Simon B. Nawrot ATNF vacation student February 2003

Transcription

1 Degn and Contructon of a Slotted Coaxal Balun and the Development of a Method to Determne Noe Temperature of LNA wth Non Standard Input Impedance. Smon B. Nawrot ATNF vacaton tudent February 3 Abtract Th paper outlne the degn and contructon of a ytem mlar to what may be connected between a propoed zgzag antenna and the frt LNA n an element of an SKA adoptng the Luneburg Len approach. It alo the objectve of th paper to outlne a procedure by whch the noe temperature of canddate LNA and the frt tage matchng for the SKA can be meaured. The procedure decrbed ha been pecfcally degned o that the noe temperature of LNA wth non tandard nput mpedance can be meaured. The 5Ω connecton requred by commercal noe fgure meter do not allow for a non tandard mpedance. Introducton CSIRO SKA team are nvetgatng the ncreae n thermal noe performance of an uncooled front operatng wth a non tandard nput mpedance other than 5Ω [1]. The paper outlne the degn and contructon of a poble front ytem operatng between 1 and 5 GHz that able to provde a tranformaton from a Ω unbalanced termnaton requred by the antenna to a 5Ω balanced termnaton requred by a tandard LNA. The reultng ytem a balun/taper combnaton. The 5Ω termnaton wa ued for th prototype, however, tranformaton to a non tandard mpedance can be acheved by followng the ame method. The performance ha been teted and reult are preented. The paper alo outlne a procedure by whch the noe temperature of an LNA or balun/taper/lna combnaton can be meaured. It recommed that the ytem a outlned n th paper be ued to meaure the noe temperature when an LNA of tandard 5Ω mpedance ued. Th wll allow the meaurement procedure to be evaluated. The ytem wll be ued n two tuaton. The frt tuaton wll allow the ytem to connect to an expermental antenna. The econd tuaton wll allow for connecton to a retor that wll be ued a a hot/cold thermal noe ource for noe temperature meaurement. Th paper wll concentrate on the latter tuaton Decrpton of requred Sytem The Sytem The ytem wll be ued n two dfferent tuaton. Thee are the Feld Meaurement tuaton n whch the ytem connected to an expermental zgzag antenna and the Bench Meaurement tuaton n whch the ytem connected to a retor. The feld meaurement ytem wll provde a mean by whch the performance of the propoed front can be teted. It wll alo provde a mean by whch noe fgure wll be meaured a the zgzag antenna drected at hot and cold ource. The bench meaurement ytem ha been contructed. By heatng and coolng a thn flm chp retor actng a a noe ource, noe power meaurement can be taken and then by ung the Y factor method [9], noe temperature can be calculated. Both ytem are mlar n that they are both ntally requred to tranform the ohm antenna mpedance down to the tandard 5 ohm requred by a tandard LNA. Both ytem alo requre a balun o that the balanced termnaton requred by the antenna can be tranformed to the unbalanced coaxal termnaton requred by an LNA.

2 Feld Meaurement The feld meaurement apparatu cont of: ) A broadband zgzag antenna a the noe ource, ) an LNA a the devce under tet, ) a coaxal cutaway balun to tranform the balanced wre ytem from the antenna termnal to an unbalanced coaxal termnal requred by the LNA, v) a taper to go between the antenna and balun termnal to provde the correct phycal pacng and correct mpedance match, v) a power meter connected to the output of the LNA o that noe fgure can be meaured. BALUN 13Ω:5Ω LNA Zgzag Antenna Tapered Secton Ω:13Ω Fgure 1. Power Meter Bench Meaurement The bench meaurement apparatu cont of: ) a chp of 18 ohm to act a the noe ource and to mulate the zgzag antenna mpedance, ) an LNA a the devce under tet, ) the ame cutaway balun a ued n the feld meaurement, v) a taper to go between the retor and balun termnal to provde the correct phycal pacng and correct mpedance match, v) the ame power meter a ued n the feld meaurement. BALUN 13Ω:5Ω LNA Noe Source Retor Ω Tapered Secton Ω:13Ω Fgure. Power Meter Decrpton and Degn of Sytem Component Zgzag antenna The antenna broadband and cover the 1-5GHz frequency range of nteret. The zgzag antenna predcted to have a nomnal nput mpedance of approxmately ohm. The nput mpedance of the antenna expected to vary by a mall amount n harmony wth the perodcty of the zgzag tructure a the frequency vared. The man beam axal to the antenna and radate n the drecton of t apex.

3 LNA A commercally avalable LNA wth 5 ohm nput and output mpedance wll be ued for ntal tetng. By later alterng the mpedance tranformaton, the ytem can be matched to the mpedance requred at the nput of a non tandard LNA to provde a mean to meaure t noe temperature. Balun The balun wa contructed from of a pece of rgd 5Ω coax. The delectrc materal ha a delectrc contant of 1.5 that wa determned from meaurement of the cable dmenon. The lo tangent unknown. The cable ha an outer conductor of alumnum and an nner conductor of copper. Approxmate dmenon are: ID = 8.3mm, OD = 9.6mm, Centre Conductor Dameter =.97mm, Outer Conductor Thckne =.7mm. The balun ha two functon: to tranform a balanced ytem to an unbalanced ytem and to provde ome mpedance tranformaton. Th acheved by cuttng a lot n the coax and gradually wdenng the lot down t length untl two parallel balanced conductor reman wth the heght of the remanng held beng equal to the dameter of the centre conductor. At the of the balun the lot angle 33 degree. Tranton from a balanced to an unbalanced ytem acheved by the tapered geometry of the lotted coax that enure that all current are gradually confned to the nde urface of the coax when the unbalanced termnal reached []. The rate at whch the lot wdened down the length of the coax determned by the requred charactertc mpedance contour of the mpedance tranformaton. The charactertc mpedance contour determned by the Klopfenten Taper [3] that optmum n the ene that t ha mnmum reflecton coeffcent n t pa band for a pecfed length of taper. The choen length of the taper wa cm and at the lowet frequency of 1 GHz th correpond to /3 of a wavelength. Wth the balun ncorporatng the Klopfenten taper the maxmum expected reflecton coeffcent at frequence above 1 GHz.1%. Calculaton for the Klopfenten taper were performed ung an teratve proce on computer ung the method n [4]. Determnaton of the charactertc mpedance of lotted coax wa determned from the degn equaton provded n []. The delectrc contant of 1.5 wa ubttuted for the ar permttvty that wa ued n the paper and a new et of degn curve were drawn. An approxmaton wa made here becaue the permttvty aocated wth the degn equaton that of the entre envronment urroundng the lotted coax and not retrcted to the coaxal delectrc. The effect of th approxmaton wa modelled for the cae where the feld ha the leat contanment.e. at the of the balun where the lot angle 33 degree. The dfference n charactertc mpedance between the cae where the delectrc flled the entre envronment and the cae where the delectrc wa retrcted to the coaxal delectrc wa only 7 ohm. Th wa not condered gnfcant and the approxmaton wa deemed atfactory. The requred Klopfenten Taper and the mpedance of the lotted coaxal cable are gven n the fgure 3 and 4 repectvely.

4 Fgure 3. Charactertc mpedance along Klopfenten Taper 5 Charactertc Impedance (ohm) Poton along balun (x/l) Fgure 4. Charactertc Impedance of Slotted Coax (Zo = 5 ohm, er = 1.5) Charactertc mpedance (ohm) Slot angle (degree) Zo upper Zo lower Average From the curve t can be een that wth a lot angle of 33 degree the charactertc mpedance 13 ohm, however, the requred mpedance at the antenna ohm. In order to tranform from 5 to ohm t neceary to contnue the Klopfenten taper nto the tapered ecton between the balun and retor..e. The balun wll contan that part of the mpedance contour between 5 and 13 ohm and the tapered ecton wll contan that part of the mpedance contour between 13 and ohm. Th correpond to the balun contanng the frt 17mm of the taper. The functon of the lot angle wth repect to the dtance along the balun approxmated a two lnear ecton and wa determned from a combnaton of the reult hown n Fgure 3 and Fgure 4. Th hown n fgure 5.

5 Fgure 5. Slot angle along balun angle (degree) (9,7) (17,33) 5 (,4) dtance along balun (mm) The degn drawng of the balun hown n Appx A. Contructon To cut away the lot n the coax a number of dfferent contructon technque were attempted. Some had more ucce than other. To cut away the lot n the coax, one choen method wa to etch the requred pattern wth hydrochlorc acd. A template wa made on a pece of paper and th wa wrapped around the cable o that the pattern could be crbed on the urface wth a knfe. A number of method to mak the dered porton of the cable were tred wth varyng level of ucce. The frt method attempted nvolved dppng the cable n molten wax. The pattern that wa prevouly crbed on the cable wa tll vble through the wax and th allowed the removal of the wax wth a mall knfe. Wth the undered porton of the alumnum now expoed the cable wa then mmered n 33% hydrochlorc acd oluton. Th method, however, wa unucceful. The prncpal reaon beng that the localed heatng generated by the reacton caued the wax to often and th reulted n unacceptable under etchng and n ome cae, complete detructon of the mak. Other makng materal were tred. Flexble PVC tape wa tred, however, localzed heatng alo caued the tape to come away at the edge, although n ome place the etch wa very clean. It thought that ung a weaker acd oluton may produce better reult n th cae. Other makng materal tred were Dulux flat black enamel pray pant and photographc ret. Before coatng an outlne of the requred lot wa maked on the coax wth 1.7mm crepe makng tape. The enamel pant wa appled by prayng and the photographc ret wa appled by dppng. In both cae after coatng, the tape wa removed to expoe bare alumnum n the hape of the lot permeter. In the cae where the photographc ret wa ued, the balun wa baked at approxmately 8 C for about one hour n an attempt to harden the coatng. Unfortunately the makng materal n both cae wa detroyed through the etchng proce. The enamel pant flaked off n ecton and the photographc ret wthtood the acd for ome tme before detructon. It thought, however, that ar bubble n the ret coatng may have been a contrbutng factor to t falure. It may be poble that good reult can be acheved f the photographc ret bruhed on to provde a thnner more unform coatng.

6 Other urface coatng for ue a a mak may need to be tred n future. A btumnou type pant ha been uggeted. Fgure 6 Some faled etchng attempt. The black coatng enamel pant, the red coatng photographc ret. The balun that ha been produced wa contructed ung a paper template that wa wrapped around the cable. Expoed alumnum wa then removed carefully ung a rough bladed hackaw and any excee removed by flng. Care wa taken to mnme damage to the delectrc materal durng cuttng. Chp Retor The retve termnaton cont of a 18Ω thn flm chp retor. The retor State of the Art ze SO4 approxmately correpondng to dmenon of.5mm x.5mm. The retor mounted on the of the taper on the PCB. Taper from balun to chp retor The taper from balun to chp retor cont of two parallel plate etched on a ngle ded PCB wth.76mm ubtrate thckne and 17um conductor thckne (Roger RT durod 6). Delectrc contant.94 and lo tangent.1. The taper provde a reducton n conductor pacng from 3mm at the balun termnal down to 1mm at the chp retor. The taper alo provde the remander of the Klopfenten mpedance contour from 13 to ohm. At the nterface between the balun and the PCB the two part were oldered together. Th rapd tranton dd have ome effect on the ytem performance but atfactory reult were tll obtaned. Degn of the taper The PCB taper uppoed to provde that part of the Klopfenten taper between 13Ω and Ω. For th requrement the taper 7.35 cm long. A number of pont along the taper were defned. The poton of thee pont are hown n fgure 7 below.

7 Fgure 7. From the reult dplayed n fgure 3 the requred mpedance along the taper are hown n Table 1. Table 1. Pont no. Dtance from pt.1 (cm) Requred Z Termnaton To determne the correct track wdth and pacng a fnte dfference two dmenonal (FDD) feld olvng program wa ued [5]. The program allowed the entry of a two dmenonal cro ecton of an arbtrary lne nto t graphcal nterface. Th allowed the geometry of the ubtrate and conductor to be pecfed. The requred charactertc mpedance at each pont along the taper wa obtaned by varyng the wdth and pacng of the track by tral and error. The reult obtaned by the program are hown n Table. Table. pont no. Z obtaned L (uh/m) C (pf/m) 8 V ( 1 m / ) W (mm) (mm) Where: L the dtrbuted nductance, C the dtrbuted capactance, v the velocty of propagaton, W the wdth of the track and, the pacng between track.

8 Contructon of the Taper The Taper wa photographcally etched on a 1mm x 4 mm pece of Roger RT Durod 6 board. The mak requred for etchng wa drawn n Soldwork and prnted black onto a tranparency heet wth a colour prnter. Calculatng the Lo n the PCB Taper In order to determne the lo n the PCB taper t neceary to form ome equaton for the lo n term of the varable provded by the FDD program n Table. The total lo of the PCB taper contrbuted to by the delectrc lo and the conductor lo. From [6], the attenuaton contant n db/metre gven by: R α = GZ db / m Z.(1) where: R the dtrbuted retance of the lne n Ω/m, G the dtrbuted conductance of the lne n S/m, R 4.34 the conductor lo.(1a) Z 4.34GZ the delectrc lo..(1b) 1. Calculaton of the Dtrbuted Retance R Equaton (6.3) n [7] can be modfed to ut the geometry of the cro ecton for the taper to gve the dtrbuted retance of a ngle conductor: R Rn gle =.() W where: 1 πfµ R = =,.(a) σδ σ σ = 58MS / m for copper, µ the permeablty of free pace, W twce the wdth of a track..e. The approxmate cro ectonal permeter of the track ued n accordance wth the above aumpton. Becaue there are two lne n the taper t neceary to multply R n n () by and ue the proxmty factor P determned a n appx for the calculaton of R: R R = P.(3) W Combnng (a) wth (3) the requred expreon for R obtaned: gle R = πfµ σ W P.(4)

9 . Calculaton of the dtrbuted conductance G From equaton (3.1) n [6] the dtrbuted conductance can be calculated by: G = πfc tanδ.(5) eq Where tanδ eq the equvalent lo tangent at a pont along the lne.e. t a combnaton of the lo tangent of the ar tan δ ar =, and the lo tangent of the ubtrate tan δ that ha the equvalent effect of a unform delectrc at that pont. Equaton (3.11) n [6] can be converted to a more arbtrary form ueful for our purpoe o that the equvalent lo tangent can be found n term of tan δ, ε and ε eq : ε ε eq 1 tanδ eq = tanδ ε eq ε 1..(6) Where: ε the delectrc contant of the ubtrate, ε the equvalent delectrc contant at a pont along the lne..e. It the combnaton of the ar eq delectrc contant ε ar =1 and ubtrate delectrc contant ε at a pont along the lne that ha the equvalent effect of a unform delectrc at that pont. ε eq can be determned f the velocty of propagaton v at a pont along the lne known. c ε eq =.(7) v Where c the velocty of lght. Subttutng (7) nto (6) and then (6) nto (5) the requred expreon n term of obtaned: v πfcε 1 tan δ c G =.(8) ε 1 tan δ, ε, and v 3. Determnaton of Conductor Lo, Delectrc Lo, and Attenuaton Contant Subttutng (4) nto (1a) the conductor lo obtaned. πfµ = 4.34 σ WZ P (db/metre).(9) Lo conductor Subttutng (8) nto (1b) the delectrc lo obtaned. v πfcε 1 tan δ 4.34 c Lo = delectrc Z (db/metre).(1) ε 1 Addton of (9) and (1) yeld the total lo or the attenuaton contant α n db/metre.

10 1 α = 4.34 WZ πfµ P + Z σ v πfcε 1 c ε 1 tanδ (db/metre).(11) 4. Reult To approxmate the total lo of the taper, the taper wa broken up nto element. Each element wa agned the data from a pont a hown n fgure 8 below: Fgure 8. Numercal value of the requred varable are gven n Table. Some other requred value are: ε =.94, tan δ =.1, σ = 58MS / m, 7 µ = 4π 1, 8 c = 3 1 m / Table 3 how ome ntermedate reult for the lo calculaton. Reult are gven for each element n the taper. The proxmty factor value were calculated a n Appx. Table 3. Lo conductor G / f R / f Lo Element delectrc ( db / Hz) Element no. ε eq tan δ eq ( S / m / GHz) P ( Ω / m / Hz) Length (cm) ( db / GHz) E E E E E E E E E E E E E E E-7 total E-7 Table 4 how reult for the Delectrc lo, Conductor lo, and total lo over the entre PCB taper for frequence between 1 and 5 GHz. The fnal column gve an ndcaton of a lo per unt length.

11 Table 4. frequency (GHz) Delectrc lo n PCB (db) Conductor Lo n PCB (db)total Lo n PCB (db) db/m Note: In mcrotrp tranmon lne t normally expected that the delectrc lo wll upercede the conductor lo at around the frequence hown n table 4. Th, however, not the cae n the reult hown n Table 4 for an open wre PCB conductor geometry. There are three reaon for th:. The PC board ha low lo.. The geometry of the open wre lne on the PCB mean that a large proporton of the feld n ar a well a n the PCB and th reduce the delectrc lo.. The wde flat conductor of the lne caue the current to be le evenly dtrbuted n the conductor and th reult n an ncreaed proxmty factor and therefore ncreaed conductor lo. Modellng of the Heat Conducton when the noe ource heated and cooled Concern were raed n regard to the heatng and coolng of the LNA a a reult of heat conducton through the taper and balun when the noe ource heated and cooled. Recommaton were made that nvolved buldng a ecton of the taper from copper plated tanle teel that ha a much lower thermal conductvty to act a a thermal barrer. The heat conducton wa approxmately modeled ung Fourer One Dmenonal Heat Tranfer Equaton for a fnte bar wth fxed temperature [8]. Dervaton of the model can be found n [8]. The model provde a conervatve (wort cae) ndcaton of the heat dtrbuton along the length x of the taper and balun at dfferent tme t. 1. Aumpton and Approxmaton. Modellng the bench meaurement apparatu a a thn rod The meaurement apparatu condered to be a thn rod upon whch Fourer One dmenonal heat tranfer equaton can be appled. The temperature dtrbuton only condered n one dmenon (over the rod length) n th model. No conderaton gven to the cro ectonal area of the rod. Th can be done f the contant of thermal permvty ( m / ) for the materal ued whch take nto account the correpondng ncreae n thermal ma due to an ncreaed cro ectonal area.. Fxed End temperature Each of the rod held at a fxed temperature. Th abolutely true only at the chp retor that heated or cooled to a fxed temperature. The bar however made uffcently long (1m) o that the other (fxed at room temperature) kept a uffcent dtance from the pont at whch the LNA located (approx.5m from the chp retor) to prevent t from affectng the temperature at th pont. Lookng at the fnal plot of the temperature dtrbuton over tme t can be een that the rod at a contant 98K for the tme hown over a conderable dtance from the 1m fxed temperature pont. Th aumpton ha ncreaed credblty when the thermal ma of the apparatu (connectng cable and power meter)

12 condered. We can afely aume therefore that from about.4m and greater the temperature a contant 98K and the fxed temperature aumpton can be appled to both.. The rod laterally nulated The model take no account of heat radaton or convecton from the rod to the urroundng envronment. A we are concerned about mnmzng heat tranfer to the LNA we are ntereted n a conervatve etmate of the LNA temperature. Becaue the bench meaurement apparatu orgnally at 98K ambent temperature, the model wll gve u a conervatve or wort cae etmate. Heat tranfer to the LNA therefore predcted to be even le than that ndcated by the model. v. The thermal permvty for the whole apparatu taken a that of copper. Although the apparatu contructed from both alumnum and copper a well a other materal, the thermal permvty of the entre tructure taken a that of copper. Th becaue t ha the greatet permvty of all the materal ued n the balun/taper. Becaue we are requrng a conervatve etmate th wll be a atfactory aumpton.. Varable ued n the model u L = 77K temperature of the chp retor noe ource. 77K the mot dtant temperature from the ambent that wll be ued n the experment and wll therefore have the greatet effect on heat conducton n the apparatu u R = 98K Other temperature (ambent) u = 98K ntal temperature of the apparatu (ambent) L = 1m length of the rod α =.117 m / thermal permvty of copper 3. The Model After dervaton, the heat dtrbuton along x at dfferent tme t gven by: HeatDtrbuton( x, t) = n C n nπx n e L α n π t L u R u + L L x + u L where :.(1) C n = ( u u ) [ ] ( u u ) ( ) n L nπ ( 1) n 1 + R nπ L 1 Subttutng n the varable and contant and evaluatng for the tme t =, 4, 6 and 8 econd and plottng over the length x reult n the oluton gven n fgure 9. The heat dtrbuton at the dark blue lne and at 4 t green etc. The plot ha been produced wth the ad of MATLAB. The code n appx 3 and baed on the code provded n [8]. It can be een from the plot that after (a tme that condered adequate for a noe fgure meaurement) the temperature at the LNA (x =.3m) ha changed by le than one degree. It can be concluded, therefore, that a tanle teel thermal barrer not neceary n the contructon of the taper.

13 Fgure 9. 4 B ar Tem perature D trbuton Over Tm e 35 3 Temperature (K) D tanc e (m ) Bracket and Clamp A mple bracket and clamp wa contructed from acrylc a a mean for provdng mechancal rgdty between the balun and PCB taper. Th protect the ytem from breakage and alo enure repeatable reult when meaurement are made. Care wa taken to avod havng the acrylc n cloe proxmty to conductor where the charactertc mpedance would be gnfcantly altered or where the hgh lo tangent of the acrylc materal mght ncreae the ytem lo. Havng any acrylc materal n cloe proxmty to the conductor of the PCB taper would gnfcantly effect the lo. A gap therefore provded n the bracket at the PCB connecton pont a hown n the fgure 11. Fgure 1. The completed balun/taper

14 Fgure 11. The underde of the balun/taper. The hape of the bracket can be een. Notce the gap at the pont where the balun connect to the PCB. Performance Reult A number of tet were performed on the balun/taper. Thee ncluded: 1. Return lo of balun/taper wth bracket. Termnated wth a hort crcut.. Return lo of balun/taper wthout bracket. Termnated wth a hort crcut. 3. Return lo of balun/taper wth bracket. Termnated wth 18Ω. 4. Return lo of balun/taper wthout bracket. Termnated wth 18Ω. For the hort crcut termnaton, a older brdge wa formed at the of the PCB taper. For the 18Ω termnaton, a 18Ω chp retor wa oldered to the of the PCB taper. Meaurement were performed ung an RF brdge and reflectometer. A dagram of the etup hown n fgure 1. Fgure 1 Balun/Taper Termnaton RF n. Sweep 1-5 GHz RF Brdge To Reflectometer

15 The reult for tet 1 and are hown n fgure 13. Reult for Tet 1 are ndcated by the blue lne and reult for Tet are ndcated by the red lne. From th, an ndcaton of the magntude of lo n the balun/taper can be obtaned. Becaue the ytem termnated n a hort crcut, all power hould be reflected and deally the reflectometer hould regter a db return lo. Becaue loe have occurred a the feld travel toward the termnaton and back toward the load, the reflectometer regter the amount of lo over the return trp of the gnal. In theory, the lo of the balun/taper half the lo regtered by the reflectometer. In practce however, there have been ome loe due to radaton and a lght lo of power due to ome current flowng down the outde of the coax. Lookng at the fgure 13 below t can be een that the preence of the bracket dd not gnfcantly affect the lo of the ytem. The lo etmated at about.db. Fgure 13. The reult for tet 3 and 4 are hown n fgure 14. The reult for Tet 3 are ndcated by the blue lne and the reult for Tet 4 are ndcated by the red lne. The return lo appear to be around 14 db over the frequency range, correpondng to a voltage reflecton coeffcent of % and an SWR of 1.5.

16 Fgure 14. The Klopfenten Taper ued n the ytem wa degned o that the voltage reflecton coeffcent would not exceed %, however, there are a number of reaon why th target ha not been reached.. The tranton from the coaxal balun to the PCB taper reult n an abrupt change n the geometry of both the conductor and the delectrc. Reflecton would occur at th pont. The taper wa degned to termnate n Ω, however, 18Ω the cloet value avalable. Even f the taper wa perfect, the mmatch caued by th 18Ω retor on t own would reult n a 5.% reflecton coeffcent whch already exceed the.1% pecfed n the taper degn.. The balun wa contructed from hand tool and accurate realaton of the Klopfenten taper wa dffcult to obtan. It predcted that the etchng proce would provde a more accurate repreentaton of the Klopfenten Taper. v. It thought that the track wdth of the PCB taper are lghtly n error near the pont where the coaxal balun connect at pont 1,, and 3 (ee fgure7). It beleved that the mulaton oftware wa not allowed to perform the adequate number of teraton requred for the oluton to converge completely n th ecton of the taper. Th, however, may not be detrmental to the ytem performance nce the track wdth are narrower than that requred for the pecfed charactertc mpedance at thee pont. Th may provde ome compenaton for the abrupt change n geometry at the connecton pont between the balun and taper by reducng the capactance at th pont. Performance Evaluaton In general the balun/taper ha performed well. It exhbt low lo and the return lo of approxmately 14dB a relatvely good reult. The pleang thng about thee reult the robutne of the degn. That, the balun wa contructed from farly rudmentary technque not aocated wth hgh precon, the chp retor doe not provde the deal match and there

17 the preence of the abrupt tranton. Depte all th the performance good. Th ndcate that performance can be ealy mproved f more prece contructon method are ued. Makng the Noe Temperature Meaurement Theory behnd noe meaurement and error To determne the noe temperature of a certan devce t neceary to take at leat two meaurement of noe power at the output of the devce under tet wth the noe ource at two dfferent temperature. Makng the meaurement requre a etup mlar to that hown n Fgure 15. Fgure 15. Noe Source Tranmon lne and /or approprate matchng Devce Under Tet Tranmon lne Power meter The method ued to determne the noe temperature baed on the Y factor method [9]. A power meaurement taken wth the noe ource at ambent temperature and th reult recorded. The noe ource retor then cooled to lqud ntrogen bolng pont temperature of 77K and another power meaurement taken and recorded. The reult are then plotted wth ther correpondng temperature on a graph mlar to that hown n fgure 16. Fgure 16. It can be een from the graph that the ntercept of the extrapolated lne wth the temperature ax gve the negatve noe temperature Te of the devce under tet [9]. The extra noe added by the devce under tet denoted N a. It can be een from the graph that t only neceary to determne a rato of N to N. It not neceary to obtan the magntude of each. A long a the h c meaured power are meaured n correct proporton to each other, the ntercept at the ame. Te wll reman Provded that the noe meaurement are accurate, and ytem loe and reflecton reman contant at dfferent noe ource temperature, the value for T e obtaned wll be accurate.

18 Unfortunately th not the cae when a practcal noe temperature meaurement performed. The requrement to meaure low noe fgure below 1 db make hgh meaurement accuracy dffcult to obtan. If the varou reflecton coeffcent remaned contant over meaurement at dfferent temperature, the effect of reflecton n the meaurement of N h and N c would be the ame. Snce th would not alter the proporton between the two meaurement the ntercept at the temperature ax would provde an accurate ndcaton of the noe temperature. Th becaue the determnaton of T e requre only ratometrc power meaurement. The problem aocated wth reflecton become great when the ytem reflecton change a the noe ource heated and cooled. Reflecton are the greatet ource of error n determnngt e. Conder fgure 15 n whch the reflecton coeffcent lookng nto the noe ource and the reflecton coeffcent lookng nto the nput of the Devce Under Tet (DUT). From [1], the power from the noe ource dpated by the LNA nput termnal gven by: 1 P d = b.(13) 1 and the power ncdent on the nput termnal of the LNA gven by: 1 P = b.(14) 1 where b the avalable power of the noe ource. A defned n [11], the avalable noe power at the nput to the LNA the noe power that would be aborbed by the LNA f t were perfectly matched. In the perfectly matched cae when =, equaton 14 become P = b the power Po that appear at the output termnal of the LNA. Therefore P o = GP.(15) Where G the gan of the LNA. 1 And Po = G b..(16) 1. It the ncdent power P that amplfed by the LNA to obtan Where G b the avalable power at the output termnal of the LNA. Rearrange equaton 16 to obtan: 1 G b = P o..(17) Knowng the ampltude and phae of and enable the determnaton of G b from P o. Unfortunately, only the magntude of and can be ealy meaured or etmated. Wth only the magntude of and t only poble to determne the value of ome lmt. Thee lmt are: ( + ) MAX = o 1 G b P and ( ) MIN o 1 G b = P..(18) b G wthn

19 Therefore: P ( ) G b P ( 1 + ) o 1 o.(19) Knowng thee lmt gve the level of uncertanty of the avalable noe power at the termnal of the LNA when P o known. It aumed here that the power meter well matched to the tranmon lne that connect between telf and the LNA output termnal o that any rereflecton between the LNA and the power meter are kept neglgble. To enure that re-reflecton do not occur t recommed that a utable attenuator be placed at the power meter nput termnal o that any poble reflecton from the power meter wll be aborbed. For th reaon, uncertanty due to mmatch wll only be condered on the nput de of the LNA. Th leave another uncertanty to conder. The uncertanty aocated wth the power readng obtaned from the power meter. Th mean that the power avalable at the LNA output termnal Po may alo le wthn ome lmt..e. Po LowerLmt Po Po UpperLmt.() P P % P P 1+ P % ( ) ( ) MEASURED 1 E o MEASURED E Where P MEASURED the power meaurement taken from the power meter, and P E % the percentage error aocated wth the power meter. Combnng (19) wth () and lettng P N = G b, ( P %)( 1 ) N P ( 1+ P %)( 1 + ) MEASURED 1 E MEASURED E..(1) Where N the noe power that plotted on the graph n fgure 16 for the hot and cold meaurement N and N. c h The upper and lower error due re-reflecton (not ncludng power meter error) are gven n percentage n the table 5 below for varou combnaton of and. Calculated value are from (1).

20 Table 5a - Upper percentage error due to re-reflecton Table 5b - Lower percentage error due to re-reflecton It can be een from the above two table that even f the Devce Under Tet ha a reflecton coeffcent that hgh n magntude, the error can be kept low f the reflecton coeffcent of the noe ource kept low. From the graph t obvou that the noe temperature T e can be calculated from N c ( Th Tc ) Te = Tc..() N N h c The approxmate error aocated wth the determned value of T e n term of the error n the cold meaurement and the hot meaurement are gven by Tc + Te Tc + Te ( ) Error = E + + c Eh 1..(3) Th Tc Te Where E c the upper percentage error lmt aocated wth the cold meaurement, and E h the upper percentage lmt aocated wth the hot meaurement. E c and E h can be approxmated a the um of the error due to re-reflecton and the power meter error. An ndcaton of how thee error and the expected value of T e affect the overall error n the determnaton of T e hown n the table 6.

21 Table 6. Te=1K Approxmate percentage error of Te Ec Eh Te=K Approxmate percentage error of Te Ec Eh Te=3K Approxmate percentage error of Te Ec Eh Te=5K Approxmate percentage error of Te Ec Eh Te=7K Approxmate percentage error of Te Ec Eh It can be een from table 6 that even a mall error n the hot and cold meaurement uch a 4% can compound nto a large error n the fnal determnaton of T e.

22 Applyng noe temperature meaurement to the LNA and Balun/tranformer Cae 1. Ung balun/tranformer to meaure noe temperature of LNA. In th cae the connecton hown n fgure 17 are requred Fgure 17 Chp Retor Balun/Taper LNA Tranmon lne 5 ohm Power meter From the performance meaurement of the balun/taper, the magntude of can be etmated at about. at 98K (aumng that the magntude of the reflecton coeffcent of the balun/taper equal on t nput and output de). not known for 77K but for the purpoe of th example t wll be aumed to be. alo. The magntude of dep on the value of S 11 for the LNA and th could be a hgh a.9. To examne what the effect of reflecton n th arrangement would have on the error, conder the value of and to be. and.6 repectvely for both the hot and cold meaurement. Lookng at table 5a and aumng that the power meter error mall, t can be een that power meaurement made for N c and N h could be n error by approxmately 5% (upper lmt). Aumng the noe temperature to be around 5K and lookng then at table 6, t can be ent that th error reult n a fnal error for T e omewhere between +/-18% and +/56%. Th clearly not a good ndcaton of the noe temperature and t therefore not recommed to ue the balun/taper to meaure the noe temperature of the LNA n th way. Cae. Ung a mcrotrp lne to meaure noe temperature of LNA. Due to the large reflecton coeffcent aocated wth the balun/taper, the noe temperature of the LNA vrtually mpoble to meaure wth uffcent accuracy n the prevou cae. It therefore recommed to employ a low lo mcrotrp lne of contant charactertc mpedance between the noe ource retor and the LNA. Th mlar to the approach adopted n [1]. The mcrotrp lne can be ealy manufactured and wll provde for a much better match for the noe ource retor. The retance of the chp retor and the mcrotrp charactertc mpedance wll be equal to that requred by the non-tandard nput mpedance of the LNA. Fgure 18. Chp Retor Mcrotrp lne of contant Z LNA Tranmon lne 5 ohm Power meter

23 Conder now that the retor matched to the mcrotrp lne wth a reflecton coeffcent of only.1 at room temperature. Takng a.1 for the hot meaurement and.5 for the cold meaurement and a.6 and lookng n table 5, t can be een that the upper error lmt for the hot meaurement about 1% and the upper error lmt for the cold meaurement about 6%. Aumng that the expected noe temperature of the LNA about 5K, the expected error aocated wth the determnaton of T e omewhere between +/-% and +/-36% (from table 6). Th a vat mprovement to the cae n whch the balun and taper were ued to connect the noe ource to the LNA. It can be een from th example how crtcal the correct matchng of the noe ource to the lne to achevng a value of T e wth mnmum error. Cae 3. Meaurng Noe Temperature of the Balun/taper and LNA together The Noe Temperature of the balun/taper and the LNA combned together a one Devce Under Tet can be determned wth better accuracy than n the frt cae where the balun/taper ued n an attempt to determne the noe temperature of the LNA alone. Fgure 19. Chp Retor Tranmon lne Balun/ taper L N A Tranmon lne 5 ohm DUT Power meter It can be een from the above dagram that t now requred to determne for the Devce Under Tet whch cont of both the balun/taper and the LNA. Th dffcult to determne, but an upper lmt for th can be determned f the nput reflecton coeffcent of the LNA and the Balun/Taper known. Refer to fgure. Fgure. 1W Balun/Taper LNA B L L can ealy be determned from S 11 of the LNA. A an example L gven the value.6. Aumng that the magntude of the reflecton coeffcent of the Ω de of the balun/taper equal to t 5Ω de (whch may not necearly be the cae) gven the value of. that wa meaured on the 5Ω de. B

24 Conder 1W of power beng ncdent at the pont hown. Due to B the power ncdent on the nput termnal of the LNA equal to 1 B = 1. =. 96Watt. The power that never reache the LNA B =. 4Watt and th reflected back toward the ource. The magntude of the reflecton coeffcent at the LNA termnal L and of the.96watt ncdent,.96 L =.96.6 =. 3456Watt reflected back to the ource. Addng up the reflected power ( =.3856W), the reflecton coeffcent of the entre Devce Under Tet can be determned by fndng the quare root of th reflected power to determne the reflected voltage. A a reult, become.6. In ummary, B can be calculated ung: ( 1 ) B L = +.(3) Th value for the upper lmt for the reflecton coeffcent of the Devce Under Tet. An exact value of cannot be determned ealy. Th value wa calculated baed on the aumpton that the reflecton coeffcent of the balun/taper the ame at both. If a balun/taper wth a non tandard coaxal connecton other than 5Ω ued wll be even more dffcult to etmate becaue the devce cannot be connected to tandard tet equpment. In th cae one wll need to make a conervatve etmate of takng nto account t effect on the value of. In order to make th etmate, one hould look at how varou value of B affect the value of. Conder the table below. Table 7. Determnng B L Return Lo (db) For example the reflecton coeffcent of the LNA known to be.6 but the reflecton coeffcent of the balun at the balanced uncertan. What may be known, however, that the reflecton coeffcent better than.4 correpondng to a return lo better than 8 db. Knowng th we can place an upper bound on at.68. Knowng a value for t now neceary that the noe ource retor well matched to the unbalanced tranmon lne between the retor and balun/taper. Th lne neceary to provde ome thermal olaton between the balun/taper and noe ource. A n the prevou cae the error n N c and N h can now be determned and fnally the error n T e alo. A n cae, t very B B

25 mportant to enure that the noe ource retor well matched to the connectng tranmon lne o that a mnmum error can be obtaned. General Procedure for determnng noe temperature The followng outlne a procedure for determnng the noe temperature of a devce under tet. An example gven multaneouly for the tuaton gven n Cae 3 n whch the overall noe temperature of the balun taper and LNA determned. The numercal value gven n the example do not apply to the balun/taper that ha been contructed and are purely hypothetcal. 1. Determne from LNA degn, or where approprate fnd the upper lmt of from the procedure outlned n Cae 3. It known from the LNA S11 that the magntude of t reflecton coeffcent.6. The reflecton coeffcent of the balun/taper at the balanced termnal unknown, however, the return lo known to be at leat better than 1dB. Lookng at table 7 to ee where the 1dB return lo row nterect wth the =. 6 column, t can be een that the upper lmt of the DUT reflecton coeffcent L equal to.65.. Determne or upper lmt of for noe ource at both hot temperature and cold temperature. Th can be determned by the followng method: If the charactertc mpedance of the tranmon lne Z L at the pont of attachment of the retor known, and the DC retance of the retor meaured at both hot and cold temperature, at both thee temperature can be ealy determned from: R Z L =.(4) R + Z L It known for example, that the noe ource chp retor attached to a balanced PCB twn lne of whch the charactertc mpedance accurately known at 18Ω. The probe of a DC ohmmeter are appled to the unbalanced termnal and the retance of the chp retor at room temperature (e.g. 9K) meaured at 184Ω. The chp retor then mmered n lqud ntrogen and after the vgorou bolng ha ceaed another DC retance meaurement made. At th tme the retance 163Ω. From thee two meaurement can be determned from the equaton above at both 9K(hot) and 77K(cold) temperature. In th cae, ( hot ) =. 1and ( cold ) = Check that the noe temperature to be obtaned wll le wthn reaonable error lmt. Ue table 5 and 6. Or ue equaton 3. Lookng at table 5 t can be een that the upper percentage error mmatch lmt of the hot meaurement approxmately 1.3% and upper percentage error mmatch lmt of the cold meaurement approxmately 6.6%. The power meter meaurement error %. E and E can be approxmated a the um of the mmatch uncertanty error and the power h meter meaurement error. Therefore, E h =3.3% and E h =8.6%. Etmatng the noe temperature to be omewhere near 5K equaton 3 or table 6 can be ued to determne the expected error. Lookng at table 6 for 5K t can be een that the expected error wll be around 4-48%. 4. Connect ytem a n fgure 15. c

26 Snce both the balun/taper and the LNA are the devce under tet, the arrangement n Cae 3 wll be ued. It neceary to provde ome open wre tranmon lne between the of the taper and the noe ource retor a hown n fgure 19. A n part t neceary to enure that the tranmon lne charactertc mpedance accurately known. Alo the tranmon lne mut be long enough to prevent gnfcant coolng of the balun/taper and LNA (or whatever the DUT may be) when the noe ource cooled. 5. Make a power meaurement wth the noe ource at room temperature. Ue an attenuator at the power meter nput to enure that any poble re-reflecton are mnmed. Record the room temperature n Kelvn along wth the power meaurement N h. For example, aume that the power meaured wa 11mW at T = 9K. 6. Immere the chp retor n Lqud Ntrogen and wat untl the vgorou bolng ubde before makng another power meaurement. Record th meaurement N c wth 77K noe ource temperature. Do not wat longer than neceary when makng th meaurement. Oberve the heat conducton model to enure that the Devce Under Tet not beng gnfcantly cooled. The heat conducton model can apply to any long thn copper tructure. It therefore vald for the connectng tranmon lne a well a the balun/taper. Aume that the power meaured wa 4mW at T=77K. 7. Ue equaton and 3 or ue the preadheet to obtan the value of T e and an error. The preadheet mpler to ue and provde a more accurate error reult and therefore recommed. An explanaton of the preadheet calculaton gven n appx 5. In the preadheet enter the value.5,.1,.65, and for G(cold), G(hot), G, and Pe% repectvely. Enter the cold and hot temperature of 77K and 9K a well a the correpondng meaurement of 4 and 11mW. Power unt are not mportant a long a they are on a lnear cale. The noe temperature calculated to be approxmately 47K wth an error of +/-48%. Concluon The degn and contructon of the requred balun/taper ha been preented. Wth only mple contructon method and component the balun and taper acheve good return lo of about 14dB between 1 and 5 GHz. Delectrc and conductor lo combned le than.db wthn the frequency range. It can be een that good reult have been acheved even wth the preence of varou dcontnute and mmatche. The degn therefore very robut and an mprovement n the reult could be ealy acheved. If t requred to produce mlar balun t recommed that the etchng proce be perfected o that contructon eaer. However, buldng a balun for a non-tandard mpedance match would not requre a pece of commercally avalable coax. A hollow copper tube would probably be needed ntead. Th would not be compatble wth the etchng proce decrbed n th paper becaue the nner urface of the tube would not be protected by delectrc materal. One would probably need to reort to awng or machnng n th cae.

27 It ha been outlned n th paper that ung the balun/taper a a matchng devce between a chp retor and LNA would produce noe temperature meaurement that have exceve error. An alternatve ha been uggeted and th requre that a mcrotrp lne be ued a the connecton between the LNA and noe ource. Th would mplfy the problem of achevng a good match at the noe ource. A method ha, however, been uggeted that would allow the noe temperature meaurement of a balun/taper and LNA combnaton a a ngle devce under tet. Fnally, a number of preadheet tool have been produced for Klopfenten Taper degn, charactertc mpedance of lotted coax, and a preadheet that calculate the noe temperature wth error of a devce. What tll need to be done to provde method by whch the heat dtrbuton n the connectng lne between the noe ource and the DUT can be accurately modelled. From th, a method of calculatng the noe contrbuton of the connectng lne can be determned o that a compenaton can be made n the fnal reult for noe temperature. If th not adopted t eental that th connected lne exhbt low lo. Reference 1. A. Parftt, L Mlner, The Degn of Actve Recevng Antenna for Broadband Low- Noe Operaton, CSIRO.. J. W. Duncan and V. P. Mnerva, 1:1 Bandwdth Balun Tranformer, Proc. IRE, vol. 48, pp , February R. W. Klopfenten, A Tranmon Lne Taper of Improved Degn, Proc. IRE, vol. 44, pp , January M. A. Groberg, Extremely Rapd Computaton of the Klopfenten Impedance Taper, Proc. IEEE, vol. 56, pp , September J. Carlon, L Haelgren, D. Nunez, U. Lundgren, J. Delng, M. Hoerln, A Sytematc Methodology for the Generaton of SPICE Model Feable for EMC Analy, SP Swedh Natonal Tetng and Reearch Inttute, 6. W. Jackon, Hgh Frequency Tranmon Lne, Methuen and Co Ltd, London, John Wley and Son Inc, R. A. Chpman, Theory and Problem of Tranmon Lne, McGraw-Hll, J. R. Whte, Mathematcal Method (1/4.539) X. Analytcal Soluton of PDE Example 1. Heat Tranfer n a Fnte Bar wth Fxed End Temperature, Unverty of Maachuett Lowell. 9. T. H. Lee, Noe Fgure Meaurement, Stanford Unverty, 1. A. Lymer, Improvng Meaurement Accuracy by controllng Mmatch Uncertanty, Aglent Technologe. 11. H. T Fr, Noe Fgure of Rado Recever, Proc. IRE, pp 419-4, July J. G. Bj de Vaate, E. E. M. Woetenburg, R. H. Wtver, R. Pantaleon, Decade Wde Bandwdth Integrated Very Low Noe Amplfer, Netherland Foundaton for Reearch n Atronomy.

28 Appx 1 Degn Drawng of Balun

29 Appx Determnng the proxmty effect on current n the PCB Taper Lne An approxmate value of the proxmty factor calculated ung a relatvely crude method, however, the reult are deemed atfactory for etmaton purpoe. To calculate the proxmty factor t neceary to determne the current dtrbuton n the tranmon lne conductor. The more evenly dtrbuted the current are wthn the kn depth of the conductor the lower the proxmty factor and the lower the retve loe..e. When current are evenly dtrbuted around the permeter of the conductor the proxmty factor at t lowet value of 1. To determne the current dtrbuton along the conductor the two dmenonal cro ecton of the tranmon lne broken up nto a ere of pont ource. In the frt teraton the current dtrbuton condered to be equal along the conductor and each pont ource gven a current level of 1.Thee pont ource are then ued to determne the H feld at an equal dtance around the permeter of the conductor. A very crude applcaton of Ampere law then performed around each pont and the relatve current dtrbuton between pont then determned from the relatve trength of the H feld. The current are then normaled wth repect to the hghet current level and th new current dtrbuton then ued n the next teraton. The teraton are repeated untl the current dtrbuton have converged. Example. Conder a twn lne PCB tranmon lne wth wdth w=4 and pacng =3. The lne cro ecton broken up nto pont. Each pont on a conductor agned the current magntude 1. The drectonal ndcator repreent the drecton of current flow n the two conductor. It then requred to fnd the relatve H feld trength n the poton marked n the dagram below: To do th t neceary to compute the vector um of each relatve contrbuton from each pont on the conductor at the marked poton. To ee how the contrbuton of each pont affected by dtance t neceary to look at Ampere Law.

30 from a pont ource wll be gven by: 1 H relatve =. r I = H dl (A) In the cae n the dagram, evaluatng the lne ntegral around the cloed contour of radu r, the expreon for current become: I = H πr and I H = πr whch mean that the magnetc feld nverely proportonal to the dtance. In the cae of the model the feld trength relatve to a dtance of one element pacng To um the contrbuton from each pont t neceary to determne the dtance between pont and to determne the horzontal and vertcal component of the magnetc feld trength. From the above dagram and takng the potve drecton to be upward and rght: a = tan 1 x, 1 1 r = =, co a co(tan 1 x) 1 H = = co(tan 1 x). r The horzontal component of the H feld at the pont gven by: Hh = H co a = H co(tan 1 x) Takng nto account the drecton of the current n each conductor the relatve H feld at the pont hown n the dagram above can be found by: Hh = 8 x= 4 co (tan 1 x) 1 x= co (tan 1 x) It alo neceary to determne the vertcal H feld at the pont hown below: 3 x= 1 co (tan 1 x)