**EMRFD Message Archive 14650**

MessageDateFromSubject14650 2018-04-25 11:04:35 iq_rx Sideband Inversion Math Hi All,

Allison has it right, as usual. The reason she has it right is more subtle--she's thought about the math while designing and building radios, and perhaps even troubleshooting this particular issue when it came out wrong. The best math is what you use to describe something you observe in the lab. In fact, the Scientific Method requires the connection between theory and experiment. An aeronautics professor may be able to write all the equations for aircraft stability, but if you are going to fly through a storm, you might prefer a pilot who had thought about the theory while acquiring thousands of hours of practice. I always read Allison's posts carefully, because she's done both.

One poster asked for a response from W7ZOI or KK7B. I just chatted with Wes, and thought I'd remind the denizens of this web page why we wrote EMRFD. Our perception was that too many RF Design textbooks emphasized the math and theory, but missed the on-going connection to Experiment. Not canned college lab experiments, but open-ended Experimental work that asks questions without answers printed in the back of the textbook. Experimental work as in Bell Labs or Jet Propulsion Labs, where the emphasis is on the advanced understanding that happens when rocket scientists who are adept at math and physics spend their careers doing experimental work.

Keep asking the good questions, but rather than looking for a simple formula or an answer in a book, do a simple experiment. On the particular question of sideband inversion, it is worth noting that incorrect lore has been published many times, for half a century, in handbooks and journals. It's easy to get the minus sign wrong, but trivial to check your work at the bench with a radio you've designed and built. For the past half century much RF writing seems to have been done by people who didn't have an experimental bench to check their work. It is also worth noting that the Scientific Method has historically been the tool we use when people speak with great authority on topics they haven't personally experienced.

Best Regards,

Rick KK7B

14652 2018-04-26 07:07:36 tim Re: Sideband Inversion Math If you get the minus sign wrong you wind up with negative frequencies

or with a mixing product far off from what you want.

I *can* tell you exactly from the math whether you will get sideband

inversion or not from a mixer based on the input frequencies and the

chosen output frequency. It doesn't require any experimenting at all.

Experiments will only confirm the math.

This math has been known for hundreds of years.

This only gets difficult when you try to conflate filtering, which

cannot invert sidebands, with mixing which can invert sidebands.

tim ab0wr

14653 2018-04-26 09:18:34 kb1gmx Re: Sideband Inversion Math Tim,If you get the sign wrong the math you did was incorrect or not sufficiently tested.Testing on the bench is instructive as to how you get to the wrong result but in mathit is possible to test and see errors.I showed the work and how it was tested as well. If I got the sign wrong the mathwould not be "ok" it would be wrong. Going to the bench would confirm it.In over 45 years in engineering the best results came from errors. Because theconfirmation step show it was wrong and also opened a door to a possibleimprovement if only in the mathematical model. The last bunch of years in researchwas a proof of that as much of it was modeling things that should work onlyto build it and find its flaws.Allison14654 2018-04-26 14:46:16 tim Re: Sideband Inversion Math 1. If you get the sign wrong, *you* got the sign wrong. The math is

just the math. Garbage in, garbage out.

2. Perfect models give perfect results. The simple arithmetic of mixing

products provides a perfect model and the perfect model provides

perfect results.

3. Mixing actually is *not* a simple process. Non-linear processes

never are. We are discussing macro, first order results. Those results

can be perfectly modeled.

4. The best results do not come from errors. The best results identify

previously unknown effects. Like studying the zika virus in mice with a

perfectly designed experiment that gives the exact result expected, but

which *also* provides a totally unexpected result that impacts cancer

research.

5. Failure is *not* an error. Ask Edison.

tim ab0wr

14657 2018-04-28 10:57:31 Don Lewis Re: Sideband Inversion Math BRAVO!-DonN5CID=======================================14659 2018-04-28 11:27:41 gollum@f-m.fm Re: Sideband Inversion Math Hi All;I have been following this with great interest. Lurking if you may. I am in the process of building up an R2PRO. This topic has always confused me and I WILL be setting up some experiments to "verify" to my little brain the actualities and the math.. :-) .This is a great answer Rick!73Guy N1GMM from sunny (NOT) VA.14660 2018-04-28 11:28:09 mleblanc0 Re: Sideband Inversion Math Well said, Rick. I'm reminded of a quote that has been attributed to Richard Feynman: "I cannot understand something that I cannot build."-Michael VE1LEB14672 2018-04-30 17:56:58 lawrence_joy Re: Sideband Inversion Math The following is from an old Watkins-Johnson catalog found at www.rfcafe.com, called "Mixers: Part 1, Characteristics and Performance, v8-2.The intermediate frequency is so termed because it falls between the RF and information frequencies. This is simply stated as: fI = ±m fR ±n fL where, m = 0, 1, 2, 3, etc. n = 0, 1, 2, 3, etc. The output products most generally desired are the sums and differences of the fundamentals of the received and LO signals. This is the case for which. m = n = 1 giving, fI = ±fL ±fR While this formula implies that negative frequency products occur, these can be ignored in practical mixer applications in much the same way as incorrect roots can be ignored when calculating quadratic equations. For the case where fL > fR, which is called highside LO, fI , = fL ± fR. When fL < fR, which is called low-side LO, fI = ±fL + fR.WN8P, Larry