I've never really understood how a mixer circuit in a typical radio receiver produces the sum and difference frequencies between the incoming RF signal and the local oscillator. I understand it requires a non-linear circuit, but I can't quite see how the signals subtract to produce the IF frequency.
For example, if the RF input is 1 mHz and the IF is 455 kHz, the local oscillator should be running at 1.455 mHz. How do we combine
1 mHz and 1.455 mHz to get 455 kHz?-Bill
local
Kevin Aylward has already posted the trig identity, showing how the multiplication of sine waves produces sum and difference frequencies. It's also worth pointing out that not all mixers are driven with sine waves: often, the local oscillator input is a square wave.
Switching mixers, such as diode ring mixers, multiply the input by +1 for half the LO cycle and -1 for the other half. The diode "switches" simply reverse the connections to the mixer output transfomer.
If you have a signal f1 and square wave LO drive f2, since the latter is the sum of an infinite series of odd harmonics, it's like having an infinite number of local oscillators! The mixer outputs are f1 +/- f2, f1 +/- 3f2, f1 +/- 5f2 e.t.c. The unwanted products are removed by the post-mixer filter.
The basic idea is the standard trig identity:
sin(x)sin(y) = [cos(x-y) - cos(x+y)]/2.
So, one has to generate a sin(x)sin(y), i.e. a multiplication.
If a device is non-linear it may typically be represented by:
Vo = a + b.Vi^2 + c.Vi^3 ++...
If Vi = VpSin(w1t) + VpSin(w2t), i.e. a simple sum of two input signals, then
Vo = a + b.(VpSin(w1t) + VpSin(w2t))^2 ++...
Epanding this gives a VpSin(w1t).VpSin(w2t) term
Kevin Aylward snipped-for-privacy@anasoft.co.uk
For a pragmatic rather than mathematical explanation, which has helped some people, try this
'Mixers' are just phase sensitive rectifiers. If you want physical insight as to how that difference frequency somehow turns up, It can be handy to just to draw out 10 cycles of a 50:50 square wave a piece of squared paper (2 square high, 2 squares low). Pretend this is the local oscillator running at say 1MHz. This now switches the rectifier device that will be rectifying the incoming RF input signal and somehow generating those sum and difference frequencies (and many others). The rectifier can be something as simple as a CD4066 ON/OFF switch. The rectifier does not *have* to be a diode or some strange device with a non linear bend in it. In fact, the ON/OFF type switch is the best of them all.
For the RF input signal, draw a line of (say) 7 square waves underneath the local oscillor signal, 3 square high, 3 squares low, =666kHz. Start them at the same point but make sure they are correctly sized (phased) relative to the top line.
Now for the rectification/mixing/multiplying/modulating action ... Draw a third "0V" output line under the previous two. Every time the local oscillator is high then the RF signal passes through to the output (is rectified), so just copy to the output line, the segment of the 'RF' square wave that sits under the local oscillator during it's high periods.
After doing all 10 then look at the resulting mishmash of blocks and half blocks and visually average them (a human RC low pass filter). Notice there is a low frequency undulating component present (about 3 cycles over the run ='340kHz')). This is the 'oddball' I.F frequency. regards john
Well, the basic idea is: signal can be "modulated" into higher frequencies or "demoluated" from lower frequencies. In plain English, the reason to do that is: in the space we live, only some portion of the spectrum can carried the signal with less attenuation. So, we would like to use that portion of spectrum to transmit the signal.
You might try
for more information. It is with a collection of links so that you can find the associated information from there.
John,
Yes, that's a good illustration. My graph paper wasn't quite wide enough for 10 cycles, so I drew an 8 cycle square wave for the oscillator (using 4 squares per cycle) and 5.33 cycles for the RF signal (using 6 squares). The result plots out to 2 high squares, followed by 6 low squares, followed by 1 high and 3 low for a total of
12 squares. The sequence then repeats, so the frequency of the combined pattern works out to 2.66 cycles, which is the difference of 8 and 5.33. Very good illustration.-Bill
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.