Coupler Theoretical Main-Line Loss Calculation
(AN-30-004)
1.
Introduction
The main-line loss of a coupler is defined as the loss between the input and
output ports. Theoretical loss is defined as that of a perfect (lossless)
coupler, for which the input power is the sum of the (main-line) output
power and the power at the coupled port. Therefore, the theoretical main-line
loss is dependent upon the fraction of the input power that is outputted at the
coupled port. The conversion between them can be expressed
mathematically. This application note derives the formula and provides a
conversion table.
2.
Derivation
A lossless coupler transfers all input power to the output and coupled ports:
Pin = Pout + Pcoupled
(1)
In practice, positive decibel values are given for main-line loss and coupling
(the fraction of the input power that is outputted at the coupled port):
ML (main-line loss in dB) = 10 log10(Pin / Pout), and
(2)
CPL (coupling in dB) = 10 log10 (Pin /Pcoupled)
(3)
With these three equations, the CPL to ML conversion can be obtained.
From equation (1), Pout/Pin = 1 – Pcoupled/Pin
(4)
From equation (3), Pcoupled /Pin = 10 –CPL/10
(5)
Substitute (4), and then (5), into (2):
ML = 10 log10 (Pin / Pout) = 10 log10 [1/(1 – Pcoupled/Pin)]
= 10 log10 [1/(1 – 10 –CPL/10 )]
AN-30-004
Rev.: A
M150261 (04/14/15) FileAN30004.doc
This document and its contents are the property of Mini-Circuits.
(6)
Page 1 of 3
3.
Insertion Loss vs. Coupling table
Coupling
dB
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
Insertion Loss
dB
3.021
2.570
2.205
1.903
1.651
1.438
1.256
1.101
0.967
0.850
0.749
0.661
0.584
0.517
0.458
0.405
0.359
0.319
0.283
0.251
0.223
0.198
0.176
0.157
0.140
0.124
0.110
0.098
Coupling
dB
17
17.5
18
18.5
19
19.5
20
20.5
21
21.5
22
22.5
23
23.5
24
24.5
25
25.5
26
26.5
27
27.5
28
28.5
29
29.5
30
AN-30-004
Rev.: A
M150261 (04/14/15) FileAN30004.doc
This document and its contents are the property of Mini-Circuits.
Insertion Loss
dB
0.088
0.078
0.069
0.062
0.055
0.049
0.044
0.039
0.035
0.031
0.027
0.024
0.022
0.019
0.017
0.015
0.014
0.012
0.011
0.010
0.009
0.008
0.007
0.006
0.005
0.005
0.004
Page 2 of 3
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AN-30-004
Rev.: A
M150261 (04/14/15) FileAN30004.doc
This document and its contents are the property of Mini-Circuits.
Page 3 of 3