A Simple Theory for Predicting the Electromagnetic Performance of Enclosures Using Impedance and Polarizability Measurements

Abstract

The th e o ry o f Madle and H o e f tH l f o r un der ­ s t an d in g th e magnetic f i e l d a t t e n u a t i o n of e n c lo s u re s has been r e f i n e d so t h a t i t can be used t o q u a n t i t a ­ t i v e l y p r e d i c t th e e le c t ro m a g n e t i c performance of e l e c t r i c a l l y small e n c l o s u r e s . Using th e t r a n s f e r impedance of th e j o i n t s , th e s u r f a c e impedance of sh i e ld e d a p e r t u r e s , and th e p o l a r i z a b i l i t y o f a p e r ­ t u r e s , t h i s th e o ry p r e d i c t s th e s u r f a c e magnetic f i e l d a t t e n u a t i o n ( t h e r a t i o o f th e s u r f a c e magnetic f i e l d on th e e x t e r i o r o f th e e n c lo su re t o th e mag­ n e t i c f i e l d i n s id e th e e n c l o s u r e ) . I n t ro d u c t io n The s o l u t i o n of many e l e c t ro m a g n e t i c c o m p a t i b i l ­ i t y problems r e q u i r e s th e a n a l y s i s o r p r e d i c t i o n of t h e e le c t ro m a g n e t i c performance o f s h i e ld e d e n c l o ­ s u r e s . The l i t e r a t u r e does not c o n ta in any s h i e ld i n g a n a l y s i s te c h n iq u e t h a t could be used t o ana lyze the s h i e ld i n g performance o f a wide range of e n c lo s u re s us ing fundamental p h y s i c a l p r i n c i p l e s such as c u r r e n t d i f f u s i o n , a p e r t u r e c o u p l in g , and j o i n t r e s i s t a n c e . This lack o f a c r e d i b l e , v a l id a t e d a n a l y s i s te ch n iq ue i s a major reason f o r e x p e r im e n ta l l y e v a l u a t i n g s p e c i f i c e n c lo su re d e s ig n s on a c a se b y -c a se b a s i s . A c r e d i b l e a n a l y s i s te ch n iq u e would be a tremen­ dous a s s e t t o a s h i e l d i n g des ig n program because i t would a l low th e d e s i g n e r t o choose th o se c o n s t r u c t io n t e ch n iq u es t h a t were a p p r o p r i a t e t o th e s p e c i f i c q u a n t i t a t i v e r e q u i rem en t . He could a l s o i n c o rp o ra t e c o n s t r u c t i o n te c h n iq u e s t h a t o f f e r e d a p o s i t i v e b e n e f i t w i th r e s p e c t t o c o s t and avoid p r a c t i c e s t h a t were d i f f i c u l t o r expensive to manufactu re whi le p rov id in g on ly marg inal improvement. Of p a r t i c u l a r importance was th e use o f g a s k e t s . These a re expen­ s iv e t o i n s t a l l and m a in t a in , and t h e r e i s no q u a n t i ­ t a t i v e method to d e te rm ine i f they a re needed. Along with th e d e s i r e t o have a c r e d i b l e s h i e ld i n g a n a l y s i s t e c h n iq u e , a b e t t e r method f o r s p e c i fy i n g s h i e l d i n g e f f e c t i v e n e s s i s d e s i r e d . The IEEE d e f i n i t i o n of s h i e l d i n g e f f e c t i v e n e s s ( i . e . , the r a t i o o f th e f i e l d a t a p o i n t , w i th and w i th o u t the e n c lo su re ) i s ve ry p r a c t i c a l , bu t i t i s no t based on f i rm p h y s i c a l p r i n c i p l e s s i n c e i t does no t t a k e in to account th e i n t e r a c t i o n / s c a t t e r i n g o f th e f i e l d by th e e n c l o s u r e , and th e d e f i n i t i o n seems in a p p r o p r i a t e when th e e n c lo su re i s p a r t o f a l a r g e r s t r u c t u r e . The su cces s t h a t s u r f a c e t r a n s f e r impedance has en joyed in t h e c a b l e a r e a has r a i s e d hopes t h a t a s i m i l a r i n t r i n s i c p r o p e r ty could be found to be a p p l i c a b l e t o s h i e ld e d e n c l o s u r e s . In f a c t , one could v i s u a l i z e a s u r f a c e t r a n s f e r impedance of an en c lo su re as th e r a t i o o f th e average e l e c t r i c f i e l d a t th e i n s id e s u r f a c e o f th e e n c lo su re t o th e mag­ n e t i c f i e l d a t t h e o u t s i d e s u r f a c e . U n fo r tu n a te ly , measuring th e e l e c t r i c f i e l d on th e i n s id e s u r f a c e i s d i f f i c u l t s i n c e one does n o t have a conven ien t c e n t e r conductor which could "average" th e f i e l d , as in a c a b l e . An in t e r im s o l u t i o n i s t o use s u r f a c e mag­ n e t i c f i e l d a t t e n u a t i o n , d e f in e d in t h i s s tudy as the r a t i o o f th e s u r f a c e magnetic f i e l d on the o u t s i d e of t h e e n c lo su re to t h e magnetic f i e l d i n s id e th e e n c l o ­ su r e . This has v i r t u e in t h a t measurements a re well d e f i n e d , r e s u l t s a re c o n c e p tu a l ly in th e same form as th e r e q u i r e m e n ts , and th e e f f e c t s o f e x t e r n a l co up l ing a r e e l im in a te d from th e s p e c i f i c a t i on /pred i c t i o n . Measurement o f th e s u r f a c e magnet ic f i e l d a t t e n ­ u a t io n of a wide range o f e n c lo su re s 12 ,3 ] have shown t h a t c u r r e n t d i f f u s i o n i s im po r tan t on ly a t low f r e ­ q uen c ies ( l e s s than a few t e n s o f k i l o h e r t z ) o r when t h e e n c lo su re wal l i s very t h i n . P r a c t i c a l examples o f t h e l a t t e r c o n d i t i o n in c lu d e wire mesh f o r f r e ­ q uenc ies below 1 MHz and m e t a l l i c c o a t in g s f o r f r e ­ q uenc ies below se v e ra l t e n s o f MHz. For most e n c lo s u re s made o f metal a t l e a s t 1 mm (0 .040 inch) t h i c k , th e predominant co up l ing mechanism between th e o u t s i d e and in s i d e of th e e n c lo su re i s th e r e s i s t a n c e o f th e j o i n t s and a p e r t u r e c o u p l in g . When e n c lo su re s a re f i l l e d w i th e l e c t r o n i c s , conduc t ive p e n e t r a t i o n s such as th e power and s ig n a l w ir in g may c o n s t i t u t e an o th e r coup l ing mechanism. However, conduc t ive p e n e t r a t i o n s a re g e n e r a l ly not cons id e red t o be p a r t o f th e e n c lo su re and w i l l no t be in c luded in th e t h e o ry p re s e n te d in t h i s s tud y . Thus, th e primary o b j e c t i v e o f a th e o ry f o r p r e ­ d i c t i n g t h e e le c t ro m a g n e t i c performance of an en c lo ­ su re i s t o account f o r p r a c t i c a l im p e r f e c t io n s or d e f e c t s such as a p e r t u r e s and j o i n t r e s i s t a n c e . I t would a l s o be d e s i r a b l e f o r th e th e o ry t o account f o r c u r r e n t d i f f u s i o n so th e performance of conduc t ive e n c lo su re s can be analyzed a t f r e q u e n c ie s where the e f f e c t i v e wall t h i c k n e s s i s l e s s than a sk in dep th . The e le c t ro m a g n e t i c a n a l y s i s o f e n c lo s u re s can be s i m p l i f i e d by on ly c o n s id e r in g s i t u a t i o n s where th e e n c lo su re i s e l e c t r i c a l l y sm a l l . For th e se c a s e s , t h e r e i s no s i g n i f i c a n t phase d i f f e r e n c e between f i e l d s , c u r r e n t s , and v o l t a g e s a t d i f f e r e n t p o in t s on th e e n c l o s u r e ; and th e a n a l y s i s can be c a r r i e d ou t us ing lumped p a ram e te r s . Using t h i s s i m p l i f i c a t i o n does n o t impose a s e r io u s l i m i t a t i o n on th e a n a l y s i s s i n c e most e n c l o s u r e s , in c lu d in g r a c k s , a re l e s s tha n a few mete rs in s i z e and t h e r e f o r e a re e l e c t r i c a l l y small f o r f r e q u e n c ie s below about a hundred megaher tz . Equipment boxes a re s m a l l e r ; t h e r e f o r e th e s i m p l i f i c a t i o n does not i n t r o ­ duce s e r io u s u n c e r t a i n t i e s u n t i l h ig h e r f r e q u e n c ie s a r e reached . The p r e s e n t s tudy i s concerned with p r e d i c t i n g th e e le c t ro m a g n e t i c performance of e n c lo s u re s when th e source i s o u t s i d e . The th e o ry could be extended to c a se s where th e source i s in s id e th e e n c l o s u re , but t h i s e x t e n s io n would r e q u i r e assumptions conce rn ­ ing th e boundary c o n d i t i o n o u t s id e th e e n c lo su re and t h e i n t r o d u c t io n o f c on cep t s such as s l o t an ten n as , e t c . , t o account f o r a l l t h e ph ys ica l p r i n c i p l e s . Note t h a t th e magnetic f i e l d a t t e n u a t i o n i s g e n e r a l ly no t th e same in both d i r e c t i o n s . In th e 1950s, Quine!4 ! developed some in n o v a t iv e te c h n iq u e s f o r per forming p r a c t i c a l a n a l y s i s of e n c l o s u r e s , e s p e c i a l l y when th e source was i n s i d e . In 1981, CaseyiS] t h e o r e t i c a l l y i n v e s t i g a t e d a p e r ­ t u r e s covered wi th cond uc t ive f i lm s and wire mesh. Among o th e r t h i n g s , he in t ro du ced th e ide a of an e f f e c t i v e magnet ic p o l a r i z a b i l i t y o f a d i s t r i b u t e d