HOW RF TRANSFORMERS WORK AND HOW THEY ARE MEASURED

Transcription

1 HOW RF TRANSFORMERS WORK AND HOW THEY ARE MEASURED ONTRIBUTIONS BY: DAXIONG JI HAIPING YAN WEIPING ZHENG AUTHORED BY: FRED LEFRAK REVIEWED BY: RADHA SETTY AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 1 of 15

2 HOW RF TRANSFORMERS WORK AND HOW THEY ARE MEASURED APPLIATIONS FOR RF TRANSFORMERS RF ransformers are widely used in elecronic circuis for Impedance maching o achieve maximum power ransfer and o suppress undesired signal reflecion. Volage, curren sep-up or sep-down. D isolaion beween circuis while affording efficien A ransmission. Inerfacing beween balanced and unbalanced circuis; example: balanced amplifiers. TRANSFORMER IRUITS AND IMPEDANE RELATIONSHIPS When signal curren goes hrough he primary winding, i generaes a magneic field which induces a volage across he secondary winding. onnecing a load o he secondary causes an A curren o flow in he load. I is generally necessary o conrol erminaing impedances of RF signal pahs, especially in wideband applicaions where pah lenghs are no negligible relaive o wavelengh. Wideband RF ransformers are wound using wised wires which behave as ransmission lines, and he required coupling occurs along he lengh of hese lines as well as magneically via he core. Opimum performance is achieved when primary and secondary windings are conneced o resisive erminaing impedances for which he ransformer is designed. Transformers having a urns raio of 1:1, for example, are ypically designed for use in a 5- or 75-ohm sysem. In his applicaion noe, reference is coninually made o erminaing impedances which he user should provide for ransformers, boh for performance esing and in acual use. For he sake of consisency in he discussion, ransformers wih urns raio greaer han 1:1 will be described as sep-up; ha is, he secondary impedance is greaer han he primary impedance. In acual use, however, connecion can be sep-up or sep-down as needed. In Figure 1, hree ransformer winding opologies are illusraed. The one in Figure 1a is he simples. alled an auoransformer, his design has a apped coninuous winding and no D isolaion. The ransformer in Figure 1b has separae primary and secondary windings, and provides D isolaion. The RF performance of hese configuraions is similar, however. The relaionship of volage and curren beween primary and secondary windings, as well as he erminaing impedances, are given by he following equaions. AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. of 15

3 V = N V and I = I N, where N is he urns raio. 1 1 Since Z = V I and Z 1 = V 1 I 1, Z = N Z 1. Tha is, he impedance raio is he square of he urns raio. Figure 1a Auoransformer Figure 1b Transformer wih D Isolaion The secondary winding in Figure 1c has a cener-ap, which makes he ransformer useful as a balanced signal splier; excellen ampliude and phase balance are obainable wih well designed RF ransformers having his configuraion. Figure 1c Transformer wih ener-apped Secondary In he equaions for Figure 1c which follow, he urns raio N refers o he enire secondary winding. V = N V, and V = V = N V When he wo halves of he secondary are conneced o equal erminaing impedances Z and Z, hen 3 I = I 3 = I 1 N; Z = N Z 1, and Z = Z 3 = Z = N Z 1 AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 3 of 15

4 A variaion on he ransformer of Figure 1c, favoring high frequency performance, is shown in Figure. I adds a ransmission-line ransformer in cascade a he inpu, o conver an unbalanced signal o balanced a he inpu o he cener-apped ransformer. Feaures of his design: Wide bandwidh, exceeding 1 MHz. Excellen ampliude and phase balance. Higher reurn loss (lower VSWR) a he primary side. Figure High-frequency Transformer wih Balun on Primary Side TRANSFORMER PERFORMANE HARATERISTIS Inserion Loss and Frequency Bandwidh Inserion loss of a ransformer is he fracion of inpu power los when he ransformer is insered ino an impedance-mached ransmission sysem in place of an ideal (heoreically lossless) ransformer having he same urns raio. Acual inserion loss is affeced by non-ideal characerisic impedance of he ransformer windings, as well as winding and core losses. Typical inserion loss variaion wih frequency is illusraed in Figure 3 which shows he 1 db, db, and 3 db bandwidhs, referenced o he midband loss as hey are usually specified. Inserion loss a low frequency is affeced by he parallel (magneizing) inducance. A low emperaure, low-frequency inserion loss ends o increase because of decreasing permeabiliy of he magneic core. High-frequency inserion loss is aribued o inerwinding capaciance, series (leakage) inducance, and core and conducor losses. A high emperaure i ends o become greaer due o increase in he loss componen of core permeabiliy. AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. of 15

5 Figure 3 Typical Frequency Response of an RF Transformer A furher influence on ransformer inserion loss is high A or D curren. Mos RF ransformers are used in small-signal applicaions, in which ypically up o 5 mw of RF or 3 ma of unbalanced D curren pass hrough he windings. In he ineres of small size and wides bandwidh, he smalles pracical size of cores is used. When inserion loss specificaions mus be me wih greaer RF power or D curren applied, his mus be aken ino accoun in he ransformer design o preven sauraion of he magneic core and consequen bandwidh reducion. How is inserion loss of a ransformer measured? This quesion is especially perinen for impedance raios oher han 1:1 because accommodaion mus be made for he impedance of es insrumenaion, which is generally a consan 5 or 75 ohms. There are hree mehods: Three ransformers are esed in pairs: A and B, A and, B and. Each pair is measured back-o-back; ha is, he high-impedance windings are direcly conneced o one anoher, and he low-impedance windings face he source and deecor of he insrumenaion which mach he ransformer impedance. This resuls in 3 values of combined inserion loss, so ha he values of he 3 unknowns (he individual A, B, inserion losses) can be calculaed. A ransformer is measured individually wih a minimum-loss pad as a maching circui conneced beween he high-impedance winding and he insrumenaion. This has been found pracical for esing 5-ohm o 75-ohm ransformers, for which maching pads are readily available. The loss of he maching circui (in db) has o be subraced from he measured value o yield he inserion loss of he ransformer iself. This mehod is applicable where only connecions are made o he secondary. AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 5 of 15

6 Figure shows he performance of a 5- o 75-ohm ransformer, model T1.5-1, esed by his mehod. The loss of he maching pad was deermined by measuring wo of hem back-oback, and dividing he db-value by. 1 3 If he ransformer has a cener-apped secondary winding, hen i can be conneced as a 18E power splier. Each half of he secondary mus be erminaed by a maching impedance N Z 1, referring o he equaions given for Figure 1c. This requires a maching nework o be used beween he ransformer and he sensing es-por of he inserion loss insrumenaion. Because an individual es por sees only one oupu, boh 3 db for he spli and he loss of he maching nework mus be subraced from he measured value of inserion loss. By sensing boh oupus, ampliude and phase unbalance can also be measured by his mehod. Elemen values and loss of he maching nework are lised in Table 1. Noe: because insrumenaion requiring proper source erminaion is conneced o one or boh oupus in his mehod, special design consideraions apply o he maching nework, and i should no be a minimum-loss pad. This is discussed in deail in he secion eniled Measuremen of Ampliude and Phase Balance of ener-apped Transformers, where design crieria, elemen values, and inserion loss for suiable maching neworks are given. To demonsrae he usefulness of his mehod for cener-apped ransformers having a wide range of impedance raios (N values), inserion loss vs. frequency is shown in Figures 5, 6, and 7 for he following models: Figure No. Model Impedance raio, 1:N 5 ADTT1-1 1:1 6 ADT-1WT 1: 7 ADT16-1T 1:16 Acual midband inserion loss is noed above each graph. AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 6 of 15

7 Figure 5 Model ADTT1-1 Inserion Loss Figure 6 Model ADT-1WT Inserion Loss relaive o midband loss a 5 deg. (.8 db) relaive o midband loss a 5 deg. (.77dB ) db:.5-9 MHZ db:. - MHZ 3 db:.3-3 MHZ db: 6-5MHz db: 3-6 MHz 3 db: - 775MHz Frequency, MHz Frequency, MHz deg. 5 deg. 85 deg. - deg. 5 deg. 85 deg. Figure 7 Model ADT16-1T Inserion Loss relaive o midband loss a 5 deg. (.89 db) db: 5-65 MHz db: 3-15 MHz 3 db: MHz Frequency, MHz deg. 5 deg. 85 deg. Impedance and Reurn Loss Impedance looking ino he secondary winding is measured wih he primary winding erminaed in is specified impedance (usually 5 or 75 ohms), and compared wih he heoreical erminaing value (Z, Z, or Z in Figure 1). 3 Reurn loss, or VSWR, is measured a he primary winding, wih he secondary erminaed in is heoreical impedance; e.g., Z primary for a 1: impedance-raio (1:1.1 urns-raio) ransformer. PHYSIAL PARAMETERS OF A TRANSFORMER The performance of RF ransformers can be undersood wih he help of he equivalen circui in Figure 8. AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 7 of 15

8 / R1 L1 L R 1:N 1 Rc Lp / Figure 8 - Equivalen ircui of Transformer L and L are he primary and secondary leakage inducances, caused by incomplee magneic 1 coupling beween he wo windings. Because heir reacance is proporional o frequency, hese inducances increase inserion loss and reduce reurn loss a high frequency. R and R are he resisance, or copper loss, of he primary and secondary windings. Skin 1 effec increases he resisance a high frequencies, conribuing o he increase in inserion loss. Inra-winding capaciances and, as well as inerwinding capaciance, also conribue 1 o performance limiaions a high frequency. However, he disinc advanage of he ransmission line design used in RF ransformers is ha much of he inerwinding capaciance is absorbed ino he ransmission line parameers ogeher wih he leakage inducance (parallel capaciance and series inducance), resuling in much wider bandwidh han is obainable wih convenional ransformer windings. L is he magneizing inducance, which limis he low frequency performance of he p ransformer. I is deermined by he permeabiliy and crossecional area of he magneic core, and by he number of urns. Inserion loss increases and reurn loss decreases a low frequency. Furher, permeabiliy of many core maerials decreases wih a decrease in emperaure, and increases above room emperaure. This accouns for he spread of he lower frequency porion of he inserion loss curves in Figure 3 as explained above. Temperaure variaion of he capaciances and he leakage inducances is relaively small. The winding resisances do vary, increasing wih emperaure, and conribue o he spread of he high frequency porion of he curves in Figure 3. The resisance R c represens core loss. There are generally hree conribuions o his loss: eddy-curren loss, which increases wih frequency hyseresis loss, which increases wih flux densiy (applied signal level) AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 8 of 15

9 residual loss, due parially o gyromagneic resonance We can picure he applied RF signal as causing vibraory moion of he magneic domains of he core maerial, which behave as paricles having ineria and fricion. The moion herefore causes a loss of energy. Higher frequency signals cause faser moion, hus greaer core loss, and his is represened by a decrease in he value of R c. A high emperaure, random hermal vibraion is greaer and adds o he energy which he RF signal mus expend o conrol he movemen of he magneic domains. Thus, core loss conribues o he increase in inserion loss and decrease in reurn loss a high frequency. These effecs are accenuaed a high emperaure as shown in Figure 3. MEASUREMENT OF AMPLITUDE AND PHASE BALANE: ENTER-TAPPED TRANSFORMERS Definiions Ampliude balance, someimes called unbalance, is he absolue value of he difference in signal ampliude, in db, beween he wo oupus of a cener-apped ransformer using he cener ap as a ground reference. Phase balance, someimes called unbalance, is he absolue value of he difference in signal phase beween he wo oupus of a cener-apped ransformer using he cener ap as a ground reference, afer subracing he 18-degree nominal value of he phase-spli. Measuremen Mehod: Maching Nework Beween Each Half of he Transformer Secondary and Sensing Por in he Tes Insrumenaion I was menioned above, oward he end of he secion on inserion loss measuremen, ha a ransformer having a cener-apped secondary can be esed like a power splier. There is a difference which mus be considered, however: A device buil as a power splier has an inernal circui which provides isolaion beween he oupus; ha provision ensures consan impedance looking ino each oupu por independen of he load on he oher oupu. A ransformer on he oher hand, being a simpler device, lacks isolaion. Thus, he design of he maching nework mus ake ino accoun no only he primary source impedance ransformed by he primary-o-half-secondary raio, bu anoher impedance in parallel wih i: he inpu impedance of whaever is erminaing he oher half-secondary winding. The siuaion is illusraed in Figure 9. R is he source and sensing por impedance of he es insrumenaion, as well as he impedance for which he primary of he ransformer is designed. The oal secondary mus be erminaed in N R. Therefore, each of he maching neworks, while is oupu is erminaed in R, mus have an inpu impedance N R. AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 9 of 15

10 The oupu source impedance of each maching nework, because i has o feed a cable presening a load R, mus also equal R. This mus be while he maching nework is being fed from a source impedance which is he parallel combinaion of wo impedances as follows: One is he ransformed source impedance R which appears a he half-secondary as (N ) R. The oher is he inpu of he oher maching nework, N R, coupled from one half- secondary o he oher. The resulan is N R 6. HALF-SEONDARY NT/ urns PRIMARY T urns MATHING NETWORK R R R MATHING NETWORK R N ) R N R / R ( N R / Figure 9 Impedance Relaionships for ener-apped Transformer wih Maching Neworks The impedance consrains for he maching nework require hree opologies depending upon he value of he ransformer impedance raio N, as shown in Figures 1a hrough 1c. 1a. N < 3 1c. N > 3 1b. N = 3 Figure 1 Impedance Maching onsrains For each of he wo non-rivial cases, 1a and 1c, he requiremens for inpu and oupu AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 1 of 15

11 impedance o he nework provide wo equaions o solve for he wo unknowns R s and R p. For N < 3, referring o Figure 1a, he equaions are: R % R s R p ' N R and N 6 R R p % R s ' R The soluion is: R s ' R 1& N N R p ' R 1 & N 1 & N %1 %1 & N For N > 3, referring o Figure 1c, he equaions are: R p R % R s ' N R and N 6 R % R s R p ' R The soluion is: R s ' R N 3 N 3 &1 % N 6 R p ' R N 3 N 3 &1 For N = 3, R s = R and R p is infinie. For accurae RF phase balance measuremen, he consrucion of he maching neworks and he connecions o hem should be such as o provide elecrical symmery beween he wo halves of he circui. To show he effeciveness of he above mehod, i was used o es ransformers for ampliude and phase unbalance, wih resuls shown in Figures 11, 1, and 13. These are he same ransformers for which inserion loss was given in Figures 5, 6, and 7. AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 11 of 16

12 Figure 11 Model ADTT1-1 Ampliude, Phase Unbalance Figure 1 Model ADT-1WT Ampliude, Phase Unbalance Frequency, MHz Ampl. Unbal. (Y1) Phase Unbal. (Y) Frequency, MHz Ampl. Unbal. (Y1) Phase Unbal. (Y) Figure 13 Model ADT16-1 Ampliude, Phase Unbalance Frequency, MHz Ampl. Unbal. (Y1) Phase Unbal. (Y) AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 1 of 16

13 I:N R Vi Vi NVi NVi N R N R Figure 1 - Volage Relaionships for Transformer wih Mached Secondary Terminaions The remaining ask is o derive expressions for he inserion loss of he maching nework, so ha i can be subraced from measured values o yield inserion loss for he cener-apped ransformer iself when i is esed by he power splier mehod described above. As a reminder, 3 db (for he spli) mus also be subraced from he measured values. Figure 1 shows volage relaionships for a ransformer wih he secondary erminaed in mached resisive impedances. The volage across he primary is half he open-circui source volage V i, because he impedance looking ino he primary is R. The power delivered o each erminaing resisor is he square of he volage divided by he resisance: P O ' NV i N i R ' V 8R AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 13 of 16

14 Figure 15 shows wha happens when he various maching neworks are insered afer he half-secondary, and he mached load per Figure 1 is replaced by R which represens he sensor por in he insrumenaion. Rs 15a. N <3 NVi Rp R R NVi R+Rs Rs 15b. N =3 3 Vi R Vi 3 Rs 15c. N >3 NVi Rp R Rp R Rp R+Rs NVi Figure 15 Volage Relaionships for Power alculaion Figure 15a includes he N < 3" maching nework of Figure 1a. The power delivered o he load R is P (he subscrip L designaes he low N case): OL P OL ' R R %R s N V i i ' R N V 16 R 16 R %R s Loss ' P O / P OL ' R %R s N R Figure 15b illusraes he N = 3 case per Figure 1b: P O3 ' V i Loss ' P 1R O / P O3 ' 1.5 Figure 15c is for N > 3, corresponding o Figure 1c (he subscrip H in P OH designaes he high N case): P OH ' R p R R p R %R p R s %R R s N V i 16R Loss ' P O / P OH ' R R %R R %R R p p s s N R p R AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 1 of 16

15 Table 1 liss he maching-nework resisance values, normalized o R, as well as he nework loss in db, for values of impedance raio for which Mini-ircuis offers cener-apped RF ransformers. Resisors available for he maching neworks are ypically he 1% values. Their nominal values, having incremens of %, could hus differ from he Table 1 values of R s and R p by as much as ± 1%. The resuling error in he loss of he nework is greaes if R s and R p depar from Table 1 in opposie direcions, and amouns o.1 db for N = 5, for example, in he case of 1% resisance error. If greaer accuracy is needed, loss should be calculaed by subsiuing he acual resisances in he equaions following Figure 15. The above discussion abou resisor precision perains o measuremen of inserion loss of a ransformer; ampliude balance is no affeced by resisance error as long as he wo maching neworks are equal. Table 1 Maching Neworks for Tesing ener-apped Transformers Z raio, 1:N R (Figure 1) R (Figure 1) Loss of Nework, db s 1:1.866 R.683 R 8.3 1: R 1.91 R :.77 R.1 R.6 1:.5.61 R 5.56 R :3.5 R None : R. R : R R 8.3 1:8 3. R 1.65 R : R 1.1 R : R 1.19 R : R 1.66 R p AN--1 Rev.: B M1561 (/15/15) File: AN1.W61 This documen and is conens are he propery of Mini-ircuis. Sh. 15 of 16

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