How to Calculate the RMS Value of an Arbitrary Waveform

by Adrian S. Nastase

Previous articles on MasteringElectronicsDesign.com talked about how to calculate the RMS of simple signals like a sine wave, trapezoidal and triangle signals, pulse and square signals. But, what about an arbitrary waveform? How do we calculate its RMS? Starting with the definition, as shown in previous articles, applying the integral, might not be an easy task. We need a different method. Enters the square root of the sum of squares.

The RMS value based on the square root of the sum of squares

If we have a few signals going through the same heating element, each signal heats the element independently of the other signals. This is valid, as long as the signals can be considered uncorrelated, that is, independent one of each other. The formula can be written as follows:

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Categories: Analog Design, RMS, Waveforms

Design a Unipolar to Bipolar Converter the Easy Way with Microsoft Mathematics

by Adrian S. Nastase

Many analog circuits can be calculated with simple algebra. This may involve an equation or a system of equations, but the calculations are quite simple. Take the differential amplifier, as an example. In a previous article, MasteringElectronicsDesign: Design a Differential Amplifier the Easy Way with Mathcad, I showed how to design the differential amplifier by solving a system of two equations with two unknowns using Mathcad. Since then, readers asked me if there is any other substitute for Mathcad that they can use to solve the system of equations. And the answer is, yes, there is one.

Microsoft Mathematics is a free application which is loaded with features. Besides its graphing, math formulas and units converter, it has an equation solver that can easily handle systems of equations. By changing a few values and letting the application calculate the unknowns, a user can tweak his circuit to match the design requirements.

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Categories: Analog Design, Differential Amplifier, Electronic Circuits Examples

Tenma 72-7745 Multimeter Review

by Adrian S. Nastase

A few weeks ago I received a Tenma 72-7745 multimeter and I have been using it since. When I opened the box I liked it right away. Small and light, with plenty of functions, Tenma 72-7745 is a digital multimeter perfectly fit for anybody’s lab. It measures DC voltage, true RMS voltage, DC and AC current, resistance, capacitance, diodes, frequency, duty cycle and temperature. It has features like auto ranging, relative measurements and hold. The multimeter is part of a family, 72-7735, 72-7740 and 72-7745. It has a RS-232 interface, so that one can use a computer to log measurements. Here are a few tests and notes I made for this review.

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Categories: Analog Design

Open-loop, Closed-loop and Feedback Questions and Answers

by Adrian S. Nastase

One of my readers posted the following questions in the comment section of MasteringElectronicsDesign.com: An Op Amp Gain Bandwidth Product.

I am doing a work on fully differential Negative feedback op-amp with capacitive divider configuration. I have some questions and confusions, can you please clarify?

What is the difference between closed loop gain and open loop gain, and are they dependent to each other?

How can we calculate the unity gain frequency if I have a 3-dB frequency of 100Hz and closed loop gain of 40dB?

Does the feedback factor (BETA) has importance with respect to any other parameters?

How will it help in finding the closed transfer function of the system assuming the op-amp as a single pole system?

The answers needed some space, more than the comment section could offer, so here is a post on the topics of op amp open-loop, closed-loop and feedback.

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Categories: Analog Design

How to Derive the RMS Value of a Sine Wave with a DC Offset

by Adrian S. Nastase

I noticed a question posted on one of Yahoo’s Q&A sites, asking what is the RMS value of a sine wave with a DC offset. The chosen answer as being “the best” was actually wrong. The next comment, which was trying to correct “the best” answer, was wrong too. I am not going to post the Yahoo link here. What I can do, is to show how to derive the RMS value of such waveform.

Let’s derive first the RMS value of a sine wave with no DC offset

Let’s start with the RMS value of a sine wave, with no DC offset, which is shown in Figure 1. It is well known that the RMS value of a sine wave is 0.707 times the signal peak level, but how can you prove this?

sine-wave-with-zero-offsetFigure 1

As shown in this article, MasteringElectronicsDesign.com: How to Derive the RMS Value of a Trapezoidal Waveform, or other RMS articles in this website , let’s start with the RMS definition.

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Categories: Analog Design, RMS, Waveforms

My Interview in EEWeb

by Adrian S. Nastase

I was recently interviewed by EEWeb for the Featured Engineer edition. EEWeb, an electrical engineering publication, has many remarkable sections, including Analog Design, RF Design, tools, jobs, projects, and even a comic section. Of interest is the EEWeb forum, which is a growing discussion board organized in categories.

Here is an excerpt from the interview:
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Categories: Analog Design, Opinion

Become a Mentor

by Adrian S. Nastase

For a few years now I mentor students at Ocean View High School in Huntington Beach, California. My activity is part of a program called Business Academy developed at Ocean High in the last years. Every spring, students meet accomplished professionals and business people who become their mentors. The goal of the program is to teach and show students the path to a professional life and what to do to pursue their goals.
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Categories: Education, Opinion

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