Author Archives: mathscinotes

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 →

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 →

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 →

I have been designing circuits with resistors since I was a kid working on science fair projects – I still remember building my first Radio Shack photocell project. While I have always thought of resistors as simple devices, I recently discovered that I have been laboring under a misconception about the standard resistor values.

Until last week, I believed that the values of the E-series standard resistor values were selected to ensure that if I needed a resistor within x% of a specific value, I simply needed to choose a resistor from the x% tolerance set. For example, Figure 1 shows the E12 series (i.e. ±10%) values – notice that each tolerance range overlaps the adjacent ranges. This means that you can always find an E12 resistor value within 10% of your required value. Continue reading →