How does a RF mixer circuit work?

[Bill Bowden]

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

 

[Kevin Aylward]

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?

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
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Andrew Holme]

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

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.

 

[[email protected]]

For a pragmatic rather than mathematical explanation, which has helped
some people, try this
http://www.davidbridgen.com/mixers.htm

 

[john jardine]

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

'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

 

[[email protected]]

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
http://www.ScienceOxygen.com/Trigonometrics.html
http://www.SicenceOxygen.com/signal188.html

for more information. It is with a collection of links
so that you can find the associated information
from there.

 

[Bill Bowden]

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) .

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

 

[foTONICS]

Bill Bowden wrote:
> 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

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.

neat, I didn't know that