A little radio receiver question for your Sunday morning...

[McPete]

Hey all,

I'm just doing some introductory comms theory, and I've come across a question that's got me a bit stumped... Could someone please give me a pointer as to how to attack this?:

So, say I've got a Super-het receiver listening to a square wave of about 200Hz, modulated at some frequency, into an upper sideband. My receiver's IF stage is set at 3kHz, so as one would expect from a square wave signal, I get fairly strong harmonics up to the 7th, where they're chopped down mercilessly by the IF filters...

Now say some scoundrel comes along and adjusts the tuning on my set up by 100Hz, so I'm not quite pointing at my signal... What comes out of my receiver now?

Cheers,
Pete

[xygor]

Ok, do you know what would come out if the baseband signal were a 200 Hz sine wave instead of a square wave?

[McPete]

I'd imagine I'd get a fairly clean sine wave. I can't see a cause for harmonics, outside random noise... I do dully remember something about the subsequent harmonics being upshifted.

[xygor]

I'm not clear whether the carrier is suppressed at the tx.  I sounds like the tx is ssb, so the carrier is suppressed.

I'm also not clear what type of detector is being used in the rx.  Is it envelope detection (AM) or product detection (SSB) or FM?  Are you looking at the output to the speaker?

[McPete]

Yes, it's a SSB system, using product detection. I'm pretty sure the result is that the fundamental is lost, and the subsequent harmonics are all shifted up by 100Hz...  Not 100% on that though.

[xygor]

You're really close.

Why do you think the fundamental goes away?  (I think you are wrong about that.)  What's special about the fundamental?  It is true that if the frequency goes low or high enough, it will be attenuated somewhere.  Most communications receivers don't have much response below 200 Hz due to the audio circuit and speaker.

Why do you think the frequencies go up instead of down? (I think you are wrong about that.)

List what the output frequencies are before and after the tuning change?  (just the fundamental and first 3 harmonics.  enough to tell you have the right idea.)

If you have access to a SSB receiver, do the experiment.  Set USB mode, pick something to listen to, and turn the dial up.  What happens to the frequencies you hear?

[McPete]

Ugh, I think I see it now... The RF input is attenuated due to the Fc not being centred on the SB, but the fundamental plus harmonics are still present. However, because they're being mixed with the wrong frequency from the local oscillator, they all have the 100Hz offset of the tuning... Being too high a LO frequency, the resulting IF is too low, resulting in the demodulated baseband being too low by that offset. The IF is also overly attenuated by the IF filters.

Result; muffled, low frequency audio.

Sorry, I've had the dumb today. Thanks for your help!

[xygor]

Yes, the fundamental and all its harmonics are shifted down in frequency by 100 Hz.

Is it still a square wave (or more precisely, an approximation of a square wave, since it didn't have infinite bandwidth to begin with) then? 

[McPete]

No. The baseband fundamental is being attenuated fairly badly, I would presume, so I'm thinking an almost saw-tooth looking wave would result.

[xygor]

You are correct.  No longer a square wave.  The reason though is that the harmonic relationship no longer exists.   A 100 Hz square wave requires harmonics at 300, 500, 700, etc. Hz, each at a specific phase.  What you have after the shift is 100, 200, 400, 600, etc. Hz.  I don't actually know what that would look like.  Those are the right harmonics for a triangle, but the amplitudes and possibly phases are not correct.