Welcome to the RF Cafe Website

Search:                 | Sitemap

About RF Cafe | Homepage Archive

Kirt Blattenberger (KB3UON)

Advertise on RF Cafe (Advertisers)

RF Cafe Live Blog | Forums

Copyright 1999-2030

Electronics & RF | Mathematics

Physics & Mechanics | Quotes

Crosswords | Humor | Podcasts

Quizzes | Cogitations | Articles

Parts & Services | Videos

Radar Handbook | Cool Things

Selected Vintage Magazine Articles

Electronics World | Radio-Electronics | OFA

Radio & TV News | QST | Popular Science

Popular Mechanics | Radio-Craft | Electronics

Popular Electronics  | Mechanix Illustrated

Short Wave Craft | Saturday Evening Post

RF & Electronics Symbols for Visio & Office

RF & Electronics Stencils for Visio

RF Cascade Workbook | Espresso Workbook

TotalTemp Technologies (Thermal Platforms) - RF Cafe



RF Electronics Shapes, Stencils for Office, Visio by RF Cafe
Rigol DHO1000 Oscilloscope - RF Cafe

Correspondence: Ladder Lingo
January 1967 Radio-Electronics

January 1967 Radio-Electronics

January 1967 Radio-Electronics Cover - RF Cafe[Table of Contents]

Wax nostalgic about and learn from the history of early electronics. See articles from Radio-Electronics, published 1930-1988. All copyrights hereby acknowledged.

Mr. Milton Badt submitted this "Ladder Lingo" response to the "What's Your EQ?" feature in the June 1966 issue of Radio−Electronics magazine. Interestingly, while he pointed out the significance to the relation to phi (φ), defined as (1+√5)/2, he did not also note that the fraction is commonly referred to as the Golden Ratio, and its result, 1.618034... is called the Golden Number. A rectangle with side lengths who's proportions are according to a/b = φ is called a Golden Rectangle.

Correspondence: Ladder Lingo

Ladder Lingo Radio-Electronics January 1967 - RF CafeDear Editor:

About the problem on the resistance of an infinite ladder network, which appeared in "What's Your EQ?" in the June issue. This has an interesting sidelight, especially for electronics men interested in mathematics.

The answer, (-1 + √5)/2, is equal to

the reciprocal of "tau" (also called "phi"), which appears many times over in geometric design, architecture, and art, as well as in mathematics. Evidently we may now add electronics to the list.

Briefly stated, tau is the ratio of length to width (aspect ratio) of a rectangle, the semiperimeter of which bears the same ratio to its length, as its length bears to its width. Tau is approximately equal to 1.618034.

A curious property of tau is that it is the only positive number which becomes its own reciprocal by subtracting 1 from it. In view of the ladder network problem this means that if you add a single 1-ohm resistor in series with the input, the new network has a resistance equal to tau, or (1 + √5)/2. A little manipulation will verify that this is the reciprocal of the original expression above.

Another interesting aspect of tau, which for the astute observer will tie it in directly with the ladder network problem, is the following alternate way of expressing it:

IMAGE HERE

[Tau or phi - it's Greek to me. - Editor]

Milton Badt, Jr.

APO, N.Y.

 

 

Posted April 4, 2023

RF Cascade Workbook 2018 - RF Cafe

About RF Cafe

Kirt Blattenberger - RF Cafe Webmaster

Copyright:
1996 - 2024

Webmaster:

Kirt Blattenberger,

BSEE | KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while tying up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

Copyright  1996 - 2026

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website: AirplanesAndRockets.com | My Daughter's Website: EquineKingdom

KR Electronics (RF Filters) - RF Cafe



Innovative Power Products Passive RF Products - RF Cafe