# integration using "db"

Integration using "db", a forum discussion on Cleverscope Mixed Signal USB Oscilloscopes. Join us for more discussions on Integration using "db" on our Questions forum.

bnevins

7 Feb 2012
Posts: 19

I have the maths graph set up as source = spectrum graph
and b = integral of a.
When Y-axis is in "V" the integral looks correct.

When the spectrum graph is set to display in "db",

Then the db value is integrated, not the voltage.

I want to be able to look at the spectrum in db, and still do integrals
on the voltage!
bartschroder

10 Feb 2012
Posts: 427

The goal here is to find total power in mW and dBm. To do this display power density in the spectrum graph, in mW/Hz, integrate it, and then display power in both mW and dBM in the Maths graph.

For maximum voltage accuracy, I used the Flat Top FFT Window. I set the transform type to Power Density. I assume a 50 ohm load, with a 1mW reference. Using V = sqrt (RP) = sqrt (50 * 0.001) = 0.224V, I set the Channel A reference to 0.224V in Analog Names and Units.

I set the Frequency Graph Linear A Units to mW/Hz and the name to Pwr Density. The spectrum source is Scope.

For the Maths graph I set the A units to dBm and name to log Pwr, and the B units to mW and Pwr.

I was using a 5V p-p waveform. This is 1.77 Vrms. So we expect P = V2/R = 62.5mW. With a Flattop window, the power is distributed over about 4 frequency bins. In this example each bin is 977 wide, so the power density per bin is about 62.5/(4 x 977) = 16 uW/Hz. We display the power density in the spectrum graph. We see a peak of about 17 uW, which is about right.

The Maths equation graph integrates the power density, showing total power at the right hand end. We send it to the B channel as mW, and find 10 log(P) for dBm and send it to the A channel. This means that you see both linear and dB on the same graph. Use Fit to make the Y axis right.

The Maths graph has the X axis set to Hz and Freq (in Analog Names and Units), and the source set to Spectrum.

We hope this works for you! See the Scope, Spectrum and Maths Graphs below.
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