A Rambling Wreck: Book 2 of The Hidden Truth by Hans G. Schantz

Author:Hans G. Schantz [Schantz, Hans G.]
Language: eng
Format: azw3, epub
Published: 2017-07-01T04:00:00+00:00

Those circles… those arcs… I tilted the center line. It looked remarkably like the background on MacGuffin’s yin-yang diagram. I raised my hand. “Professor Fries, what is this graph?”

“That is a Smith Chart. You’ll need to make copies of this sheet,” he announced to the class. “We’ll be using it to solve impedance matching problems graphically.”

I remembered the words from MacGuffin’s manuscript – that “Mr. Bini” (Majorana) said the yin-yang diagram followed from the work of an American named Smith and a Russian mathematician. I may have finally found the elusive Mister… Doctor? Professor? Smith. I couldn’t believe my good fortune. I’d been searching the library for the last couple of weeks looking for a physicist named Smith, and here he was in my microwave circuits textbook: Phillip Hagar Smith. Only, apparently he was an electrical engineer, which explained why I hadn’t found him.

My eagerness to solve the rest of the mystery overcame my discretion. “Is there a Russian mathematician known for his work with Smith?”

“No,” Professor Fries paused, searching his memory. “I don’t recall Smith collaborating with anyone in particular let alone a Russian mathematician. Of course, Schelkunoff came up with the concept of impedance in the 1930s, so Smith’s work followed from Schelkunoff’s.”

“And Schelkunoff was Russian?”

“I believe he was American.” Professor Fries seemed amused at my sudden interest. “He may have come from Russia originally, though. We’ll be discussing him today, so hold your questions for now.”

Every electrician and electrical engineer knows Ohm’s law: voltage equals current times resistance (V = I R). A little algebra tells you that resistance is the ratio of voltage to current (R = V/I). Heaviside, along with Lodge and a few others, extended Ohm’s law to cover AC or alternating current circuits. In the modern representation, voltage, current, and resistance become complex numbers, only the resistance gets called “impedance” and it has two parts: “resistance” (R) is the real part and “reactance” (X) is the “imaginary” part (Z = V/I = R + jX). Of course, there’s nothing truly imaginary about it. Both parts are physically real – complex numbers are just a bookkeeping method – keeping track of a voltage wave and a current wave, for instance, that may have different amplitude and phase.

Don’t ask me how impedance got denoted by the letter “Z” and reactance by the letter “X.” Maybe it’s because current already took the letter “I” and resistance had adverse possession of “R.” And don’t get me going on how electrical engineers use “j” to denote the square root of negative one instead of “i” like physicists and mathematicians. They certainly didn’t disclose such sensitive information to mere undergraduates.

Anyway, this Schelkunoff had the brilliant idea that if impedance was the ratio of voltage to current, then maybe there was an analogous kind of impedance that could be defined as the ratio of electric to magnetic field. The units make it really clear: electric field is volts per meter and magnetic field is amps per meter, so the ratio of electric field to magnetic field works out to volts over amps, just like voltage over current.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.