To explain the answer, we need to understand the concept of image rejection ratio in a super heterodyne receiver and how it is affected by the quality factor of the antenna coupling circuit.

Image Rejection Ratio:
The image rejection ratio is a measure of how well a super heterodyne receiver rejects unwanted signals that are mirrored around the intermediate frequency (IF). These mirrored signals are known as image frequencies. The image rejection ratio is typically expressed in decibels (dB) and indicates the level of attenuation of the image frequency compared to the desired frequency.

Quality Factor of Antenna Coupling Circuit:
The quality factor (Q) of the antenna coupling circuit represents the selectivity or sharpness of the frequency response of the circuit. It is a measure of how well the circuit can differentiate between the desired frequency and nearby frequencies. A higher Q value indicates a narrower bandwidth and better selectivity.

Calculating Image Rejection Ratio:
The formula to calculate the image rejection ratio is given by:

Image Rejection Ratio (IRR) = 20 log10(Q)

Given that the quality factor (Q) of the antenna coupling circuit is 150, we can calculate the image rejection ratio as follows:

IRR = 20 log10(150)
IRR ≈ 20 × 2.176
IRR ≈ 43.52 dB

This means that the image rejection ratio for the given antenna coupling circuit is approximately 43.52 dB.

Finding Image Rejection Ratio at 20 MHz:
To find the image rejection ratio at 20 MHz, we need to calculate the frequency difference between the desired frequency (20 MHz) and the intermediate frequency (455 KHz).

Frequency difference = |20 MHz - 455 KHz|
= 19.545 MHz

Now, we can calculate the image rejection ratio at 20 MHz using the frequency difference and the image rejection ratio formula:

IRR at 20 MHz = IRR - 20 log10(Frequency difference/IF)

IRR at 20 MHz = 43.52 - 20 log10(19.545 MHz/455 KHz)
IRR at 20 MHz ≈ 43.52 - 20 log10(42.9451)
IRR at 20 MHz ≈ 43.52 - 20 × 1.633
IRR at 20 MHz ≈ 43.52 - 32.66
IRR at 20 MHz ≈ 10.86 dB

Therefore, the image rejection ratio at 20 MHz is approximately 10.86 dB.

Comparing with Given Options:
The closest option to the calculated image rejection ratio at 20 MHz is option 'D' with a value of 22.536 dB. However, this option does not match the calculated value. It seems there might be an error in the options provided.

In summary, the image rejection ratio at 20 MHz for the given antenna coupling circuit with a quality factor of 150 is approximately 10.86 dB, which does not match any of the given options.

F_si = f_s + 2IF