How to calculate VFO/IFO frequencies?

Question

I am trying to build a simple superhet receiver for listening SSB signals. I read several articles about SSB and got confused so I am looking for some practical explanation.

I have 2 mixers, quartz filter between them. So there are 2 conversions. First, from HF to IF, second from IF to audio.

Let's say I want to receive LSB in range 3747-3750 KHz. If I understood LSB concept correctly 3750 KHz will become 0Hz in audio and 3747Khz will be 3kHz. Some sort of inversion. Am I wrong here?

If my intermediate frequency is 8MHz and I have some ideal filter in range 8000-8003KHz what should be first oscillator frequency?

I think like this:

8000 + 3750 = 11750 // I set DDS above the received frequency

so the lower part HF frequency will be on the high side of IF filter

11750 - 3747 = 8003

And second oscillator frequency then has to be 8003 for LSB (highest edge of the IF filter):

8003 - 8003 = 0
8000 - 8003 = 3

And if I had USB I had to set to the starting IF filter frequency (8000kHz).

Am I getting it all wrong? Can somebody give a good explanation with examples? Or good article to read.

Answer 1

Let's say I want to receive LSB in range 3747-3750 KHz. If I understood LSB concept correctly 3750 KHz will become 0Hz in audio and 3747Khz will be 3kHz. Some sort of inversion. Am I wrong here?

You're exactly right. LSB maps a 1 Hz baseband input to 1 Hz below the carrier frequency, 20 Hz to 20 Hz below the carrier, and so on. USB is the same but the modulated frequencies are above rather than below the carrier.

In other words, in LSB the carrier frequency is the highest frequency in the transmission, and in USB it is the lowest.

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A frequency mixer has two inputs, the signal you'd like to demodulate, and the VFO. Each is at a frequency $f_1$ and $f_2$, respectively. The mixer then outputs:

$$ f_\text{out} = \begin{cases} f_1 \pm f_2 & \text{if } f_1 > f_2\\ f_2 \pm f_1 & \text{if } f_2 > f_1 \end{cases} $$

If you are demodulating LSB, you want the signal's carrier frequency (3750 kHz) to fall at the top end (not the bottom, as in your example) of the filter (8003 kHz). So, you could tune your VFO to 4253 kHz, because 4253 + 3750 = 8003. Or, you could tune the VFO to 11753 kHz, because 11753 - 3750 = 8003.

Either will work, but you must also consider the image frequency. Say you tune the VFO to 4253 kHz. Your signal at 3750 kHz does get mixed to the IF as desired, but there is another solution to the equation: 12256 - 4253 = 8003. So if there is another signal or noise present at 12256 kHz also present at the input to the mixer, that also gets mixed to the IF and thus interferes with your desired signal. Alternately with the VFO tuned to 11753 kHz, the image frequency becomes 19756 kHz, because 19756 - 11753 = 8003.

Again, either choice works. Your design choices must balance the capabilities of the VFO, potential interference at the image frequency, and the requirements of the filter to remove the image frequency.