Author Archives: mathscinotes

It's Warm Out and the PVC is Getting Longer ...

Posted on 20-June-2014 by mathscinotes

I live in Minnesota -- where winter temperatures can be as low as -36 °C (-33 °F) and summer temperatures can be as hot as 38 °C (100 °F). Because most things expand when our days get hotter, we occasionally have things like doors and windows that are too tight in the summer and too loose in the winter. Today, I encountered a PVC pipe that was installed during the heat of last summer and it had ripped itself free of its mounting brackets during the cold of winter. Of course, it is summer now and the pipe is back to its installed length. I was asked by an electrical equipment installer today how much length variation should he plan for when using PVC pipe outdoors. It turns out the National Electrical Code (NEC) actually has a table that addresses this question and I will discuss in this post how that table was generated. Let's discuss the answer I gave this installer. Continue reading →

Posted in Construction, General Science | 2 Comments

Maximum Phone Line Length Math

Posted on 29-May-2014 by mathscinotes

I can see the days of the classic copper phone line coming to an end over the next few decades. Like analog video, it will eventually be replaced by digital services. For a fiber optic deployment (i.e. no copper), the old phones lines can re-purposed to carry the power needed by the fiber optic interface if AC power is not available. To carry power, the resistance of the line -- which is determined by the length and cross-sectional area of the line -- becomes very important. When carrying voice signals, phone line resistance was limited to ensure that the central office could detect the phone going off-hook. This post will use the maximum allowed line resistance to determine the maximum possible line length. Continue reading →

Posted in Electronics, Telephones | 9 Comments

Telephone Ring Trip Math

Posted on 27-May-2014 by mathscinotes

As you can tell by my recent posts, I am doing quite a bit of traditional landline phone math lately. The problems are not very complex, but their resolution is important to delivering quality voice service. Today, I have been working on the circuitry that determines when a phone has gone off-hook. Continue reading →

Posted in Electronics, Telephones | 5 Comments

Measuring Telephone Ring Power

Posted on 17-May-2014 by mathscinotes

I have been looking at some power data for telephone circuits today and this data provided a useful empirical check on the theoretical calculations that I have done elsewhere. When I showed the data to some other engineers, they had some good questions that I thought would be worth covering here. Continue reading →

Posted in Electronics | Comments Off on Measuring Telephone Ring Power

Yet Another Thermistor Discussion

Posted on 15-May-2014 by mathscinotes

I thought enough people may want to see this slight variation that it would be worth putting into a separate post. It turns out the optimal linearization value for RS is exactly the same as for my original post. This result makes sense if you think about it a bit because a nearly linear output across one resistor in the circuit implies a linear voltage across the other. You can derive this result rigorously using the same approach I used in the Appendix of my original post. Continue reading →

Posted in Electronics | Comments Off on Yet Another Thermistor Discussion

Phone Line Length Math

Posted on 8-May-2014 by mathscinotes

We make ONT products that provide telephone service in addition to data and video services. I was asked today what limits the length of a standard POTS phone line from an ONT. Most ONTs today are specified to drive a phone line less than 1000 feet long. As I started to write down my answer, I thought that this was a nice application of simple DC electronics and was worth documenting here. Continue reading →

Posted in Electronics, Uncategorized | Comments Off on Phone Line Length Math

Bisecting an Outside Wall Corner Angle

Posted on 5-May-2014 by mathscinotes

I have just returned from putting up crown molding at brother's house. It is always fun working with my brothers. In many ways, we are little different today than we were 40 years ago. During this task, I encountered a wall corner that was not square. Let's talk about how you can measure and bisect this angle. You need to bisect the angle when you want to cut the molding to fit around the corner (Figure 1). Continue reading →

Posted in Construction, Geometry | Comments Off on Bisecting an Outside Wall Corner Angle

ITU 100 GHz Frequency Grid Math

Posted on 24-April-2014 by mathscinotes

A physicist in my group and I were having a discussion about how the wavelengths (i.e. colors) for lasers are specified by an international standard and I thought this discussion would provide a nice example of a differential approximation. The widespread deployment of fiber optic cable (see Figure 1, Wikipedia) is a game changer for networking and may be our most important new infrastructure -- remember that high-speed wireless depends on cell towers interconnected with fiber optic cables. Continue reading →

Posted in Fiber Optics | Comments Off on ITU 100 GHz Frequency Grid Math

555 Timer Math

Posted on 10-April-2014 by mathscinotes

Quote of the Day With hard work, difficult material can be grasped. Step by step, incrementally, the novice can become the master. — Joshua Waitzkin. World Tai Chi champion and subject of the book 'Searching for Bobby Fischer'. He is … Continue reading →

Posted in Electronics | 8 Comments

A Lone Engineer in a Marketing Meeting

Posted on 9-April-2014 by mathscinotes

My staff is passing this video link around that illustrates what it is like being the lone engineer in marketing meeting. There is quite a bit of truth here. Continue reading →

Posted in Humor, Management | 2 Comments