How do I calculate an axial ratio from phase difference?

[Tures_s]

Hello everyone, i design a polarizer with two port on HFSS, i plot the phase different between the two port and it's around 90°, but i want to know also the axial ratio, how do i calculate the axial ratio from the phase different for the polarizer?

 

[taimur1036]

To calculate the axial ratio of a polarizer from the phase difference between its two ports, you can use the following steps:

1. **Understand Axial Ratio:** The axial ratio (AR) is a measure of how well a polarizer maintains polarization purity. It's defined as the ratio of the major axis to the minor axis of the polarization ellipse.

2. **Calculate Phase Difference:** You've already calculated the phase difference between the two ports, which is approximately 90 degrees. This indicates that the polarizer is achieving a 90-degree phase shift between its two output ports for orthogonal polarizations.

3. **Convert Phase Difference to Axial Ratio:** The relationship between phase difference (φ) and axial ratio (AR) for a polarizer is given by:

\[
AR = \frac{1}{\sqrt{1 - \sin^2(\phi)}}
\]

In your case, since the phase difference is 90 degrees, you can substitute φ = 90° into the equation:

\[
AR = \frac{1}{\sqrt{1 - \sin^2(90°)}}
\]

\[
AR = \frac{1}{\sqrt{1 - 1}}
\]

\[
AR = \frac{1}{\sqrt{0}}
\]

Since you're dividing by zero, this calculation doesn't provide a meaningful result.

4. **Interpretation:** A phase difference of 90 degrees between the two ports of a polarizer typically indicates that the polarizer is working as intended to provide orthogonal polarization outputs. However, the axial ratio calculation in this case doesn't yield a meaningful value due to the mathematical limitation when dealing with a phase difference of exactly 90 degrees.

5. **Alternative Approach:** If you want to further characterize the polarizer's performance, you may need additional measurements or simulations. For example, you could analyze the S-parameters of the polarizer to understand its polarization properties more comprehensively, including axial ratio, cross-polarization, and return loss.

If you have access to simulation software like HFSS, you can perform additional analyses to gather more insights into the polarizer's behavior beyond just the phase difference between its ports.