How to Derive the RMS Value of a Sine Wave with a DC Offset
Monday, February 20th, 2012Summary:
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.
The RMS Value of a Trapezoidal Waveform – Part 2
Friday, July 23rd, 2010Summary:
In a previous article, How to Derive the RMS Value of Pulse and Square Waveforms, I showed how to derive the RMS value of a pulse signal. In some applications, the trapezoidal signal plateau is not flat, but rather a ramp, as shown in Figure 1. A typical example is a DC-DC converter, where the transformer winding current might look like the signal in Figure 1. The waveform is still considered a trapezoidal waveform. Let’s calculate its RMS value.
Using the Summing Amplifier as an Average Amplifier
Sunday, July 4th, 2010Summary:
The summing amplifier can output the average of two, three or more signals. This is different than a signal average. The summing amplifier cannot, for example, output the average of a triangle signal. For that, you need an integrator to perform the average in the analog realm, or you need to sample the signal and calculate the average with a microcontroller. This type of average is the signal average in the time domain. I will write an article about the average of a signal in a near future.
How to Derive the RMS Value of Pulse and Square Waveforms
Sunday, June 13th, 2010Summary:
The RMS value of a pulse waveform can be easily calculated starting with the RMS definition. The pulse waveform is shown in Figure 1. The ratio t1/T is the pulse signal duty-cycle. As shown in other articles in this website (How to Derive the RMS Value of a Trapezoidal Waveform and How to Derive the RMS Value of a Triangle Waveform), the RMS definition is an integral over the signal period as in equation (1).
How to Derive the RMS Value of a Triangle Waveform
Monday, June 7th, 2010Summary:
What is the RMS value of a periodic signal? When a periodic signal is generated by a source connected to a load, a resistor for example, the RMS value is the continuous signal, the DC value which would deliver the same power to the load as the periodic signal.
This article shows how to derive the RMS value of triangle waveforms with different shapes and duty cycles.
How to Derive the RMS Value of a Trapezoidal Waveform – Part 1
Saturday, May 15th, 2010Summary:
In this article I will show you how to calculate the RMS value of a trapezoidal waveform. This periodic waveform is shown in Figure 1. It has a rise time from 0 to t1 and a fall time from t2 to t3. The plateau is between t1 and t2, and the signal is periodic with the period T. If you know this, then you can derive the RMS value of a triangle, square and pulse waveform as well.
