# 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.

Thanks for your guidance.

• 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. Jan 27, 2017 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, 2017 at 13:27
• Mixers are usually followed by bandpass (or lowpass) filters to pick off the spectrum of interest and eliminate the rest. Jan 27, 2017 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 Jan 27, 2017 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, 2017 at 18:07

## 4 Answers

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.

About local oscillator input to your mixer....
Many mixers accept a sine wave at their local oscillator port, but internally use this signal to over-drive mixer diodes, or to saturate mixer switches. You might see a minimum amplitude requirement on the local oscillator input to reach this saturation point. In such a mixer, you'll see harmonically related output similar to that you'd obtain with square-wave local oscillator input. So it is unwise to assume that a sine wave input to local-oscillator guarantees fewer harmonics at mixer output.

The local oscillator port of a saturated-switch type mixer described above should be assumed non-linear. Driving a local-oscillator port with logic signals can be done, but not casually. A mixer local oscillator port often expects to be driven by a linear source (perhaps having a 50-ohm driving impedance), even though it is non-linear itself.

Consider the NE602, double-balanced active mixer. I've used it happily into the moderate 100s of Megahertz. You can drive the Oscillator pin from a SignalGenerator, and experiment with harmonic suppression.

At the output of your mixer, you will have all the spectrum, all the possible combinations of frequencies. You have to filter them out, which is the interestd on for your application. For example the 3rd order harmonics (3*f1, 3*f2, 2*f1+/-f2, 2*f2+/-f1), are of special relevance because they are actually in your signal bandwidth and this is why 3rd order intercept point (3IP) is an important value when you characterize your mixer.

In case you are using a transistor, usually the LO si a sine wave and you need to make sure where you opperate it, to adjust your wave parameters. For example, for a resistive FET mixer the operating point is Vg=Vth for minimum LO power requirement.