# Understanding Mixer Operation

I am trying to understand the Mixer operation for frequency up/down conversion. We just multiply our RF/IF signal with Local Oscillator (square wave) to do this job. Fine. BUT, if I start looking closely on operation things are getting confusing for me!

Say below is frequency domain presentation of the signal I am trying to upconvert.

Now the frequency domain presentation of periodic square wave is like following:

Now If I multiply these two signals time domain, which is same as convolution in frequency domain, the result would look like following:

And here is my question. Say, my intention is to move the signal to $$\omega_p$$ frequency. But clearly the result would contain higher harmonics of the above frequency. The Mixer datasheet from Analog devices does not talk about filtering the resultant signal post mixing. Basically the output of Mixer MUST go through signal processing to cut out the harmonics and retain the specific frequency region of interest. Or the Mixer by itself cuts out the higher frequency?? Something is amiss in my understanding, because so far I thought that I can use the Mixer output straight way without filtering, but the way I see, it needs filtering to cut out harmonics.

Also in Mixer stage, can I use clock signals instead of square wave as inputs? I believe if I feed Sine wave as the input in LO port, I can get rid of this higher harmonics issue altogether. Is it possible to inject sine wave at the LO port. The datasheet is not explicit on this.

• The local oscillator is NOT a square wave but a sinus as pure as possible. The result of mixing, is the input is a single tone, are two tones, fin+fmixer and fin-fmixer. If the input is of a certain BW, that BW appears centered over the sum and the difference of the frequencies. Usually a superhet receiver will filter one of the two frequencies, either the sum or the difference. – Claudio Avi Chami Jan 27 '17 at 12:58
• @Claudio Avi Chami: if OP says LO Signal is square wave why do you say it is not? It's not unusual at all to use a square wave (which is just a sum of f, 3f, 5f, etc. sine waves) as LO mixer input signal. – Curd Jan 27 '17 at 13:27
• Mixers are usually followed by bandpass (or lowpass) filters to pick off the spectrum of interest and eliminate the rest. – Brian Drummond Jan 27 '17 at 13:53
• @Curd it is highly unusual to use local oscillator that is not sinusoidal but if you have an example you are more than invited to share – Claudio Avi Chami Jan 27 '17 at 15:51
• @Claudio Avi Chami: any mixers using analog switches as mixing elements are an example. E.g. look at this LF receiver design. Also synchronous rectification (commonly used in lock-in amplifiers; note section about "Digital Switching Multiplier") is nothing else but mixing with a rectangular LO signal (with additional phase correlation). – Curd Jan 27 '17 at 18:07

The Mixer datasheet from Analog devices does not talk about filtering the resultant signal post mixing

No it wouldn't because it assumes you are using it with a sine wave but harmonics will produce multiple images because a mixer is a signal multiplier.

Or the Mixer by itself cuts out the higher frequency?

No, almost certainly not (some may do but I've never heard of one). You will need to bandpass either the output or use a sine wave for $\omega_P$.

Also in Mixer stage, can I use clock signals instead of square wave as inputs?

You have to ensure that the DC content of the clock signal is either removed (capacitor in series) or that the mixer can handle the voltage range you propose.

Is it possible to inject sine wave at the LO port. The datasheet is not explicit on this.

Almost certainly, this is the norm.

You don't say which mixer type (passive vs. active) you're using. Few mixers are strictly linear multipliers, meaning that sinusoidal inputs to RF port and local-oscillator port yield no harmonically-related outputs. Unlike a linear multiplier, most mixers generate harmonic-rich output.