### Days Postings

### Blog Series

### Subscribe to Blog via Email

### Copyright Notice

© Mark Biegert and Math Encounters, 2017. 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.### Disclaimer

All 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.

# Category Archives: Electronics

## Thermal Calculation Example for a Simple Electronic Component

An circuit designer came to me yesterday with an interesting problem whose solution nicely illustrates how simple component thermal calculations are performed. He was seeking advice on calculating the junction temperature of a Schottky diode (Figure 1) used in a switched-mode power supply. Continue reading

Posted in Electronics
1 Comment

## Analysis of 555-Based PWM Circuit

I received a request for the design formulas that can be used to estimate the frequency (f) and duty cycle (DC) generated by the 555 timer-based Pulse Width Modulator (PWM) circuit shown in Figure 1. The presence of diodes in the charge and discharge paths are the main cause of the confusion. Continue reading

Posted in Electronics
Leave a comment

## Linear Temperature Coefficient Resistor Nonlinearity

Our products contain many analog circuits. These circuits often require temperature compensation in order to meet their requirements across the product's entire temperature range. To perform this compensation, we often use resistors with a specified Temperature Coefficients of Resistance (TCR). A vendor recently stopped manufacturing one of the resistors we use for temperature compensation, and we needed to find a substitute. While searching for a substitute resistor, I needed to understand just how linear the approved resistor's temperature variation is so I can find an appropriate substitute. Continue reading

Posted in Electronics
1 Comment

## Yet Another FPGA Differential Termination Example

An engineer asked me for assistance on determining the termination circuit for a Xilinx uG476 series 7 FPGA. The circuit works is slightly different manner than those termination circuits I have developed before (here and here) because there is not termination voltage, so I thought I should document my work in detail. I will be using Mathcad 15 to determining the optimal resistor values for (1) terminating the circuit in printed circuit board's characteristic impedance (Z0), and (2) ensuring that I preserve as much of the transmit signal level as possible without exceeding the input circuit's maximum voltage level. Continue reading

Posted in Electronics
7 Comments

## Temperature Sensing with a Bandgap Reference

I have decided that my next home electronics project will be a precision thermometer that I can read over the Internet. I will be mounting the sensor at my cabin in Northern Minnesota, where winter temperatures can drop to -40 °C or lower. During the summer, temperatures can rise to nearly 40 °C. My plan is to connect the unit to a Raspberry Pie that I use to provide remote monitoring and control. I decided that I going to use a Texas Instruments' LMT70 precision temperature sensor, which uses a well-known circuit called a Brokaw bandgap reference to measure the temperature of its die. Continue reading

Posted in Electronics
2 Comments

## Maximum Reach Estimates for Low-Voltage DC Power Delivery

It is no secret that I prefer Mathcad for the vast bulk of my computational work, but I live in a world in which Excel is universally available. As such, I must prepare Excel workbooks for others to use. Today, I was asked to prepare an Excel worksheet that our salesman could use for estimating the maximum range over which different combinations of wire and voltage could deliver useful power. I include my Excel workbook here for those who wish to follow along. Continue reading

Posted in Electronics
1 Comment

## Ensuring Stable DC Power Delivery To Switching Loads

I presented a seminar over lunch today on short-range DC power distribution, which I believe is one of the most exciting areas in electronics today. AC power distribution has dominated power engineering since the "War of the Currents" ended with Westinghouse's AC system winning a decisive victory over Edison's DC system back in the 1890s. Starting in 1930s Europe, high-voltage DC distribution has slowly gained a foothold in some long-haul, high power distribution applications, but most power distribution has continued to be dominated by AC. Continue reading

Posted in Electronics, Power Over Ethernet
Leave a comment

## Effect of Wire Length on Surge Protector Let-Through Voltage

While reading about how these units worked, I noticed that the amount of surge voltage they let pass (called let-through voltage) is a function of the hookup wire length. The units are tested with a hookup length of 6 inches, and the user is warned that the let-through voltage increased by ~20 V per inch of additional wire. I became curious about the origin of this rule of thumb. In this post, I will show you where this rule of thumb comes from. Continue reading

Posted in Electronics
Leave a comment

## Quick Look at a High-Power PoE Graph

I have been sitting in a meeting on a high power version of Power over Ethernet (PoE) known as IEEE 802.3bt. It supports 90 W of output power with a guarantee of 71 W at the load. During the talk, Figure 1 was discussed (my version of the chart). When I am given some mathematical information, I like to experiment with it to see if I understand what I am being told. Continue reading

Posted in Electronics, Power Over Ethernet
Leave a comment

## Using SUMPRODUCT to Evaluate Two-Variable Polynomial

One of the most common computation tasks that my customers face is estimating battery capacity based on the battery's temperature and discharge current. Figure 1 shows a example of the capacity curves for a typical lead-acid battery. Ten years ago, I chose to implement this function with an Excel spreadsheet that used a polynomial approximation for this function. An engineer today asked me to explain how my Excel implementation works, and I felt this would be a good topic for a post. This approach is implemented using SUMPRODUCT – no helper cells were required. Continue reading

Posted in Batteries, Electronics
2 Comments