What a Difference a Wave(shape) Makes

The blog A Little About RMS introduced the concept RMS (Root Mean Squared) as a way of expressing the equivalent effect of alternating current vs. direct current electricity in the power consumed by a resistive load.  Now would be an excellent time to read that one again before going ahead with this one.  As part of that blog, it was discussed that producing an equivalent effect across a resistive load with alternating current required a higher peak voltage than the constant direct current voltage that would be required to produce the same effect.  The comments in that blog were limited to one particular waveform, sinusoidal or “sine wave,” which is to my knowledge, the only waveform used in supplying electrical energy commercially today and is most familiar to most of us.  Alternating current generators supplying the grid produce sine wave current.  There are applications, however, where other waveforms are produced for special purposes.  Changing the shape of the wave moves the numbers around quite a bit and has some significant consequences.  Let’s check it out.

One of the things to point out is that in the illustrations that follow, the values for the “Time” scale have been omitted.  This is because with a recurring wave (one that repeats exactly) there is no effect of time.  It doesn’t matter if it repeats 60 times a second (60 cycle) or 400 times a second or once a minute.

First, let’s review the most common waveshape, the sine wave or “sinusoidal.”

In order to produce the same effect on a resistive load (such as an electric heater or a light bulb), a sine wave modulated electrical source requires a peak voltage of 1.414 (√2) times that of a direct current source.

Now let’s look at a different wave shape, the triangle wave.

In order to produce the same effect on a resistive load (such as an electric heater or a light bulb), a sine wave modulated electrical source requires a peak voltage of 1.733 (√3) times that of a direct current source.

How about a rectangle shape?

In order to produce the same effect on a resistive load (such as an electric heater or a light bulb), a sine wave modulated electrical source requires a peak voltage the same as that of a direct current source.

The wave shapes shown above are the classics.  But, with today’s electronics, we can intentionally (or unintentionally) create nearly any wave shape one might imagine.  Let’s imagine –

Now we have a situation where the peak voltage to produce the same result is many times the equivalent of the direct current source to produce the same result.  In fact, our “imaginary” wave form is not at all unlike many of those we see in ultrasonic systems.

 – JF –