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Why a mixer to combine two frequencies?

Discussion in 'General Electronics Chat' started by carbonzit, Aug 11, 2018 at 8:13 PM.

  1. carbonzit

    carbonzit Active Member

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    Here's something I don't understand: let's say I want to combine two signals of different frequencies and derive a beat frequency from them. (Just like in a superhet radio receiver where the tuned RF signal is reduced down to IF using a local oscillator.)

    I don't see why I need a mixer to do this. It seems to me that a simple circuit like this would do the trick, by simply combining the two signals:

    Freq. mixing.gif
    Would this not work? I look at it this way: instead of electronic signals, I think about sounds of two different frequencies that combine, with no mechanism other than the transmission medium, the air. In this case we can clearly hear the two beat frequency tones, one subtractive, the other additive, and extract them if we want to. Why wouldn't this work with electrical signals? Won't they simply cancel and reinforce each other to produce the two beat frequency signals that we can then extract (using the LC filter shown here)?

    I'm not sure why we need a "mixer" circuit to do this. From my reading I understand that there's something about mixers operating in a non-linear way that makes them work, but I'm not sure why. (I'm not building anything using this; just curious about general principles.)
     
  2. crutschow

    crutschow Well-Known Member Most Helpful Member

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    Adding (or subtracting) two different frequencies does not give the sum and difference frequencies.
    You just end up with the two frequencies together.
    Do the math and you will see.
    To get the sum and difference frequencies you need to multiply them together and that requires a non-linear (mixer) circuit.
    Again, do the math.

    If you can hear sum or difference frequencies than that means there is a non-linear process involved.
    What are the conditions where you "can clearly hear the two beat frequency tones, one subtractive, the other additive..." and how do you "extract them".
     
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  3. RadioRon

    RadioRon Well-Known Member

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    Seconding what crutshchow said, when you have two sinusoidal voltages and simply add them together, you simply don't get any new components at any other frequencies. Only when you combine the two while also distorting them do you create new frequencies. It takes some non-linearity to cause the distortion. Here's another way to think about it...when you hear two different tones of sound with your ears and if those tones are pure and they are not too loud, you only hear those tones, you don't hear anything else, right? Take the alternative to an extreme, if simply adding two tones together (again, if the tones are pure and if the volume is not too loud) were to create a sum and difference, how could you possibly listen to any music and not have it sound completely polluted with many many sums and differences? You don't because at reasonable volumes, your ear is operating linearly and not distorting the sound. If the volume is cranked up very high, the speakers probably begin to operate non-linearly and your ears also start to be non-linear and then you hear harmonics as well as sum and difference products, and the tones (or the music) become a real mess. Its pretty obvious. Why? Well, I was taught this effect by using mathematics to show how when you add one sin(x) plus a second sin(y) all you get is sin(x)+sin(y). Nothing creates sin(x-y) or sin(x+y). Now, if you multiply sin(x) times sin(y) the result is very different, and you have sin(x), sin(y), sin(x+y) and sin(x-y) all in the result. A mixer (or any non-linear circuit) does this multiplication. Again, its easiest to see if you do the math, just as crutschow says.
     
  4. dave miyares

    Dave New Member

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  5. Nigel Goodwin

    Nigel Goodwin Super Moderator Most Helpful Member

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    A lot of confusion arises over the term 'mixer' - as it applies to two completely different techniques.

    In this case it's actually a 'multiplier' for RF mixers, but for audio mixers it's an 'adder'.

    There's also mixers for cakes, and concrete! :D
     
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  6. crutschow

    crutschow Well-Known Member Most Helpful Member

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    As well as Social ones. ;)
     
  7. audioguru

    audioguru Well-Known Member Most Helpful Member

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    Your extremely simple "circuit" is shorting together the outputs of where they came from which might kill one or both signals and/or damage the outputs. A adder can be made with a current-limiting resistor in series with each signal then connect the free ends of the resistors together to make the resulting added signal.
     
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  8. dave miyares

    Dave New Member

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  9. carbonzit

    carbonzit Active Member

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    I'd like to be able to (do the math). I'm quite willing to be shown it--you know, sine, cosine, omega, all that. Actually, that would be the best way for me to understand this concept.

    I'm confused again by something you said. Why would you need to multiply the frequencies? Wouldn't you be adding and subtracting them?

    So far as sound is concerned, I'm pretty sure I've heard beat frequencies resulting from two tones being played together, but I can't point to anything concrete or specific.
     
  10. crutschow

    crutschow Well-Known Member Most Helpful Member

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    Absolute not.
    As previously stated, adding and subtracting does not mathematically (or in reality) generate new frequencies.
    If you put two different frequencies into an opamp adder circuit you simply end up with the two frequencies combined in the single output.
    No new frequencies are formed.
    If new frequencies were generated (called IM distortion in amplifiers) it would be impossible to record and store music obtained from different studio microphones as is commonly done.

    You have to multiply them to get the sum and difference frequencies.
    Perhaps this article will help.
     
  11. carbonzit

    carbonzit Active Member

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    Thanks. I'll study up on that. (Unless I can find a better explanation somewhere else.)
     
  12. rjenkinsgb

    rjenkinsgb Active Member

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    Just to clarify things, although the signals have frequencies, the addition or multiplication is of the instantaneous voltages of the signals.

    Even distortion like clipping the signal(s) will give frequency-mixing effects - an overdriven guitar amp input (or distortion/overdrive/fuzz pedal) does just that.
     
  13. JimB

    JimB Super Moderator Most Helpful Member

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    A practical demonstration.

    Connecting two signal sources to a display, using three 100 Ohm resistors:
    Test Setup.png
    On the scope, we see this:
    Added 01.JPG

    A 100kHz sinewave superimposed on a higher frequency signal which the scope shows as a band of signal.

    But looking on the spectrum analyser, we see:
    Added 02.JPG

    Just the 1MHz signal and the 100kHz signal.
    (And the image of the 100kHz signal, which is just there because of the way the analyser works and is set-up).

    But if we change the resistive network for a diode ring mixer (OK so it is a home made lash-up based on an SBL-1, that I made some time ago in the hope that it would give me some good results at low frequencies. All in all it was not a great success.):
    The Mixer.JPG

    On the scope we see this:
    Mixed 01.JPG

    The typical output of a balanced mixer.
    If the balance was better, the zero crossing points would be sharp nulls.
    Note that this is NOT an conventional Amplitude Modulated signal, it is a Double SideBand Suppressed Carrier signal.

    Looking on the spectrum analyser:
    Mixed 02a.jpg

    We do not see the 100kHz signal, that does not pass through the balance mixer.
    The 1MHz carrier is 30dB down on the two side frequencies at 0.90 Mhz and 1.1 Mhz.
    If the mixer balance was better, the 1Mhz signal could be supressed down into the noise.


    JimB
     
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