Happy Friday the 13th.
“In the field of observation, chance favors the prepared mind.”
Look’t that poor, tired sum’ bi’ch…
Haven’t posted for a while (ten days) ’cause I had a design problem’s teeth sunk deep into my derriere. Couldn’t crack it. So, I started to write a report explaining to my client why I couldn’t solve their problem, and something weird happened.
I perceived a solution.
Maybe I’ll discuss that later, but pro’ly not here. Here is where I want to talk about how it happened.
Last October is when this project started. I emailed a fellow who had liked my work from the past to let him know of my ‘availability’… He had something… It was hard to see how to proceed, but when you’re hungry you’ll maybe try things. And as the searching, searching, searching, for the answer continued it seemed like I might not get ‘lucky’ after all.
“Let me tell you the secret that has led me to my goal. My strength lies solely in my tenacity.”
Heh. I quoted forty hours to survey known antenna designs and recommend the best variant. I’m way-y-y-y past that now. The trouble was that I had looked at perhaps six or eight published designs that purported to work the way I needed them to work. Some didn’t because of a quirk in my client’s statement of work. Some didn’t because they just didn’t. (Maybe I didn’t understand what the authors were trying to say, or maybe I did and they were just wrong.) In order to satisfy myself that they wouldn’t work I had to try really hard to make them work. And I had wanted something to work. But nothing did, so I decided I had to give up.
“I am on the verge of mysteries and the veil is getting thinner and thinner. The nights seem to me too long…”
I wanted to show the essential difference between a ‘wire’ antenna and a ‘slot’ antenna in a clear way. So I made a WIPL-D model of two loops of wire that were identical except for they way they were fed. One loop was fed in series and the other in parallel. My intention was to show that the parallel fed loop acted like a ‘slot’ antenna and the series fed loop acted like a ‘wire’ antenna. Here they are, the series fed loops are the first and third and the parallel fed loops are the second and fourth:
On the left we see the relative magnitude of the current density of the two loops at resonance. (Although the absolute current densities are different the relative distributions in the two different configurations are the same.) On the right we see the relative phase of the current flowing in the two loops at resonance. Here the two pictures look completely different.
Now look at the radiation fields of the two loops. Again, the series fed loop is on the left and the parallel fed loop is on the right. You don’t need to know a bunch of antenna lingo to see that these two pictures are very different. The difference has to be related to the relative phase difference of the current in the two loops.
Now, the wire antenna on the left and the slot antenna on the right are understood to be related theoretically by Huygen’s Principle, sometimes called the principle of complementarity. You can read about the theory of complementarity here and here, but I just want to quote a little slice from Wikipedia:
“From Babinet’s principle, a dipole antenna is complementary to a slot antenna consisting of a slot the same size and shape as a dipole cut from an infinite sheet of metal; both give the same radiation pattern.”
I believe Babinet’s Principle because it’s true. The trouble was, Babinet’s principle didn’t apply to these two structures because even though they were duals they were not complements! Again, from Wikipedia:
“Let B be the original diffracting body, and B’ its complement, i.e., the body that is transparent where B is opaque, and opaque where B is transparent.“
Everybody I know thinks about slot antennas this way. I used to, too.
“He who proclaims the existence of the Infinite, and none can avoid it — accumulates in that affirmation more of the supernatural than is to be found in all the miracles of all the religions; for the notion of the Infinite presents that double character that forces itself upon us and yet is incomprehensible. “
As this little golden nugget of Truth seeped into my brain I began to get this giddy feeling, like when in my dreams I can fly. I stood up and went to the kitchen for a cup of coffee and it felt like my knees might bend backwards and send me falling onto my face. I came back and sat in a different chair and just stared at the back of my computer like it was iconography.
And I knew I was going to crack it. But I had received this epiphany during the very act of formally writing out my terms of surrender.
luck chance coincidence providence…