© Mark Biegert and Math Encounters, 2022. Publication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Mark Biegert and Math Encounters with appropriate and specific direction to the original content.
DisclaimerAll content provided on the mathscinotes.com blog is for informational purposes only. The owner of this blog makes no representations as to the accuracy or completeness of any information on this site or found by following any link on this site. The owner of mathscinotes.com will not be liable for any errors or omissions in this information nor for the availability of this information. The owner will not be liable for any losses, injuries, or damages from the display or use of this information.
Monthly Archives: May 2016
We have Memorial Day off from work and that can only mean one thing – time to work on some circuits for home projects. I have another inductive sensor project for which I want to generate a frequency that depends on the inductance value. The Colpitts oscillator is a good circuit for this type of application.
This is a quick note to document how I analyzed a circuit that I found on a tutorial and verified a statement made on the tutorial about the minimum gain required to startup the oscillation. I also derived an expression for the oscillation frequency. Continue reading
Years ago, I read the book Parallax (Figure 1) and really enjoyed the tale of how 19th century astronomers measured the distance to the nearest stars. This measurement was critical to providing scientists some idea as to the scale of the universe.
The book Parallax describes how simple trigonometry, along with the introduction of large telescopes coupled to precision measurement gear, could be used to measure the angular parallax of a star as the Earth revolved around the Sun – a method called trigonometric or stellar parallax. During my recent perusing of the Wikipedia, I discovered that there was an alternative form of parallax measurement, called dynamical parallax, that allows one to estimate the distance to stars that are beyond the limits of trigonometric parallax. Continue reading
I regularly receive questions on the handling requirements for Printed Circuit Boards (PCBs). In a previous blog post, I stated that I recommend that service personnel always wear gloves when handling outdoor electronics because electronics in an outdoor enclosure are required to function with an internal ambient temperature of 85 °C. The PCBs themselves usually operate a 10°C above the internal ambient temperature. So a maintenance technician could have to handle a PCB that is 95 °C (203 °F) – just short of the temperature of boiling water. I have measured PCB temperatures at Fort Mojave, AZ, and I can confirm the 95 °C value is real. Figure 1 illustrates how the temperature “stack up” works for a typical outdoor installation. Continue reading
I was reading a Wikipedia article on the star Iota Apodis (Figure 1), which is a binary star, and noticed that three apparent visual magnitudes were listed for the two stars: 5.41 (5.90/6.46). The visual magnitudes listed represented the combined and individual brightness of the two components (in parentheses). I became curious as to how the magnitudes were summed. Continue reading
For the last two years, I have been working from the standing position. While I would like to say I work standing because it is supposed to be healthier, I actually work while standing because I was having some issues with numbness in one of my feet, and working from a standing position eliminated this problem. While it took a bit of time to get used to, I now prefer working from the standing position. In fact, I am now setting up my garage-based shop area for standing work. Continue reading
I was reviewing an industry standard when I saw Figure 1, which clearly looked wrong – the asymptotes seem like they are in the wrong place. I decided to take a closer look at this figure and see if I could determine what the correct version of this chart would be. Continue reading
Many analog circuits are designed so that their critical performance characteristics are a function of the ratio of resistances (e.g. Figure 1). For example, I worked on analog pacemakers as a student intern. Those pacemakers were hybrid analog circuits with a number of parameters that were set using laser-trimming. In fact, a goal of many analog designers is for their creations to be ratiometric.
While you can laser trim values in production, this operation is expensive and may not be necessary if you can achieve a sufficiently accurate resistor ratio value using standard E-series resistors. Continue reading
It seems like the presidential selection process has gone on forever, and we still have months to go before it is over. To show my unhappiness about the whole process, I have hung an election poster for Admiral Ackbar outside of my cube. His one word slogan is a simple one – “Trap”. I have always thought it was telling that the admiral leading the rebel alliance was the last one to know that he had led his troops into a trap. Continue reading
gave a seminar today on the use of Mathcad 15 in an engineering organization. The discussion was mainly on Mathcad basics, plus my exhortations on properly documenting your math work so that it can be understood and supported by others – and years from now, YOU. I have given this presentation before, and it went well. During these seminars, I like to include examples of my standard process for doing engineering mathematics using a computer algebra systems. Continue reading
I recently had the need to be able to set precisely a non-standard resistance value in production. Historically, I have used potentiometers, mechanical or electronics. Potentiometers are undesirable in production because they tend to be expensive, unreliable, mechanical units require adjustment accessibility, and they can drift.
While I was researching options, I ran across an interesting approach that uses three resistors to realize any resistance from 10 Ω to 1 MΩ within 0.1 % using three resistors from a set of 70 standard resistance values plus short and open values. Continue reading