trap to band-pass.
“Trap the interferer” is lesson 1 of 6 in Oscillator Outcrop, Signals & Wireless (RF) World 2. Free with an account. Lessons unlock in order, so you’ll do the 7 before it first.
Questions people ask
What is the difference between a notch filter and a band-stop filter?
A notch is a narrow band-stop: it removes one frequency, or a thin slice around it, and passes everything else. A band-stop filter can remove a wider range. A series LC trap is the simplest notch.
How do I calculate the capacitor for an LC trap?
Pick the coil, then C = 1 ÷ (4π² × f² × L). To trap 1.5 MHz with a 10 µH coil, C = 1 ÷ (4π² × (1.5 × 10⁶)² × 10⁻⁵), about 1.13 nF. Use a trimmer or a close standard value and tune it on the bench.
Can an LC notch remove 50 or 60 Hz mains hum?
In principle, but the parts get huge: trapping 50 Hz with a 1 H coil needs about 10 µF. Audio and measurement gear use an active twin-T notch, or a digital notch in software, instead.
Related topics
- LC resonant frequency explainedA coil and a capacitor swapping energy at one frequency: f₀ = 1 ÷ (2π√(LC)), tanks and tuning.
- What is impedance?Resistance and reactance combined: why 3 kΩ and 4 kΩ make 5 kΩ, and what phase means.
- Capacitive and inductive reactance explainedWhy a capacitor passes treble and a coil passes bass: X_C, X_L and Ohm's law for AC.
- Amplitude modulation (AM) explainedTurn a carrier's height up and down with a voice: modulation depth, sidebands, and why past 100% it tears.