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RF Isolator S-Matrix | RF Isolator scattering matrix

This page describes RF Isolator S-Matrix (scattering matrix). It also covers basics of RF Isolator.

What is RF Isolator?

As we know RF Isolator is a 2-port microwave device which forwards the signal in one direction and blocks the signal in the other direction. It is used for wide variety of applications such as protection of test and measurement equipments, delicate devices such as MMIC amplifiers and attenuators etc. The figure-1 depicts working of RF Isolator. As shown RF signal can pass from port-1 to port-2 only with port-3 terminated. Following are the typical specifications of isolator device.
• Operating frequency range
• Isolation from port-2 to port-1
• Insertion Loss from port-1 to port-2
• VSWR (Voltage Standing Wave Ratio)

RF Isolator S-Matrix | RF Isolator scattering matrix As Isolator is a 2-port device, let us consider simple 2-port network as shown in the figure-2. Waves travelling towards n-port are ai = (a1, a2, ...., an) and waves travelling away from n-port are bi = (b1, b2, ...., bn). Relation between ai and bi can be expressed by following equations.
b1 = S11*a1 + S12*a2
b2 = S21*a1 + S22*a2 From the above S-matrix can be written as follows.
Isolator S-matrix =
|S11 S12 |
|S21 S22 |
Here, S11 is input reflection coefficient with output terminated by matched load, S21 is forward transmission from port-1(input) to port-2(output), S12 is reverse transmission from port-2 to port-1 and S22 is output reflection coefficient.

Here
➨S11 = b1/a1, S12 = b1/a2, S21 = b2/a1, S22 = b2/a2
The figure-2 depicts RF Isolator S-matrix i.e. Scattering matrix.