Applyng Computatonal Methods to Test Ste and Antenna Desgn By Glen Dash, Ampyx LLC, GlenDash at alum.mt.edu Copyght 000, 005 Ampyx LLC In the past, mathematcs and expementaton wee the only tools engnees had to undestand test ste and antenna desgn. Today we have the Method of Moments. Antennas commonly used n EMC wok nclude dpole, concal, log peodc and hon types. These ae used on calbated test stes fo pecson measuements. In the past, engnees had to ely on electomagnetc theoy along wth good deal of tal and eo to desgn antennas and test stes. Today, we have computatonal tools that engnees of 30 yeas ago could only have deamed of. In ths atcle, we wll apply the elegant and poweful Method of Moments to the desgn of a half wave dpole and a bconcal antenna. We wll also use t to deve a ste attenuaton model. But fst we need to evew the physcs of an antenna that does not, and cannot, exst, yet s the antenna aganst whch all othes ae measued. It s called the sotopc adato. Fgue 1: Enegy fom an sotopc adato popagates outwad evenly n all dectons, fallng off accodng to the nvese squae law. An sotopc adato s an antenna that adates equally n all dectons. An mpulse of enegy suppled to the antenna s temnals esults n a sphecal shell of enegy popagatng outwad at the speed of lght. Snce enegy must be conseved, the shell s enegy pe unt aea must fall as t
expands. In fee space, the ate of fall s popotonal to 1/4π. The pupose of a ecevng antenna s to ntecept some of ths outwad adatng enegy. Fo example, consde the case of a theoetcal ecevng antenna consstng of a one-mete squae, pefectly absobng sheet placed at a dstance fom the sotopc adato. The amount of enegy pe unt tme (powe absobed by the sheet wll be: 1 1 d t 4π Whee: d The powe absobed n watts by the 1 mete squae sheet (powe densty) t The powe tansmtted n watts The powe s tansmtted n the fom of an electomagnetc feld composed of othogonal electc and magnetc feld components. Theefoe, the powe densty ncdent on ou ecevng antenna s the coss poduct of these two felds: d H ( Whee: d owe densty n watts pe squae mete The electc feld at the locaton of the ecevng antenna n volts pe mete H( The magnetc feld at the locaton of the ecevng antenna n ampees pe mete Futhe, n fee space the ato of the two felds s equal to the fee space mpedance, 377 ohms. 377 H ( d 377 Usng these elatons we can deve an expesson fo the electc feld poduced by an sotopc adato at a gven dstance : t d 4π d 377 d 377 377 4π t 5.5 Note that ths elatonshp s deved puely fom the consevaton of enegy. 1 We wll be assumng hee that the dstance s geate than λ/π (fa feld). t
The sze of the ecevng antenna can, of couse, be othe than 1 squae mete. Futhe, ts effcency may make the antenna seem to be ethe lage o smalle than ts physcal sze. These factos can be olled nto an effectve aea fo an antenna. The amount of powe eceved s the powe ncdent upon an antenna tmes ts effectve aea. Fo a 100% effcent 1m pefectly absobng sheet, the effectve aea would be 1. A sheet of.5m physcal sze, 50% effcent, would have an effectve aea of.5. ( A d eff Aeff t 4π Whee: ( owe eceved n watts A eff The antenna s effectve aea The ecevng antenna s usually desgned to convet the eceved powe nto a voltage fo measuement. Snce each antenna wll have ts own chaactestc mpedance (a adaton esstance ), a tansfe functon can be deved whch elates the powe ncdent on the ecevng antenna to the voltage at the antenna temnals: R ant Aeff ( t 4π Whee: The voltage at the eceve antenna s temnals R ant The eceve antenna s adaton esstance A tue sotopc adato eally exsts only n theoy. actcal antenna types commonly used n EMC wok nclude the dpole and bconcal types. The Dpole ehaps the smplest pactcal antenna s the half wave esonant (tuned) dpole. Its patten s not sotopc. Instead, n the plane of the antenna (the azmuth ) the electc feld t poduces s n the shape of a boad fgue eght. Tansmtted powe s focused n the fowad and eawad dectons. Snce enegy must be conseved, ths means that the dpole exhbts a powe gan ove sotopc. Theoy pedcts that ths powe gan s equal to 1.64, o expessed logathmcally,.14 db: Whee: G owe gan ove sotopc G ( db) 10log G
G (db)owe gan ove sotopc n db We can confm theoy by usng the computatonal Method of Moments. The method s utlzed n numbe of softwae packages and the one we wll use s EZNEC (Refeence 5). We wll set the fequency to 100 MHz and the length of the antenna to 1.44 metes, whch should poduce esonance. We wll make ou theoetcal antenna out of #1 AWG coppe we. EZNEC calculates the antenna s chaactestcs, ncludng ts azmuth patten, ts gan ove sotopc (calculated to be.11 db) and ts nput mpedance (close to 73 ohms) (Fgue 3). The slght dffeence n gan ove sotopc fom the theoetcal s due to the fact that ou antenna s not pefectly esonant, and s bult of coppe whch has some ohmc losses. A gan ove sotopc of.11 db s equal to a powe gan of 1.61. Fgue : Among the smplest of antennas, the half wave esonant dpole s a good statng pont fo antenna analyss.
Fgue 3: Usng a Method of Moments pogam, we can calculate the azmuth and elevaton plots of a half wave, tuned dpole n fee space. Based on ths smulaton, ou half wave tuned dpole wll poduce a feld stength at a gven dstance equal to: 5.5 G t G 1.61 7 t
Fgue 4: We add a ecevng antenna thee metes fom the tansmttng antenna of Fgue 3. Ths allows us to calculate ste attenuaton. Note that just the pesence of the ecevng antenna bows out the feld slghtly. Usng EZNEC, we now add a ecevng antenna to the smulaton, placng t 3 metes fom the tansmttng antenna. The antennas ae co-plana as shown n Fgue 4. EZNEC geneates the esults shown. Note that the feld poduced by the tansmttng antenna has been dstoted somewhat by the pesence of the ecevng antenna. Accodng to Refeence, the effectve aea of a tuned half wave dpole s:
π λ 4 eff G A Theefoe, the eceved powe wll be: 16 ) ( 16 ) ( 4 ) ( G G G A t t t eff π λ π λ π Snce the electc feld s popotonal to the squae oot of the powe: G E E t λ π λ 13. 4 ) ( Futhe, snce the antennas ae dentcal, the ato of the voltage dvng the tansmttng antenna ( ) to that measued at the eceve ( ) wll be the same. λ 13.
Fgue 5: A test ste has a gound plane whch eflects some of the tansmtted sgnal, causng lobes n the adated feld. The amount of sgnal eceved theefoe depends on the heght of the antennas above the gound plane. The smulaton shown s fo esonant half wave dpoles opeated at 100 MHz. We now place a pefectly eflectng gound plane 1.67 metes unde the two antennas. The effect of the gound plane s to eflect some sgnal, changng the amount of sgnal eceved. The effect can be obseved fom the EZNEC computed elevaton plot shown n Fgue 5. (The elevaton plot maps the electc feld n a plane pependcula to the gound plane and passng though the cente of the tansmttng antenna.) The pesence of the gound plane causes lobes to be poduced. The shape of these lobes s a functon of the heght of the tansmttng antenna above the gound plane and the fequency. Fo the confguaton shown n Fgue 5 (whch places the ecevng antenna n the lobe of maxmum eflected sgnal) the gan n electc feld esultng fom addton of the gound plane s appoxmately 1.67. Ths nceases the ato of eceved to tansmtted sgnal: λ λ (1.67)(1.3).
Fo example, opeatng at 100 MHz (λ3 metes):. That s, f we put 1 volt nto the tansmttng antenna,. volts wll be measued on the eceve. The tansmsson loss, also known as the ste attenuaton, s 13. db. Fgue 6: A system consstng of a tansmttng and ecevng antenna can be modeled as a two-pot netwok. The ato of sgnal out ( ) to the sgnal n ( I ) s known as the ste attenuaton. We wll also fnd t useful to calculate the electc feld ncdent on the ecevng antenna fom the voltage obseved on a eceve:
( A d d ( eff Theefoe, the voltage at the eceve nput wll be: Whee: f MHz Fequency n MHz. 0 0 50 ( 377 d G λ 377 4π MHz MHz f Gλ 4π 1.64 50 λ.13 λ 377 4π 300 λ f 0 1 39.6 0 39.6 f Ths equaton s usually wtten n ts logathmc fom: MHz G λ 377 4π 1 0 fmhz 39.6 db) 0log 0 ( db) 0log0 db) 0 ( db) + 0log fmhz 31.9 Let AF 0log fmhz 31.9 db) ( db) + AF The tem AF s known as the antenna facto. By addng the antenna facto to the voltage obseved on the eceve, the electc feld ncdent on the antenna can be calculated. Fo a pefect half wave tuned dpole, the antenna facto s: 0
AF 0log fmhz 377 4π f G 0log 300 50 db) ( db) + AF 0 MHz 31.9 The method also woks fo antennas of the bconcal and log peodc type, though fo those antennas the antenna facto must be geneally be deved empcally. Ste Attenuaton The fact that the tansmsson loss between a tansmttng and ecevng antenna can be so eadly pedcted means that a test can be devsed to measue the qualty of test stes. In the 1950 s, the Fedeal Communcaton Commsson (FCC) began to develop such a test based on the ste attenuaton pncple. Fgue 7 shows a typcal test ste. The ecevng antenna can be ased o loweed ove a 1 to 4 mete ange n ode to pck up the lobe of maxmum emssons. The tansmttng antenna s fxed at a heght of two metes. Both antennas ae hozontal.
Fgue 7: Ste attenuaton s llustated. Two dpole antennas ae placed thee metes apat. The tansmttng antenna s hozontal and s fxed two metes above the gound plane. The ecevng antenna s thee metes away and can be ased o loweed though a dstance of one to fou metes. The mnmum loss at each fequency should follow the cuve shown. The sold poton of the cuve s deved theoetcally, the dotted poton empcally.
Usng the analyss above, and assumng that each antenna adds.5db of loss, the ste attenuaton should be: SA 0log fmhz 5.7 Thus, at 100 MHz the ste attenuaton should be 14.3 db. Ths equaton was ncopoated n FCC Bulletn OST-55. The equaton woks well only above 80 MHz due to the estcted heght of the ecevng antenna. Below that fequency, OST-55 equed test stes to meet an empcal cuve. In the 1980 s, ANSI Accedted Standads Commttee C63 developed a moe geneal test fo ste attenuaton. In addton to specfyng ste attenuaton tests fo 3, 10 and 30 mete test stes n both vetcal and hozontal polazaton, the standad s flexble enough to be used wth any well calbated, lnealy polazed antenna. The Bconcal The use of concal antennas goes back to the dawn of the ado age. In the ealy 1900 s, Macon found that a concal antenna poduced bette esults than a sngle we and bult tansmttng antennas usng concal desgns. Fgue 8: Macon s oldhu staton n England (1905). Although geneally not appecated at the tme, the concal desgn of the antenna was a key to ts success. Afte Refeence 4. The eason that concal antennas poved supeo was that Macon s spak tansmtte was a boadband souce. When combned t wth a boadband antenna, Macon was able to tansmt fa moe enegy than he could of have had he been lmted to the esonant fequency of a sngle we. Macon s antenna was known as a dscone, a cone shaped stuctue placed vetcally ove a
gound plane. Combnng two such cones back to back poduces a b-concal antenna. Though the geneal chaactestcs of concal antennas have been known fo almost a centuy, pecse mathematcal models pedctng the behavo poved llusve. o to the development of computatonal technques, eseaches had to ely mostly on expemental data to desgn the dscone o bconcal antennas. Fgue 9: A typcal bconcal antenna used fo EMC wok. Key paametes ae the cone length (, the oveall length (L) and the angle fomed by the cone and the hat. Some of that data s shown n Fgue 10. At esonance, the mpedance of a dscone antenna s a functon of ts cone angle. Note that at a gven cone angle the mpedance s elatvely flat ove a wde fequency ange. Futhe, the azmuth patten of a dscone antenna s a boad fgue eght, just lke a dpole, and t etans ths shape ove a wde fequency ange. The elatvely flat mpedance combned wth the elatvely stable azmuth patten makes the dscone antenna an deal choce fo boadband tansmsson. The same s tue fo the bconcal antenna. Snce the bconcal antenna s made up of two dscones back to back, mpedance cuves fo the bconcal antenna can be deved smply by multplyng the cuves n the Fgue 10 by two.
Fgue 10: Befoe the advent of computezed methods, concal antennas wee desgned usng empcally deved chats and tables, such as those shown hee. The key to the bconcal s unusual chaactestcs s ts elatvely flat mpedance and t dpole lke azmuth patten. Afte Refeence 1. The bconcal style antenna commonly used fo EMC testng uses a cone made of sx to eght ndvdual ods. The ods ae ted togethe at the antenna s extemtes by bendng them nto a hat. As a pactcal matte, the hat has only a mno effect on pefomance. These antennas have easonably good pefomance fom 60 to about 00 MHz. Below 60 MHz antenna s SWR becomes hgh. The antenna s smply too shot to exhbt a good mpedance match at low fequences. Rathe than behavng as a bconcal antenna, t s smply a shot, fat, msmatched dpole. To have low SWR, the ato of to λ should be geate than.5. To peseve a good azmuth patten the ato of L to λ should be less than.75 (Fgue 10).
Fgue 11: Wdely used fo EMC wok, the typcal bconcal antenna exhbts hgh SWR below 60 MHz. It s smply too shot to be well matched thee. Stll, the antenna can be used f well calbated. Afte Refeence 3. In ecent yeas, manufactues have attempted to deal wth the low fequency pefomance ssues of the bconcal antenna though the use of loadng elements placed at ethe end of the antenna. Ths can mpove pefomance somewhat. We can use the Method of Moments to smulate a bconcal antenna. The desgn we chose to model s smple, consstng of 4 ods smulatng each cone. Lke commecally avalable antennas, ou bconcal woks easonably well above 60 MHz. Fo antennas used n fee space, only a mnmal numbe of ods ae needed. Howeve, neaby stuctues such as the feed lne o a gound plane can mbalance the antenna, so fo pactcal applcatons moe ods ae needed. Whee sevee loadng s expected, sold cones may be equed.
Fgue 1: We desgned ou own bconcal antenna and tested t usng the Method of Moments. Wth L.737 metes and θ60 degees, the antenna woks well fom 60 MHz to ove 00 MHz. At the low end, SWR ses, as t does fo most pactcal bconcal desgns. SWR shown s nto 100 ohms.
Fgue 13: Azmuth pattens fo ou model bconcal antenna ae shown. Refeences: 1. ey Hgh Fequency Technques, Rado Reseach Laboatoy of Havad Unvesty, olume I, Chapte 4, McGaw Hll (1947).. W. K. Robets, A Gude to FCC Equpment Authozatons, publshed by Wllma K. Robets, (1980). 3. I. Staus, A New Bconcal Antenna Fo Use n the Fequency Range of 175 to 1000 Megahetz, ITEM (1985). 4. J. Kaus, Antennas, McGaw Hll (1988). 5. EZNEC s avalable fom Roy Lewallen, W7EL,.O. Box 6658, Beaveton, OR 97007. Fo ths atcle, EZNEC.0 was used.