Image frequency

• In a standard broadcast receiver (and , in fact , in the vast majority of all receivers made ) the local oscillator frequency is made higher than the incoming signal frequency for reasons that will become apparent .

• It is made equal at all times to the signal frequency plus the intermediate frequency.

• Thus $f_0=f_s+f_i or f_0=f_s-f_i$, no matter what the signal frequency may be .When $f_0$ and $f_s$ are mixed , the difference frequency , which is one of the by-products , is equal to $f_i$ .

• As such , it is the only one passed and amplified by the IF stage.

• If a frequency $f_{si}$ manages to reach the mixer, such that $f_{si}=f_o+f_i$ , that is , $f_si=f_s+2f_i$, then this frequency will also produce $f_i$ when mixed with $f_0$.

• Unfortunately, this spurious intermediate-frequency signal will also be amplified by the IF stage and will therefore provide interference.

• This has the effect of two stations being received simultaneously and is naturally undesirable.

• The term $f_{si}$ is called image frequency and is defined as the signal frequency plus twice the intermediate frequency .Reiterating , we have

  $f_{si}=f_s+2f_i$

• The rejection of an image frequency by a single –tuned circuit , i.e., the ratio of the gain at the signal frequency to the gain at the image frequency , is given by

  $α=\sqrt{1+Q^2 ρ^2 }$

where $ρ=\frac{f_{si}}{f_s} -\frac{f_s}{f_{si}}$

Q=loaded Qo ftuned circuit

• If the receiver has an RF stage, then there are two tuned circuits , both tuned to f_s .The rejection of each will be calculated by the same formula , and the total rejection will be product of the two.

• Whatever applies to gain calculations applies also to those involving rejection.

• Image –rejection depends on the front-end selectivity of the receiver and must be achieved before the IF stage.

• Once the spurious frequency enters the first IF amplifier, it becomes impossible to remove it from the wanted signal.

• It can be seen that if $\frac{f_{si}}{f_s}$ is large , as it is in the AM broadcast band , the use of an RF stage is not essential for good image-frequency rejection , but it does become necessary above about 3MHz.

  Double spotting

• This is well-known phenomenon, which manifests itself by the picking up of the same shortwave station at two nearby points on the receiver dial.

• It is caused by poor front-end selectivity , i.e., inadequate image-frequency rejection .That is to say, the front end of the receiver does not select different adjacent signals very well , but the IF stage takes care of eliminating almost all of them .

• This being the case, it is obvious that the precise tuning of the local oscillator is what determines which signal will be amplified by the IF stage.

• Within broad limits, the setting of the tuned circuit at the input of the mixer is far less important (it being assumed that there is no RF amplifier in a receiver which badly suffers from double spotting).

• Lack of selectivity is harmful because a weak station may be masked by the reception of a nearby strong station at the spurious point on the dial .

• As a matter of interest , double spotting may be used to calculate the intermediate frequency of an unknown receiver , since the spurious point on the dial is precisely 2f , below the correct frequency .(An improvement in image-frequency rejection will produce a corresponding reduction in double spotting .)