Bill, I remember in your Soldersmoke book that you had difficulty for a long time trying to understand how a mixer created the sum and difference frequencies, and how this was accomplished in a diode ring mixer. I know that you've got it all sorted out now, but I thought this was a good topic for a video anyway.
Here's my video on the subject:
73,
Alan
Alan: Thanks. Great stuff. Yea, I've been looking at the innards of mixers for a long time. In my book, I try to explain how I have come to understand the physics of the mixing action -- how the use of a non-linear element causes two signals to "multiply" and how this "multiplication" results in sum and difference frequencies. I tried to go beyond the trig functions because for me the trig didn't really explain anything.
In the book I was looking at the classic two diode mixer (beloved of Doug DeMaw!). A few years later, on the blog, I was looking at the action of the diode ring. I concluded that there is a big difference between how the diode ring works and how the two diode mixer works. RSGB provided a great diagram:
73 Bill
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I guess one way of describing the difference between a two diode mixer and a diode ring would be to say that the more simple mixer multiplies the signal by 0 and 1 (if it is operating in "switching mode), while the diode ring multiplies by 1 and -1.
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The one thing I'd add to this discussion is that the multiplication effect needed to obtain sum and difference frequencies of mixing can be seen with the more simple on/off single diode situation by recognizing the the nonlinearity of the current equation for the diode. There is some mixing due to just the binary on/off but you get a more broad spectrum of mixing products if you break down the nonlinear current characteristic into a Taylor series, where you see that there is a squared term in current. Since the applied current contains the two input frequencies (cosines), the two cosines get squared, giving you the trig identity sum and difference frequencies and some other mixing products as well.
ReplyDeleteI don't think that this picture of mixing is very intuitive and so I personally feel that some elements of the mixing process will always be most easily "visualized" by looking at the algebra and trig. Still I like knowing that fundamentally there is this "squared term" in nonlinear elements that gives rise to the mixing products, it provides more explanation than just saying "diodes multiply signals", although it's not a pretty visual picture obviously. - Bert WF7I
Very good comments, Bert. Some people 'get things' better visually. Others get a better feel for things mathematically. So thank you for adding that perspective.
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