IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 32, NO. 1, FEBRUARY 1990 66

Short Papers Resonances in Electromagnetic Penetration of Deep Slots

Abstmct-This paper discusses the influence of depth on the trans- mission of narrow slots and presents curves of calculated and measured transmission that exhibit depth resonances. At these resonances, the transmission is much higher than predicted by zero-depth models.

I. INTRODUCTION

Many problems involving electromagnetic penetration of joints or cracks require a model that accounts for the depth of the crack. An overlapping cover, for example, could form a narrow opening of appreciable depth if the seal were not perfect. The higher the frequency under consideration, the more important depth becomes. This paper discusses the influence of depth on the transmission of narrow slots and presents calculated and measured slot transmission for deep slots.

The problem of interest is the effect of increasing depth on the transmission of narrow, finite-length slots in a plane conducting screen. Leviatan and Harrington’s work with small circular aper- tures [l] indicates that resonances due to depth exist. Harrington and Auckland [23 and Taflove et al. [3] studied depth resonances of infinitely long slots in thick conducting screens. These results, although useful for qualitative analyses, did not give quantitative re- sults for finite-length deep slots. To evaluate the effects of depth resonances of finite-length overlapping joints, the problem of a nar- row, finite-length slot in a plane conducting screen of finite thickness was solved, and these results were compared with measurement.

Lyon and SangsteF’s solution of the problem of finite-length slots in a thick-walled waveguide [4] illustrates an efficient method-of- moments approach to this problem. The solution presented here [5] is an application of this approach to this problem. There are, however, some important differences. Reference [4] dealt with the properties of slot antennas of a given fixed depth in thick-walled waveguides. The present study focuses on the variation of the transmission of slots as a function of depth. Instead of a waveguide radiating into a half-space through a narrow slot of finite depth, a plane wave in one half space was couped into a second half space through a narrow slot in a thick conducting screen. Accordingly, the Green’s function for the waveguide in [4] was replaced by the Green’s function for a half space. A convergence-inducing technique by Shanks [6] was applied in this solution to allow longer slots to be considered.

A frequency scan by the resulting computer code predicted the effect of depth on the transmission of the slot. Measurements of the transmission of a deep, dielectric-filled slot validated those predic- tions.

11. MEASUREMENT APPROACH

The measurements were made by illuminating the front face of an aluminum box that is 50 cm on each side. Fig. 1 shows the geometry of the test object. A slot is cut in the center of the front face. With the exception of the front, the interior walls of the box are lined

Manuscript received September 30, 1988; revised July 20, 1989. The author is with the Microwave Physics Division, Sandia National Lab-

IEEE Log Number 893 197 1. oratories, Albuquerque, NM 87185.

50 X 50 X 50 cm AI box

to power meter -

dielectric filled waveguide

standard gain horn

Fig. 1. Geometry of test object.

with absorbing material to reduce reflections. Thus, the box interior simulates an infinite half space behind a conducting plane.

A slot that is adjustable in depth yet still able to maintain its shape and good RF contact is difficult to construct. This problem was solved by building a section of waveguide with the same cross section as the slot. This waveguide was inserted into the slot from the rear and served to extend its depth. The waveguide section was made by wrapping copper sheet around a Lucite slab. A 12.5-by-10.0-cm copper sheet with a similar slot cut in it was placed over the rear of the extender to simulate part of the other side of the thick conducting plane. A dipole probe was placed at the rear of the box on the axis normal to the slot to measure the transmitted power density.

A solid aluminum front face was used first to quantify leakage into the box via unwanted paths. The leakage signal was below the noise floor of the instrumentation (-65 dBm) and was at least 28 dB below the minimum signal observed in the actual measurements.

III. RESULTS

To compare measurements of slot transmission with calculated val- ues, it is helpful to define a transmission coefficient 7. Place a probe behind the slot at position r , (where t-, is a position vector of magnitude r, whose origin is at the center of the front face of the slot), and measure a transmitted power density S,. If the transmit- ted power density were uniform over the half space behind the slot, the slot would have to transmit a total power P, equal to 2?rrkS,. Define the transmission cross section 7 as that area of the incident wave that contains power P,. In other words

where Si is the power density of the wave incident on the slot. Since S, is proportional to r;’ in the far field and Si is a constant, 7 is a function of the direction of the probe from the slot (due to the slot’s pattern) but not of the distance of the probe from the slot.

Figs. 2 and 3 show the transmission cross section 7 of a slot that is 4.1-cm long, 0.51-cm wide, and 9.0- and 10.0-cm deep, respectively. 7 is shown as a function of frequency from 2.0 to 4.0 GHz. The solid curves are the calculated values; the dotted curves are the measurements.

For a slot length of 4.1 cm and a Lucite dielectric constant of 2.57, the half-wave resonance should appear at about 2.3 GHz. Both the calculations and measurements in Figs. 2 and 3 show a peak there. The second length resonance, where the slot is one and one half wavelengths long, occurs at three times this frequency. The other three peaks in the figures, then, are not slot length resonances but are instead depth resonances. Notice that when the slot depth is changed,

001 8-9375/90/0200-0066$01 .00 0 1990 IEEE

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 32, NO. 1, FEBRUARY 1990 67

DEEP SLOT TRANSMISSION 60 . 1

- D = S O 50

5 * MEAS i 40

E!

rn 2o

e 30 U W (II

(I) 0 0: I O U

0 2 2.5 3 3.5 4

FREQUENCY, GHZ Fig. 2. Transmission cross-section for 9-cm deep slot.

DEEP S L O T TRANSMISSION

I

or seams is important in the assessment of system susceptibility to electromagnetic interference.

ACKNOWLEDGMENT

R. P. Toth contributed greatly to the success of the measurements described in this paper. Discussions with J. M. Hoffman on both the code and the measurements were quite helpful.

REFERENCES Y. Leviatan and R. F. Harrington, “Electromagnetic transmission through apertures in a cavity in a thick conductor,” in IEEE Antennas Propgat. Int. Symp. Dig., 1982, pp. 491-492. R. F. Harrington and D. T. Auckland, “Electromagnetic transmission through narrow slots in thick conducting screens,” IEEE Trans. An- tennas Propagat., vol. AP-28, no. 5, pp. 616-622, Sept. 1980. A. Taflove et al., “Detailed FD-TD analysis of electromagnetic fields penetrating narrow slots and lapped joints in thick conducting screens,” IEEE Trans. Antennas Propagat., vol. 36, no. 2, pp. 247-251, Feb. 1988. R. W. Lyon and A. J . Sangster, “Efficient moment method analysis of radiating slots in a thick-walled rectangular waveguide,” Proc. Inst. Elec. Eng., vol. 128H, no. 4, pp. 197-205, Aug. 1981. L. D. Bacon, “FDSC: A microwave coupling code for slots of finite depth,” Sandia National Laboratories Rep. SAND85-0561, Apr. 1985. D. Shanks, “Non-linear transformations of divergent and slowly con- vergent sequences,’’ J . Math. Phys., vol. 31, no. 1, pp. 1-42, 1955.

A 20-Hz-to-200-kHz Magnetic Flux Probe for EM1 Surveys

2 2.5 3 3.5 4

FREQUENCY, GHZ Transmission cross-section for 10-cm deep slot. Fig. 3.

the upper three peaks change position, whereas the length resonance stays fixed.

It is not too surprising that these resonances should occur. The interior of the slot forms a very narrow waveguide through which the transmitted signal has to propagate. Reflections from the rear face of the slot change the input admittance at the front face, causing the admittance to repeat every half wavelength in the waveguide. The frequencies at which these depth resonances occurred corresponded to the depth D being an integral number of half wavelengths in the guide.

Two facts account for the lower-than-expected measured transmis- sion at the resonances. First, to get enough signal for the measure- ment, the dipole probe was built to have a large effective area. Since the scattering area of the probe was also large, the fields in the slot could interact with the probe’s scattered field. One way to mitigate this problem would be to use a smaller, less sensitive probe with a more sensitive receiver. Another approach would be to account for its effects by including scattering from the probe in the code. Sec- ondly, the calculation did not account for losses. Since the resonances are of fairly high Q, losses would significantly reduce the measured response at the peaks.

IV. CONCLUSIONS

The results are significant in that they change our earlier assump- tions about the effect of slot depth. We had assumed that slot length was the most important parameter in determining slot transmission and that depth served only to attenuate the coupled signal. Length is an important parameter, but at certain frequencies in this exam- ple, depth effects increased the transmission significantly over that predicted when slot depth is ignored. Thus, the depth of such cracks

JAMES P. HAUSER

Abstmct-A small magnetic flux probe has been developed, and it exhibits a magnetometer-like response over the frequency range of 20 Hz to 200 kHz with an effective antenna height of 1 m. The E-field equivalent noise floor of this device is -10 p V h & at 10 kHz. A switchable high-pass filter is included to allow the measurement of VLF fields in the presence of strong 50-400-Hz power-line fields.

The distinguishing features of this probe are its method of winding and shielding. This paper describes both the theory of operation and practical construction of such a probe.

I. INTRODUCTION

In response to a need for a convenient means of determining the optimum location to mount a VLF H-field antenna on aircraft, a small (2 x 12 cm) magnetic flux probe has been developed. This probe exhibits a magnetometer-like response in the frequency range of 20 Hz to 200 kHz. That is, unlike a simple coil, the probe output is proportional to field strength only and is not a function of frequency.

The first part of this paper discusses the theory of operation and some of the design considerations for the probe. The second part describes its practical construction and calibration. Somewhat larger probes (2.5 x 20 cm) have been constructed, and they extend the lower frequency response to 5 Hz and reduce the electronic noise floor by 10 dB. However, they will not be discussed here.

11. THEORY A N D DESIGN

Numerous articles and texts have been written about shielded loops for the measurement of time-varying magnetic fields (see, for exam-

Manuscript received December 1, 1988; revised July 28, 1989. The author was with the Aero Spectra Corporation, Boulder, CO. He is

currently with the Naval Postgraduate School, Monterey, CA 93943. IEEE Log Number 8931974.

0018-9375/90/0200-0067$01 .OO 0 1990 IEEE