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What's Your EQ?
August 1966 Radio-Electronics

August 1966 Radio-Electronics

August 1966 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.

Here are two more circuit problems for you from the August 1966 issue of Radio-Electronics magazine. The first is a fairly familiar tapered resistance network where you are asked to determine the input resistance of the infinite network. Out of curiosity, I asked Arya, ChatGPT 4.1, Grok 3, and Gemini 2.5 Pro, to calculate the given formula to 75 decimal places. I received four different answers. All agreed to 33 decimal places, and three of them agreed to 51 places, then everything fell apart. Once again I warn: Do not blindly trust the results of AI clients. Verify everything important!!! The other problem is to determine the output waveform of a duo-diode vacuum tube circuit. The semiconductor equivalent is a pair of PN junction diodes with the anodes at the top.

What's Your EQ?

What's Your EQ?, August 1966 Radio-Electronics - RF CafeConducted by E. D. Clark

Three puzzlers for the student, theoretician and practical man. Simple? Double-check your answers before you say you've solved them. If you have an interesting or unusual puzzle (with an answer) send it to us. We will pay $10 for each one accepted. We're especially interested in service stinkers or engineering stumpers on actual electronic equipment. We get so many letters we can't answer individual ones, but we'll print the more interesting solutions - ones the original authors never thought of.

Write EQ Editor, Radio-Electronics, 154 West 14th Street, New York, N. Y. 10011.

Answers to this month's puzzles are on page 91.

 

Tapered Network - RF CafeTapered Network

The diagram shows an example of a tapered ladder network that extends to infinity. What is the input resistance?

- Paul J. Nahin

 

 

 

? ? ? Circuit - RF Cafe? ? ? Circuit

Under the conditions shown in the diagram, can you determine the waveform and range of the output voltage developed between terminal A and ground? The internal resistances of both input voltage sources are assumed to be negligible. Also, the resistance and self-potential of the diodes are negligible. 

- Kendall Collins

Quizzes from vintage electronics magazines such as Popular Electronics, Electronics-World, QST, Radio-Electronics, and Radio News were published over the years - some really simple and others not so simple. Robert P. Balin created most of the quizzes for Popular Electronics. This is a listing of all I have posted thus far.

RF Cafe Quizzes

Vintage Electronics Magazine Quizzes

Vintage Electronics Magazine Quizzes

Vintage Electronics Magazine Quizzes

Answers to What's Your EQ?

These are the answers. Puzzles are on page 40.

Tapered Network Solution - RF CafeTapered Network

If the first section of the network is removed, the remaining portion looks like Fig. 1. This new network is identical to the original except that each of the resistors has been multiplied by 1/2.

By a basic theorem of scaling, if a resistive network has all of its resistors multiplied by a constant factor, the input resistance will also be multiplied by the same factor. Thus, the input resistance of the modified network is 1/2R. The original ladder can then be drawn as in Fig. 2.

R = 1 + (1/2 1/2R)/1/4R

R2 - 1/2R - 1= 0

R = 1/4 (1 + √17) 

= (100 decimal places)

1.280776406404415137455352463993519134441310153866913126591484262003422437694 (Arya) 1.280776406404415137455352463993519256286799806343405108599658393273738586584 (Grok 3) 1.280776406404415137455352463993519256286799806343405056169742121389542578696 (ChatGPT 4.1) 
1.280776406404415137455352463993519256286799806343405108599658373356217779583 (Gemini 2.5 Pro)

 

? ? ? Circuit Solution - RF Cafe? ? ? Circuit

When the ac input voltage is zero, both diodes conduct. R2 and R3 are effectively in parallel, forming an effective resistance of 2/3 megohm between point A and ground. Since R1 is in series with this 2/3 megohm, the output at point A is 25 volts.

When the ac input voltage rises to +50 volts or more, the left-hand diode stops conducting and the effective resistance between point A and ground is 2 megohms (R2). The voltage divider (R1-R2) limits the maximum output voltage to +50 volts - just half the input.

As the ac input voltage drops below zero, the current through R3 and the left-hand diode increases. This decreases the current through the right-hand diode and, as a result, the output voltage decreases. When the ac input voltage reaches -50 volts or more, the right-hand diode is nonconducting and the output voltage is zero.

Correction from November 1966 What's Your EQ?

The solution to the "Tapered Network" puzzler (August 1966 EQ) contains an error. The first equation should read:
R = 1 + 1/4 R/(1/2 + 1/2 R)

Otherwise, the answer is correct as printed.

 

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   BSEE - KB3UON - AMA92498

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 lady's voice announced "You've Got Mail" when a new message arrived...

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