# Solving an exercise of superheterodyne receiver with high IF frequency

I've been struggling with this problem for several hours. I have a high IF superheterodyne receiver. The input frequency can vary from 9kHz to 3GHz. I need to calculate the minimum intermediate frequency (f_IF) if it is being used an IF filter of bandwith 1MHz. Must be kept in mind that the input frequency (f_in) is filtered using an ideal low lass filter with a cut frequency of 3GHz. Then, I must find the minimum and maximum frequency of the local oscilator (f_LO) as well as the minimum and maximum of the image frequency (f_im). Finally I must compute the range of frequencies the image rejection filter must filter, if necessary.

I have been struggling for a while. I watched a lot of videos and tried to solve it in many different ways but cannot come up with any solution.

• How can you have a 1mhz bandwidth on a 9khz RF carrier?
– user338146
May 13, 2023 at 23:31
• 1MHz bandwith of IF filter, and the carrier frequency can be between 9kHz and 3GHz. That's what it says... May 13, 2023 at 23:38
• Sorry if that is wrong, clearly I don't have strong understanding on the topic. I would appreciate if you tell me what's wrong with that. May 13, 2023 at 23:38
• This sounds like a classic upconverting spectrum analyser input. I'm struggling to find a suitable resource on the net, the best I have so far is figure 9.13 from this guide. If I do find something better, I'll make an answer. The frequencies are different, but the concept is the same. May 14, 2023 at 9:09

First of all, this sounds like an academic exercise as I don't know of a real-world application where an input frequency range of 9 KHz to 3 GHz is handled without some type of channelization (band filtering). But...

I would do an up conversion followed by a down conversion.

First up convert the input to (say) 10 GHz - 13 GHz. Call this IF1. This can be done using a fixed frequency LO (LO1) of ~10 GHz. I have no idea how many IM spurs are going to be generated by this, but we'll let that go for now.

Then, I would use a tunable LO (LO2) to down convert the 10 GHz to 13 GHz IF1 to something more manageable and that will provide the needed 1 MHz bandwidth, say 100 Mhz (so the bandwidth is 1% of IF2). That would mean an LO2 of ~10.1 GHz to ~13.1 GHz, and use the difference frequency out of the second mixer.

Note that you can, on paper, change the two LO frequencies to give you a different IF1 and IF2. And that your choice of IF2 may depend on the ease of providing an IF filter bandwidth of 1 MHz, with the passband and rolloff (out of band rejection) you desire.

• Real world application, general purpose spectrum analyser like the HP8566, input 9 kHz to 2.5 GHz, first IF a bit above 3 GHz IIRC. 2nd LO at 3.321 GHz down to 2nd IF of 321 MHz, then 300 MHz to give a last IF of 21 (ish) MHz. May 14, 2023 at 6:17

The intermediate frequency (IF) can be above or below the RF frequency. In the mixer, the RF and OSC frequencies are mixed to make F1+F2 and F1-F2. I have built radios for 100 MHz with a 10.7 MHz IF or 1 MHz with a IF of 455 kHz (IF is lower than RF.) I have played with a radio for very low frequencies where the RF is lower than the IF. Example RF=9 kHz and IF = 160 kHz.

This looks like homework so we don't really have to build one. Please do the math and see if this works. IF=3.5 GHz. (strange thing to do.) What oscillator frequency is needed to receive 3 GHz? 3 GHzRF + ?OSC = 6.5 GHzIF. Then on the low end what OSC frequency is needed to add to 9 kHz to have a frequency at 6.5 GHz. Please think about this and tell me what you think. Then try it for a low IF frequency.

• Note that the IFs are not always less than your RF. May 14, 2023 at 2:36