Coaxial Stub Length (λ/4)
l = c / (4 × f)
Quick answer
This calculator solves l = c / (4 × f) for Stub Length. With Frequency 10 MHz, the result is 7.495 m. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A quarter-wave coaxial stub is a length of transmission line used as a frequency-selective filter or impedance transformer. An open-circuited quarter-wave stub presents a short circuit at its resonant frequency and can be used as a notch filter to reject interference. A short-circuited quarter-wave stub presents an open circuit at resonance and passes the desired signal. Stubs are commonly used in amateur radio duplexers, harmonic filters, and phasing harness systems for antenna arrays.
Variables
- l — Physical stub length (m)
- f — Center frequency (Hz)
Practical Notes
The physical length must be multiplied by the velocity factor of the coaxial cable used. Common velocity factors: RG-58 (solid PE) = 0.66, RG-8X (foam PE) = 0.78, RG-213 (solid PE) = 0.66, LMR-400 (foam PE) = 0.85. Quarter-wave stubs have a bandwidth that depends on the cable impedance and the source/load impedances. Multiple stubs can be cascaded for sharper filtering.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| l | Stub Length | m | mm, cm, m, km |
| f | Frequency | MHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Frequency 10 MHz
- 2. The relation: l = c / (4 × f)
- 3. Substitute: f = 10 MHz
- 4. Result: Stub Length = 7.495 m
Worked examples
Minimum range
Given: Frequency 100 kHz
Result: Stub Length = 0.7495 km
Low range
Given: Frequency 1 MHz
Result: Stub Length = 74.95 m
Typical
Given: Frequency 10 MHz
Result: Stub Length = 7.495 m
High range
Given: Frequency 100 MHz
Result: Stub Length = 0.7495 m
Maximum range
Given: Frequency 1 GHz
Result: Stub Length = 7.495 cm
Solving for each variable
Solve for Stub Length
Frequency 100 kHz → 0.7495 km
Solve for Frequency
Stub Length 1 mm → 74.95 GHz
How Stub Length changes with Frequency
| Frequency (input) | Stub Length (result) |
|---|---|
| 1 MHz | 74.95 m |
| 2.5 MHz | 29.98 m |
| 5 MHz | 14.99 m |
| 7.5 MHz | 9.993 m |
| 10 MHz | 7.495 m |
| 15 MHz | 4.997 m |
| 20 MHz | 3.747 m |
| 40 MHz | 1.874 m |
| 70 MHz | 1.071 m |
| 100 MHz | 0.7495 m |
The same result in other units
| Unit | Value |
|---|---|
| mm | 7495 |
| cm | 749.5 |
| m | 7.495 |
| km | 0.007495 |
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<p><a href="https://vbatpower.com/formulas/coax-stub-length/">Coaxial Stub Length (λ/4)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Coaxial Stub Length (λ/4)?
Use l = c / (4 × f). With Frequency 10 MHz, Stub Length works out to 7.495 m.
What is the formula for Coaxial Stub Length (λ/4)?
The formula is l = c / (4 × f). A quarter-wave coaxial stub is a length of transmission line used as a frequency-selective filter or impedance transformer.
How do you find Frequency when you know the other values?
Rearrange for Frequency: with Stub Length 1 mm, Frequency is 74.95 GHz.
What units does Coaxial Stub Length (λ/4) use?
Stub Length is shown in mm, cm, m, km. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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