How does a quarter-wave stub create a notch?

An open-circuited quarter-wave stub connected in shunt across a transmission line presents a short circuit at its resonant frequency. At that frequency, all signal energy is diverted into the stub and reflected, creating a deep null in the transmission response. The stub length determines the notch frequency: L = lambda/4 = c/(4f sqrt(epsilon_eff)). The notch bandwidth is determined by the stub impedance relative to the main line: a higher-impedance stub produces a narrower notch. A 100-ohm stub on a 50-ohm line creates a notch bandwidth of about 10 to 15 percent. Multiple stubs at slightly different frequencies can create a wider rejection band, but a single stub provides the simplest and most predictable narrow notch.

What determines notch depth and bandwidth?

Notch depth (rejection at the center frequency) depends on the Q factor of the resonant element. A simple microstrip stub achieves 15 to 25 dB rejection with Q of 50 to 100. A coaxial cavity notch filter with Q of 5000 to 10000 achieves 40 to 60 dB rejection in a bandwidth as narrow as 100 kHz at 1 GHz. A crystal (quartz) notch filter can achieve Q of 50000 or more, providing 60+ dB rejection in a bandwidth of 10 to 20 kHz. The trade-off is always depth versus bandwidth versus size: higher Q means deeper and narrower rejection but requires a physically larger or more expensive resonator. Passband insertion loss is typically 0.5 to 2 dB depending on the technology and how close the passband edge is to the notch center.

When should I use a notch instead of a bandpass filter?

Use a notch filter when you need to remove one specific interfering frequency while passing everything else. A bandpass filter defines what you want to keep; a notch defines what you want to remove. For example, a wideband surveillance receiver covering 100 MHz to 6 GHz may need to reject a single strong FM broadcast transmitter at 101.5 MHz that overloads the front end. A notch at 101.5 MHz with 30 dB rejection solves the problem with less than 1 dB insertion loss at all other frequencies. A bandpass filter that rejects 101.5 MHz would need to be extremely narrow, adding significant passband loss and group delay distortion across the entire 6 GHz operating band.

Passive Components

Notch Filter

A wideband military receiver covering 30 MHz to 3 GHz sits 200 meters from a 10 kW FM broadcast transmitter at 98.1 MHz. The FM signal arrives at −10 dBm, overwhelming the receiver's LNA (which compresses at −20 dBm) and generating intermodulation products across the entire band. A cavity notch filter tuned to 98.1 MHz with 40 dB rejection reduces the FM signal to −50 dBm, well within the LNA's linear range. The notch bandwidth is only 500 kHz, so frequencies above 98.35 MHz and below 97.85 MHz pass with less than 0.3 dB loss. One precision rejection notch saves the entire receiver from desensitization without sacrificing wideband coverage.

Category: Passive Components

Function: Reject narrow band, pass all else

Key Spec: Rejection depth, notch BW, IL

Notch Filter Technologies

Technology	Q Factor	Rejection	Notch BW	IL (passband)	Frequency Range
Microstrip stub	50 to 100	15 to 25 dB	10 to 15%	0.3 to 0.5 dB	0.5 to 30 GHz
Lumped LC trap	50 to 200	20 to 35 dB	2 to 10%	0.3 to 1 dB	1 MHz to 3 GHz
Coaxial cavity	5,000 to 10,000	40 to 60 dB	0.01 to 0.1%	0.5 to 1.5 dB	30 MHz to 6 GHz
Crystal (quartz)	30,000 to 100,000	50 to 70 dB	0.001 to 0.01%	1 to 3 dB	1 to 200 MHz
YIG tunable	1,000 to 5,000	40 to 50 dB	0.05 to 0.2%	1 to 2 dB	0.5 to 40 GHz

Quarter-wave open stub notch frequency:
f_notch = c / (4L × √ε_eff)

Notch bandwidth (3 dB):
BW = f_notch / Q
Cavity at 1 GHz with Q = 5000: BW = 200 kHz

Rejection at center:
A_notch ≈ 20·log(1 + 2Q·Z_stub/Z₀) dB (for shunt stub)

Common Questions

Frequently Asked Questions

How does a stub create a notch?

An open λ/4 stub presents a short circuit at resonance, diverting signal energy. Length sets frequency. Stub Z relative to line Z sets bandwidth. 100 Ω stub on 50 Ω line: ~10 to 15% notch BW, 15 to 25 dB rejection.

What controls depth and bandwidth?

Q factor of the resonator. Stub: Q ~100, 20 dB, wide. Cavity: Q ~5000, 50 dB, narrow. Crystal: Q ~50000, 60+ dB, extremely narrow. Higher Q = deeper + narrower but larger/costlier. Passband IL: 0.5 to 2 dB.

Notch vs. bandpass?

Notch removes one frequency, passes everything else. Bandpass passes one band, rejects everything else. Use a notch when one interferer threatens a wideband receiver. A bandpass would add loss and distortion across the full operating band.

Related Terms

← Noise Temperature OFDM →

Filter Design

Notch Filter Designer

Enter interference frequency, required rejection depth, and acceptable passband loss. Compare stub, cavity, and crystal implementations for your application.

Design a Notch