Question

In a Broadcast superheterodyne receiver having no RF amplifier, the loaded Q of the antenna coupling circuit (at input of mixer) is 100. If the intermediate frequency (IF) is 455 KHz, calculate the image frequency (f_si) and its rejection ratio (α) at 1000 KHz.
1. f_si = 1190 KHz and α = 1.386
2. fsi = 1455 KHz and α = 138.6
3. fsi = 1910 KHz and α = 1.386
4. fsi = 1910 KHz and α = 138.6

Answer 1

Correct Answer - Option 3 : fsi = 1910 KHz and α = 1.386

Concept:

Image frequency: The frequency at which signal  causes interference is called ‘image frequency’

Image frequency and intermediate frequency is related as follows:

fsi = fs + 2 IF

fs: carrier frequency of the tuned station

fsi: image frequency

IF: Intermediate frequency

The image frequency rejection ratio (α) is the ratio of the intermediate frequency (IF) signal level produced by the desired input frequency to that produced by the image frequency. 

Calculation:

Given:

intermediate frequency (I.F) = 455 kHz

Tuned signal frequency is fs = 1000 kHz

Image frequency is

fsi = 1000 kHz + 2 × 455 kHz

fsi = 1910 kHz

Image frequency rejection ratio( α ) = \(\frac{f_{si}}{f_s}-\frac{f_s}{f_{si}}\)

α = \(\frac{1910}{1000}-\frac{1000}{1910}\) = 1.38