1. Mixers Theory and Applications

2. BITX20 bidirectional SSB transceiver

3. BITX20 bidirectional SSB transceiver

4. Summary of our radio waveforms
Audio Frequency (AF)
Beat Frequency Oscillator (BFO)
Intermediate Frequency stage (IF)
Local Oscillator (LO)
Radio Frequency stage (RF).

5. 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 F+G and F-G and no harmonics.
Lets remind ourselves what these waveforms are like before we look in more detail at real mixers.

6. The inputs to the ideal mixer
2000Hz
2200Hz

7. The output from the ideal mixer
200Hz
and
4200Hz

8. 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(f+g)/2

9. A simple unbalanced Mixer

10. Diode Characteristic
Voltage in volts
Current in milliamps

11. 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

12. BITX20 bidirectional SSB transceiver

13. A diode ring Mixer

14. Ring Mixer G Positive

15. Ring Mixer G Negative

16. Advantages of the ring mixer
Good carrier rejection
Good Input rejection

17. 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

18. A Double balanced Mixer

19. G input positive on left

20. G input positive on Right

21. 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)

22. Real devices: MC1496

23. Real devices:SA602A

24. Orthogonality
Two things are orthogonal if changing one doesn’t 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.

25. Orthogonality Example
If you feed sine waves at frequencies F and G into a mixer you get sine waves at frequencies F+G and F-G.
If F=G then you get 2F and DC out
So if you take the DC average of the output you will get zero unless F=G. (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

26. 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

27. The Fourier transform
Previously we said that when you mix F and G and F=G 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.

28. 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.

29. A square wave to be Fourier transformed

30. Mixer input G to measure the fundamental

31. Mixer output for the fundamental
Note the strong positive DC average

32. Mixer output for the 2nd harmonic
Note the average is zero (even harmonic)

33. 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

34. Mixer output for the 4th harmonic
Note the average is zero (even harmonic)

35. Mixer output for 5nd harmonic
Note the 6 positive peaks 4 negative. Average is 2/10. This is 1/5 of the fundamental signal

36. Mixer output for the 6th harmonic
Note the average is zero (even harmonic)

37. Mixer output for 7nd harmonic
Note the 8 positive peaks 6 negative. Average is 2/14. This is 1/7 of the fundamental signal

38. 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

39. Mixer output for the Fundamental Cosine
Note the average is zero (anti-symmetric about centre)

40. Mixer output for the 2nd Harmonic Cosine
Note the average is zero (anti-symmetric about centre)

41. Mixer output for the 3rd Harmonic Cosine
Note the average is zero (anti-symmetric about centre)

42. 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

43. 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.

44. Questions?