Properties of Directional Couplers

2020年5月13日

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The properties of an ideal directional coupler are as follows.

All the terminations are matched to the ports.
When the power travels from Port 1 to Port 2, some portion of it gets coupled to Port 4 but not to Port 3.
As it is also a bi-directional coupler, when the power travels from Port 2 to Port 1, some portion of it gets coupled to Port 3 but not to Port 4.
If the power is incident through Port 3, a portion of it is coupled to Port 2, but not to Port 1.
If the power is incident through Port 4, a portion of it is coupled to Port 1, but not to Port 2.
Port 1 and 3 are decoupled as are Port 2 and Port 4.

Ideally, the output of Port 3 should be zero. However, practically, a small amount of power called back power is observed at Port 3. The following figure indicates the power flow in a directional coupler.

Directional Coupler Indicating Powers

Where

$P_{i}$ = Incident power at Port 1
$P_{r}$ = Received power at Port 2
$P_{f}$ = Forward coupled power at Port 4
$P_{b}$ = Back power at Port 3

Following are the parameters used to define the performance of a directional coupler.

Coupling Factor $C$

The Coupling factor of a directional coupler is the ratio of incident power to the forward power, measured in dB.

C = 10 l o g 10 P i P f d B

Directivity $D$

The Directivity of a directional coupler is the ratio of forward power to the back power, measured in dB.

D = 10 l o g 10 P f P b d B

Isolation

It defines the directive properties of a directional coupler. It is the ratio of incident power to the back power, measured in dB.

I = 10 l o g 10 P i P b d B

Isolation in dB = Coupling factor + Directivity

Two-Hole Directional Coupler

This is a directional coupler with same main and auxiliary waveguides, but with two small holes that are common between them. These holes are $λ_{g} / 4$ distance apart where λg is the guide wavelength. The following figure shows the image of a two-hole directional coupler.

Two-hole Directional Coupler

A two-hole directional coupler is designed to meet the ideal requirement of directional coupler, which is to avoid back power. Some of the power while travelling between Port 1 and Port 2, escapes through the holes 1 and 2.