# Capacitor Self-Resonance

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1 Capacitor Self-Resonance By: Dr. Mike Blewett University of Surrey United Kingdom Objective This Experiment will demonstrate some of the limitations of capacitors when used in Radio Frequency circuits. After completing the experiment, the student should be able to a. Measure the self-resonant frequency of a capacitor. b. Measure the corresponding equivalent series resistance. c. Avoid the problems associated with connecting capacitors in parallel. d. Select suitable capacitors for various decoupling and coupling applications. Equipment Spectrum Analyser with Tracking Generator up to 1 GHz. 50 ohm Microstrip Test Jig ( See Appendix) off Coax Cables, 50 ohm BNC to BNC, 0.5m long 10dB BNC Coaxial Attenuator ( Pad) rious capacitors Equipment Set-Up Connect the equipment as shown in Fig. 1. Remove any capacitors from the Test Jig and check that the insertion loss is 10 db over the entire frequency range of the spectrum analyser. Any small variation can be corrected by normalising the display. Always have at least 10dB on the input attenuator of the spectrum analyser. Fig. 1 Equipment Set-up 1

2 Theory Rp Fig. Capacitor equivalent circuit Figure shows the equivalent circuit of a capacitor. R p, the parallel leakage resistance is usually many Megohms and can be ignored at RF. The inductance is mainly due to the leads of the capacitor. The electrode structure has inductance but is usually only significant in leadless surface mounted types and large capacitors with spiral wound electrodes. At the self-resonant frequency of the capacitor the impedance ( Z ) will be equal to the series loss resistance R s. C Fig. a. Equivalent circuit assuming Rp = infinity Test Capacitor Tracking Generator Output 50 Vs C Spectrum Analyzer Input 50 Fig. 3 Equivalent measurement circuit From the equivalent circuit at resonance, Fig. 3, we can calculate the attenuation. Here we assume the system impedance is 50 ohms. With the test capacitor (Z) disconnected, the input voltage to the spectrum analyser () will be = Vs 50 V 50 5 Vs/ Fig. 3a Thevenin Equivalent of source

5 For general-purpose use, a double-sided printed circuit board with 50-ohm BNC connectors is used. A 1.6 mm thick epoxy glass substrate (FR4 / GF) requires a track width of 3 mm for 50 ohms. The foil pattern of a suitable Test Jig is shown below. Note the four small holes near the centre of the Jig connect the top and bottom ground planes. This makes the ground impedance low at the point where the test capacitor is connected. These experiments have been submitted by third parties and Agilent has not tested any of the experiments. You will undertake any of the experiments solely at your own risk. Agilent is providing these experiments solely as an informational facility and without review. AGIENT MAKES NO WARRANTY OF ANY KIND WITH REGARD TO ANY EXPERIMENT. AGIENT SHA NOT BE IABE FOR ANY DIRECT, INDIRECT, GENERA, INCIDENTA, SPECIA OR CONSEQUENTIA DAMAGES IN CONNECTION WITH THE USE OF ANY OF THE EXPERIMENTS. 5

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