Serving the worldwide community of radio-electronic homebrewers. Providing blog support to the SolderSmoke podcast: http://soldersmoke.com
Podcasting since August 2005! Listen to Latest SolderSmoke
Sunday, September 20, 2026
Scott K6AUS gets a Drake 2-B from Steve KW4H
Monday, July 6, 2026
How Hans G0UPL Cracked the Code for Stable I and Q from the Si5351
Back in 2018, I remember Farhan telling me that "Hans has cracked the code" getting stable I and Q from the Si5351. But I never really appreciated the importance of this breakthough until I recently started looking at the receiver from Macedonia. Then I asked AI (Google Gemini) for a readout on who was responsible for the I and Q innovation. Here is what I got yesterday from Gemini:
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The credit for solving this problem and unlocking stable, single-chip I/Q quadrature generation from the Si5351 goes to Hans Summers, the British QRP developer and founder of QRP Labs.
While other talented developers in the amateur radio community—most notably Jason Mildrum (NT7S)—wrote the definitive, widely used standard open-source Arduino libraries for basic Si5351 tuning, it was Hans Summers who fundamentally cracked the math required to force the chip into a stable 90 degree phase shift over a wide frequency range without breaking lock.
The Breakthrough Discovery
Around 2014 to 2015, while designing highly compact, low-cost transceivers like the QCX and ultimate VFO kits, Summers realized that standard programming libraries were completely incompatible with generating stable quadrature signals.
He pioneered a completely reversed architectural method to control the chip, which became the blueprint for homebrew SDR builders everywhere:
Flipping the Fractional Math: Standard libraries fixed the primary internal Voltage Controlled Oscillator (VCO/PLL) at an integer value and used the second stage (the MultiSynth fractional dividers) to dial in the exact frequency. Summers realized this broke the phase shift. He discovered that you must lock the MultiSynth divider to a fixed even integer and force the first stage (the PLL VCO) to do the fractional math instead.
The "No Reset" Discovery: Standard practices issued a soft PLL reset command to the chip every time the user turned the tuning dial to ensure clean frequencies. This reset caused the phase relationship to drop out or randomize. Summers proved that after an initial startup reset to align the phases, you can smoothly glide the VCO frequency up and down via the I2C bus without resetting the PLL, keeping the I and Q signals locked in a perfect mathematical embrace.
Thanks to Hans Summers publishing his detailed engineering application notes and open-sourcing his mathematical methods, developers around the world were able to write the code that modern microcontrollers (like the ESP32 in your receiver) use today to keep the I/Q phase rock-solid as you dial across the bands.
Sunday, June 28, 2026
Update: How Many Drake 2-B Receivers Were Made? Can Someone Send a Drake 2-B to Scott?
Scott K6AUS has been involved since the very beginning and continues to look at the mathematics:
https://nomadiq.net/blog/post/how-many-drake-2bs-were-ever-made
Scott has given us a very useful update based on additional serial numbers provided by SolderSmoke listeners.
How many? About 11,300. Check out Scott's page for some interesting mathematical details.
Thanks a lot Scott!
BTW: SCOTT K6AUS DOES NOT HAVE A DRAKE 2-B. THIS IS JUST WRONG! HE HAS DONE SO MUCH FOR THIS RECEIVER! HE SHOULD HAVE ONE! IS THERE ANYONE OUT THERE WHO CAN SEND A DRAKE 2-B TO SCOTT?
Wednesday, October 15, 2025
The Perils of Overreliance on Math
On the Importance of Really Understanding Radio and Radio Circuitry
In the first version of my book I included (in bold letters) sections in which I described my efforts to deeply understand how the circuits I was using really worked. I mentioned that this yearning for understanding probably had its roots in the influence of Jean Shepherd: Shep seemed to expect true radio hams to really understand the gear that they worked on. As a child, James Clerk Maxwell would often ask about how things worked: “What’s the go of it? What’s the particular go of it?” That is the kind of understanding that I wanted. But as I progressed, I would often come across hams who had other notions about what constituted “understanding.” These people were often Electrical Engineers, deeply schooled in mathematics. For them, knowing the math was synonymous with understanding how circuits worked. Asked, for example, how a mixer mixed, they would spit out trigonometry formulae. I found this kind of understanding insufficient and unsatisfying. I was not alone:
In 1990, after seven years of teaching at Harvard, Eric Mazur, now Balkanski professor of physics and applied physics, was delivering clear, polished lectures and demonstrations and getting high student evaluations for his introductory Physics 11 course, populated mainly by premed and engineering students who were successfully solving complicated problems. Then he discovered that his success as a teacher “was a complete illusion, a house of cards.”
The epiphany came via an article in the American Journal of Physics by Arizona State professor David Hestenes. He had devised a very simple test, couched in everyday language, to check students’ understanding of one of the most fundamental concepts of physics—force—and had administered it to 8 thousands of undergraduates in the southwestern United States. Astonishingly, the test showed that their introductory courses had taught them “next to nothing,” says Mazur: “After a semester of physics, they still held the same misconceptions as they had at the beginning of the term.”
The students had improved at handling equations and formulas, he explains, but when it came to understanding “what the real meanings of these things are, they basically reverted to Aristotelian logic—thousands of years back.”
To Mazur’s consternation, the simple test of conceptual understanding showed that his students had not grasped the basic ideas of his physics course: two-thirds of them were modern Aristotelians. “The students did well on textbook-style problems,” he explains. “They had a bag of tricks, formulas to apply. But that was solving problems by rote. They floundered on the simple word problems, which demanded a real understanding of the concepts behind the formulas.”
From: http://harvardmagazine.com/2012/03/twilight-of-the-lecture
Sunday, July 30, 2023
Understanding Maxwell's Equations (video)
Friday, April 16, 2021
What Kind of Car Would Have this Plate?
We are proud to say that the owner is a SolderSmoke listener. Can you figure out what kind of car he is driving?
(See comments for answer).
Thursday, February 18, 2021
Phasors and the Propeller Analogy from Walla Walla University
Wednesday, February 17, 2021
Wednesday, April 29, 2020
Applied Science -- Electrical Impedance Tutorials
Part 1 appears above, Part 2 is below.
Ben Krasnow has a KNACK for explaining technical things. I liked his videos on impedance. At the end of the second video, he said he'd do a third one that would focus on impedance in coaxial cables. But I couldn't find it on his channel. I hope it was made -- this is very interesting and useful.
Ben's YouTube channel is here: https://www.youtube.com/user/bkraz333
Friday, March 27, 2020
Excellent Video on Maxwell's Equations
Really well-done. He gets to the essence without getting bogged down in the math. Great graphics too.
Sunday, April 14, 2019
Understanding Fourier Transforms
Lots of wisdom and insight here:
http://www.jezzamon.com/fourier/index.htm
Strongly recommended for those trying to understand mixers and harmonics.
Monday, May 30, 2016
Movie Review: "The Man Who Knew Infinity" FIVE SOLDERING IRONS
My wife and I went to see this flick about the mathematician Srinivasa Ramanujan. It was filmed at Trinity College, Cambridge -- if you look at the dedication to "SolderSmoke -- Global Adventures in Wireless Electronics" you will see a picture of my kids at Cambridge. Alas, that picture was taken at Kings College, not Trinity; nonetheless, the Cambridge connection got us interested. Then there was the Indian aspect of the story, which is very intriguing. There was also the "amateur makes good" angle that all of us should, I think, find very encouraging.
The movie did not disappoint. We really liked it. The presentation of the cultural clash was very well done. Elisa told me that as she watched Ramanujan struggle with England, she found herself wanting to tell him, "You are just going through culture shock. Be patient! I've been through this many times!" They included just enough math to give the viewer a sense of what Ramanujan was working on.
I got a real kick out of one scene in which old Professor Hardy, seeking to motivate young Ramanujan, took him into the Wren Library and showed him the manuscript of Newton's Principia. I had seen the same manuscript in the library of the Royal Society in London -- they had take it out on the occasion of the visit to the library of Stephen Hawking and NASA Director Mike Griffin. They also had on the table the reflecting telescope that Newton himself had made. That was quite a day.
Great movie. I give it the coveted rating of five soldering irons.
More about Ramanujan here:
https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
Tuesday, April 23, 2013
King of the Nerds
Submit a tape and possibly win 100K.
http://nerdking.net/
Our book: "SolderSmoke -- Global Adventures in Wireless Electronics" http://soldersmoke.com/book.htm Our coffee mugs, T-Shirts, bumper stickers: http://www.cafepress.com/SolderSmoke Our Book Store: http://astore.amazon.com/contracross-20
Thursday, March 14, 2013
Almost forgot! Happy Pi Day!
3-14 Get it?
And happy birthday Albert Einstein!
Our book: "SolderSmoke -- Global Adventures in Wireless Electronics" http://soldersmoke.com/book.htm Our coffee mugs, T-Shirts, bumper stickers: http://www.cafepress.com/SolderSmoke Our Book Store: http://astore.amazon.com/contracross-20
Thursday, February 28, 2013
73 -- The BEST Number
"The best number is 73. Why? 73 is the 21st prime number. Its mirror (37) is the 12th and its mirror (21) is the product of multiplying, 7 and 3. ... In binary, 73 is a palindrome, 1001001 which backwards is 1001001."
-Dr. Sheldon Cooper, (Jim Parsons), "Big Bang Theory"
"Just to invite your attention to "73" in Morse code--also a palindrome."
-W9JEF
Our book: "SolderSmoke -- Global Adventures in Wireless Electronics" http://soldersmoke.com/book.htm Our coffee mugs, T-Shirts, bumper stickers: http://www.cafepress.com/SolderSmoke Our Book Store: http://astore.amazon.com/contracross-20
Wednesday, March 14, 2012
Happy Pi - Einstein Day!
The card is for a special event sponsored by the Lake Effect Amateur Radio Club:http://www.lakeeffectarc.info/Event-PiEinsteinDay/PiDay.htm
I've been reading "Math and the Mona Lisa" so lately I've been more into Phi than Pi. When will we have Phi Day? January 6th?
Our book: "SolderSmoke -- Global Adventures in Wireless Electronics"http://soldersmoke.com/book.htmOur coffee mugs, T-Shirts, bumper stickers: http://www.cafepress.com/SolderSmokeOur Book Store: http://astore.amazon.com/contracross-20
Tuesday, August 23, 2011
German Tanks and Drake 2-Bs: We Have the Number!
Hi Bill,
Finally getting back to you. I crunched the numbers... I saw a total of 23 serial numbers reported. The important thing is that these numbers be reported somewhat randomly with no biases etc. I think this is the case, and the fact we have 23 numbers is very very good in terms of the power of this experiment. The highest number reported was 12955. Let m = 12955. The number of reports was 23 so let k = 23. The equation to use (from wikipedia) is below...
The lowest serial number reported to SolderSmoke was 2008, so you wouldn't need to subtract more than that. You can think of this equation intuitively (a very SolderSmoke thing to do!). Imagine what happens when we have a single observation. k = 1, so our estimate is about 2 times what our highest observation is. This makes sense because you would guess your observation is most likely to be about half way between 0 and the true top number. If k = 2, then our estimate is about 1.5 times our highest observation. If k = 3, then our estimate is about 1.333 times our highest observation.... as we observe more numbers, we are more likely to have observed the top number so as k goes to infinity, our estimate moves towards our top observed number, which it should.
I hope my explanation made sense. Anyway I highly recommend SolderSmoke listeners who want to know more, to read the wikipedia page. Its quite well written and offers a lot for people who like hard formal explanations and an intuitive description. Keep up the good work!
I love the podcast - hopefully we may catch each other one day on the bands.
73 Scott (K6AUS)
Our book: "SolderSmoke -- Global Adventures in Wireless Electronics"http://soldersmoke.com/book.htmOur coffee mugs, T-Shirts, bumper stickers: http://www.cafepress.com/SolderSmokeOur Book Store: http://astore.amazon.com/contracross-20
Wednesday, May 18, 2011
How many Drake 2-Bs? The German Tank Problem
-------------------
Hi Bill,
I was just listening to your latest soldersmoke podcast and your
discussion about how many Drake 2Bs were made. Without knowing the
exact serial number for the last Drake 2B before the Drake 2C was
made, you can estimate what that number might have been by knowing a
few of the real serial numbers that are being used by people today.
This is a mathematical problem related to the somewhat famous "German
Tank" problem. Check out:
http://en.wikipedia.org/wiki/German_tank_problem.
If you were to ask your listeners to report to you their Drake 2B
serial numbers you could estimate the largest serial number there ever
was from the formula on that wiki page. This could be a fun exercise
:) I've never had a Drake 2B so I can't contribute. But I could do the
estimate for you if you gave me the numbers.
Cheers and 73
Scott (K6AUS)
Monday, March 14, 2011
Happy Pi Day! (3.14 Get it?)
One of the many benefits of having a kid in elementary school is that you are made aware of important days that otherwise might escape your attention. Like today: International Pi Day. While the mathematical connections might be a bit flaky, I liked the above video.
Slashdot put it this way:
I'm not saying it's as good as Lady Gaga or Justin Bieber or something, but it's a great way to get ready for Pi day which is tragically still not a federal holiday. Write your congressman.
Friday, January 22, 2010
Does Math Lead to Understanding?
In "SolderSmoke -- The Book" I describe the quest for deep understanding of the circuits that we build and use. There is some discussion in the book of the role of mathematics in this quest. A while back a reader e-mailed me on this subject. In the hope of stimulating a discussion, I'll present the key paragraph from that e-mail here (the author will, for now, remain anonymous):I appreciate your quotes from Feynman, Asimov, etc. about not
really being able to fully understand everything. As a math teacher
I can say that one of the biggest misunderstandings about math
is that it "explains" the phenomena of physics and engineering.
(Science and math teachers are notorious for saying to a student
who has just asked a "why" question things like, "well the math is
a little bit more complicated than what you can handle right now.
Wait untilyou have had a year or so of calculus.") In reality it's
the exact opposite! The math equations actually hide the answers.
They are very good at accurately describing phenomena, or at
predicting what will happen next, but they can never answer the
question of why one equation works and another does not. We
get very comfortable with allowing the familiar math equations
to hide our inability to really answer the "whys."
This really resonated with me. In my effort to get a better grasp of mixer theoy a lot of people seemed to be simply pointing me to the trig equations, and equating a knowledge of those equations with an understanding of how the mixer circuits really work.
Of course, I don't mean to be anti-math here, but I thought the e-mail on the limits of mathematics was very interesting. In "Empire of the Air" Tom Lewis wrote, "At Columbia, Edwin Howard Armstrong developed another trait that displeased some of the staff and would annoy others later in life: his distrust of mathematical explanations for phenomena of the physical world. All too often he found his professors taking refuge in such abstractions when faced with a difficult and seemingly intractable conundrum... Time and again as an undergraduate at Columbia, Armstrong had refused to seek in mathematics a refuge from physical realities."




