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Consider a superheterodyne receiver designed to receive the frequency band of 1 to 30 MHz with IF frequency 8 MHz.

a) What is the range of frequencies generated by the local oscillator for this receiver?

b) An incoming signal with carrier frequency 10 MHz is received at the 10 MHz setting. At this setting of the receiver we also get interference from a signal with some other carrier frequency if the receiver RF stage bandpass filter has poor selectivity. What is the carrier frequency of the interfering signal?

My solution:

part a)

        1M+8M     < f(local oscillator) <   30M+8M
           9M Hz  < f(local oscillator) <   38M Hz

part b)

The image station will be at = fc+  2f(intermediate) 
                             = 10M+2(8M)
                             = 26M Hz

Please look at my answer and correct me if something is wrong.

This is one of the problems in chapter 5 of Modern Digital and Analog Communication Systems, 4th edition. I couldn't find the solution manual for this edition, only for 3rd edition which did not include this question.

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    \$\begingroup\$ Just a comment on this example. This is a horrible IF selection for a superhet receiver. You typically want the IF frequency to be far away from the frequency you want to receive so that the Image frequency can be filtered out. Notice, in this case, that the image frequency at 26 MHz is in the desired band, so your receiver cannot easily filter it out. The LO is also in band, giving you spurs. If the IF frequency was at 45 MHz, for example then the LO would be 46-75 MHz, easily filtered out. The image would be at 91-120 MHz, easily filtered out. \$\endgroup\$
    – rfdave
    Apr 18, 2015 at 1:48
  • \$\begingroup\$ @Dave, upvoted, but isn't it usually preferable to pick an IF that's lower than the frequency band you're interested in? I'm genuinely curious; this isn't really my field, but I'm studying up because my next electronics project is going to be building a superhet receiver. I've never seen an IF higher than the desired band before. For example, the typical IF for FM seems to be 10.7 MHz, and for AM 455 kHz. \$\endgroup\$ Oct 21, 2016 at 19:54
  • \$\begingroup\$ Well, you need to figure out your requirements, and like all engineering problems, there's no perfect solution, just ones that work with varying tradeoff's. For example if you were designing a receiver for 1 MHz to 30 MHz, then if you used a 455 kHz IF freq, the IF oscillator would be at 455 kHz + FReceive. This frequency is going to be in-band across most of the receive bandwidth, quite possibly creating intermod products inband. It's a somewhat complicated subject, too complicated for a small edit window. Google search for Mixer Spurs and IF frequency selection for more info. \$\endgroup\$
    – rfdave
    Oct 22, 2016 at 0:26

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Your answers are correct. Another way to think about the image is, that you'd set the oscillator to 18 MHz (so that 18-10 MHz gives 8 MHz for the I.F.). With that setting, you can pick up a signal that's 8 MHz away in the other direction, that being 18+8 MHz, which is the answer you got.

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  • \$\begingroup\$ thank you for your answer and comment. I answered the question according to the equations with a little understating of what's going on in the problem . your comment wide my understating , In real life we don't want that interference to happen !! HOW DID THEY SOLVE THIS PROBLEM ? IS IT RELATED TO ( Pre-emphasis, de-emphasis SYSTEMS ) ? \$\endgroup\$ Apr 18, 2015 at 1:58
  • \$\begingroup\$ @user3136052 You would use a different IF. It has nothing to do with pre-emphasis. \$\endgroup\$
    – user207421
    Apr 18, 2015 at 6:36
  • \$\begingroup\$ If you have more questions, it's better to post them as new questions. In this example, they gave you a hint: "...if the receiver RF stage bandpass filter has poor selectivity". The idea is to have a filter than can pass the 10 MHz signal while filtering out the 26 MHz one. This "RF stage" goes between the antenna and your conversion stage. \$\endgroup\$
    – gbarry
    Apr 18, 2015 at 7:07
  • \$\begingroup\$ To obtain the best "frequencies" of the local oscillator and of the "IF", one can draw a graph showing "all" the various combinations of the frequencies in play (band to be received and local oscillator) with all the interferential multiples. The area on the paper that is not crossed by any "straight" line is the best place ... \$\endgroup\$
    – Antonio51
    Jul 1, 2021 at 11:18

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