IEEE Consultants' Network of Long Island

RMS of A Square Pulse Train - John Dunn, Consultant, Ambertec, P.E., P.C.

You can find the root-mean-square (RMS) value of a unipolar square pulse train as sketched below using an average responding voltmeter, typically, a digital multimeter and a scope.

The RMS value equals the average value divided by the square root of the waveform's duty cycle:

 
While there are true-RMS meters that can conveniently yield this waveform's RMS value, such meters have crest factor limitations which become of concern for low values of duty-cycle. For this waveform, this method has no such limitation.

 

A Little Fun With Geometry - John Dunn, Consultant, Ambertec, P.E., P.C.

I am certainly no math historian, but having picked up a little bit here and a little bit there, we may consider the following.

We don't actually know for certain, but the Pythagorean Theorem might have been proven in ancient Greece this way:   

 

Were not restricted to the usual 3:4:5 right triangles that get shown to middle-schoolers. This construction is completely general.

Truchet Tiles - John Dunn, Consultant, Ambertec, P.E., P.C.

Truchet tiles are named for their inventor, Sébastien Truchet, 1657-1729. Please see http://www.irisa.fr/faqtypo/truchet/truchet3E.html and then let's have some fun with this:  

 

The value of logarithms - by Marty Kanner

John Dunn just wrote about looking for and finding exponontial functions that will represent experimentally taken data points. I would like to suggest that possibly the most important mathematical function to physical man is the logarithim. The characteristic sensitivity of man's five physical senses all track a logarithmic function.

The function is applied by engineers all over the place such as RF power transmission levels and sound levels in DB's (affectionately called doobies). The so called audio taper volume control really tries to track a logarithimic function. And, I hope you will forgive me for pointing out that the copper wire table can easily be memorized by recognizing that it can be represented by a single logarithmic equation.

My point is that if you are trying to apply a function to some physically taken data points, try the logarithim.

Marty Kanner

Fitting Exponential Equations to Data - John Dunn, Consultant, Ambertec, P.E., P.C.

Most physical processes in nature have exponential properties. Radiation half-life is one example, thermal transitions from hot to cold or cold to hot are another example.

Often, a set of data from some process can be a little messy, a little noisy. However, if the data points look exponential, the underlying process is probably exponential and its fairly easy to find an equation for that exponential behavior:

We can go from this:  

to something that looks like this:

A Letter on Logarithms from Uncle Morty - by Marty Kanner

Dear Shiran, Lee-Ad, and of course Shilee (Renee and Udi too),

I called today and spoke to Shiran who gave me a rundown on how everyone is. He also told me that he was busy studying and told me he was having trouble with the logarithm in math. I was thinking about it as this happens to be something that had become very important to me in my work and now I find it important on how I look at life in general. I decided to write you about this and when I went to my computer file holding the letters I sent you, I find that I haven't written (other than e-mails) in over 10 years-sorry about that.

I was wondering why Shiran and so many students find this difficult to understand and are quick to forget about it once they passed the course. I came to the conclusion that the great difficulty starts when the student sees no reason to understand or handle this mathematical function. I therefore conclude that if one is to teach the subject, then the first thing to do is provide  purpose for what you are teaching. Additionally, the next thing the student should be taught is how this function relates to the linear system we first learn about. The last thing to present the student is how to handle the logarithm. Unfortunately, this is usually the first and only thing the student is presented with.