Discussion: Figure 1 shows an overall view of the test comprised of a pair of square shielded loops connected to an Agilent N1996A spectrum analyzer set up to perform a two port insertion loss measurement. The two loops are positioned end-to-end and held in place with paper tape on the back of the loops. A close-up of the two loops is shown in Figure 2. The semi-rigid coax used to form the loops is encased in the plastic seen in the figures.


Figure 3 shows the resulting plot of insertion loss (unnormalized) between 10 MHz and 1 GHz. Notice the significant dip of around 30 dB at about 394 MHz. This feature has the appearance of a resonance that can be explained with reference to Figure 4.



The capacitance between the shield segments shown in Figure 4 form a resonant circuit with the inductance of the two loops. The current path for the resonance is shown by red arrows. The loops I used were one inch on a side, so the effective loop for the resonant circuit is approximately two inches by one inch. The Missouri University of Science and Technology inductance calculator gives an inductance of about 125 nH for such a loop assuming a wire (shield) radius of 10 mils. The resonant frequency of 394 MHz then yields a capacitance of about 1 pF for the total capacitance in the tuned circuit of Figure 4. But how is energy coupled into this resonant circuit? There are a number of ways to explain how this happens, but the important point is that it does happen. Adding ferrite to the coax cables feeding the loops did not change the characteristics of Figure 3 so the current loop of Figure 4 is the controlling feature.

One possible simplified explanation is as follows: Current flowing in the center conductor of the driven loop generates inductive voltage drop (Ldi/dt) around the loop. A shielded cable is nearly an ideal transformer, so the voltage drop on the center conductor under each of the two shield segments is magnetically coupled into the shield segments as Mdi/dt. The mutual inductance, M, between the center conductor and the shield, is the inductance of the shield itself. This driving voltage on the two shield segments causes current to flow around the four shield segments coupled by the parasitic capacitance between the loop shields as shown in Figure 4 thus driving the resonant circuit. In this discussion, I am treating the circuit as composed of lumped elements since each segment and the loops themselves are small compared to a wavelength at 400 MHz.


If a resonance caused by the current path of Figure 4 is the reason for the dip in plot in Figure 3, then moving the loops apart should increase the resonant frequency. This would happen because the capacitance between the loops is reduced. Figure 5 shows the test setup modified to space the loops one cm apart. The two loops are taped to a plastic ruler to maintain the spacing during the measurement. A close-up of the spaced loops is shown in Figure 6.




The resulting two port insertion loss plot is shown in Figure 7. Note that the resonant dip has moved to about 495 MHz. This would represent a significant drop in capacitance on the order of 40%.


As the loops are moved further apart, the capacitance between all parts of the loops begin to contribute an increasing portion of the capacitance between the loops complicating the picture somewhat. One would not expect the capacitance to decrease as much as just that of the facing sides as the loops are separated.

A future Technical Tidbit will show how this effect can result in errors during troubleshooting a circuit using signal injection. The problem is that using a shielded loop can sometimes give a false sense of security that electric field effects are not important.