The equations presented here make it possible to predict and analyze the resonant behavior of microwave circuits enclosed in rectangular shields.
Shielded enclosures are commonly used as protection for microwave printed-circuit boards (PCBs). While the enclosure can guard a PCB from environmental effects, it can also alter the electrical performance of the circuit. Understanding the effects of the enclosure and how to predict them can improve the accuracy of most modern computeraided-engineering (CAE) simulation tools. As Part 1 of this two-part article series explored last month, the effects of the shielded enclosure can be minimized by precisely predicting the frequency, location, and nature of enclosure-induced resonant modes, and the techniques for doing this were outlined in Part 1.
One of the keys to avoiding unwanted resonant modes involves knowledge of the maximum electric (E) and magnetic (H) fields and their corresponding resonant frequencies. The effects of resonant modes can be greatly reduced by careful placement and routing of circuits on a PCB. To demonstrate the approach, two filters were placed in proximity of a shield. The first filter (filter A) was placed in the center of the shield, resulting in TM110, TM210, and TM310 modes with E-field hotspots and expected field excitations at 4.1, 7.2, and 8.3 GHz.
In contrast, the second filter (filter B) was placed toward the bottom of the shield cavity. The field magnitudes are much less in this area, with less resonant effects expected than for the first filter's placement. A simulation with Ansoft HFSS electromagnetic (EM) software also predicted that resonant effects would be considerably less for the placement of filter B (Fig. 10).
Another example shows the effect of undesired coupling from one circuit to another (Fig. 11). The circuit connected from port 1 to port 2 consists of a grounded microstrip stub. The circuit connected from port 3 to port 4 is a stepped impedance microstrip lowpass filter. Both circuits are in the vicinity of high H-fields for all the five modes described in the table. So we should expect to see resonant effects at 4.2, 5.9, 7.2, 8.0, and 8.3 GHz. The energy from port 1 appearing at port 3 is plotted in Fig. 12. Note that there are five peaks of fairly high transmission at the predicted resonant frequencies.
If the same circuits are shifted inside the can (Fig. 13), where the single grounded stub is placed at an H-field null for the TM110 mode, it is expected that this mode excitation should be reduced (Fig. 14).
The other peaks are still pronounced, since the location of the H-field null for the TM110 mode is actually the location for high or even maximum H-field concentrations inside the shield for the other modes.
The above simple simulations are used to illustrate the point that placement and routing of RF circuitry inside the shield has an impact on the degree of excitation of the resonant modes. Also, as can be seen in the above E- and H-field plots, if higher-order modes are excited, then the entire shield becomes hot fairly rapidly, so circuit placement to reduce excitation of resonant modes may very well be a moot point.
Finally, a point that cannot be overstated is that effective circuitry placement only reduces the resonant effects, but does NOT get rid of them completely. The only way to get rid of the problematic resonances is to change the dimensions of the shield such that the resonant frequencies are far removed from any frequencies that are present in the design or by use of RF absorbers which in effect change the dimensions of the can (refer to ref. 4 for good overview of RF absorbers).
The information presented here is provided as a general overview for resolving and solving shield and cavity resonance issues that can plague RF design. Rough estimates of the resonant modes and frequencies can be determined from the simple equations provided here. Dominant and minor mode hotspots should be determined prior to layout to avoid the pitfalls of exciting unexpected modes. Optimum shield dimensions should be determined to reduce the effects of shield resonances. Also, the information provided here should provide an engineer with a troubleshooting aide for an existing design having shield resonance issues and as a tool to identify locations where to place RF absorbers or metal posts to break up resonant modes.
1. David K. Cheng, Field and Wave Electromagnetics, Addison-Wesley Publishing Company, Boston, MA, 1992.
2. N. Marcuvitz, Waveguide Handbook, IEEE, London, 1993.
3. B. Whitfield Griffith, Jr., Radio Electronic Transmission Fundamentals, Noble Publishing, Norcross, GA, 2000.
4. Paul Dixon, "Dampening cavity resonance using absorber material," RF Design, May 2004.
5. Lance Lascari, e-mail: email@example.com.