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Let's look at this definition of mixers (reference):

A real mixer cannot be driven by arbitrary inputs. Instead one port, the "LO" port, is driven by a Local Oscillator with a fixed amplitude sinusoid.

  • In a down-converting mixer the other input port is driven by the "RF" signal and the output is at a lower "IF" intermediate frequency

  • In an up-converting mixer the other input port is driven by the "IF" signal and the output is the "RF" signal

Now let's consider the wikipedia definition of mixer (taken from the italian page):

In telecommunications, a mixer is a non-linear circuit, that is, a device that accepts two frequency signals at the input and outputs a combination of the two signals at different frequencies. In the most common output applications a signal is produced which can be: 1) the sum of the frequencies of the input signals (fout = f1 + f2) 2) the difference between the frequencies of the input signals (fout = f1 - f2)

Now I have some questions: I) which is the correspondence between up and down converters circuits and circuits which perform sum and difference of frequencies?

I'd say that:

  • down converting mixer: takes RF as input and gets fIF = fRF - fLO
  • up converting mixer: takes IF as input and gets fRF = fIF + fLO

II) Exactly what does IF represent? Let's consider for instance a receiver. The signal that arrives at the antenna is the result of an amplitude or frequency modulation through which a signal which contains some informations (for instance an audio signal) is shifted in frequency and carried by a high frequency carrier signal. Then the receiver will have to reconstruct the original information signal. So does IF represent this signal? Or is the down - conversion to IF an intermediate stage?

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  • \$\begingroup\$ Could you please edit your post by typing in the text from the image, and if you're feeling ambitious, editing out of the image? It'll make the question more consistent, searchable, and translatable. \$\endgroup\$
    – TimWescott
    Jan 9 '20 at 19:15
  • \$\begingroup\$ Yes, I'll write it \$\endgroup\$
    – Kinka-Byo
    Jan 10 '20 at 16:57
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    \$\begingroup\$ A real mixer can take arbitrary inputs in certain ranges. The common mixers may only work in narrow frequency ranges, but more expensive ones based on a Gilbert cell can work down to DC (though depending on the design you may have problems using them at rf) \$\endgroup\$
    – Hearth
    Jan 10 '20 at 17:47
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    \$\begingroup\$ @Hearth : I'm not sure if it's what you meant, but diode ring mixers will take the LO input and square it up -- and this is a good thing, because such a mixer has less intermodulation distortion the less time that is spent with the diodes "sorta on". Ditto for FET-ring mixers (which I've only seen schematics of, but never used). I suspect that even a Gilbert cell mixer would perform better just at mixing if it were designed so the LO port were driving hard. \$\endgroup\$
    – TimWescott
    Jan 10 '20 at 18:12
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I) which is the correspondence between up and down converters circuits and circuits which perform sum and difference of frequencies?

To clarify the concept of a "mixer";

What a mixer ideally is, is just an analog multiplier, which takes two input signals and multiply them together to get the output, this is why the multiplication symbol is used to represent an ideal mixer.

It turns out that if you multiply to sine functions with different frequencies, let's call the frequencies fa and fb, then the result is two new sine functions, one with frequency fa+fb, and one with frequency fa-fb (you also get fb-fa, but one of the latter are going to result in a negative frequency, which is out of the scope of this answer)

In order to get either an up-converter, or a down-converter, you just filter out the signal that you don't want after the mixer. Let's say that you wan't to down-convert, well just add a low pass filter after your mixer, and you are only going to get the difference of the frequencies. You wan't to up-convert? add a high-pass filter after the mixer..

What I have described until now is just how to think of ideal mixers, what they do, and how you can think of the difference between an up-converting mixer, and a down-converting mixer, it is all just to do with the filter you use. However, the ways that up and down converting mixers are made in reality depends completely on the application, typically in RF applications any type of non-linear amplifier can be used, with the filter in its feedback path, and the signals can be added together on the input. This will give a similar result to an actual analog multiplier, and after the filter you still only get the signal that you want.

II) Exactly what does IF represent? Let's consider for instance a receiver. The signal that arrives at the antenna is the result of an amplitude or frequency modulation through which a signal which contains some informations (for instance an audio signal) is shifted in frequency and carried by a high frequency carrier signal. Then the receiver will have to reconstruct the original information signal. So does IF represent this signal? Or is the down - conversion to IF an intermediate stage?

"IF" Stands for "intermediate frequency", and in most cases this is not the final output that you are looking for.

The IF signal is indeed an intermediate stage, as the name suggests. Let's take the case of an AM modulated signal, after down-conversion you still have an AM modulated carrier, it is just at a lower frequency. The same is true for FM, you just get an FM modulated IF which is at a lower frequency than your original RF signal.

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It's complicated. And ever-changing (at least, if you have a collection of RF books stretching back to the days when a pentode was "that newfangled tube").

which is the correspondence between up and down converters circuits and circuits which perform sum and difference of frequencies?

  • Any circuit that multiplies two sinusoids puts out a signal at the sum and difference of those two frequencies.
  • In practice, most mixer circuits put out signals at the sum and difference of the incoming "signal" port, and just about every possible harmonic of the "LO" port. This is because multipliers are inherently nonlinear, and a good way to manage that nonlinearity is to concentrate its effects on the LO signal.
  • When there is a difference at all, it's because an "up converter" or a "down converter" is followed by filters that filter out the unwanted mixing products and only keep the desired one -- so it's as much the filter that determines the "up" or "down" part as anything else*.

Exactly what does IF represent? Let's consider for instance a receiver. The signal that arrives at the antenna is the result of an amplitude or frequency modulation through which a signal which contains some information (for instance an audio signal) is shifted in frequency and carried by a high frequency carrier signal. Then the receiver will have to reconstruct the original information signal. So does IF represent this signal? Or is the down - conversion to IF an intermediate stage?

"IF" literally means "intermediate frequency**". You can think of a superheterodyne receiver as being a really well optimized fixed-frequency receiver that sits behind a tunable frequency converter -- and that frequency converter is the mixer stage (or the up- or down-converter).

In general, all of the radio frequency communications modes impress a signal on a carrier (or they generate a signal that's referenced to some, possibly suppressed, carrier). A frequency conversion step preserves the structure of the signal, but just moves it in frequency. The signal still needs to be demodulated and processed as necessary for consumption (i.e., an AM signal needs to run through a peak detector, an FM signal needs to be run through a discriminator, etc.)

* Some mixers inherently have a "low frequency" port and a "high frequency" port -- that's too complicated for this answer, though.

** And again too complicated for this answer -- the IF isn't always lower than the RF. There's a lot of "HF" receivers that work from 1MHz to 30MHz or so that convert the RF up to an IF in the 45 to 70MHz range, and then do the rest of their processing.

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Term "local oscillator" (=LO) is historical. Radio equipment had initially an oscillator as the transmitter. Having an oscillator also in the receiver (to shift the signal to IF in the mixer) needed a new term and that became LO.

Let's have a signal named A. Let's input A to a mixer and let's simultaneously input from an oscillator (=from the LO) a sinewave which has frequency Fo. If the mixer works ideally, one can separate with spectrum analysis two simultaneous output signals. Every moment the voltage in the output is the sum of these mixing products:

1) frequency sum: every spectral component of A is shifted amount +Fo upwards in the frequency scale

2) frequency difference: every spectral component of A is shifted amount +Fo downwards in the frequency scale. If the resulted frequency is negative, the minus sign can be omitted.

Ideal mixer is actually a voltage controller amplifier or attenuator, where the local oscillator signal controls proportionally how much A is amplified or attenuated.

Term up-conversion isn't as clear as it can at first seem to be. Amplitude modulated radio signal contains simultaneously both ideal mixing results. If the transmitted audio signal covers frequency range say 100Hz...5kHz and the "LO" signal is at 1MHz, the mixer outputs simultaneously the audio signal at bands 1000100Hz...1005000Hz and 995000Hz...999900Hz.

To be exact an additional DC component (=0Hz) is added to the audio signal and that generates an additional mixing product, the carrier at 1Mhz, which is needed to make the conversion back to audio (=the detection) easy in AM receivers. We say the AM radio signal has frequency 1MHz although it's distributed between 0,995MHz and 1,005Mhz.

The carrier and one of the copies of the signal above or below the carrier is theoretically unnecessary. They waste both signal power and frequency space. We have SSB (=single side band) radio systems where the unnecessary parts are suppressed with filters or clever phasing circuits, but they make the receiver complex and degrade audio quality, so the simle AM radio signal is still in use. For analog television a version of AM which radically reduced the unnecessary parts but transmitted them as band-limited was used.

In digital signal processing ideal mixing with multiplication is used widely. In analog circuits perfect multiplication is possible only with low frequency op amp circuits. In radios bad mixing was so serious problem that some workarounds were needed. The most common workaround was to replace multiplication with switching.

With spectral math (=trigonometric equations or Fourier transforms) one can show that the sinusoidal local oscillator signal in ideal mixing can be replaced by square wave. The result is like the signal A is either switched ON-OFF with switching frequency=the LO frequency (=Fo) or the polarity of A is swapped with the LO frequency. We skip the math, but if we believe the the frequency shift in the ideal mixer, we see that the switching creates the mixing results also between A and the harmonics of the square wave at freq Fo.

In practical mixers no linear multiplication is attempted, the mixers do the switching with diodes or transistors. The voltage of the LO signal is so high that the switching is possible. Signal A gets thru half of the time in balanced mixers or all the time in double balanced mixers, but half of the time as inverted (=multiplied by minus 1)

The unwanted mixing results with the harmonics of the LO signal are filtered off. The system designer has selected the used frequencies so that filtering is possible.

About IF: Radio receivers need often high signal amplification to be able to receive weak signals and as well they need sharp filtering to receive only the interesting radio station. These things can be too expensive with variable frequency circuits except if the interesting station makes an ovewhelming strong signal which covers the others which simple receivers would pass through at the same time.

Mass produced "Super Heterodyne" receivers as early as in 1930' shifted with a mixer the interesting signal to about 450kHz intermediate frequency, where the final filtering, amplification and detection to audio happened. Shifting to 450kHz was actually shifting upwards when the signal was at Long Wave band. MW and HF bands needed shifting downwards.

Direct shifting with mixing to 0Hz or direct conversion receiving is possible with phase locked or synchronizing oscillation analog circuits if there's at least somehow helping bandpass filtering in front of the conversion. Also digital signal processing can be used if there's some amplification, signal level normalization and filtering available before the AD conversion.

IF has also been used in radio transmitters to make modulations easier. It's especially useful in microwave range, where everything complex is difficult at the final transmission frequency.

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The IF is, as others have said, is just an intermediate frequency between the source RF and the final frequency you will analyze. But keep in mind that there can be more than one IF. Here's an example.

Say you have an 8 GHz (X-band) input that you want to, somehow, mix down to 500 MHz, at which point it can be sampled by a high speed ADC. One way to do this would be to mix the 8 GHz input with an 8.5 GHz LO, and use the 500 MHz difference output.

Another way would be to mix the 8 GHz input with that same 8.5 Hz LO, only this time you use the sum frequency out the the mixer, 16.5 GHz. This is an IF, but it's not your final IF. Then you mix the 16.5 GHz with another LO at, say, 17 GHz and take the difference frequency, 500 MHz, and ship it over to your ADC.

Which approach is best depends on many things. But one of the main reasons for one approach over another has to do with spur management and suppression, with a spur just being an undesired frequency that comes out of the mixer or any other non-linear part in the receive chain.

Receiver designers spend lots of time and effort figuring out the right approach.

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