Mixers Theory and Applications

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MixersTheory and Applications
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BITX20 bidirectional SSB transceiver
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BITX20 bidirectional SSB transceiver
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Summary of our radio waveforms
Audio Frequency (AF) Beat Frequency Oscillator
(BFO) Intermediate Frequency stage (IF) Local
Oscillator (LO) Radio Frequency stage (RF).
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The ideal mixer (A reminder)
An ideal mixer multiplies rather than adds
waveforms. In a moment we will look at the
electronics of mixers. If you feed two sine
waves at frequencies F and G into a multiplier
you just get sine waves at frequencies FG and
F-G and no harmonics. Lets remind ourselves what
these waveforms are like before we look in more
detail at real mixers.
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The inputs to the ideal mixer
2000Hz
2200Hz
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The output from the ideal mixer
200Hz
and
4200Hz
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Some maths
Last time we noted that the output waveforms were
90 degree phase shifted sine waves of half the
amplitude. For many purposes this makes no
difference. However we will look at this in more
detail later in the talk (but avoiding
maths). Sin(f) Sin(g) Cos(f-g)/2
Cos(fg)/2
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A simple unbalanced Mixer
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Diode Characteristic
Voltage in volts
Current in milliamps
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Disadvantages of the simple mixer

• No carrier rejection (G)
• No input rejection (F)
• High drive voltage needed on all inputs
• Harmonic distortion on all signals

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BITX20 bidirectional SSB transceiver
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A diode ring Mixer
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Ring Mixer G Positive
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Ring Mixer G Negative
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Advantages of the ring mixer

• Good carrier rejection
• Good Input rejection

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Disadvantages of the ring mixer

• High drive current needed on carrier input
• Harmonic distortion (on carrier input)
• Expensive discrete components
• Needs transformers to work properly

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A Double balanced Mixer
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G input positive on left
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G input positive on Right
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Advantages of the double balanced mixer

• Almost linear on each input
• Great carrier and input rejection
• Low drive signals needed.
• Low harmonic distortion on both inputs
• Well suit to IC manufacture
• No transformers
• Cheap (due to IC process)

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Real devices MC1496
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Real devicesSA602A
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Orthogonality
Two things are orthogonal if changing one doesnt
change the other. In geometry this is a right
angle. For example Latitude, Longitude and
Altitude over sea are orthogonal. Over land they
are not. Sine waves of different frequencies are
Orthogonal. Most other waveforms are not
orthogonal.
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Orthogonality Example
If you feed sine waves at frequencies F and G
into a mixer you get sine waves at frequencies
FG and F-G. If FG then you get 2F and DC
out So if you take the DC average of the output
you will get zero unless FG. (Only true for
orthogonal waveforms such as sine waves) So if
we use an accurate signal generator for G then
the DC value is a measure of the harmonic of F at
G
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The spectrum analyser
If we vary the frequency of our signal generator
G into our mixer then we can measure the strength
of the signal F at a range of frequencies. (Just
like tuning a radio) If the signal F that we are
measuring is not a pure sine wave then as we tune
the generator we will only measure the sine wave
component of the signal F at the frequency of our
generator G. So by sweeping G we can measure the
spectrum of F
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The Fourier transform
Previously we said that when you mix F and G and
FG you will get a DC average. This is only true
if F and G are in phase. If F and G are antiphase
you get a negative DC value. However if F and G
are 90 degrees apart you will get zero. So you
can measure the phase of F by measuring at both 0
and 90 degrees (I and Q). Note that sine and
cosine waves at the same frequency are orthogonal.
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The Fourier transform
A Fourier transform is like a spectrum
analyser. Multiply the original waveform by sine
waves of each harmonic in turn and take the DC
averages. These give you the sine wave
harmonics. Now do the same thing with cosine
waves, This gives you the cosine wave harmonics.
(90 degrees shifted) We will see that for a
Square wave you get the 1/3, 1/5 1/7 ratios (odd
harmonics) we used in the signals talk.
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A square wave to be Fourier transformed
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Mixer input G to measure the fundamental
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Mixer output for the fundamental
Note the strong positive DC average
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Mixer output for the 2nd harmonic
Note the average is zero (even harmonic)
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Mixer output for the 3nd harmonic
Note the 4 positive peaks 2 negative. Average is
2/6. This is 1/3 of the fundamental signal
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Mixer output for the 4th harmonic
Note the average is zero (even harmonic)
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Mixer output for 5nd harmonic
Note the 6 positive peaks 4 negative. Average is
2/10. This is 1/5 of the fundamental signal
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Mixer output for the 6th harmonic
Note the average is zero (even harmonic)
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Mixer output for 7nd harmonic
Note the 8 positive peaks 6 negative. Average is
2/14. This is 1/7 of the fundamental signal
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But what about the cosine components?
So far we have only looked at the sine wave (in
phase) components. We should check if there are
any Cosine (90 degree phase shifted) components.
Note the Cosine is symmetric about the centre
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Mixer output for the Fundamental Cosine
Note the average is zero (anti-symmetric about
centre)
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Mixer output for the 2nd Harmonic Cosine
Note the average is zero (anti-symmetric about
centre)
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Mixer output for the 3rd Harmonic Cosine
Note the average is zero (anti-symmetric about
centre)
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Summary of the components of a Square wave
We have seen that you do get the 1/3, 1/5 1/7
ratios (odd harmonics) we used in the signals
talk. The even Sine harmonics have equal numbers
of plus and minus (half wave) peaks so are
zero Odd Sine harmonics all have two more
positive peaks than negative out of a total of
double their harmonic number. Hence the 1/3, 1/5,
1/7 etc. ratios. Cosine harmonics are all
anti-symmetric and thus zero
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The Inverse Fourier transform
In the signals talk we took the harmonics of a
square wave and combined them. This was an
Inverse Fourier transform! (If done correctly
these transforms are reversible and lossless) We
may look at the Fast Fourier transform (FFT) in a
later talk. Its just a quicker way of doing
Fourier transforms.
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Questions?