Mixers

 

The aim of these notes is to provide an explanation of mixers, i.e. mixers generally associated with r.f., from an approach which is perhaps a bit different from the normal.
Audio and video mixing are not the same thing, as should become obvious.  In those disciplines it really should be called adding, and in r.f., multiplying. 


Introduction

The need for "mixers" arose in the early days of radio. When thermionic valves became available and were used to amplify r.f. it soon became apparent that the design of fixed frequency amplifiers was simpler than that of tuneable ones. This led to the superheterodyne architecture replacing t.r.f. (tuned radio frequency), in which the r.f. signal was amplified in a series of (tuneable) stages prior to detection.

The idea of the superhet is to convert the frequency of the desired station, whatever its frequency may be, to a fixed frequency so as to permit its easier amplification and filtering.
This conversion is achieved by using a stage originally called a frequency changer and which we now know as a mixer, in conjunction with an oscillator, the so-called local oscillator.


Basics

At the most basic level a mixer is no more than a non-linear device, but it will be useful to first look at linear ones. 


If a signal is applied to a linear device, stage, or system, the output will be linearly related to, i.e. directly proportional to, the input.
A graph of current through, versus voltage across, a resistor will serve to illustrate the point.

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If the voltage across the resistor is increased, or decreased, then the current through it will also increase or decrease by the same factor. It is said that the current is linearly related to the voltage.

Now look at this graph of input versus output voltage of an (ideal) amplifier with a voltage gain of 10.

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You can see that the output voltage is linearly related to the input voltage, and consists of a copy 10 times bigger, and nothing else. If the input is a single frequency the output will be a single frequency.

What happens if the amplifier is not linear, such as might be represented by the next graph ?

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The number of times the output is greater than the input, i.e. the amplification, depends on how big the input is to start with. 

 

It is a characteristic of a non-linear device that if the input is a single frequency, the output will consist not only of that frequency but harmonics of it too. Not surprisingly, this is called harmonic distortion.

However, the situation is more complex than this, much more.  In addition to the original frequency and its harmonics, the output will contain components which are the sums of the various frequencies, the differences between them and harmonics of those too. 

They are known collectively as inter-modulation products, or i.m.ps. Remember that name, particularly the word "modulation". I shall mention it later.

I said at the beginning of this section "at the most basic level a mixer is no more than a non-linear device".

There is no non-linear device more basic than a diode.

Just look at its voltage/current curve.

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A diode is the most basic mixer

 

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Mixers (etc)

So how is a mixer and local-oscillator used?
The next diagram shows the first few stages of a radio receiver.

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The signals from the antenna go to the mixer. The output from the oscillator also goes to the mixer. The output of the mixer goes to a filter, which is often at the output of an amplifier.  The output of this may receive further amplication and filtering. 

The mixer, being a non-linear device, will produce, at its output, the two inputs (signals from the antenna and that from the oscillator), harmonics of them, their sum, their difference, harmonics of the latter two, sums and differences of all the above etc, etc.

The signals from the antenna may be numerous - tens, or perhaps even hundreds of frequencies Ė and we need to be able to select just one of them which will be passed, after conversion (mixing) to the (fixed-tuned) amplifier/s. 

The oscillator produces a frequency which is different from that of the signal we want to receive and is usually higher. In a tuneable receiver this difference is constant irrespective of the frequency to which the receiver is tuned, and it is this difference frequency to which the stage/s between the mixer and subsequent "detection" are tuned. 

 

Letís take a look at some typical figures such as those associated with a medium-wave a.m. broadcast receiver. 


It is designed to receive frequencies from 540kHz to 1600kHz.
The oscillatorís frequency will have a fixed difference from the above range and be higher. That difference is typically 455kHz. The oscillatorís range of frequencies will, therefore, be 995kHz to 2055kHz.

The tuning of the radio is achieved by adjustment of the oscillatorís frequency. 


If we want to receive a station at, say, 600kHz, setting the receiverís tuning control to this indicated frequency will set the oscillator to 600 + (the fixed difference of) 455 = 1055kHz. 


Apart from the station at 600kHz, which we want to hear, there will inevitably be others whose signals will be present at the mixerís input.
To keep things simple weíll assume thereís just one more, at 800kHz.


The mixer has, as inputs, frequencies of 600 and 800kHz from the antenna and 1055kHz from the oscillator.
At its output will be those three frequencies, their sums, their differences, harmonics, and every possible combination of all the above. For the sake of brevity Iíll enumerate only the first few:

 

the input frequencies
       
600
         
800
         
1055
 
their sums
600
+
800
=
1400
 
600
+
1055
=
1655
 
800
+
1055
=
1855
 
their differences
800
-
600
=
200
 
1055
-
800
=
255
 
1055
-
600
=
455

 

Of these, and indeed the many more, the one of interest is the last, 455kHz.
It is to this frequency to which subsequent amplifiers and/or filters are tuned. We call it the intermediate frequency, or i.f.

The other frequencies at the mixerís output will be rejected (attenuated) by the i.f. filter/s.

Another example wonít go amiss.

This time the receiver is tuned to 1300kHz.
The oscillator will be at 1300 + (the fixed difference of) 455 = 1755.

 

Mixer inputs
1300
1755
 
Mixer outputs
1300
1755
1300
+
1755
=
3055
1755
-
1300
=
455

 

Again, of the various frequencies present at the output it is only the latter can pass through the i.f. section

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Now, for the (etc) bit.

Consider an a.m. transmitter.
An a.m. transmitter has an oscillator, one or more r.f. amplifiers and a modulator. The modulator too is a series of (audio) amplifiers. Itís a bit of misnomer because modulation takes place in the last r.f. stage.
The final r.f. amplifier has applied to it not only the r.f. but the audio too.

Suppose we have a transmitter whose carrier frequency is 1 MHz (1,000 kHz) and we apply a 1 kHz tone as modulation.
At the final amplifierís output, and sent to the antenna, will be the carrier at 1 MHz, the lower sideband at 999 kHz and the upper sideband at 1001 kHz. There will also be a component at 1 kHz but as the output of the transmitter will have a circuit tuned to 1MHz the amplitude of this component will be insignificant.

Now consider the most simple of all radio receivers, the crystal set.
It consists of a tuned circuit to select the station you want to listen to, and a detector (the crystal Ė which is a diode.)

Letís tune it to the a.m. transmitter above.
The detector has at its input three frequencies, 999 kHz, 1000 kHz and 1001 kHz.
Remember the diode curve above? Itís hopelessly non-linear. It should come as no surprise, therefore, that at the output there will be the original three input frequencies plus their sums and their differences. The circuit which follows the detector will respond only to audio frequencies Ė itís very often no more than just a pair of high impedance Ďphones. So we can ignore the sum frequencies. It is the difference frequencies which will be heard. In this case 1 kHz (the original modulation frequency) and 2 kHz (2nd harmonic distortion.)

Does what is happening in the a.m. transmitter and the crystal detector sound familiar?
It ought to. Itís the same thing

For a.m., modulation, demodulation (detection) and mixing are exactly the same process. They have historically been given different names presumably because they were perceived to be different. Theyíre not.

There are two special kinds of mixer. The balanced mixer and the double balanced mixer.
In the balanced mixer one of the inputs is "cancelled". It will appear at the output, but attenuated by some 40dB or more compared with the other components.
The double balanced mixer is similar in as much as it "cancels" both inputs so that only the various sums and differences appear at the output.

Finally, Iíll pass on the following observation/comment regarding receivers.  It has helped some beginners in the past.
When you listen to a radio station with a receiver you are hearing just a part of the radio frequency spectrum through a narrow "window."  The width of this window is that of the i.f. filter/s.  When you tune the radio you are effectively sliding the window up or down the spectrum.

A scanning receiver (scanner) does this automatically and repetitively, stopping when it detects a station.
A spectrum analyser is a special, and rather expensive, variant of a scanning receiver, in which the detected output is presented on a screen as a graph of amplitude versus frequency.

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