White Paper. Method of Modeling Differential Vias. Abstract. Issue: 2.1 Date: Jan25, 2011

Transcription

1 White Pape Method of Modeling Diffeential Via Iue:. Date: Jan5, 0 Lambet Simonovich, Signal Integity & Backplane Specialit, Lamim Entepie Inc., limonovich@lamimentepie.com D. Eic Bogatin, Signal Integity Evangelit, Bogatin Entepie, eic@bethesignal.com D. Yazi Cao, Potdoctoal Fellow, Dept. of Electonic, Caleton Univeity, yazi.cao@hotmail.com Abtact Accuate, model fo via in a multilaye cicuit boad ae neceay to pedict link pefomance in the GHz egime. Thi pape decibe a methodology to build a high bandwidth, calable fit appoximation cicuit model uing imple tanmiion line of long via typically ued in thick backplane deign. Sytem achitect and backplane deigne fo example can quickly model vaiou inteconnect topologie fo what-if cenaio and to et the diection fo a moe detailed deign evaluation. It include neceay paamete to tudy and quantify the though and tub effect when effective dielectic contant and via impedance ae vaied. A an added benefit, thi imple modeling technique alo povide a mean to validate and anitize late model built with 3D field olve when ue have a limited kill et in the ue of the tool. Copyight 00

2 Autho Biogaphy Lambet (Bet) Simonovich gaduated in 976 fom Mohawk College of Applied At and Technology in Hamilton, Ontaio, Canada a an Electonic Engineeing Technologit. Ove a 3 yea caee at Bell Nothen Reeach and Notel, he helped pionee eveal advanced technology olution into poduct and ha held a vaiety of R&D poition, eventually pecializing in backplane deign ove the lat 5 yea. He i the founde of Lamim Entepie Inc. poviding innovative ignal integity and backplane olution. He i cuently engaged in ignal integity, chaacteization and modeling of high peed eial link aociated with backplane inteconnect. He hold two patent, two IEEE publication and co-autho of an awad winning DeignCon009 pape elated to via modeling. Eic Bogatin eceived hi BS in phyic fom MIT and MS and PhD in phyic fom the Univeity of Aizona in Tucon. He ha held enio engineeing and management poition at Bell Lab, Raychem, Sun Micoytem, Anoft and Inteconnect Device. Eic ha witten 4 book on ignal integity and inteconnect deign and ove 00 pape. Hi latet book, Signal and Powe Integity- Simplified, wa publihed in 009 by Pentice Hall. He ha taught ove 4,000 enginee in the lat 0 yea. Many of hi pape and column ae poted on the web ite. Yazi Cao eceived the B.S. and Ph.D. degee in electical engineeing fom Wuhan Univeity, Hubei, China, in 004 and 008, epectively. Hi eeach inteet include neual netwok, deign and modeling of RF/Micowave cicuit. Since 009, he ha been a potdocto in the Depatment of Electonic, Caleton Univeity, Ottawa, Canada. Recod of Change: Iue.0 -Apil 8, 00 Initial eleae Iue.0 -Januay 7, 0 - Page 4, the equation diectly above (6) 3.60E-9 coected to actually ead 3.60E+3. Iue.-Januay 5, 0- Page 3 Coected typo in equation fo to ead 0.GHz and coected fo equation below with.0e0.

3 Intoduction Peent integated cicuit (IC) technology advancement ae allowing data ate in exce of 0 Gb/. PCB though hole via paaitic ae becoming moe of a facto affecting bit eo ate (BER) pefomance. Accuate via modeling fo topology imulation ae a mut and often equie ophiticated 3D modeling tool. Mot of thee tool ae complex, expenive and equie a high level of expetie to opeate. With copoate R&D budget hinking, boad deign enginee ae equied to take on moe divee eponibilitie. In many cae, they lack the neceay kill et and o expetie to ue ophiticated modeling tool popely becaue they lack the time to invet in leaning it popely, o they ue the tool too infequently. Peonal expeience ha poved mitake can happen when dawing o inputting paamete leading to inaccuate eult. Often thee ae no imple method to anitize the eult epecially if thee ae no meauement available that can be ued fo model anitization. Behavioal model and cicuit topology model ae two geneic kind of model ued to imulate high peed eial link. S-paamete ae called behavioal model becaue they decibe the behavio of the tuctue with epect to incident wavefom fom calibated pot. They can be ued a a behavioal epeentation of the actual tuctue once the device i meaued. Meaued S-paamete behavioal model ae limited becaue they epeent eveything connected between the calibated efeence plane of the VNA. Elaboate de-embedding and calibation cheme ae needed to emove fixtue effect fom the meauement to leave behind jut the -paamete tuctue of inteet. Even then, they epeent only one ample of a given contuction. It i impoible to pefom what-if, wot cae min/max analyi with a ingle behavio model. Thei uefue in model development i to help build, calibate and validate cicuit topology model. A cicuit topology model on the othe hand, i a chematic epeentation of the tuctue. When un in a cicuit imulato, it pedict a meaueable pefomance of the tuctue. Thee model can be paameteized o that wot cae, min/max analyi can be exploed quickly. Fo any phyical tuctue, thee can be moe than one cicuit topology that decibe it. All can give the ame pefomance, up to ome bandwidth. Thi wok i pat of a follow-up tudy fom the DeignCon009 pape Pactical Analyi of Backplane Via, by Bogatin, Simonovich, Gupta and Reo [5]. Ou goal of thi pape wa to develop an analytical methodology and equation to develop a cicuit topology model of a diffeential via tuctue in the abence of meaued data. The model hould be imple, yet match the meaued pefomance up to a high bandwidth. It hould be validated againt a 3D field olve and coelated back to meaued eult. 3

4 Anatomy of a Diffeential Via Stuctue An example of a diffeential via tuctue though a pinted cicuit boad (PCB) tack-up i hown in Figue. It i epeentative of via ued to connect uface mounted component o backplane connecto to intenal laye tace a oppoed to via ued to tanition between laye when ignal ae outed between inne laye. It fom the bai of a via modeling methodology peented in thi pape The via bael i a plated though hole extending the entie length of a PCB tack-up. The outide diamete equal the dill diamete. The inide diamete i the finihed hole ize (FHS) afte plating. Pad ae ued on laye to enue thee i ufficient coppe fo tack attachment afte dilling opeation. When ued in thi fahion, they ae efeed to a functional pad. Anti-pad ae the cleaance hole of plane laye to pevent hoting to the via bael o pad. Anti-pad Pad Via Dielectic Typ. Stub Via Bael Coppe Plane Typ. Figue Diffeential Via Stuctue Though a Multilaye PCB The via potion i the length of the via bael connecting one ignal laye to anothe. It i often efeed to a the though via ince it i pat of the ignal net. The tub potion i the emainde of the via bael extending to the oute laye of the PCB. In high peed deign whee the via tub i geate than 300mil/BR, whee BR i the bit ate in Gb/, it can be the pimay caue of ignal degadation and eye cloue [6]. High peed point-point eial link baed backplane ae often thick tuctue due to the ytem achitectue and cad-cad inteconnect equiement. Back-dilling the via tub i common pactice on thick PCB to minimize tub length fo bit ate geate than 3Gb/. 4

5 Conventional FR4 type laminate ae fabicated with a weave of gla fibe yan and ein. The effective dielectic contant (Dk) i a function of gla to ein atio of the laminate ued fo the PCB tack-up. When a ignal popagate in a tipline fahion though a fibegla einfoced laminate, the electic field i in the z-axi and othogonal with epect to the uface of the boad. Howeve, when a ignal popagate though a pai of via diven diffeentially, the electic field i in the x-y axi and ee a diffeent combination of gla weave and ein content with diffeent ditibution a illutated in Figue. Thi make the mateial aniotopic in natue. Dankov et al [4] ha hown the effective dielectic contant in the x-y axi can be 5-0% highe than the z axi. E-field VS Fibegla E-field Rein Highe gla to to ein atio between chage => => Highe effective dielectic contant (Dkxy) Lowe gla to to ein atio between chage => => Lowe effective dielectic contant (Dkz) Figue Electic field diection in the laminate of the two diffeent egion. Between via bael (left) and in the tipline inteconnect (ight) The diffeential via tuctue can be epeented by a twin-od tanmiion line geomety. The ditibuted exce capacitance ove it entie length i due to the via bael` poximity to the anti-pad. The malle the anti-pad diamete, the geate the ditibuted exce capacitance will be. Thi ultimately eult in lowe via impedance theeby inceaing eflection. In all high peed eial link deign, it i common pactice to emove all non-functional pad and to maximize the anti-pad cleaance a much a pactically poible. Oval anti-pad ae often ued in thi egad to futhe mitigate exce via capacitance. 5

6 Twin-Rod Tanmiion Line Geomety A twin-od tanmiion line geomety a illutated in Figue 3 i one of thee coectional geometie that have exact equation fo chaacteitic impedance. The othe two geometie ae coaxial and od-ove-plane. All thee elationhip aume the dielectic mateial i homogeneou and completely fill the pace wheneve thee ae electic field. Figue 3 Twin-od geomety howing electo-magnetic field elationhip The elationhip between capacitance, inductance and impedance of twin-od geomety ae decibed by the following equation: Ctwin 7.06E 3 Dk Len () Ltwin 0.6E 9* * Len () 6

7 Zdiff Ltwin Ctwin 0.6E 9* 7.06E 3 * Len Dk Len 0 Zdiff (3) Dk Whee: Ctwin = Capacitance between twin-od - F Ltwin = Inductance between twin-od H Zdiff = Diffeential impedance of twin-od - Ω Dk = Dielectic contant of mateial Len = Length of the od - inche = Radiu of the od - inche = Space between the od - inche When diven diffeentially, the electo-magnetic field ceate a vitual etun plane at exactly one half of the pacing between the od. Each od theefoe behave like a ingle od-ove-plane geomety. Twin-od Rod-ove-plane L Vitual Retun L/ + - C L/ C C Figue 4 Twin-od v Rod-ove-plane 7

8 The odd mode capacitance i the capacitance of each od to vitual etun plane and i equal to twice the capacitance between od. Codd.4E Dk Len (4) The odd mode inductance i the inductance of each od to vitual etun plane and equal to one half the inductance between od. Lodd 5.08E 9* * Len (5) The odd mode impedance of each od i half of the diffeential impedance, and i equivalent to the od-ove-plane impedance. Lodd 60 Zodd (6) Codd Dk Coaxial Tanmiion Line Geometie The coaxial tanmiion line geomety conit of a cente conducto imbedded within dielectic mateial and uounded by a continuou hield a illutated in Figue 5. In thi ymmetical tuctue, the electo-magnetic field ae contained within the hield. Figue 5 Coaxial tanmiion line tuctue howing inductance (Blue) and capacitance (Red) 8

9 The elationhip between capacitance, inductance and impedance of coaxial geometie ae:.4e Ccoax Dk Len D D (7) D Lcoax 5.08E 9 Len (8) D Zo Lcoax Ccoax D 5.08E 9 Len D.4E Dk Len D D 60 D Zo (9) Dk D Whee: Ccoax = Capacitance - F Lcoax = Inductance H Zo = Chaacteitic Impedance - Ω Dk = Effective Dielectic contant Len = Length of the od - inche D = Diamete of conducto - inche D = Diamete of hield - inche Figue 6 Elliptic coaxial tanmiion line tuctue. An oval vaiation of a coaxial tuctue i a fom of an elliptic coaxial tuctue hown in Figue 6. Gunton [8] deived the elationhip between capacitance, inductance and impedance of elliptic coaxial geometie a: 9

10 Cellip.4E Dk Len W ' b w t (0) Lellip W ' b 5.08E 9 Len () w t Zo Lellp Cellp W ' b 5.08E 9 w t.4e Dk W ' b w t Zo 60 Dk W ' b w t () Tet Vehicle The tet vehicle ued to coelate imulated eult wa the ame one ued in the DeignCon009 pape [5]. Specific ae ummaized in Figue 7. The lage dip in the inetion lo ae a diect eult of the ¼ wave eonance of the dangling tub. Thi eonant fequency i a good fit ode meaue of the effective dielectic contant aociated with the ignal popagating down the tub. Fom the meaued eonant fequency and the tub length, the effective dielectic contant can be etimated uing the following equation; c Dkeff 4* _ * (3) Stub length f Whee: c = Speed of light (.8E0 inche/ec) Stub_Length in inche f = ¼ wave fequency in Hz Uing the tub length of 70 mil and eonant fequency of 4.3 GHz, a Dkeff = 6.4, which matche the value extacted a the bet fit of the paameteized model to the 0

11 meaued data. Once the effective Dk wa known, the odd-mode via impedance wa eaily calculated to be 3.5 Ω uing the od-ove-plane impedance fomula (6). Zdiff Zvia Zvia Zvia Dk eff 59 8 Figue 7 Tet vehicle ummay fom DeignCon009 pape [5]. Building a Simple Scalable, Cicuit Baed Model Ou peviou analyi [5] uggeted a imple twin-od model fo a diffeential via tanition, coniting of a unifom diffeential pai, can be ued to accuately decibe a

12 eal diffeential via to vey high bandwidth when calibated to meaued data. At the time of that publication, it wa not poible to ditinguih between a highe dielectic contant and a ditibuted capacitive loading due to coupling to the plane. It wa thought the only way to ditinguih thee two effect wa with a 3D field olve. Since thi wok i a continuing tudy of diffeential via, the model can be futhe implified to ue imple coupled tanmiion line and etting the even mode paamete the ame a the odd mode paamete a illutated in Figue 8. Figue 8 Agilent ADS cicuit baed twin-od via model. In a ubequent neual net via modeling pape by Cao, Simonovich and Zhang [7] a Dk_xy of 4.3 wa ued fo an HFSS 3D model imulation of the ame phyical via tuctue. Thi value gave the bet coelation to meauement. Pat of that wok howed the dielectic mateial had an aniotopic facto appoximately 8% highe in the x-y axi ove the aveage Dk in the z-axi. Thi cooboate well with Dankov et al wok [4] howing gla einfoced laminate have an aniotopic facto between 5-0%. The wok alo helped anwe peviou quetion we had in [5] and made it poible to ditinguih between a highe effective dielectic contant and a ditibuted capacitive loading fom coupling to the plane. In fact it tun out to be a little of both. It coect a peviou theoy we had uggeting the effective dielectic contant in the x-y axi wa pedominated by the gla fibe denity uounding the via hole tuctue [3]. It i now poible to develop analytical equation fo effective Dk and via impedance to be ued in a paameteized cicuit model.

13 Developing Analytical Equation fo Dkeff and Zodd A cloe look at the anatomy of the diffeential the via tuctue unde tudy i illutated in Figue 9. Via capacitance i mainly influenced by the oval anti-pad. t w W b Figue 9 EM Field elationhip of twin-od via model with oval anti-pad. Even though the hield i not continuou, the capacitance fo each via uounded by an oval anti-pad on the plane laye can be etimated uing the elliptical coaxial tanmiion line equation (4). The thinne the dielectic between coppe plane laye, the moe accuate it will eemble a coaxial tuctue fom an electotatic point of view. In ode fo the magnetic field to behave like a coaxial tuctue, the hield mut be continuou ove the entie length. Since thi i not the cae, the magnetic field behave moe like a twin od tuctue when the via ae diven diffeentially. Theefoe the odd-mode capacitance Cvia can be appoximated a;.4e Cvia Dkavg Len W ' b w t (4) and the odd-mode inductance Lvia can be calculated a; 3

14 Lvia E Len (5) and the odd-mode impedance Zvia can now be appoximated by; Zvia Lvia Cvia E Len.4E Dkavg Len W ' b w t Zvia 3.60E 3 Dkavg W ' b w t Zvia 60 Dkavg W ' b w t (6) Whee: Lvia = Odd-mode via inductance - H Cvia = Odd-mode via capacitance - F Zvia = Odd-mode via impedance - Ω = via to via pitch inche = adiu of via bael = Dill dia - inche (Dkxy Dkz) Dkavg W ' b = Oval dimenion pe Figue 6 w t The bulk dielectic contant Dkavg i due to the combination of ein and gla weave ditibution. If a diffeential ignal i popagated between the twin od, it would ee thi bulk dielectic contant. Howeve, it alo ee the capacitive loading fom the finge 4

15 5 field between the bael and the plane it pae though. Thi ditibuted capacitance effectively lowe the odd-mode impedance of the via and inceae the effective dielectic contant. The effective dielectic contant can be evaluated baed on how much the via odd-mode impedance i deceaed. Baed on the twin od fomula, the via odd-mode impedance can be expeed a; 60 Dkeff Ztwin Zvia Subtituting the odd-mode impedance fom equation (6) into the equation above, and olving fo Dkeff yield; 60 Zvia Dkeff ' t w b W Dkavg Dkeff t w b W Dkavg Dkeff t w b W Dkavg Dkeff ' '

16 Dkeff Dkavg W ' b w t (7) Model Paamete Validation Uing D and 3D Field Solve The model accuacy wa compaed againt Quickfield D [9] and Anoft HFSS 3D [0] field olve to tudy the effect of anti-pad vaiation in capacitance and Dkeff epectively. In ode to emove any ambiguity of aniotopic facto fom the dielectic, a Dk = wa ued in all field olve and analytical equation. Fo both cenaio, the antipad dimenion wee vaied fom x0.053 ound to oval whee the oval length wa vaied in 5 mil incement up to long. Quickfield Capacitance and Inductance Coelation Figue 0 how the electotatic plot and equipotential line ditibution of ound v oval coaxial tuctue. A the oval inceae in length, the equipotential line pacing become wide apat in the y-axi accounting fo the educed capacitance. 6

17 Y X Figue 0 Electotatic field of cicula v oval hield. Dk = Uing equation (4), via capacitance wa calculated uing Dk = fo epective anti-pad vaiation. The eult lited in Table and plotted in Figue in mot cae how bette than % coelation to Quickfield D field olve. Table Compaion of Calculated Via Capacitance v Quickfield D Field olve. Dk = 7

18 Figue Compaion of calculated v Quickfield D field olve fo via capacitance. Dk = Figue how the magnetic field elationhip of a twin-od via tuctue when diven diffeentially uing Quickfield D field olve. The calculated odd-mode inductance uing equation (5) wa appoximately 7nH compaed to the Quickfield calculated 6.3nH. The dicepancy can mot likely be attibuted in pat to the tudent veion of oftwae having a 55 node limitation fo the meh. The ize of the model limit the meh o accuacy i affected. 8

19 Lodd Lodd Lodd E E e 9H/in 59 8 * Len * Lodd =.497E-7 nh/m/ 39.4 in/m = 6.3nH/in Figue Magnetic field twin-od via tuctue. Simulated v calculated inductance. 9

20 HFSS Dkeff Coelation Figue 3 Anoft HFSS model oval anti-pad vaiation. Dk= The HFSS model hown in Figue 3 wa developed fo a neual net via modeling pape [7]. It wa eued fo thi pape to validate the cicuit model againt Dkeff fo vaiou anti-pad length. The PCB tack-up dimenion ued in the model wee the nominal engineeing pecified value. A Dk = wa ued a one of the model paamete fo the imulation to implify the analyi and emove any aniotopic ambiguity. The equivalent via cicuit model wa then compaed againt the HFSS geneated touchtone -paamete file uing Agilent ADS []. Both tet topologie ued fo the imulation ae hown in Figue 4. Ideal Balun tanfome wee ued to implify the diplay of diffeential -paamete. Fo each anti-pad dimenion, a epective Dkeff wa calculated baed on the ¼ wave eonant fequency uing equation (3) fo each epective HFSS -paamete file. The eult ae peented in Table, and plotted in Figue 5. They how excellent coelation to HFSS field olve eult with le than % accuacy fo oval anti-pad length to width atio of le than.:, and 5% fo.5: atio. 0

21 Figue 4 HFSS touchtone S-paamete file (Dk=) v Agilent ADS tet topology cicuit model.

22 Table Compaion of Dkeff calculated v HFSS 3D field olve fo Dk= Stub_Len inch A-pad_W inch A-pad_L inch Re Feq HFSS Sim Hz Dkeff_Sim HFSS Dkeff_Cal Fomula Delta % Zodd Cal ohm E % E % E % E % E % E % E % 65.5 Figue 5 Compaion of Dkeff calculated v HFSS 3D field olve fo Dk= Compaing the inetion and etun loe (Figue 6-Figue ) how excellent coelation fo uch a imple model. Table 3 ummaize the ¼ wave eonant fequency notche and how the cicuit model ha bette than 5% accuacy ove the entie ange of oval anti-pad vaiation.

23 db(s(7,7)) db(s(3,3)) db(s(8,7)) db(s(4,3)) db(s(5,5)) db(s(,)) db(s(6,5)) db(s(,)) m m f eq= 7.630GHz db(s(,))= Valley m m f eq= 7.60GHz db(s(6,5))= Valley feq, GHz Figue 6 Compaion of inetion and etun lo HFSS v cicuit model. Oval antipad; Dk = ; Anti-pad = x m3 m4 m3 f eq= 7.750GHz db(s(4,3))= Valley m4 f eq= 7.70GHz db(s(8,7))= Valley feq, GHz Figue 7 Compaion of inetion and etun lo HFSS v cicuit model. Oval antipad; Dk = ; Anti-pad = x

24 m5 m5 feq= 7.980GHz db(s(6,5))=-5.05 Valley m6 feq= 7.990GHz db(s(0,9))= Valley m6 Figue 8 Compaion of inetion and etun lo HFSS v cicuit model. Oval antipad; Dk = ; Anti-pad = x0.060 m7 m7 feq= 8.90GHz db(s(8,7))= Valley m8 feq= 8.0GHz db(s(,))= Valley m8 Figue 9 Compaion of inetion and etun lo HFSS v cicuit model. Oval antipad; Dk = ; Anti-pad = x

25 m9 m9 feq= 8.330GHz db(s(0,9))=-4.76 Valley m0 feq= 8.450GHz db(s(4,3))= Valley m0 Figue 0 Compaion of inetion and etun lo HFSS v cicuit model. Oval antipad; Dk = ; Anti-pad = x0.070 m m feq= 8.430GHz db(s(,))= Valley m feq= 8.650GHz db(s(6,5))= Valley m Figue Compaion of inetion and etun lo HFSS v cicuit model. Oval antipad; Dk = ; Anti-pad = x

26 m3 m3 feq= 8.50GHz db(s(4,3))= Valley m4 feq= 8.870GHz db(s(8,7))= Valley m4 Figue Compaion of inetion and etun lo HFSS v cicuit model. Oval antipad; Dk = ; Anti-pad = x0.080 Table 3 Quate-wave eonant fequency compaion ummay fo HFSS-GHz fo Calc-GHz Delta % % % % % % % Invetigating the Stub Potion of the Via The tub potion of the diffeential via unde tudy i illutated in Figue 3. In the PCB tack-up, the efeence plane laye have oval anti-pad, while the ignal laye have coppe plane-fill with ound anti-pad. Thoughout Stub thickne, the anti-pad altenate between ound and oval. The Stub thickne epeent the powe plane laye with thinne dielectic between plane and thicke coppe laye. The ed potion of the co-ection epeent the electic field while the blue ing epeent the magnetic field. The electic field line though Stub will pead onto the cavitie between efeence plane to oughly the extent of the ound anti-pad diamete a 6

27 hown except fo the thickne of the oval anti-pad coppe laye whee the electic field will be contained to the oval dimenion. To implify futhe analyi, thee laye will be ubtacted fom Stub oveall thickne and added to Stub thickne becaue they will have the ame popetie a Stub. Since exce via capacitance of Stub will be lowe than Stub, it will inceae the peed of popagation though thi ection. Theefoe, Dkeff will be lowe than Dkeff. Vitual Retun + - Stub Dkeff TD STUB Dkeff TD Stub Dkeff TD Figue 3 Stub potion of diffeential via. Oval anti-pad on efeence plane laye and ound antipad on ignal laye The elationhip between tub length and eonant fequency uing a ine wave example i illutated in Figue 4. When a ignal ente the via tuctue fom the top, it tavel along the though potion of the via until it eache the junction of the intenal tack and tub. The ignal plit with ome of the ignal continuing along the tace, and ome continuing along the tub. When the ignal eache the end of the tub, it eflect and tavel back up the tub whee it will again meet the attached ignal tace. A potion will combine with the oiginal ignal and a potion will continue back towad the ouce. If the ound tip delay TD i half a cycle, the two wave ae 80 degee out of phae, and the eulting amplitude at the eceive will be educed. 7

28 The wot cae fo inetion lo i one half a wavelength delay. It occu when the total delay though the tub, (TD) i ¼ wavelength. The fequency whee thi maximum cancellation occu i called the ¼ wave eonant fequency fo. 0 TD TD 3 TD 4 TD t o t 0 o 3t o t o fo fo 4 fo fo Figue 4 Stub eonance illutation. The pecific of the diffeential via anti-pad ae hown in Figue 5. The ound anti-pad ovelap each othe due to the via-via pacing (). 8

29 w t B W 0.059" W ' 0.073" W ' W ' B 0.066" w t 0.08" w t b W 0.059" W ' 0.073" b 0.053" w t 0.08" Figue 5 Round v. oval anti-pad detail of the tet vehicle. The popagation delay though the tub vaie a the effective dielectic contant uounding the via hole tuctue change. The total time delay, TD i the um of TD and TD. A vaiation in ignal peed due to vaiation in effective dielectic contant though the tub will detemine the final ¼ wave fequency notch in the S inetion lo plot. Theefoe, the ¼ wave eonant fequency (Hz) can be expeed a; fo 4TD 4 TD TD to to to to fo fo (8) fo fo fo fo Whee;.8E 0 fo Hz 4 Stub _ len l Dkeff fo fo.8e 0 Hz 4 Stub _ len Dkeff 9

30 30 t w B W Dkavg Dkeff ' t w b W Dkavg Dkeff ' = via to via pitch inche = adiu of via bael = Dill dia. - inche Stub_len; Stub_len = Stub length - inche Dkz) (Dkxy Dkavg t w B W ' = Round anti-pad dimenion pe Figue 5 t w b W ' = Oval anti-pad dimenion pe Figue 5 Once the ¼ wave eonant fequency i calculated, the new Dkeff and Zvia epeenting the entie tub length could be calculated uing the following equation fo each anti-pad dimenion. _ fo length Stub E Dkeff ) Stub Zvia Stub (Zvia Zvia Whee; t w B W Dkavg Stub Zvia ' 60 _

31 Zvia _ Stub 60 Dkavg W ' b w t = via to via pitch - inche = adiu of via bael = Dill dia. - inche Stub_len =Stub length - inche (Dkxy Dkz) Dkavg Cicuit Model v HFSS Via Model Validation Uing the HFFS model epeenting the actual tet vehicle tack-up and long tub via pad/anti-pad tack, Dkeff and Zvia wee calculated uing the paamete lited below. The dielectic contant wee povided fom upplie data heet fo the mateial ued to fabicate the tack-up. HFSS Via Paamete; = = Dill adiu = 0.04 Via_length = 4.7mil Stub_length =.9mil ** Stub_length = 56.3mil ** Stub_length = 69.3mil Aniotopy = 8% W = Anti-pad Length = b = Oval anti-pad width = B= Round anti-pad width =0.066 w = t = Dill Diamete=0.08 Dk_z = 3.65 Dk _ xy Dkavg 3.96 **The combination of ound anti-pad coppe powe plane and dielectic thickne fo Stub defined by the HFSS tet vehicle model i appoximately 0.3. Subtacting thi fom total tub length of 0.69 leave a length of appoximately fo Stub (which include the um of the oval anti-pad coppe thicknee of Stub a explained ealie). Cicuit Model Calculated Via Paamete; Dkeff Dkavg 6.00 W ' B 0.39 w t

32 ' t w b W Dkavg Dkeff GHz E Dkeff length Stub E fo GHz E Dkeff length Stub E fo _ _ GHz E E E E fo fo fo fo fo _ E E fo length Stub E Dkeff ' 60 _ t w B W Dkavg Stub Zvia 8 3. ) Stub Zvia Stub (Zvia Zvia 8 3. ' 60 _ t w b W Dkavg Stub Zvia

33 The imulated S-Paamete fom the equivalent via cicuit model wa compaed againt the HFSS imulated touchtone -paamete file uing Agilent ADS []. Both cicuit topologie ued fo the imulation ae hown in Figue 6. Ideal Balun tanfome wee ued to implify the diplay of diffeential -paamete. Compaing the imulated inetion and etun loe of Figue 7 how excellent coelation between thee two computation method up to appoximately 3GHz fo uch a imple model. It i alo emakable the ¼ eonant fequency calculated (fo = 4.4GHz) agee exactly to the imulated model. 33

34 Figue 6 ADS chematic of HFSS touchtone S-paamete file (Dkxy =4.3) v. cicuit model uing calculated value. 34

35 db(s(3,3)) db(s(,)) db(s(4,3)) db(s(,)) m m m feq= 4.40GHz db(s(,))= Valley m feq= 4.40GHz db(s(4,3))= Valley feq, GHz Figue 7 Simulated inetion and etun lo compaion of cicuit model (blue, cyan) againt HFSS imulation (ed, magenta) epectively. Cicuit Model v Tet Vehicle Validation Thee ample via tuctue ae illutated in Figue 8. They epeent a long, medium and hot via tub of the tet vehicle and ued to validate the tanmiion line cicuit model accuacy. The equivalent via cicuit model fo the long tub via cae wa compaed againt the HFSS geneated touchtone -paamete file and meaued tet vehicle eult uing Agilent ADS []. The tet topologie ued fo the imulation ae hown in Figue 9. The top cicuit topology imulate the meaued -paamete of the tet vehicle. The middle cicuit topology imulate the HFSS -paamete model fo both via and pcb tace. The bottom cicuit topology tet the tanmiion line cicuit model uing analytical fomula paamete fo via and tace. Ideal Balun tanfome wee ued to implify the diplay of diffeential -paamete. 35

36 Via = 4.7 mil L Via = 06 mil L0 Via = 0 mil Stub = 69.3 mil Stub = 78 mil L0 Stub = 64 mil Figue 8 Illutation of laye meaued howing long, medium, hot tub length fom tet vehicle tack-up. Figue 30 how the coelation of calculated eult ued in the cicuit model againt the meaued tet vehicle tuctue and HFSS model of the long tub via. The calculated eult fo Dkeff = 6.5 and Zvia=3.8 Ω enable the model to be in excellent ageement with the meauement to about 3 GHz. It i a ueful a a good fit appoximation to to pefom what-if topology analyi o even povide a level of confidence the 3D model have been deigned a expected. Figue 3and Figue 3how the coelation of calculated eult ued in the cicuit model againt the meaued tet vehicle fo the medium and hot tub via epectively. Similaly, when Zvia = 3.8 Ω; Dkeff = 6.5 fo medium tub and 6.57 fo hot tub, they how excellent ageement with meaued eult. 36

37 Figue 9 ADS chematic of tet vehicle (top), HFSS (middle) and cicuit model (bottom) ued fo imulation compaion. The HFSS topology include both via and tack -paamete modeled fom [7]. 37

38 TDR_ TDR5_5 TDR3_3 db(s(,)) db(s(5,5)) db(s(3,3)) db(s(4,3)) db(s(6,5)) db(s(,)) m f eq= 4.380GHz db(s(,))= Valley m f eq= 4.40GHz db(s(6,5))= Valley m m3 m m3 f eq= 4.390GHz db(s(4,3))= Valley feq, GHz feq, GHz time, nec Figue 30 Long tub (L) via inetion, etun lo and TDR plot compaion of cicuit model (blue) againt HFSS imulation (geen) and tet vehicle meauement (ed). Dkeff = 6.5, Zvia = 3.8, Df =

39 TDR_ TDR5_5 db(s(,)) db(s(5,5)) db(s(,)) db(s(6,5)) feq, GHz feq, GHz time, nec Figue 3 Medium tub (L0) via inetion, etun lo and TDR plot compaion of cicuit model (blue) againt tet vehicle meauement (ed). Dkeff = 6.5, Zvia = 3.8, Df =

40 TDR_ TDR5_5 db(s(,)) db(s(5,5)) db(s(,)) db(s(6,5)) feq, GHz feq, GHz time, nec Figue 3 Shot tub (L0) via inetion, etun lo and TDR plot compaion of cicuit model (blue) againt tet vehicle meauement (ed). Dkeff = 6.57, Zvia = 3.8, Df =

41 Concluion Thi wok ugget a eally imple cicuit model fo a diffeential via tanition, coniting of two imple, coupled tanmiion line cicuit model, can be ued to accuately decibe a eal diffeential via to vey high bandwidth. The imple od ove plane fomula can be ued to pedict the odd-mode inductance. The elliptical coaxial fomula fom [8] can be ued to pedict via capacitance due to anti-pad ize to within % when compaed againt a D field olve [9]. Thi wok ha anweed many of the quetion fom oiginal pape [3], [5] & [7]. Due to the aniotopic natue of the dielectic mateial, the effective dielectic contant in the x-y axi i typically highe than the dielectic contant in the z axi. Thi tudy evealed the dielectic mateial had an aniotopic facto of 8% and cooboate wok done by [4]. It wa poible to quantify and ditinguih between a highe dielectic contant and a ditibuted capacitive loading fom coupling to the plane. In the abence of meaued data, applying thi methodology ha poved to be emakably accuate a a fit appoximation fo calculating via impedance and effective dielectic contant. The value can eaily be adjuted in the cicuit model to quickly quantify the effect of adjuting vaiou paamete fo enitivity analyi o to optimize the pefomance of via in a channel model and to help anitize ubequent model geneated with a 3D EM-field olve. Uing the developed fomulae, a value of Dkeff = 6.5 and Zvia=3.8 Ω wee found to be in excellent ageement with the meauement up to about 3 GHz. 4

42 Refeence [] Pak Electochemical Cop., [] Eic Bogatin, Signal Integity Simplified [3] Simonovich, L., "Relative Pemittivity Vaiation Suounding PCB Via Hole Stuctue," Signal Popagation on Inteconnect, 008. SPI 008. th IEEE Wokhop on, vol., no., pp.-4, -5 May 008 [4] Dankov, P.I.; Levcheva, V.P.; Pehlov, V.N., "Utilization of 3D imulato fo chaacteization of dielectic popetie of aniotopic mateial," Micowave Confeence, 005 Euopean, vol., no., pp. 4 pp.-, 4-6 Oct. 005 [5] E. Bogatin, L. Simonovich, S. Gupta, M. Reo, Pactical Analyi of Backplane Via, DeignCon 009, -5 Feb [6] Eic Bogatin, Optimizing Via fo High Speed Seial Link Application, SI- Inight (6) Apil, 009. [7] Yazi Cao, Lambet Simonovich, and Qi-Jun Zhang; A Boadband and Paametic Model of Diffeential Via Hole Uing Space-Mapping Neual Netwok, IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 9, NO. 9, SEPTEMBER 009 Pg. 533 [8] M.A.R. Gunton, Micowave Tanmiion-Line Impedance Data, Van Notand Reinhold Company LTD. 97 [9] Quickfield Student, Tea Analyi Ltd., Veion SP [0] HFSS Veion Anoft Copoation, 007 [] Agilent ADS, Agilent EEof EDA, Veion 009 4