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Friday, September 18th

Measuring Structural Resonances in the Time Domain – Part 1


Figure 1. Experimental Setup with Parallel Plates and Connecting Wire


Abstract: Oscilloscopes are more common in most engineering labs than network analyzers or spectrum analyzers, so measurement methods that use oscilloscopes maximize the return on lab equipment for many companies. A method of measuring structural resonances using an inexpensive pulse generator and an oscilloscope is described and results are presented.

Discussion: In the June 2006 Technical Tidbit, I described a method of using a spectrum analyzer or a network analyzer to measure structural resonances in electronic equipment. But what if you don’t have one of these instruments? Figure 1 shows the test setup for an alternate method using an oscilloscope and an inexpensive pulse generator. This setup was used to generate the data presented in this Technical Tidbit. The test setup is composed of two copper clad boards connected by the red test wire and separated by about two cm to simulate two circuit boards in proximity or a circuit board mounted over a chassis. The wire connecting the board “ground planes,” while on the long side, is not any worst than many board to board or board to chassis ground connections I have seen in industrial equipment and some medical equipment.There are two wire loops (a.k.a. magnetic field probes) placed near the red wire so that one side of each loop is parallel to the wire. One loop is connected to a pulse generator, model TG-EFT, from Fischer Custom Communications that is shown in Figure 2. The general method of using this pulse generator and magnetic loops to couple pulsed noise into circuits is described in the October 2007 Technical Tidbit on this site. The second loop is connected to a 50 Ohm input of the scope. A detailed picture showing construction details of one of the loops is shown in Figure 3.

Figure 2. Fischer TG-EFT Pulse Generator
The TG-EFT pulse generator was set to 166 Volts open circuit for this test. The pulse voltage coupled into the red wire has a risetime of about 300 ps and a duration of about 4 ns. This stimulus results in ringing at the resonant frequency of the setup. In some cases, more than one resonant frequency may be present.

Figure 3. Loop Used for Noise Injection

Figure 4 shows a close-up of the loops coupled to the red “grounding” wire. The mutual inductance between each loop and the wire is likely on the order of about 10 nH of the total loop self-inductance of about 80 nH. The loops are separated to minimize direct coupling between the pulse generator driven loop and the sensing loop connected to the scope. Excessive direct coupling between the loops can result in too much loop output to the scope from the initial pulse, making it difficult to see the resonance without overloading the scope input.

Figure 4. Close-up of Loops Coupled to Wire Connecting the two Boards

Figure 5 shows the output of the loop connected to the scope. Since I knew the resonance would be at a relatively low frequency, I used  the bandwidth limit on the scope vertical amplifier to filter out the initial pulse from the generator and show only the resonance of the boards and connecting wire. The amplitude of about 20 mV is of little importance being determined by the generator output, the mutual inductance between the loops and the wire, and the vertical amplifier bandwidth limit used in the scope.

Figure 5. Resonance of Plates and Wire

In Figure 6, the first few cycles of Figure 5 are expanded to measure the ringing frequency. The scope indicates a frequency of about 37 MHz (readout near bottom of screen). A frequency in this range is to be expected given the circuit dimensions.


Figure 6. Frequency Measurement of Resonance, ~37 MHz

This method is especially useful for systems where boards and system components are connected by wires having resonances below 100 MHz. One could also use RF injection probes and current probes to do similar measurements on longer system cables at lower frequencies. Higher frequencies will be the topic of Part 2 of this Technical Tidbit.


Summary: A simple method of injecting pulses into circuits for measuring  resonant frequencies is described. This method is useful for resonances below 100 MHz. Considerations for higher resonant frequencies will be covered in a second Technical Tidbit on this topic.


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