Directional Coupler Calculator
Coupling factor, directivity and isolation, the power at every port, and how much directivity limits a return loss reading.
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Worked example: a 20 dB coupler on a 100 W transmitter
Through port: 49.90 dBm
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How it works
Coupling factor, directivity and isolation
A directional coupler passes most of the power on a line to its through port and taps a sample of the power travelling one way to its coupled port. The coupling factor is how far that sample sits below the input, in dB. Directivity is how far the sample sits above what leaks to the isolated port, so it sets how well the coupler tells forward from reflected power, and isolation, from the input to the isolated port, is coupling plus directivity.
The tapped power comes off the main line, so even a lossless coupler has a through loss, and a real one adds its dissipative loss on top. When a coupler is used to measure return loss, the leakage set by its directivity adds to the reflected sample, in or out of phase, so a reading stands for a range of true return loss.
C = P₁ − P₃
D = P₃ − P₄
I = P₁ − P₄ = C + D
L = P₁ − P₂, at least Lmin = −10 log₁₀(1 − 10^(−C/10))
Γ = 10^(−RL/20); true Γ = Γmeas ± Γdir, with Γdir = 10^(−D/20)
- P₁, P₂, P₃, P₄
- power at the input, through, coupled and isolated ports, in dBm
- C
- coupling factor, in dB
- D
- directivity, in dB
- I
- isolation, in dB
- L, Lmin
- through (insertion) loss, and its lossless minimum, in dB
- Γ, RL
- magnitude of the reflection coefficient, and the return loss in dB
Worked example
Worked example: a 20 dB coupler on a 100 W transmitter
A 100 W transmitter, +50 dBm, feeds its antenna through a 20 dB coupler with 25 dB directivity and a 0.10 dB datasheet insertion loss.
| Step | Working | Result |
|---|---|---|
| Coupled port | 50 − 20 | 30.00 dBm |
| Isolation | 20 + 25 | 45.00 dB |
| Isolated port | 50 − 45 | 5.00 dBm |
| Lossless through loss | −10 log₁₀(1 − 10^(−20/10)) | 0.04 dB |
| Through port | 50 − 0.10 | 49.90 dBm |
The coupled port takes 1 per cent of the input power, so even a lossless 20 dB coupler loses 0.04 dB on the through path; the other 0.06 dB of the datasheet loss, about 1.27 W, is dissipated in the coupler. A 10 dB coupler on the same line would put 40.00 dBm on the coupled port and lose at least 0.46 dB, and a 3 dB coupler at least 3.02 dB.
FAQ
Frequently asked questions
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What is the coupling factor of a directional coupler?
The coupling factor, or coupling, is how far the power at the coupled port sits below the input power, in dB: C = P₁ − P₃. A 10 dB coupler sends 10 per cent of the input power to the coupled port, a 20 dB coupler 1 per cent and a 30 dB coupler 0.1 per cent. Some datasheets give it as a negative number, such as −20 dB; that is the same 20 dB coupler, and the calculator takes it as a positive number.
How is the coupled port power calculated?
The coupled port power is the input power minus the coupling. A 10 dB coupler taps a sample 10 dB below the input, so a +43 dBm input gives a +33 dBm coupled level.
Why does the through port lose power even in a perfect coupler?
The power that reaches the coupled port comes off the main line. Even a lossless coupler therefore has a through loss of −10 log₁₀ (1 − 10^(−C/10)), which is small for loose coupling (about 0.04 dB for 20 dB) and large for tight coupling (about 3 dB for 3 dB). A real coupler adds its dissipative loss on top.
What is the difference between coupling, directivity and isolation?
Coupling is how much power the coupler taps to the coupled port. Directivity is how well it separates forward from reflected power, which sets the quality of any measurement it makes. Isolation is the total loss from the input to the isolated port and equals coupling plus directivity, so any two define the third.
How does coupler directivity affect a return loss measurement?
Leakage set by the directivity adds to the reflected sample, so a reading corresponds to a range of true values rather than a single number. For example, a 20 dB reading through a coupler with 25 dB directivity could be anywhere from about 16 to 27 dB of true return loss. The narrower you need that range, the further the directivity must exceed the return loss you are measuring; the calculator shows the range so you can judge it.
Who is this tool for?
It is for systems integrators and RF technicians who use off the shelf couplers in a signal path. It covers port levels, part selection and measurement accuracy. It does not cover the design of the coupler itself.
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