IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 34, NO. I, FEBRUARY 1992 23

Radiation Properties of a Pigtail-Terminated Coaxial Transmission Line

Hassan A.N. Hejase, Member, ZEEE

Abstract-The method of moments is used to study the shield- ing effectiveness of a pigtail-terminated shielded wire (coaxial line) above a perfectly conducting ground plane. Numerical computations are performed in the RF frequency range, i.e., 25-1000 MHz. Pigtail wires on either or both ends of the shield are considered. Results are compared to those from the un- grounded case (floating shield). Results show that the presence of pigtail wires as ground connections at RF frequencies is undesirable and may further enhance radiation. The impedance termination have also been studied showing a small effect on the shielding effectiveness of the antenna structure.

Shield

I

Fig. 1. Geometry of the problem.

I. INTRODUCTION

N a previous work [1]-[3], the problem of a coaxial I line (shielded wire) placed vertically above a perfectly conducting ground plane was treated. Pigtail wires were used across the shield gap to connect the shield to ground and thus suppress any currents along the outer shield surface. These currents constitute the major source of EM1 coupling and radiation. Thus, it was shown that pigtails, although small in electrical or physical size, play an important role in coupling and shielding effectiveness.

In the present paper, we study a coaxial transmission line placed horizontally above a perfectly conducting ground, as shown in Fig. 1. The line is excited on one end through a coaxial line-ground feed and terminated on the other end by an impedance load. A small section of the shield is discontinued on each end leaving part of the inner conductor exposed to outside interference and coupling. Ideally, the shield would be extended over the entire length of the inner conductor and circumferentially bonded at each end to ground. However, i t is more practical to use pigtail wires as shield-to-ground connections. This is a common practice in missile systems where some wiring circuitry is run on the outer missile skin and shielded to prevent any coupling with other electronic circuitry inside the body. Usually, shield breaks exist on each end and use of pigtails to ground the shield is not uncommon. The quality of the pigtail wire connection is defined in terms of the shielding effectiveness introduced in [l], [3].

Paul [4], [SI carried out an extensive theoretical and exper- imental study of the effect of pigtails on coupling and cross talk at frequencies up to 100 MHz. He concluded that the elimination of pigtail wires could improve the effectiveness of the shield, and that pigtails have a dominant role in coupling and cross talk. The contribution of our paper is to provide

Manuscript received May 18, 1990; revised June 27, 1991. The author is with the Department of Electrical Engineering, University of

IEEE Log Number 9104204. Kentucky, Lexington, KY 40506-0046.

a better understanding of the pigtail-grounding mechanism in the 25-1000 MHz frequency range.

The logical question is: How effective are pigtails? The answer does depend on the configuration used. In the paper [ l ] , the use of single short pigtails and multiple medium size pigtails resulted in a good improvement of shielding effectiveness. However, the configuration studied here is rather different. At RF frequencies, the loop(s) formed between transmission line and ground through stray capacitances induce magnetic moments which may help increase or decrease the susceptibility of the system to EM1 depending on whether they add or subtract. Numerical restrictions prevent us from placing the line too close to ground in order to reduce the impedance between the line and ground. Throughout this study, we assume a solid shield in order to isolate the effect of the pigtail connection. Practical RF cables have braided shields. The small apertures formed between braids could become electrically visible at high frequencies and may present a major source of RF leakage and interference.

For numerical results, the transmission line was assumed to be lossless with a 50-0 characteristic impedance. The thin-wire approximation is invoked by assuming all line cross-sectional dimensions to be very small compared to the line length and the wavelength. The coaxial ground feed is modeled as a delta-gap voltage source just touching ground. Other models could have been used as well [1], [3]. The moment method WIRES code will be used to analyze the system as a wire-antenna problem. More about the WIRES code is found in previous literature [6], [7]. The thin-wire approximation will allow us to model the line configuration as an antenna problem. The effect of the transmission line interconnection of the exposed wire antennas and the loading effects are yet to be incorporated. Assuming only the quasi-TEM mode to be propagating along the coaxial line, the impedance matrix relating voltages and currents at the end ports of the line is obtained. The latter is then represented by two coupled lumped networks across the end ports [see Section 111. The

0018-9375/92$03.00 0 1992 IEEE

24 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 34, NO. 1, FEBRUARY 1992

Fig. 2. Simplified geometry for numerical computations.

equivalent antenna configuration is shown in Fig. 2. The coupled lumped networks resulting at the shield break ports are incorporated into the antenna moment method WIRES code in the form of impedance loading as will be discussed in Section 11.

Numerical results are presented in Section 111. The trans- mission line antenna of Fig. 2 is analyzed for several pigtail configurations and several load impedance terminations. Plots of antenna currents, input impedance, and maximum power gain are provided. Power radiated from the pigtail-terminated case is compared to that radiated from the ungrounded shield case, with each normalized to its corresponding input power to determine the shielding effectiveness of the antenna struc- ture. For pigtail connections at the feed end, the antenna current (on the outer shield surface) is reduced moderately in the lower frequency range. Hence some improvement in shielding effectiveness is obtained (less than 20 dB below 200 MHz). A pigtail at the load end proved to be unimportant because it cannot block the feed current from propagating along the shield section. At frequencies above 200 MHz, no significant improvement in shielding effectiveness is ob- served from the case when pigtails are absent. Results demon- strate that a change in cable impedance termination and the pigtail presence have a small effect on the shielding effectiveness of the structure. Hence, pigtails may become unnecessary. Stray capacitances between shield and ground provide the proper grounding mechanism at high frequencies. Another important aspect is the insensitivity of the feed section (generator) to the type of termination used when computing maximum power gain and shielding effectiveness. This characteristic could be exploited further at very high frequencies [SI, [9].

11. THEORY-INCORPORATION OF TRANSMISSION LINE COUPLING INTO THE MOM CODE

The radiation problem of a transmission line over a conduct- ing ground is treated using the method of moments. If the outer diameter of the line is much smaller than the line length and wavelength, the line can be modeled as a thin-wire antenna. The internal transmission-line coupling between end ports representing the shield discontinuities will be incorporated into the radiation MOM code in the form of lumped loading.

The moments method [6] converts an integro-differential equation in terms of the unknown current distribution into a matrix equation of the form

The procedure consists of subsectioning the wire antenna into -V short dipole segments connected together. The end points

of two adjacent segments define a port in space [lo]. Hence an N-port network is formed. If there is no lumped voltage generator or impedance across the port, the port is said to be short-circuited. The generalized impedance matrix [Z ] is determined by applying a current source to each port in turn, and calculating the open circuit voltages at all ports. The elements of matrix [Z ] depend only on the wire geometry used and the source frequency. The elements of voltage array [VI will be nonzero if the corresponding port is source-driven, and zero if the port is short-circuited. Once matrices [Z] and [VI are determined, the current array [ I ] is obtained by matrix inversion or other numerical analysis techniques. However, before [ I ] is determined, we have yet to include the effect of lumped impedance loading, lumped voltage excitation, and transmission-line interconnection between ports.

For a lossless coaxial transmission line of length L and characteristic impedance 20, port voltages and currents could be easily shown to be related by equations

= zTZz 11 + zTzJ 1 3 (2) (3)

(4) ( 5 )

< = ZT, ~ 1% + ZT,,

z T a 1 = ZT,, = jz, cot (k L ) ZTZJ = ZT,, = - 3 2 0 csc.(k L )

where the 2-parameters are given by

and k is the wavenumber. The transmission line could then be modeled as a thin-wire antenna of radius equal to the line outer radius and loaded at both ends by lumped networks representing (2) and (3). Consider the wire configuration as an N-port network with two ports i and j interconnected by a transmission line [ll]. Assume that these ports are loaded by lumped impedances ZL, and ZL, and excited by lumped voltage sources VG, and LrGJ. Fig. 3 shows the particular ports with two lumped networks representing all the above. Voltages across each port are then given by

where the quantity between parentheses models the transmis- sion-line interconnection between ports as derived in ( 2 ) and (3). From the generalized matrix equation (l), we can write the equations for port voltages $5 and Vj as

Substitution of (7) and (8) into (6) yields

HEJASE: RADIATION PROPERTIES OF A TRANSMISSION LINE 2s

I I I I

I I I \ Shield I

!I: t'

Fig. 3. Network modeling of internal coupling between the end ports of the shielded transmission line (ports i and j ) .

VGj = ( 2 3 % - ZTJz)Iz + ( 2 1 3 + ZL,, - ZT,,)Ij \

-k ZjkIk. (10) k = l

k # z J

Thus lumped impedance loading is applied at a port by adding the load impedance to the corresponding diagonal element in [Z]. Lumped voltage excitation is applied by replacing the corresponding zero in [VI by the voltage source value. If a transmission-line interconnection is present, the generalized impedance matrix [ Z ] is altered by subtracting Z T ~ ~ ( I C = i , j ) from the diagonal elements Z,, and Z13, and subtracting Z,_ ( I C # m = 2.3) from the off-diagonal elements Z,, and z,, .

111. NUMERICAL RESULTS

Moment method computations [6], [7] have been carried out for the circuit of Fig. 2 with the perfectly conducting ground plane replaced by the image antenna. The coaxial transmission line is assumed to be air-filled with a characteristic impedance 2, = 60ln(b/a) of 50 R. Hence b /u = 2.3. The antenna dimensions used are L = 1 m, D = 0.05 m, H = 0.04 m, a = 0.001 m, b = 0.0023 m, c = 0.0015 m. The antenna is driven by a I-V sinusoid on one end (feed end) and terminated with 50 R (2, = 2,) or 1000 R (typical high value) load impedances on the other end (load end). Computations are done in the frequency range 50- 1000 MHz. At these frequen- cies the transmission-line antenna is electrically 0.1 to 3.33 wavelengths long. At the lowest frequency, the electrical size of the loop formed between the wire antenna and ground (perimeter) is about 0.2 A. Pigtail wires on either or both ends are considered in addition to the floating shield case (no pigtails). Pigtail wires are treated in the WIRES code as wire junctions. The code also accepts multiple radius changes along the antenna. Current computations are performed along the inner conductor, antenna and pigtail segments of Fig. 2 at 100 and 800 MHz, with typical load impedances of 50 and 1000 R. Only a 4-cm long pigtail wire is being considered. Longer or shorter pigtails make a small difference since stray capacitances between antenna and ground become dominant at high frequencies.

Fig. 4 indicates currents at the feed ( I F ) , load ( I L ) , pigtail ( 1 ~ ~ . Ip,) and shield ( I S ) sections. The latter represents the current induced on the exterior of the coaxial transmission line (outer shield surface). Fig. 5(a) and (b) show current

Fig. 4. Structure currents: I F = current on feed section; IS = current on shield section; I L = current on load section; IpL . IpR = currents on feed and load end pigtails, respectively, 1~ and 1s denote positions along feed and shield sections, respectively.

7 1

- 6 Pigtail at Feed End - Pigtail at Load End

2 - 4

2 3

- 5 Pigtails at Both Ends

.w

5 6 2

$ 1

0

No Pigtail Pigtail at Feed End Pigtail at Load End Pigtails at Both Ends

Position Along Feed Section ( I F / A )

( b)

Fig. 5 . Current magnitude along (a) feed, and (b) shield sections (f = 100 MHz, ZL = 50 Q).

magnitude plots on the shield ( I s ) and feed ( I F ) sections at 100 MHz for a 5 0 4 termination. Currents on the pigtail(s) (IpL.IpR) and load section ( I L ) were computed but are not shown here. Computations not shown here show that the shield current is strongly excited for the ungrounded (no pigtail) and load-end pigtail cases. A pigtail at the feed end reduces the shield current by about 25% with respect to the ungrounded case (no pigtails). Although the pigtail effectiveness is diminished by the influence of the magnetic moments produced by the antenna-to-ground loops due to stray capacitances, the pigtail on the feed end results in improved shielding effectiveness. Further shield current reduction is observed when pigtails are connected at both ends.

Current computations were also performed at 800 MHz for a 50-R load and different pigtail configurations. Results show that a pigtail at the load end excites shield currents that are greater than those of the ungrounded case (almost 50% more) and hence it further enhances radiation. On the other hand, the configurations of a pigtail at the feed end and pigtails at both ends reduce the shield current to about 25 and 50% of

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 34, NO. 1 , FEBRUARY 1992

5200

4400

3600

2 2800 - 0 ; 2000

26

3600

3240

2880 - 5 2520

y 2160

1800

1440

L 1080 - 120

360

n

: ~ 1 1 ~ I '

,'

- No Pigtail Pigtail at Feed End ' Pigtail at Load End 1 Pigtails at Both Ends 1 '

~.~~ ~~~

- -

I (

n 100 200 300 400 500 600 i o 0 800 YOO 1000

Frequency (MHz)

Fig. 6. Input resistance versus frequency (Z, = 50 0).

~ No Pigtail Pigtail at Feed End Pigtail at Load End

. . ~ ~

- - Pigtails at Both Ends ~

I I -2000

-2800

I

0 I O 0 200 300 400 500 600 700 800 YO0 1000

Frequency (MHzj

Fig. 7. Input reactance versus frequency (Z, = 30 n).

that induced in the absence of pigtail connections. However, at 800 MHz, the shield is electrically long (8/3 wavelengths) and even a small current distributed along its length will radiate effectively. For a 1000-R load termination, the cases of pigtails at the feed end or at both ends are equally effective in reducing radiation at 100 MHz but they become less effective at 800 MHz due to shield electrical length. A pigtail at the load end enhances radiation at both frequencies.

Computations of other quantities such as input impedance, maximum power gain, and shielding effectiveness were also performed. Figs. 6 and 7 show plots of input resistance and reactance as a function of frequency and type of pigtail connection for a 50-0 load. Plots for a 1000-R load were also obtained but are not shown in this paper. Note that at certain resonant frequencies rather high values of input impedance are observed. Also, in the upper frequency range, both input parameters tend to oscillate between nearly fixed bounds. This suggests that for frequencies higher than 1 GHz bounds for the input impedance could be established and hence bounds for induced currents are found. This information could then be used to predict the behavior of the structure at very high frequencies [8]. Except at some select resonant frequencies, the input parameters remained unaffected by an increase in the load impedance from 50 R to 1000 R.

Fig. 8 shows the maximum power gain for a 50 R load. Note that at frequencies up to 200 MHz, pigtail connections at both ends reduce the gain by an average 15 dB with respect to the ungrounded case. Above 200 MHz, a floating shield (no pigtails) appears to be the best option. Pigtail connections on

10

0 B 2 -10

6 5 L -20

2 -30

'2 -40

-50

E' 5

-60 0 I00 200 300 400 500 600 100 800 YO0 1000

Frequency (MHz)

Fig 8 Maximum nower gain versur freouencv (ZT = 50 0).

~ Pigtail at Feed End Pigtail at Load End ....

- - Pigtails at Both Ends

-- I II -25 ' '

0 100 200 300 400 500 600 700 800 900 1000

Frequency (MHzj

Fig. 9. Shielding effectiveness versus frequency (Z, = 30 Q).

either end enhance radiation throughout the whole frequency range. Plots not shown here show that a change in load impedance does not alter the power gain significantly.

Fig. 9 shows the shielding effectiveness (SE) defined to be the ratio of total power radiated with no pigtail present to total power radiated in the presence of pigtails, with both powers normalized to the input power in each case. Positive decibels indicate that the pigtail configuration radiates less than the floating shield case (no pigtail). With pigtails at both ends, up to 20 dB of improvement in SE is obtained in the lower frequency end. Above 200 MHz, SE is reduced. All other configurations fail to improve SE at all frequencies. Larger loads show some improvement in SE for a pigtail at the feed end and a lower SE for pigtails at both ends, as shown in Fig. 9. Plots of shielding effectiveness for a 1000-R load are also obtained but are not shown here. Except near resonance, SE appears to be insensitive to the load impedance used [8], [9]. Therefore, except for the small improvement that a pigtail at the feed end and pigtails at both ends provide at frequencies below 200 MHz, the shielding effectiveness does not improve with shield-to-ground connections.

IV. CONCLUSIONS The effect of pigtail connections has been analyzed by

the method of moments. For a shielded wire placed parallel to a perfect ground, pigtail connections could reduce the effectiveness of the shield. Hence, the elimination of pigtails is necessary at RF frequencies. For lines longer than two wave- lengths ( f > 600 MHz), the load type appears to have little

HUASE: RADIATION PROPERTIES OF A TRANSMISSION LINE 27

effect on shielding effectiveness and input parameters. The insensitivity of the feed section to the termination type would allow establishing approximate bounds for input impedance

[9] A.T. McMahon, J. Weber, A Prothe, and A. Pesta, “Shielding effec- tiveness measurements for a SHFEHF field-to-wire coupling model,” presented at the 1989 IEEE Nat. Symp. on Electromagn. Compat., 1989, nn. 414-417. r r

and induced current at very high frequencies, where use of the computer code becomes formidable.

[IO] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design. New York: Wiley, 1981, p. 344.

11 11 R. Mittra, Computer Techniques for Electromagnetics. New York:

REFERENCES

H. A. Hejase, A. T. Adams, R. F. Harrington, and T. K. Sarkar, “Shield- ing effectiveness of pigtail connections,” IEEE Trans. Electromagn. Compat., vol. EMC-31, no. 1, pp. 63-68, Feb. 1989. H. A. Hejase, A. T. Adams, and R. F. Harrington, “A Quasi-static tech- nique for evaluation of pigtail connections,” IEEE Trans. Electromagn. Compat., vol. EMC-31, no. 2, pp. 180-183, May 1989. H. A. Hejase, “Radiation from a coaxial transmission line with a pigtail termination,” Ph.D. dissertation, ECE Dep., Syracuse Univ., Syracuse, NY, June 1987. C. R. Paul, “Effect of Pigtails on cross talk to braided-shield cables,” IEEE Trans. Electromagn. Compat., vol. EMC-22, no. 3, pp. 161 -172, Aug. 1980. -, “Basic EMC technology advancement for C3 systems-shield, a digital computer program for computing cross talk between shielded cables,” Tech. Rep. RADC-TR-82-286, vol. IV-B, Nov. 1982. R. F. Harrington, Field Computation by Moment Methods. Malabar, FL: R.E. Krieger, 1983. D. C. Kuo and B. J . Strait, “Improved programs for analysis of radiation and scattering by arbitrary bent wires,” Tech. Rep. AFCRL-72-0051, Rep. 15, Syracuse Univ., Syracuse, NY, Jan. 1972. A. T. Adams, J. Perini, M. Miyabayashi, D. H. Shau, and K. Heidary, “Electromagnetic field-to-wire coupling in the SHF frequency range and beyond,” IEEE Trans. Electromagn. Compat., vol. EMC-29, no. 2, pp. 126-131, May 1987.

- - Hemisphere, 1987.

Hassan A. N. Hejase (S’86-M’86-M’87) was born in Torreon, Mexico on August 10, 1959. He re- ceived the B.S. degree with honors in industrial electrical engineering from La Laguna Institute of Technology, Torreon, Mexico, in 1980, the M.S.E.E. degree from Monterrey Institute of Technology and Superior Studies, Monterrey, Mexico, in 1982, and the Ph.D. degree in electrical engineering from Syracuse University, Syracuse, NY, in 1987.

From 1980 to 1982, he was part-time instructor of Mathematics and Physics, Monterrey Institute

of Technology. During 1982 he was employed as an Electrical Design Engineer by HYLSA Steel Company, Monterrey, Mexico. During 1983 he was employed as a Technical Marketing Engineer by PROLEC transformer company, Monterrey, Mexico. From 1984 to 1987 he was a Graduate Research Assistant in the ECE Department at Syracuse University, working on radar signal processing and moment method applications to EM problems. Since August 1987 he has been with the Department of Electrical Engineering at the University of Kentucky, Lexington, KY. His research interests include the application of computational methods (MOM) to EM problems.

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