Saturday, June 30, 2012

Oscilloscope Peak Via Slope

The first oscillating magnetic field superconductor levitation tests yesterday went great. With the Peavey power amplifier driving the electromagnet, the superconductor levitated at frequencies up to 164 Hz. An interesting measurement problem arose that required the use of a math trick to compensate for the limitations of the oscilloscope. Our oscilloscope has a maximum vertical range of 5 volts per division. There are 8 vertical divisions on the screen, so as long as the oscillating voltage from the amplifier is less than or equal to 40 volts peak to peak, we can read its peak value by counting divisions on the oscilloscope screen. To attain the necessary levitation force however, the oscillating voltage applied to the electromagnet had to be greater than 40 V peak. Instead of readable trace like the one shown above, the oscilliscope looked like:

There aren't enough divisions on the scope screen to read the voltage. This is where the math trick comes in. We know the frequency of the sine wave and we can measure the slope of the wave as it crosses zero. Using that information, we can calculate the peak value. The equation for a sine wave is:

Where A is the peak value of the sine wave that we can't see on the screen.

The derivative, or slope, of a sine wave is:

The cosine of 0, (the value where where the sine wave crosses the x axis), is 1, so we can setup an equation:

Now, if we know the frequency and measure the slope as rise over run on the oscilloscope screen, we can calculate the unknown peak value A.

Picture of the Day:

From November2006

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