Discussion: This Technical Tidbit details an example of using the resonant frequency of a circuit to determine a desired circuit parameter, in this case the capacitance of a BNC barrel adapter. I have used measurements and caclulations like this many times to derive circuit parameters where I did not have access to a network analyzer. In some of the earlier cases, I am not sure network analyzers were available at all.

Figure 1 shows the experimental setup composed of a one inch (~2.5 cm) square wire loop connected to a BNC barrel adapter, covered with yellow heat shrink tubing, and a black plastic covered square shielded loop of the same size held over the plain wire loop. One way of constructing a square shielded loop is given in my December 2000 Technical Tidbit. Figure 2 shows a picture of the wire loop and BNC barrel adapter. Sometimes I feed the loop high voltage electrical transient waveforms, as in the November 2007 Technical Tidbit. For those applications, soldering the wire to the BNC barrel is important for safety. For the method of this article, soldering the wire is not critical but leads to a physically robust loop. The 16 AWG brass wire used to form the loop is stiff enough to hold its shape, is easy to solder, and just fits into the center pin hole of the BNC adapter.


The black plastic covered square shielded loop is driven from the tracking generator of a spectrum analyzer and its return loss relative to 50 Ohms plotted in Figure 3. One could also plot SWR or reflection coefficient and get a similar result. The June 2006 Techical Tidbit describes how to optimize the measurement parameters of the instrument. A directional coupler can also be used to measure the reflected power from the loop if the instrument cannot directly measure it. For this test, a shielded loop is preferred for connection to the tracking generator signal source to minimize errors caused by capacitance between the loop and the structure to be measured.

In Figure 3, note the sharp dip of about 2 to 3 dB in the return loss of the shielded loop at about 363 MHz. At that frequency, the inductance of the wire loop and the capacitance of the BNC barrel adapter is resonant and the resulting tuned circuit absorbs energy from the shielded loop above it. The result is the dip evident in Figure 3.


That the dip in Figure 3 is due to the wire loop and its BNC barrel adapter forming a resonant circuit can be shown by Figures 4 and 5. Figure 4 shows the two loops separated by a distance greater than the size of the loops and Figure 5 shows the resulting return loss plot. As can be seen in Figure 5, there is no dip at 363 MHz., just the small series of ripples in the return loss. The gradual downward trend in Figure 5 of increasing return loss as frequency increases is mostly due to loss in the RG174 coax cable used to connect the shielded loop to the analyzer.


Using the inductance calculator at Missouri University of Science and Technology, one can determine the inductance of the yellow wire loop as being about 80 nh. Since the frequency of an LC resonant tank circuit is given by:


and we know F_R = 363 MHz. and L = 80 nH, the capacitance of the circuit (which is mostly in the BNC barrel adapter) must be about 2.4 pF. I have used techniques like this to develop electrical models of connectors and other physical structures when a network analyzer was not available.