Leakage from coaxial cablesM.M. Rahmann, M.Sc., J.E. Sitch, B.A., M.Eng., Ph.D., and Prof. F.A. Benson,

D.Eng., Ph.D., C.Eng., F.I.E.E.

Indexing terms: Cables, Coaxial cables

Abstract: The leakage properties of a large number of coaxial cable samples have been measured over a widefrequency range, up to 3-5 GHz in some cases. The surface transfer impedance per unit length ZT, and theequivalent surface transfer impedance due to mutual capacitance Zp, are evaluated and compared with valuescomputed using formulas found in the literature.

1 Introduction

Modern electronic systems require the interconnection ofvarious units, and coaxial cables are widely employed forthis purpose. Interference between pieces of equipment inclose proximity, or between different parts of a singlesystem, must be reduced to acceptable levels if properfunctioning is to be ensured. The leakage of energy intoand out of coaxial cables is an important source ofinterference.

If the cable is truly coaxial there are two types ofleakage. Most important is usually that due to transferimpedance per unit length (ZT),X whereby current flowingwithin the coaxial line (i.e. in the circuit consisting of thecentre conductor and the outer) gives rise to an e.m.f. thatappears in another circuit containing the cable's outerconductor. The second coupling mechanism arises becausesome electric flux can pass through the outer conductor,giving rise to electric-field coupling between the twocircuits. Although this electric coupling is often measuredas a mutual capacitance, it may be expressed as an equiv-alent transfer impedance ZF, Reference 2.

If the outer conductor of a coaxial cable were an homo-geneous tube of high-conductivity material, leakage wouldbe virtually eliminated at all but the very lowest frequencies.This is due to skin effect, and is readily observed in solidjacketed cables of various types.1 Coaxial cables withbraided outer conductors are pliable, lightweight and lowcost; these factors mean they must be used even in circum-stances where freedom from interference is important.

It seems obvious at first sight that energy can escapethrough the interstices of the braid; analysis shows that aswell as providing the route for the escape of electric flux,the holes in the braid contribute a mutual inductance toZT. This is called the gap inductance, Lg. Increasing thefraction of the dielectric outer surface that is covered bythe braid as opposed to the gaps, does not always reducethe surface transfer impedance.3'4 A second mutualinductance is required to explain this phenomenon. This isthe braid inductance Lb, caused by the woven nature ofthe braid.s For braid angles less than 45° (readers shouldrefer to Appendix 9.1 for an explanation of braidparameters) Lb acts in opposition to Lg; so that reducingLg actually increases the overall mutual inductance(Lg + Lb) if Lb is greater than Lg and acts in the oppositesense. Optimised leakage characteristics arise when Lb and

Paper 549A, first received 30th May and in revised form13th November 1979Mr. Rahmann, Dr. Sitch, and Prof. Benson are with the Departmentof Electronic and Electrical Engineering, University of Sheffield,Mappin Street, Sheffield Si 3JD, England

74

Lg are nearly equal in magnitude, making the overall mutualinductance so small that a dip appears in the ZT versus fre-quency characteristic. The dip is caused by skin effect, asthe skin depth becomes less than the conductor thicknessthe mutual resistance becomes less than the total resistance.Fig. 1 shows variations of ZT with frequency for ordinaryand optimised braids and for a solid tube.

Braid optimisation relies on balancing two opposingquantities; maintaining the balance would be a difficult jobin volume production. It is also achieved at the expense ofgreater electric field coupling, compared to conventionalbraids for which the braid inductance predominates, theholes in the braid have to be made larger to increase the gapinductance.

The object of the work presented here was to measurethe leakage properties of a large number of cables over awide frequency range (100kHz to 3-5 GHz for somesamples) and to compare the measured results with theoreti-cal predictions.

2 Apparatus and experimental procedures

The properties to be measured are ZT, the surface transferimpedance per unit length, the polarity of the inductivecomponent of ZT, and ZF, the equivalent surface transferimpedance per unit length due to electric flux leakage.

01 1 10frequency, MHz

Fig. 1 Transfer impedance ZT with frequency

(a) solid screen(£>) non optimised braid(c) optimised braid

IEEPR0C. Vol. 127, No. 2, Pt. A, MARCH 1980

0143-702X/80/020074 + 7 $01-50/0

At frequencies below 150 MHz, a triaxial tester of thetype described in BSS2316 may be used (Fig. 2). Theresults obtained from this may be corrected for travelling-wave effects,6 but if the test length exceeds a quarter wave-length, (X/4) the correction factor gets rapidly larger andthis adversely affects the accuracy. ZF also becomesimportant as the length of the sample approaches X/4. Forthe reasons outlined above, a i m test length was used forfrequencies up to 30 MHz, for frequencies up to 150 MHz a500 mm length was used. As the length is made shorter,the influence of the ends increases, so the test sectionlength cannot be shortened very much below 500 mm inorder to extend the frequency of operation.

To make measurements at uJi.f. and above, a differentapproach is needed, standing waves are avoided and thevelocities in the two lines are made equal. The use of acorrection factor is obviated, even if the test section isseveral wavelengths long, provided that ZF is small com-pared to Z T . The equipment, which is similar to that usedby Discheid,7 is shown diagrammatically in Fig. 3. Thesliding short circuits are used to present open circuits inthe planes of the T-junctions, to match the outer-systemat the operating frequency. The use of the sliding shortcircuits give rise to two effects, firstly, the apparatus must betuned up at each test frequency and secondly, because theposition for tune is about X/4 from the Tee, there is a mini-mum operating frequency which is related to the overalllength of the setup. In the work presented here, thisminimum frequency is 100 MHz, a value which allows someoverlap with the frequency coverage of the other apparatus.The upper frequency limit is marked by the onset ofpropagating waveguide modes in the outer line, these upsetthe matching and propagate at a different phase velocity.Propagation of the TEn mode becomes possible above2-9 GHz in this equipment and was apparent in trans-mission and reflection measurements of the inner line above3 GHz. The most serious drawback of this equipment is thatit can only be used with one size of cable. Matching of thecircuit containing the outer line requires that it shall have50 £2 characteristic impedance. Since the dielectric constantof the filling is determined by the need to maintain equalvelocities on the inner and outer lines, the internal diameterof the outside tube is determined uniquely by the braiddiameter. Cables with a mean braid diameter of 7-7 mm(e.g. URM67) can be measured in the existing apparatus.

shorting cop(brass)

toz.

detector zscreen undertest shielded load

resistor

Fig. 2 Low frequency triple coaxial apparatus (not to scale)

braid undertest

from / tosource / load

annular slidingshort circuits

Fig. 3 High-frequency triple coaxial apparatus (not to scale)

IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980

The polarity of the overall mutual inductive componentof ZT is obtained by using the low-frequency triaxial testerdriven from a pulse generator. The step function response(obtained using a wide pulse with a fast rise time) can beviewed on an oscilloscope and consists of an inductivespike plus a resistive level shift (Fig. 4). The sense of theinductive part is readily observed.

The triaxial tester shown in Fig. 1 may be modified tomeasure mutual capacitance (CJ2) from which ZF can becalculated. The matched load is removed from the boxleaving a screened open circuit, and the shorting cap is alsoremoved from the outer tube. The outer circuit is excitedby a pulse generator, the outer tube is 'live' and the braidis earthed. The response of the inner conductor is used tocalculate Cl2 and hence \ZF\ which equals ioCyiZ^Z^where Z01 and Z m are the characteristic impedances ofthe inner and outer coaxial lines, respectively.

3 Calibration and measurements

For both test-sets Z T is given by

\ZT\ = 2 -TT^ (1)

where

/

K

= output voltage

= input voltage

= input source impedance

= test length

= correction factor7

The value of |K22/^il is measured by attenuator substi-tution, in the case of 75 £1 cables a matching transition ofknown loss is used.

Three standards were tested in order to check the ZT

measurements. The first of these consists of the core (innerconductor plus dielectric) of URM67 cable with a solidstainless-steel outer conductor 0-91 mm thick.* The othertwo standards have perforated tube outer conductors with120 5 mm diameter holes and 100 2 mm diameter holes permetre, respectively. The wall thickness is 1 mm (19 s.w.g).

J_ shift dueto braidresistance

100 ns

time

Fig. 4 Sketch of oscilloscope traces used to determine the sign ofmutual inductive part ofZT

Negative mutual inductance is shownupper trace = input currentlower trace = output voltage

* Conductivity 80 X 10s Sm'

75

It can be seen from Fig. 5 that good agreement existsbetween the calculated and measured values of ZT. For theperforated tubes, the mutual inductive component of ZT

was calculated; for the solid walled tube, the only contribu-tion is due to the resistance, modified by skin effectscreening.

Unfortunately, the standards could not be used in thehigh-frequency triaxial apparatus, this could only be checkedby comparing measurements in the frequency range from100 to 150 MHz where samples of the same cable couldbe measured in both setups.

The errors in ZT measurements are estimated to be lessthan ±15%. Sample-to-sample variations in excess of 20%have been observed in measured ZT values for nominallyidentical cables so manufacturing tolerances may beresponsible for large variations in ZT.

4 Results

Fig. 6 shows the transfer impedances versus frequency ofcable Uniradio M57 and M67. These cables have the samebraid design and dielectric, but the inner conductor con-struction is different, URM57 has 75 £1 characteristicimpedance while that of URM67 is 50 ft. In principle,ZT is a function of the braid construction alone, whereasZF depends only on the braid and the dielectric constantsof materials inside and outside the braid. The results agreewith this, the difference between the two cables' character-istics is the same magnitude as the variation betweensamples of the same cable.

10

0-1 1 10frequency, MHz

Fig. 5 Z>p against frequency for standardscalculated

Homogeneous tube

120 X 5 mm hole tube

100 X 2 mm hole tube

measured Acalculatedmeasured •calculatedmeasured •

Cable

Table 1: Measured and calculated results at 10 MHz,all values in m&m' 1

URM 57/67 URM 102 URM43 M43 tape

\zT\(measured)

(Reference 5)

(Reference 5)

(Reference 8)

(measured)ZF(Reference 2)ZF(Reference 8)

60

81

10

7123

581-8

1-9

18

3-4

54-3

21-7

32-648-2

6-120

5-2

31

170

160

14

14635

1252-2

2-3

27

100

62

25

3730

321-7

2-9

23

Table 1 shows measured and calculated values of trans-fer impedance at 10 MHz, the formulas given by Tyni5

have been used to calculate the braid and gap inductancesseparately; the overall inductance is the difference betweenthese two. Vance8 has published a theoretical expressionfor the mutual inductance caused by the holes in the braid.It is seen that changes in the value of the gap inductancehave little effect on the overall mutual inductance, this isbecause the braid inductance is so much larger than the gapinductance that it completely dominates the overallinductance.

The polarity test yields a negative sign for the mutualinductance, confirming that the braid inductance is greaterthan the gap inductance (the braid angle is 25-8° so thebraid inductance will be negative).

The value of ZF, due to electric field coupling throughthe interstices of the braid, is also shown in Table 1. Thecapacitance is measured at low frequencies, and is taken tobe independent of frequency when calculating ZF at10 MHz. Values of ZF have also been caluclated and aregiven in the Table. Expressions given by Vance8 andFowler2 have been used and it is seen that values calculatedusing Fowler's formula agree more closely with experi-mental results than those computed using the expressiongiven by Vance, this is observed for all the cables tested.Fowler's analysis takes into account the effect caused bythe finite thickness of the braid, apart from this factor, thepredictions of the two theories are very similar.

Cable Uniradio M102 has an optimised braid, its leakageproperties are shown in Fig. 7. Although the low-frequencybraid resistance is greater than for cable URM67, forfrequencies above 7 MHz, ZT is more than ten times smaller.The mechanism responsible for the reduction of mutualinductance is clearly seen from the calculations, comparedto URM67 Lb is smaller and Lg is larger, so the differencebetween them is much less. In this case the method ofcalculating Lg assumes great importance, use of Tyni'stheoretical value does not give such good agreement withexperiment as Vance's expression.

The optimisation process magnifies errors in calculatingboth Lb and Lg, thus yielding a sensitive test of any theory.For nonoptimum cables where Lb is dominant, calculationdoes give fairly good agreement, indicating that the theoreti-cal value of Lb is quite accurate. There is no strong reasonto suppose that Lb is inaccurate for optimised cables, sothese results can be used, in the absence of any measure-ments on braids whose properties are dominated by Lg, as

76 IEEPROC. Vol. 127, No. 2, Pt. A.MARCH 1980

a measure of the accuracy of calculated values of Lg.Vance's method seems to be the more accurate of the twoin these circumstances.

An interesting feature of the results of the measurementson both cables is that ZT seems to deviate from its lineardependence on frequency at about 3 GHz. It is unfortunatethat errors are expected at this frequency because of thepropagation of another mode in the outer coaxial line;measurements on smaller diameter cables are needed todetermine whether or not ZT depends linearly on frequencyat 3 GHz and above.

Fig. 8 shows the leakage characteristics of cable UniradioM43 and an equivalent tape-braided cable. The resultsindicate that the theories are equally valid for tape and wirebraids, and that there is little to choose between them fromthe point of view of leakage.

5 Further results

The leakage characteristics of 33 different cables have beenmeasured, copies of the results and details of the cables'

construction may be obtained by writing to the authorsat the University of Sheffield.

6 Conclusions

The leakage characteristics of a large number of cableshave been measured and compared with values calculatedfrom formulas in the literature. Although no one theoryaccurately predicts the performance of all cables, Tyni'sassumption of two opposing inductances appears to be valid.A synthesis of the expressions given by Vance8 for the gapinductance and Tynis for the braid inductance gives thebest fit with experimental data. Fowler2 gives an accurateexpression for the prediction of ZF. The accuracy of all thepredictions is ultimately limited by the uncertainty in thedefinition and estimation of the dimensions used in theexpressions, especially as these dimensions are sometimescubed or exponentiated.

The value of ZT increases linearly with frequency up toat least 2 GHz, further work is required to determine

10

10

10

10

10

0-1 10 100frequency. MHz

IGHz

Fig. 6 ZTandZF for cables URM6 7 and URM5 7

Measured ZT values for URM67 high-frequency rig *1 low-frequency rig •Measured ZT values for URM57 high-frequency rig A1 low-frequency rig *Measured ZF for URM67 OCalculated ZF at 10 MHz (Vance) •Calculated ZF for 10 MHz (Fowler2) •

IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980 77

whether the apparent rise in inductance at higher fre-quencies is genuine, or is an artifact of the test set-up.

7 Acknowledgments

This work was supported by the UK Ministry of Defence,we are grateful for their involvement.

B I.C C. and Henry Righton and Co. Ltd. kindly donatedall the cable specimens used in the experiments in particularwe wish to thank J.L. Goldberg for his interest andencouragement.

A.H. Badr of this department was involved in manyuseful discussions and Miss R.K. Sidhu and F. Yialelisperformed some measurements.

8 References

1 SCHELKUNOFF, A.: 'The electromagnetic theory of coaxialtransmission lines and cylindrical shields'. Bell Syst. Tech. J.,1934, 13, pp. 532-578

2 FOWLER, E.P.: 'Observations on the use of ZT(Q for compar-ing the breakthrough capacitance of cable braids'. IEC WorkingGroup document no. SC46A/WG1 (Fowler), 3, November 1973

3 KRUGEL, L.: 'Abschirmwirkung von Aussenleitern flexiblerKoaxialkabel'. Telefunken Z., 1958, 114, pp. 256-266

10

10

10

10

10

4 HOMANN, E.: 'Geschirmte Kabel mit optimalen Geflechtschirmen', Nachrichtentech. Z. 1968, 21, pp. 155-161

5 TYNI, M.: 'The transfer impedance of coaxial cables with braidedouter conductors'., EMC Symposium, Wroclaw, Poland,September 1976

6 JUNGFER, H.: 'Die messung des kopplungswider Standes vonKabelschirmungen bei hohen Frequenzen'., Nachrichtentech. Z.1956,12, pp. 553-560

7 DITSCHEID H.L.: 'Theorie und messung des kopplungswiderstandes . Short lecture at the NTG Conference. Berlin, 1966

8 VANCE, E.F.: 'Shielding effectiveness of braided-wire shields'.IEEE Trans., 1975, EMC-17, pp. 71-77

9 Appendixes

9.1 Braid parameters

The braid is woven using N tapes or groups of wires(spindles) which usually contain the same number of wires(«). Each spindle or tape follows a helical path, the distancemeasured along the cable axis for one turn of the helix iscalled the lay length, /. The braid angle, 0 is the anglebetween the helix and a line parallel to the axis, i.e.tan 0 = nDm/l where Dm is the mean braid diameter,assumed equal to d0 + 2-25d; d0 is the diameter overdielectric, and d is the diameter of a braiding wire or the

01 10 100frequency, MHz

I G H Z 10

F ig. 7 ZTandZF for cable URM102

. . . „ , high-frequency rig •Measured Z T values, e • „

1 low-frequency rig aMeasured braid resistance per unit length (d.c.) 0Measured Zp OCalculated ZF (Fowler) •78

IEEPROC. Vol. 127, No. 2, Ft. A, MARCH 1980

tape thickness, whichever is appropriate. Fig. 9 shows asketch of a braid.

The filling factor, Kf is defined as the proportion of thecable core covered by one hand of the lay. It is given by

Kf =nNd

2/sinfor a wire braid

for a tape braidW = tape width

(2a)

(2b)

The coverage factor or optical coverage Kc is defined as

Kc = Kf(2~Kf) (3)

9.2 Summary of theoretic predictions

Vance8 calculates the coupling through the electricallysmall diamond shaped holes by assuming their magneticand electric polarisabilities to be the same as those of

10Ar-

10

10

> • • oo

0-1 10 100frequency, MHz

Fig. 8 Zjiand Zp for cable URM43 and a tape-braided version

Measured 2 T ^1 tape braid •

(low-frequency rig). . Arf URM43 OMeasured Z p . . . , .

* tape braid A,_ . . U R M 4 3 •

Calculated ZF (Fowler) { a p e b r a j d A

Fig. 9 Sketch showing braid construction

I = lay lengthDm = mean braid diameter6 = braid angle

ellipses having similar major and minor axes. From hisanalysis, Vance obtains the following expressions:

6NK cE(e)-(l-e2)K(e)

0<45C

(4a)

6eN

d > 45° (5b)

Where ju and e are the permeability and permittivity of thecable, Cx and C2 are the capacitances per unit length of theinner and outer circuits.

e = - t a n 2 0

- cot2 0

0 < 4 5

0>45C

K(e) and E(e) are complete elliptic integrals of the firstand second kinds, respectively,

K(e) = f d 0 f

?' sin2 0 7 J<

7T/2

-el sin2

As mentioned in the text, Tynis treats two sources ofmutual inductances. The braid inductance,Lb, arises becauseequal current flows in both hands of the lay. This causes amagnetic field,Hm, between the layers. Unless the lays crossat right angles, the weaving in and out causes flux cuttingand therefore an induced e.m.f. resulting in a mutualinductance, Lh; given by

\m4rtD,

(tan2 0 - 1 ) (6)

a is the distance between the layers, assumed to be

Ida = 1 +h/d

where h is the width of the slit between adjacent spindles, i.e.

2-nDm cos 0h =

N-nd

for wire braids, for tape braids W is substituted for nd.To compute the gap inductance Tyni assumes that Hr

leaks through the slits between spindles resulting in

nd(7)

Fowler2 computes ZF by assuming that the capacitiveleakage is the same as that through square holes whose sidesare equal to h, the distance between adjacent spindles,corrected to take account of radial displacements caused bythe weave as follows:

sin 7

IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980 79

f'where Zf = Ij&KEp™! R ( f \ e x p _ /«*?} (8)

tan 7 =where R = 0 1 1 7 3 , and e l 5 e2 = relative permittivities of

h + d the inner and outer circuits.In the caluclations shown in Table 1, /x = ju0, e = 2eo

Fowler also applies a correction to take account of the and \Jexe2 =2, the values of permittivity were chosenfinite thickness of the screen (chimney effect), this is the because ZF was measured in a setup with air as the dielectricexponential term in his expression for ZF which is in the outer line, but the cables had p.v.c. jackets.

80 IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980