583 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 37, NO. 4, NOVEMBER 1995

Fig. 1). The optimal choice for the localized source will be the center of the three apertures as shown in Fig. 3. Numerical results using the FDTD method are shown in Fig. 4, which, despite the existence of a distributed source, Le., the three huygens’ sources at the three apertures, the AABC performed appreciably better than the ABC.

IV. CONCLUSION This work presented an alternative formulation to ABC’s that

was found to be highly suitable for a class of radiation EMVEMC problems having localized sources or sources distributed over a small region. By optimizing the boundary condition at each boundary cell for the highest likely direction of incidence, spurious reflections can be reduced resulting in a large dynamic range of FDTD simulations. The adaptive absorbing boundary condition is found to be well-suited for implementation into the FDTD method and it does not introduce instability in the solution.

While the AABC was found to improve the accuracy of the numerical solution, this advantage, however, comes at the expense of an additional cost in terms of either computer run-time or computer memory, but not both. This is because the parameters used in the adaptive form of Liao’s ABC have to be computed for each boundary cell. These parameters can be computed at the beginning of the run and stored for each cell, or they can be computed during the run as the boundary condition is being applied to the boundary node. The user can then make this choice depending on which computer resource is more affordable.

E. L. Lindman, “Free space boundary conditions for the time dependent wave equation,” J. Computat. Phys., no. 18, pp. 66-78, 1975. B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comp., vol. 31, no. 139, pp. 629-651, 1977. G. Mur, “Absorbing boundary conditions for the finite-difference ap- proximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat., vol. EMC-23, no. 4, pp. 377-382, 1981. R. Mittra, 0. M. Ramahi, A. Khehir, R. Gordon, and A. Kouki, “A review of absorbing boundary conditions for two and three-dimensional electromagnetic scattering problems,” IEEE Trans. Magn., vol. 25, no. 4, pp. 3034-3039, July 1989. T. G. Moore, J. G. Blaschak, A. Taflove, and G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Antennas Propagat., vol. 36, pp. 1797-1811, Dec. 1988. 0. M. Ramahi, “Boundary conditions for the solution of open-region electromagnetic scattering problems,” Ph.D. dissertation, Univ. Illinois, Urbana, IL, May 1990. S. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analysis,” Scientia Sinica (ser. A), vol. 10, no. 27, pp. 1063-1076, 1984. W. C. Chew, Waves and Fields in Inhomogeneous Media. New York Van Nostrand Reinhold, 1990.

On the Leakage Radiation from a Circumferentially- Slotted Cylinder and its Application to the EMI

Produced by TEM-Coaxial Rotary Joints

Charles M. Knop, Fellow, IEEE, and Louis F. Libelo, Senior Member, IEEE

Abstract-The amount of leakage radiation, as well as the radiation pat- tern and its gain, produced by a complete-360’ circumferential-narrow gap cut in a coaxial cable carrying a TEM mode is determined. Leakage levels for such a typical cable of approximately 26% are predicted to occur for gaps as small as about 0.0074X. The former is substantiated by measurement on a 5’’ diameter coaxial cable of 50-0 characteristic impedance operating at 2 GHZ. Estimates of the EMI levels produced by typical coaxial choked-rotary joints (where the chokes significantly decrease the gap leakage) operating at high power levels are then given.

I. INTRODUCTION

The determination of the amount and pattern of the unintentional leakage radiation which occurs when a coaxial cable’s outer conduc- tor is broken in such a way as to form a gap completely around its periphery (or which occurs from a gap in a rotary joint in such a cable) is necessary in order to quantify the EM1 so-produced.

This determination is done here by first obtaining the external (radiation) admittance of the gap using Parseval’s theorem in mode space [1]-[31. This admittance (which is independent of the cable’s or waveguide’s interior construction) in conjunction with the internal coupling capacity of the cable [4] then gives the equivalent circuit of the gapped-cylinder. From this equivalent circuit the amount of leakage radiation produced relative to the input power to the cable is determined. The radiation pattern and its directive gain are then detennined directly from the boundary value solution for the external fields; these quantities are then used to predict the EM1 power density produced at any far-field point in space relative to the input power, where consideration is given to the effect of the finite length of the cable.

Numerical results for the specific cases of typical operating sizes of TEM coaxial-cable of fixed diameter at a given frequency but of various size gaps are then given as is experimental confirmation for a specific case. Finally, estimates of the EM1 levels produced by choked-rotary joints in the above type cables are given where even though the chokes significantly decrease the gap leakage, this EM1 can cause problems under HPM (High Power Microwave) operation.

II. ANALYSIS

A. The External Fields Consider then the gap-slotted cylinder (initially taken as being

infinitely long) depicted in Fig. l(a). It is assumed that the tangential electric field at the outer surface, p = a, of the cylinder is constant over the gap and zero off it (this assumption is made even though it is realized that it is not the most accurate, such as to be found in [4] and [5]; still the fact that it gives results in good agreement with

Manuscript received October 28, 1994; revised May 11, 1995. C. M. Knop is with Andrew CorpEMRC, Orland Park, IL 60462 USA. L. F. Libelo is with the Army Research Laboratory, Adelphi, MD 20817

IEEE Log Number 9415540. USA.

0018-9375/95$04.00 0 1995 IEEE

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL 37, NO 4, NOVEMBER 1995 584

(a) cb) (c) Fig. 1. equivalent transrmssion line of a CSC, and (c) equivalent circuit of a CSC.

(a) Geometry of a CSC (circumferentially-slotted cylinder), @)

experiment justify its use):

0 off slot EO on slot

It is well known that the fields produced by (1) exterior to the cylinder can be written, for this symmetrical azimuthal case, as a Fourier integral over axial (2-directed) mode space [6], [7] as:

with: u2 = k 2 - h2, u = +(k2 - h2)l12 for Ihl 5 k , ‘u. = -j(h2-k2)1’2 forlh) 2 k , k = ( ~ T ) / x , x = free space wavelength, f@)(%) and H,(’)(x) being the Hankel functions of second kind of argument x and orders zero and one, respectively, and where a time variation of exp (+jut) is assumed. Zn (2) Ez(h) is the complex mode amplitude of E , at p = a and is given by

using (1) in (3) gives

(4) -

where U = ( h H ) / 2 . The complex mode amplitude of 234, A+(h), is, via Maxwell’s equations:

(5)

B. The External Admittance The complex power, PR, radiated by rhe gap is found by integrating

Poynting’s vector over the slot which is equivalent, via Parseval’s theorem, to [1]-[3]:

w * _ _ PR = -2x2a E,H+ dh. (6) 1,

The external admittance, Ye, is defined by:

(7)

where 1x1 is the magnitude of the voltage across the gap, /V,( = IE,IH. Substituting (4) and (5) in (6) gives:

where C = ka = (27ra)/A. Making use of the Wronskian relation- ship Qf Jo(z )Y~(z) - ~ I ( Z ) % ( X ) = - 2 / ( x x ) , inspection of (8) reveals that its real part (the external conductance G,) is only due to the modes having 0 5 Ihl 5 IC:

where: X = ha = ( h / k ) ( k a ) = C ( h / k ) , U = ( h H ) / 2 = (X/2)(H/a), V = (C2 - X2)l12, and J,(V) and Yo(V) are the zero order Bessel and Neumann functions, respectively, of argument V. Similarly, examination of (8) (letting X’ = - jha imaginary part (the external susceptance Be) is due to a suscep the entire imaginary mode spectrum 0 5 ljhl 5 00:

where: U‘ = ( X ’ / 2 ) ( H / a ) = -jU (and noting [sinU/U]2 = [sin lUl/lUl]2 = [sin U‘/V’]’), V” = C2+X’2). Fortran programs for (9) and (10) with C and H / a as parameters were then written (see below).

the real and imaginary parts, respectively, of (52) of Wait and Hill [8] (which also assumed a constant Ez field across the gap) for their coating case allowed to vanish, i.e., their Aq = A, = 0, except for the slight analytical differences between (10) of our sin U’/U’ integrand factor corresponding to the imaginary part of (28) plus all of (29), of [SI. Thus, our expressions and those of [SI for G, are identical and those for Be differ slightly. However, despite these latter analytical differences in Be, numerical computations (given below) show the results to be indistinguishable. Also, numerical results from either OS these methods agree with some limited computations 0 5 C 5 1.0, H / u = 0.100) also obtained by Parseval’s theorem using a different integration procedure as employed by Papathedorou et al. [93, as shown below.

C. The Equivalent Circuit The work of Chang [4] shows that if the cylinder

cable of outer radius a and inner radius a,, that the ab admittance, Ye, is shunted by a coupling capacitance, C,, where, the Corresponding susceptance, B, = wCc, is (valid for H / u (( I, H/X << 1, and G2 << 1):

At this point it is noted that (9) and (10) agree identically

where E,. is the relative dielectric constant of the material filling the coax. Normally, one knows the characteristic impedance, 20 = [17/(27~~;’’)] log,(a/ao) a, of the cable and its phase velocity relative to that in free space, v/c = E;”’, so, specifying 2, and v /c gives ala,. Thus, the total shunt admittance, YT, across the gap is YT = G, + ~ B T , where BT = Be + B,. This is shown in Fig. l(b), where this YT appears in series with the equivalent transmission line between the gap extremities. If the wall thickness is not negligible (as it is here based on agreement of experimental results with predicted) then the work of [lo] can be used to refine the expression of YT. One then converts YT to a series R and X : ( R + j X ) = YF1, so R = G,/(Gz + B;), X = -BT/(G: + B;), and this with the fact that the cable is taken to be terminated with its Z,, gives the equivalent circuit of Fig. l(c), where Po is the incident real-power

LEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 37, NO. 4, NOVEMBER 1995 585

at the plane passing through the bottom of the gap, i.e., at the line formed by points a' and b' as shown.

D. Power Radiated The equivalent circuit of Fig. l(c) can now be used to compute

the real power radiated, PRR, relative to the incident real power, Po, since, from power conservation Po = PL + PRR + PRL where PL is the real power delivered to the 2, load and PRL = lrI2P0 is the real reflected (returned) power (with r = reflection coefficient = (2 - Z,) / (Z + Z0), and 2 = ( R + 2,) t j X being the input impedance, so lrI2 = (R2+X2) /[ (R+2Zo)2+X2]) and where the trivial ohmic loss in the cable is neglected. From Fig. l(c) it is seen thatthenetrealpowerintothecircuitis Po(l-JI'12) = PER+PL and PRR/PL = R/Z, SO P R R / P ~ = (R/Zo)(l -lr12Y[1 + (R/Zo)l and P L / P ~ = (1 -lrlZ)/[l + (R/ZO)]. In a measurement, one normally uses the ratios of power in dB relative to Po, thus: D B L = 10 loglo (PL~P, ) , DBR = 10 log,, ( P R R / P ~ ) , DBRL = 10 loglo ( P R L / P ~ ) where DBRL is the dB return loss, -DBL is the dB insertion loss and - D B R is the dB radiation loss (where D B L , D B R, and D B RL are all negative), thus power conservation gives:

1 (12) DBRLI10 - 10DBL/10 DBR = 10loglo (1 - 10

and hence PRR/PO = loDBR/" . To make the computations, a Fortran program to determine R, X , DBL, DBR, and DBRL given GT = G, and BT = Be + B, as inputs was written (see below).

E. Radiation Patterns and Gain Using the well known methods of employing the asymptotic form

of the Hankel functions in (2) in conjunction with a stationary phase integration of it gives the radiation fields [for the infinite cylinder case in a vertical position as shown in Fig. l(a)] as 161, [7]:

where the gap width is taken as small compared to A. The directive gain, 9 9 0 , on the horizon (0 = 90") is defined as

9 9 0 = [IEO(T, go0, 4)12/l(211)1/[~RRl(4.~2~l

990 = {30112G,[J?(C) + YO2(C)]}-'

(14)

where, from (7), PRR = IV012G,/2, so that with (13), (14) becomes:

(15)

where G, (in siemens=mhos) is given by (9). The gain on the horizon, in dBi, is then G9, = 10 log,, 990. Computations for which are given below as are discussions of the effect of a finite length cylinder.

The radiation pattern expressed in dB relative to the value on the equatorial plane is

where use is made of (13), computations for which are given below [using [J:(C) + Y,"(C)]/[J:(CsinO) +Y:CsinO)] for the magnitude of the Hankel function ratios in (16)l.

B B

07 :$ '3, I

,' "/' k''

Fig. 2. H / A = 0.100.

Predicted dependence of external B and G of a CSC on C for

F. EMI The EM1 power density, S(r , 0, q5), produced at any far-field point

is given by S = IEe(r, 0, 4)12/(217) where the arguments T , 0, and 4 of S are understood, Using (16) this can be expressed as S = where S9, is S evaluated at 8 = 90°, and is also given by S g o = (PRRg90)/(4RT2), SO:

PRR 990 oDB( 8) / 1 0 S ( r , 0, 4) = 7 . 4rr computations of which are given below.

111. COMPUTATIONS

A. Test Cases on Extemal Admittance FORTRAN programs for (9) and (10) (multiplied by 1,000 to

obtain G,, and Be in millisiemens=millimhos) were written and, initially, as a test case, were first used to compare with available previous computations [9] for H / u = 0.10 with 0 5 C 5 1.0. The results are shown in Fig. 2 (where here and in the figures below, A is used for a, K for I C , GE for G, and BE for Be, for clarity). Fig. 2 also shows the results of [9] and, as seen, the two results virtually coincide. Next, H/a was maintained at 0.100 and C increased to 3.00; these results are also plotted in Fig. 2 and, were shown to virtually coincide, for 0 5 C 5 3.00, with those using (52) of [8] , (with Aq = A s = 0) which was also programmed.

B. Specific TEM Mode Coaxial Cable Next, G, and Be were computed for the case of a coaxial

cable of C = 0.465, with 0 5 H/a 5 0.20 (so 0 5 H/A = [C/ (2x ) ] (H/a ) 5 0.0148) as was BT = B, + Be using (11) (multiplied by 1,000) for the case of 2, = 50.0 R (with E, = 1.262, a / a , = 2.550), as plotted in Fig. 3(a)-1 (in this figure and in Fig. 4(a)-1 BT is denoted by BTOT for clarity). A program to compute R and X and the dB load, radiated and reflected quantities, all defined above, using GT = G, and BT as inputs was written with the results as shown in Fig. 3(a-2) and 3(b), respectively. Examination of Fig. 3(b) then shows, for example, that a 50-R cable of C = 0.465 (e.g., 2a = i'' at 2.00 GHz) with a slot of width corresponding to Wa = 0.100 (i.e., 2H = 0.0875" or H/A = 0.0074) is predicted (when terminated with a matched load) to radiate -5.91 dB (i.e., 10-5.91'10 = 0.2564 M 26%) of the power incident to the cable. This examination also reveals that as the slot width increases for

586 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL 37, NO. 4, NOVEMBER 1995

0 4

06

w . -1 - m

- I

,15 . I0 .I5 .2B E i.00 ' ' ' ' I ' ' ' I ' ' " ' I ' ' I

H i R , S L O T V i O T H / C A B L E R A D i l i S

w . -1 - m

- I

,15 . I0 .I5 .2B E i.00 ' ' ' ' I ' ' ' ' I ' ' " ' I ' ' ' '

H i R , S L O T V i O T H / C A B L E R A D i l i S

I

W

8 .

m

& W w

0.00

Flg. 3. (a) Preacted dependence of extemal B and G, total B and series R and X of a CSC-Coax on H / A for C = 0.465 and 2, = 50 0. (b) Predicted dependence of load, rachated and reflected power (relative to incident power) of a CSC-Coax on H / A for C = 0.465 and 2, = 50 R. (c) Integrands of extemal G and B of a CSC for C = 0.465 and H / A = 0.100, 3(c-1), G E ( X ) ; 3(c-2), BE(X ' ) .

a given a, Le., as H / u increases, more power is radiated, as one would expect, but the increase is very gradual (e.g., doubling the slot width from H / u = 0.10 to 0.20 only increases the radiated power by about 0.9 a). At this point it is interesting to examine plots of the integrands of G, and Be (i.e., of (9) and (lo), respectively) as shown in Fig. 3(c-1) and 3(c-2), respectively. Thus, examination of Fig. 3(c-l) discloses that virtually all of the contribution to the radiation occurs at X = C (i.e., h = I C ) , i.e., along the cable's axis (since u = 0 for h = k ) , implying that the radiation should peak as

8 approaches 0" or 180" for an infinite cable (as is verified below by examination of the predicted patterns). Similarly, examination of Fig. 3(c-2) shows that virtually all of the susceptance is associated with X' = O (i.e., j h = 0).

N. RADIATTON PAlTERNS

Fortran programming of (16) gives the results of Fig. 4 for the cases of C = 0.465 and 3.00, which are seen to be very similar.

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 37, NO. 4, NOVEMBER 1995 587

T H E T A . DEGREES FROM V E R T I C A L

Fig. 4. Predicted elevation plane pattems of a CSC of C = 0.465 and C = 3.00 and small H/A.

Note that the computations do not extend to exactly 0 = 0" or 180" since the fields become unbounded there (for the infinite-length cylinder model, as is not the case for a finite-length as discussed below), though the power radiated is still bounded since the external (radiation) conductance obtained from (9) is finite. For this reason the use of (15) to obtain the gain cannot be employed since it will, with (16), give too high a value on and near the cable's axis since its use implies that 8 extends all the way down to 0" and all the way up to 180".

V. MEASUREMENTS

A. Radiated Power-Amount

The E M coax case above (namely of 2, = 50.0 s1 and of C = 0.465) was subjected to experimental verification by using a four foot length of semi-rigid coaxial cable having 2a = 0.875 in and H = 0.100~ = 0.044 in and operating at 2 GHz (so H/X = 0.0074), a photo of which is given in Fig. 5. The cable was terminated in a 50-0 load and the insertion loss and return loss were measured in dB in an anechoic chamber. The measured results, as obtained from (12) using measured value of DBRL and DBL, along with the predictions [via Fig. 3(b)] are tabulated in Table 1. It is seen that the amount of predicted radiated power is 25.64% while that measured was 27.4%. This is good agreement. In passing it is noted that one should not be surprised by the above large (26%) radiation produced by a thin 360" gap since it interrupts all the axial current which becomes a displacement current in the gap which radiates. In fact, use is made of this efficient radiation mechanism to design coaxial colinear array antennas [ 111-[13].

B. Radiation Pattems

The far-field patterns were measured in an anechoic chamber with pyramidal absorber (of about 1' diameter) placed at each end of the coax to reduce end reflections and feed line effects. The elevation plane pattem measured is shown in Fig. 6(a) which for ease of comparison, also shows the predicted pattern of Fig. 4 for C = 0.465. The agreement is seen to be adequate except near 0 = 0" and 180" and vicinity where the predicted pattem (being for an infinitely long cable) continues rising whereas the measured pattern decreases. This decrease was also observed (not shown here) with the end-absorbers removed (since the radiation from the ends will always cancel for a finite length of cable for the TEM mode, because the H4 field does not vary with 4 and is pointing in the opposite directions at opposite azimuthal-sides for either the top or bottom of the cable). With the end-absorbers removed the cable has a much larger axial standing wave on it due to the end-reflections and the elevation plane pattern

Fig. 5 . Photo of a four foot length of 50-0 coaxial cable having a slot of WA = 0.100 (H/X = 0.0074 at 2.0 G H z ) . (Slot location is in center of cable by middle of white paper; 12-in ruler shown in center).

TABLE I PREDICTED AND MEASURED LOAD, REFLECTED AND RADIATED POWER (IN dB

RELATIVE TO INCIDENT POWER) FOR CIRCUMFERENTIALLY-SLOTTED 50-0 COAXIAL CABLE OF C = 0.465 AND H / A = 0.100 (NOTE:

RADIATED POWER IS ALSO GIVEN IN % RELATIVE TO kCIDENT POWER)

Quantity Predicted+ Measured++

Load Power, DBL, dB -2.43 -2.1 Reflected Power, DBlU, dB -7.63 -9.6 Radiated Power, DBR, dB -5.91 -5.6

Radiated Power, % 25.64 27.4

+ Infinite length. ++ Four foot length.

(not shown here) has more severe oscillations. With the end absorbers in place these end reflections are significantly reduced but, still, a small standing wave is present which produces the approximately 8 lobes (the cable being about 8X long) seen in Fig. 6(a) since the axial current on the outer surface of the coax travels, essentially, at the phase velocity of light [as seen from Fig. 3(c-l)], though it is not a surface wave per se. In either case (with or without absorber ends) the measured directive gain (obtained by pattem integration namely: 990 = Usoff 10-DB(e)'lo sin 8d0 , and in dBi, 10 log,, 990) is about -2 dBi at 0 = 90" and rises, as seen from Fig. 6(a), to a maximum of about $3 dBi near the cable's ends. The equatorial plane pattem is shown in Fig. 6(b) and is seen to oscillate by approximately f l dB about the predicted-omni-directional value, which is reasonable agreement.

VI. APPLICATION TO THE EMI PRODUCED BY ROTARY JOINTS

Rotary joints fall into major categories [14]-[16], one is broad band (including down to dc), usually TEM coaxial cables employing spring-finger or sliding contacts having no gaps, and the other either TEM coax or TMol circular waveguide having gaps but with quarter wave chokes of the type described by Fig. 7 [17]. These chokes suppress the above gap radiation since an effective short circuit appears at the gap a of Fig. 7 due to the actual short at point c, a distance X/2 from a, and since at gap b the axial current is virtually zero. For a coaxial cable a similar action occurs at the inner conductor. However, this behavior can only be done across a narrow bandwidth.

It has been observed that these latter chokes decrease the gap radiation by, typically, 4&60 dB [16], Le., the radiation from the gap with the choke as compared to that without the choke is reduced

588

4 . +

B -

E E E TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 37, NO 4, NOVEMBER 1995

- + ' 0 - a .

B W

c3 B N N L I L t .

m u LT w 3 0 [L

W 1 I

(b) Fig. 6. Predicted and measured pattems for a CSC of C = 0.465 and H / A = 0.100, (a) elevation plane and (b) equatorial plane.

(say of sensitivity -90 dBm) having, say, an isotropic receiving level, [so its effective collecting area =A2/(4.ir) = 17.90 cm2 at 2 GHz] since the power density it will be exposed to is -43.5 -9.5 + 0 -20 = -73.0 d13m/cm2 and the power received will be -73.0 4- 10 log,, (17.9) = -60.5 dBm.

VII. CONCLUSION 1) The above theoretical, computational, and experimental work

shows that use of an infinitely-long slotted-cylinder to model a finite length coaxial cable carrying a TEM mode and having a 360" gap gives, in conjunction with Parseval's theorem to obtain the gap's extemal admittance and use of Chang's [4] coupling capacity, an equivalent circuit which accurately predicts (see Table I) the fractional amount of incident power to the cable which is radiated. However, the radiation pattern from the finite cable has a much lower measured directive peak gain than that predicted for the infinite cable since there is, approximately, no radiation from the ends of the finite cable. Still, estimates of this peak antenna gain (occurring near the cable's end) can be deduced from the pattern measurements made as being at most about $3 dBi. From this amount of power radiated and this estimated pattem gain, the power density produced by typical choked rotary joints was then estimated and shown to be high enough to potentially cause serious EIvfI problems to nearby sensitive receivers.

2) The same expressions (and associated FORTRAN programs) for G, and B,, of (9) and (10) above, respectively, can be used to determine the radiation from a circumferential slot cut in a circular waveguide propagating the T M o l mode (for which C > 2.405, being typicdy equal to about 3) once an equivalent circuit for this case is derived.

APPENDIX FIRST-ORDER ANALYSIS OF CHOKE SUPPRESSION

Referring to Fig. 7 and denoting the gap impedance (that across 6) by z b and the complex propagation factor of the A/4 lines by y = a+jP andlettingA = (crX)/4,B = (pX)/4 = (2.ir/X)(X/4) = 7i/2, the impedance, 21, seen looking into the X/4 shorted-line is 2, = z,, t m h (A + j B ) , where z,, = 60 log, (aco/acz) is the Characteristic impedance of the choke-lines, with uco and ucz

Fig. 7. Descriphon of choke achon in a rotary Joint of a coaxial cable.

by this amount. Hence, the EM1 produced is given by (17) above but decreased by this amount. This value-range can also be approximately arrived at by a "first-order'' transmission line analysis of the choke as given in Appendix A. Since the cable or waveguide in which the joint is located is typically short in length (less than SA), and considering the above observed reduction in gain (for a 8X cable as compared to that predicted for an infinite cylinder) it is reasonable to assume that ggo -2 dBi and that as 0 approaches 0" or 180" g(0) will rise to perhaps at most, +3 dBi. Thus, (17) with these considerations, gives the maximum value of power density, S, for a 40 dB choke, as S = So 10-40/10. 10f3/lfl = ', where So = isotropic power density = P R R / ( ~ T ~ ~ ) and where, if the choke suppresses by 60 dB, this is further reduced by 100, etc. As an example, if the peak power to the cable is 1 KW and taking PRR = 26% of this, S at r = 10' will be 4.5. lo-' mw/cm2 (-43.5 dBm/cm2). For any other power input at any other T and any other choke suppression S in dBm/cm2 will be: S = -43.5 -20 loglo(r/lO) + 10tog(Po) - (CdB- 40), with T being in feet, Po in KW, and C ~ B the choke suppression in dEi. Thus, for Po = lo3 (1 m), T = 20',cds = 60 dB, 3 = -39.5 dBm/Cm2, etC. Similarly, even a 60-dB choke with a Po of 1 kW can present a serious EM1 problem to a nearby (say T = 30') sensitive receiver

being their outer and inner radii, respectively, as measured from the cable's axis. Hence, the X/4 line to the left is temnated with the impedance (2, + Zb) so that its input impedance, which is then seen at the gap u is 2, = Z,,[Z,, tanh ( A + J B ) + (26 + z,)]/[Zb + 21) tanh (A + j B ) + Z,,]. Using tanh (A + j B ) = (sinh A cos B+j cosh A sin B)/(cosh A cos B+j sinh A sin B ) , where here cos B = 0, sin B = 1, gives tanh(u + j B ) = l / t a n h A1 S 1/A since A << 1. Thus, 2, = 2,,(22,, + A&,)/[& + &,(A + A-')I. Since A is very small this becomes 2, G 2AZ,, (where we note that if the chokes had no loss, Le., if A = 0, then 2, = 0 and a perfect short would exist across a). Now, noting that a = [Rs/(27r)](l/ucO + l /a, ,) /[2Zo,] (where R s is the surface resistance), we see that 2, = [ R s / 2 ~ ] ( l /uco + 1/uc8)(A/4). Hence, for a silver plated choke, RS % 2.5. 10-'fl/' with f in Hz, so, for a frequency of 2 GHz (f = 2 . lo9), RS = 0.0112 $2, so, Z, = 4.45. ~ O - ~ ( A / U ~ ~ ) ( ~ +uco/ucz) M 9 . ~o-~ (A /~ , , ) since uco and ucz are almost equal. Thus, for a choke having X/uco = 3 (Le., here, uco A 2" since X 6"), 2, = 2.7. R. Hence, using the equivalent circuit of Fig. l(c) with X = 0, and R = Z,, and 2, = 50 gives (from Section II-D and noting Irl 2 0), PRR/P, = R/Zo = 5.4. lop4, Le., the leakage power is down about 43 dB with the choke. With no choke it is down about 6 dB, so the choke suppresses the leakage by an additional 37 dB.

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 37, NO. 4, NOVEMBER 1995 589

REFERF~NCES

[l] C. M. Knop and C. T. Swift, “A note on the radiation conductance of an axial slot on a cylinder,” Radio Sci., vol. 68D, no. 3, pp. 447-451, 1965.

[2] C. M. Knop and V. Gylys, “Radiation conductance of an axial slot on a dielectric coated cylinder,” Radio Sci., vol. 3, no. 4, pp. 391-395, 1968.

[3] C. M. Knop, “External admittance of an axial slot on a dielectric coated metal cylinder,” Radio Sci., vol. 3, no. 8, pp. 803-817, 1968.

[4] D. C. Chang, “Equivalent-circuit representation and characteristics of a radiating cylinder driven through a circumferential slot,” IEEE Trans. Antennas Propagat., vol. AP-21, no. 6, pp. 792-796, 1973.

[5] J. R. Wait and D. A. Hill, “Electromagnetic fields of a dielectric coated coaxial cable with an interrupted shield-quasistatic approach,” IEEE Trans. Antennas Propagat., vol. AP-23, no. 5, pp. 679-682, 1975.

[6] J. R. Wait, Electromagnetic Radiation from Cylindrical Structures. New York Pergamon Press, 1959, pp. 125-130 (recently reprinted by IEE Press, Peter Peregrinus, Ltd., London, UK). R. E. Collin and F. J. Zncker, Antenna Theory, Part 1. New York McGraw-Hill, 1968, pp. 567-574. J. R. Wait and D. A. Hill, “On the electromagnetic field of a dielectric coated coaxial cable with an interrupted shield,” IEEE Trans. Antennas Propagat., vol. AP-23, no. 4, pp, 470-479, July 1975. [Note: Private communication with J. R. Wait has revealed that the equation for A( A) following (40) of this reference should read A( A) = A’ ( 1 - E / E ~ ) ( c - b)b. Thus, A(A) vanishes for either E = E~ or c = b, as it should.] S. Papathedorou, R. F. Harrington, and J. R. Mautz, “The near field and aperture admittance of a circumferential slot in a circular cylinder,” in 7th Int. Con$ Antennas Propagat. ICAP, London, 1991, pt. 2,

R. F. Harrington and J. R. Mautz, “A generalized network formulation for aperture problems,” IEEE Trans. Antennas Propagat., vol. Ap-24, no. 6, pp. 870-873, 1976. S. I. Cohn, A. J. Hoehn, and G. I. Cohn, “Coaxial omnidirectional slot antenna arrays,” in Proc. Nut. Electron. Con$, Hotel Sherman, Chicago, IL, Oct. 4-6, 1954, vol. 10, pp. 652-662. M. C. Bailey, F. B. Beck, and W. F. Croswell, “Vertically polarized stacked arrays of omnidirectional antennas,” IEEE Trans. Antennas Propagat., vol. AP-18, no. 2, pp. 285-290, 1970. P. Volta, “Design and development of an omnidirectional antenna with collinear array of slots,” Microwave J., vol. 25, no. 12, pp. 111-115, 1982. G. L. Ragan, Microwave Transmission Circuits. New York McGraw- Hill, MIT. Rad. Lab. Ser., 1946, vol. 9, pp. 416-434. M. J. Kelly, et al., RADAR. New York Van Nostrand, 1949,

Sage Laboratories advertisement, Microwave J., p. 105, Jan. 1991, and private communication with H. C. Chapell of Sage Laboratories, Natick, MA. F. E. Terman, Electronic and Radio Engineering,4th ed. New York McGraw-Hill, 1955, p. 1024.

pp. 865-868.

pp. 832-833.

RF’ Interference Effects on PIN Photodiodes

Cheng-Kuang Liu, Member, IEEE, and Cheng-Tie Chou

Abstract-RFI effects on PIN diodes were studied experimentally for various light powers. It is shown here that operating a diode in a photovoltaic mode is much more susceptible to RFI than operating it in a photoconductive mode. The RF-frequency and RF-power dependences of the interference effect are illustrated. A method of predicting combined effects of light illumination and RFI is suggested. Methods of avoiding this interference are discussed.

I. INTRODUCTION

A study of the susceptibility of transducers to RFI is essential to an opto-electronic system, when a desired signal sending to a transducer is small. A coupled RFI may sometimes be neglected or be smoothed out by an averaging process in practical applications. However, it becomes noisome in the presence of a nonlinear device such as a diode or a transistor. Much attention has been focused on the RFI [l]. Rectification effects on diodes and bipolar transistors have been investigated [2]-[4]. The rectified, through device nonlinearity, high- frequency-interference noise can shift the level of a low-frequency signal or the quiescent operating point of the victimized transistor. Recently, it is shown that an unintentional capacitive coupling path leads to ac interference effects on the measured photovoltage [5]. However, to our knowledge, a detailed study of combined effects of light illumination and RFI has never been reported. A study of these combined effects on PIN photodiodes is thus motivated.

A noise problem is usually resolved by the method of experimental trial and error. Altematively, one may apply prediction methods to save the expense and time in debugging. These methods are based upon the understanding of interference mechanisms and theoretical models. A small signal model or a transmission line model has been developed [2]-[4] for nonlinear devices. A prediction model based upon a piecewise approximation is adopted here to analyze the combined effects of optical illumination and RFI on a PIN diode. In this paper, experimental results of RFI and light-illumination effects are shown in Section 11. Its prediction model is presented in Section III. Then, a discussion is followed in Section IV. Conclusions are finally made in Section V.

II. RFI AND LIGHT LLUMINATION EFFECTS Assume that a sinusoidal interference voltage 21, (t) = V, sin (ut)

couples through radiation or conduction into a PIN diode with a cross- section area A and a depletion layer width W. Electron-hole pairs are generated in the diode, under the illumination of a monochromatic light with photon energy near or above the bandgap energy of the semiconductor. The resulting dc photocurrent due to collection of the optically generated carriers by the junction can be expressed as [6]

IL = qAG& + L, + W ) (1)

where G is the optical generation rate, q is the electron charge, L, and L, are the diffusion lengths of hole and electron, respectively. The optically generated carriers results in an open-circuit photovoltage, V,,, when the diode is open circuited.

Manuscript received May 2, 1994: revised June 6, 1995. The authors are with the Department of Electronic Engineering, National

IEEE Log Number 9415541. Taiwan Institute of Technology, Taipei, Taiwan 10772, Republic of China.

0018-9375/95$04.00 0 1995 IEEE