Pulsed RF spectrum spreadsheet

Click here to learn about the effect of pulse width on solid-state devices

Click here to learn about spectrum analysis (from a medieval Keysight app note!)

New for April 2023: the spreadsheet that was used to create the images for this page is available in our download area, and features some improvements over the original.

New for May 2022. Pulsed waveforms are familiar to anyone that works on radar, like the terminal guidance system on the Neptune missile that deep-sixed the Moskva... Gunboat diplomacy is getting harder and harder to pull off.

Radar uses pulsed RF signals, which may or may not be frequency modulated (chirped).  Ignoring the chirp aspect, it is useful to be able to predict spectra for a pulse signal, for example, if you were creating a test plan as a remote employee with no lab access. With this in mind we created an Excel spreadsheet to do this.  It is not quite ready to be offered as a download, but if you are interested in a copy let us know.

There does not seem to be a great deal of information on the ol' world-wide web on how to predict pulsed waveform spectra.  On this awesome web site you will see a photo of a pulsed response with a nice explanation of what you are looking at (see figure 11). The spectra follows a "sinc" function (sin(x)/x). The nulls are spaced at the reciprocal of the pulse period, and the line spectra spacing is at the reciprocal of the pulse width. The RF frequency sets the center of the spectra.

We measured some pulse spectra using some really expensive Keysight gear (N9030B PXA Signal Analyzer), at 30 GHz center frequency. Why 30 GHz?  We just wanted you to be jealous if your spec-an can't reach Ka-band. We used an E8257D  Analog Signal Generator to provide the pulsed tone, with a cable that has maybe 6 dB loss between the two boxes. Fortunately, all the test equipment uses 2.4mm precision connectors so no adaptors were needed!

Before we start pulsing, here is a photo CW tone displayed, with amplitude -16.6 dBm.  Why didn't we pick a nice round number like 0 dBm? We didn't think of that!

Below is the simulated CW tone in our spread sheet.  If anyone knows of a way to plot spectral lines in Excel, we'd love to hear about that.  For now, the spreadsheet just plots dots for tones.‚Äč 

Next, we turned on pulse modulation, at 1μs pulse width and 10μs period. Check out the spectral lines. As expected there are nulls every 1 MHz (except at center frequency) and spectral line spacing is 100 kHz. The RF is said to have spattered. and the peak amplitude at 30 GHz is reduced by 20 dB. This is known as the pulse desensitization factor which we will abbreviate PSF.

Here is the spreadsheet prediction.  Looks good!  Note that there are perfect nulls at 29998, 29999, 30991 and 30002, but in reality there is a noise floor that  would obscure them in an actual measurement. 

Pro tip: there is no "sinc" function in Excel. When you blindly enter sin(x) and divide by x, at x=0, the value is incorrectly reported as zero because Excel apparently never went to college.  You need to put in an IF statement to detect for x=0, and substitute a value of 1 at that singularity.

Editor's note, April 2023: the title of this plot is wrong, it should say 10us period, 1us width... we'll fix that soon...)

Next, we used the integration option on the signal analyzer, to capture all of the spectral lines inside a window.  Doing this reveals that the average power is -26.53 dBm, 10 dB below the CW signal. Just as we'd expect for 10% duty factor.

We did not try to put an integration option into our spreadsheet... yet.

Let's increase the pulse period to 100μs, to 1% duty factor (editor's note: these parameters were corrected in April 2023). Now the spectral lines are so close to each other that you have to zoom in to see them. There are 100 of them between the nulls. The peak amplitude at 30 GHz is down 40 dB (the pulse desensitization factor for 1% duty).

Can our spreadsheet keep up with all those lines? Of course: 

So, what is the formula for pulse desensitization factor for rectangular pulsed RF? Let's call it alpha, and here it is:

Alpha=20*log10(duty factor).

Note that average power is much higher than Alpha (dare we say it is half as negative?)

Paverage=10*log10(duty factor)

Here is a table of pulse desensitization for you to memorize:

Duty Factor alpha
0.01 -40.000
0.02 -33.979
0.03 -30.458
0.04 -27.959
0.05 -26.021
0.06 -24.437
0.07 -23.098
0.08 -21.938
0.09 -20.915
0.1 -20.000

If you are interested in the spreadsheet let us know and we will try to duct tape it together soon. The hard part will be making the X-axis limits in the plots autoscale to your particular signal.

As a certain CEO used to say when he signed off of a town hall, "that's all for now!"

Author : Unknown Editor