Contribution of resonance to ground bounce in lossy thin film planes

Contribution of Resonance to GroundBounce in Lossy Thin Film PlanesSreemala Pannala,Student Member,IEEE,Jaya Bandyopadhyay,and Madhavan Swaminathan,Member,IEEEAbstract—This paper discusses the pulse propagation effects on lossy thinfilm planes.The ground bounce phenomena produced by the resonance on planes has been captured using a combina-tion of modeling techniques and measurements.Macromodeling method has been used to explain the transient phenomena on planes by using the dominant poles and residues of the system. Index Terms—Ground bounce,low impedance plane,poles, rational function model,residues,time domain measurements.I.I NTRODUCTIONS IMULTANEOUS switching noise(SSN)is a major con-cern in present day computer systems due to a combination of fast switching circuits,high clock frequencies,wide busses and low voltage levels.A major requirement to limit SSN is the need for a low impedance power distribution system over a large frequency bandwidth.Power and ground planes in a package form an integral part of the power distribution system, since they enable the supply of power to the integrated circuits with small DC drop.Planes also exhibit low impedance AC characteristics which are required for high speed computer systems.Though planes provide the necessary electrical character-istics,they are electrically large at high frequencies.This produces parallel plate waveguide modes in the structure that cause the planes to resonate at discrete frequencies.If the resonances occur within the frequency bandwidth of interest, the following problems could arise in high speed systems. 1)The impedance of the power distribution may increaseby many orders of magnitude at these resonant frequen-cies causing either a slowdown or mal-functioning of the system.A remedy for this problem is the use of decoupling capacitors[1].2)Resonances could cause coupling between various areasof the power distribution leading to transmission of electromagnetic energy.A quiet driver at a remote location may propagate this energy to the input of a receiver.For low voltage systems,this is a cause for concern due to the small threshold level of the receiver circuits.This is also a problem for mixed signal systemsManuscript received December5,1998;revised April21,1999.This paper was presented at the Seventh Topical Meeting on Electrical Performance of Electronic Packaging,United States Military Academy,West Point,NY, October26–28,1998.This paper was supported in part by the Packaging Research Center,Georgia Institute of Technology.The authors are with the School of Electrical and Computer Engineering, Packaging Research Center,Georgia Institute of Technology,Atlanta,GA 30332-0250USA.Publisher Item Identifier S1521-3323(99)06973-7.where noise sensitive analog circuits have to co-exist with digital circuits.Resonances in the frequency domain manifest themselves as an oscillatory transient waveform in the time domain, which contributes to the ground bounce on planes.This paper discusses the ground bounce phenomena exhibited on lossy thinfilm planes using a combination of modeling methods and measurement techniques.The major contributions of this paper are as follows.1)A modeling approach has been discussed for the accuratesimulation of the transient and steady state response on lossy thinfilm planes.Macromodeling methods have been used to capture the frequency domain response from an electromagnetic simulator,using which the transient response has been computed through discrete convolution in time domain.Numerical methods such asfinite difference time domain(FDTD),Method of Moments technique have been used traditionally in the past for modeling power and ground planes either in the time or frequency domain.However,the macromodeling methods discussed in this paper are not limited to any particular numerical technique and provide theflexibility of explaining the transient phenomena using the poles and residues of the system.This allows for the easy correlation between the frequency domain response and the time domain response of a system.Analysis of finite sized rectangular planes in both frequency domain and time domain has also been discussed using radial transmission line approach in[2].In[2],the time domain response was mapped from the frequency domain results using inverse fast Fourier transform and was explained by early-time and late-time constituents.The method discussed in this paper uses discrete time convolution on the residues and poles of the system and is hence different from[2].2)Time domain transmission(TDT)measurements havebeen used in this paper to capture the transient response on lossy planes.Though power/ground plane structures have been characterized using time domain reflectometry (TDR)measurements based on a non uniform transmis-sion line model in[3],the plane structure discussed in this paper provides some unique challenges.Since the impedance of the thinfilm planesissystem,modifications in the measurement setup are required to couple sufficient en-ergy onto the planes.This problem is magnified manifold due to the large frequency bandwidth requirements of the1521–3323/99$10.00©1999IEEE(a)(b)Fig.1.(a)Physical dimensions and cross section (b)1cm 21cm fabricated meshed plane structure.planes requiring the generation and propagation of high speed pulses.Details on the measurements have been discussed in this paper.3)Due to DC.losses in the structure,thin film planes attenuate electromagnetic energy which translates into a reduction in the quality factor1cm with twoplanes separated by6.5mwide conductors on a150m m via pads on the top surfaceallowing access to the bottom plane.As shown in the figure,the test structure contains a two dimensional array ofviasFig.2.5model.Fig.3.Steady state TDT response.which allows the propagation of the pulses at various via positions.The dielectric used was photodefinable epoxy resin (relative dielectric constant of 3.4)without the filler contents.Details on the materials and fabrication steps are available in [4].The fabricated thin film structure is shown in Fig.1(b).III.W IDE B AND F REQUENCY D OMAIN M ODELThis section discusses the importance of a wide band frequency model to capture the transient response on planes.For any finite sized plane structure,the step response can be analyzed using the steady state (low frequency)contribution and an initial transient (high frequency)response.Since the planes behave as a capacitor,the steady state TDT response is similar to the charging of a capacitor and can be easilycaptured using asimplemodel developed to capture the steady state response is shown in Fig.2,which consists of an inductor (20pH),two capacitors (0.23nF)anda resistor (40mIn Fig.2,the capacitance and resistance value was extracted from measurements using a 30MHz LCR meter and the inductance value was extracted using FastHenry [5],a tool for modeling and reducing an inductive network.The correlation betweenthemodel does not howevercapture the transient response on the planes due to the parallel plate waveguide modes in the structure,as shown in Fig.4.InPANNALA et al.:CONTRIBUTION OF RESONANCE TO GROUND BOUNCE IN LOSSY THIN FILM PLANES251Fig.4.Initial transient response of the 5model and macromodel.Fig.4,an oscillatory waveform expected from the reflections at the plane edges is not seen during the initial time period.To obtain a wide band frequency model two electromagnetic tools were used to extract the scattering parameters of the thin film plane structure.The first tool used a method of moments technique (SONNET [6])and the second tool was based on a TM approximation (CADENCE [7]).The resultsof both tools were comparedwithmeasurements using a network analyzer for a two-port structure with the probe tips placed on the two diagonal corners and showed good agreement over a 12GHz bandwidth.Fig.5compares the network analyzer measurements and CADENCE results.The purpose ofcomparingusing SONNET from which we can see thatthe structure is initially capacitive and resonates at 6.8GHz (first resonance).Since the structure is lossy,the Quality factorresults for the diagonal port locations.Using the scattering parameters of the structure,a rational function was developed asfollows:(1)whereare realcoefficients,are the numberof zeros and poles of the system respectively.In (1)the poles of the system are the same for all the scattering parameters,which simplifies the enforcement of the stability condition.It is assumed that the device is symmetrical and reciprocal,but (1)can be modified for other cases easily.Through the methods discussed in [8],the coefficients in (1)were computed by solving the eigen valueequationofmatrix being the hermitian transposeofmatrixcomputed in (2)has been plotted as afunction of the number ofunknownsrequired tocaptureapproaches zeroat13beyond which there is little variation.This condition was used as the criterion to select the orderof252IEEE TRANSACTIONS ON ADV ANCED PACKAGING,VOL.22,NO.3,AUGUST1999Fig.5.S21measurement comparison with CADENCE results.the solution using which the coefficients were computed from the corresponding eigen vector.A macromodel with six dominant poles was generatedfor the2-port Scattering parameters with anerrorat each frequency point over the bandwidth of interest.The comparison betweentheis (3),shown at the bottom of the previous page,for the diagonal port location,where the coefficientsare-macromodel,the transient response of theplanes was simulated using a standard250mV,35ps rise timestep source.Over the initial transition time,the macromodelshows an oscillatory waveform which is absent in thesimpleat timeinstantis the impulse response of the device.The macromodels developed can be used for simulatingthe transient response bypassing explicit convolution usingrecursive convolution formulation as described in[9]–[10].The recursive convolution formulation for a device with“”residues and“”poles attime(5)PANNALA et al.:CONTRIBUTION OF RESONANCE TO GROUND BOUNCE IN LOSSY THIN FILM PLANES253(a)(b)Fig.6.S21macromodel comparison with SONNET results.(a)Magnitude.(b)Phase.whereis the time step andTDR/TDT system is a difficult problem.The impedance254IEEE TRANSACTIONS ON ADV ANCED PACKAGING,VOL.22,NO.3,AUGUST1999Fig.7.Minimum eigen values for different orders of themacromodel.Fig.8.Block diagram of TDR/TDT measurement set-up.of the plane structureisofthe incident pulse.Hence the TDR/TDT setup was modified to include a 9V,15ps risetime source from Pico Second Pulse Labs (PSPL)which provides the necessary amplitude and bandwidth.The receiving sampling head used was still the TEK SD-24.However,since the cutoff amplitude of the SD-24is 3V,a wideband 20dB attenuator was used at the receiving head.To compensate for the 20dB attenuator,the transient behavior at the receiver input was then recreated in the Digital Sampling Oscilloscope.The experimental setup is shown in Fig.8.The structure in Fig.1was designed to make ground-signal-ground measurements at any via point on the structure.15050ps)of the measured transient responseis shown in Fig.9using a 9V,15ps risetime input,which represents the ground bounce on the structure.The amplitude of the ripple is 35–70mV for the 9V input voltage,which is measurable.VI.M EASUREMENT TO M ODELING C ORRELATIONTime domain convolution was used to generate the transient response usingthe(7)whereis the transmittedvoltage,as in (3)is the transmission of electromag-netic energy between the ports [12].Equation (7)assumes that reflections from the cable and interfaces is minimal.Fig.10shows the correlation between the macromodels using the discrete convolution equation in (7)and measurement for both diagonal and edge port locations.As can be seen in the figure,the agreement between the measured and simulated response is very good suggesting that the reflections from the interfaces is minimal.The time period of the oscillation depends on the effective distance between the probe points and the effect of the reflections from the edges of the finite plane structure.In Fig.10,the transient response (amplitude and phase)is a function of the position of the probe points suggesting the importance of resonance in the structure.The resonantPANNALA et al.:CONTRIBUTION OF RESONANCE TO GROUND BOUNCE IN LOSSY THIN FILM PLANES255Fig.9.Transient response measured using the9V PSPL source.frequencies for the various test cases have been tabulated in Table I.VII.A NALYSIS U SING THE S YSTEM P OLES AND R ESIDUES An attempt has been made in this section to analyze the pole frequencies in order to explain the transient phenomena on the planes.The specifications of the PSPL source was15 ps rise time.A pulse rise time of30ps was estimated in the experimental setup by including the effects of the cable, probes and a through calibration standard,which represents a1cm plane.The pole-residue form of the rational function developed in Section IV is given in(8).The imaginary part of the complex conjugate pairs of poles2and3correspond to oscillatory expressions in the time domain and the corresponding frequencies are6.8468and 10.0099GHz.The real part of the poles introduce damping in the transient response.Poles1and4have only an exponential term in the time domain which determine the steady state response.The damping for pole1is far greater than pole 4,hence the effect of the latter pole is dominant.The total response corresponding to these poles is found by adding each of the individual components[13]6.89GHz.For the second test case,the structure was probed along one side of the structure,the distance between the two ports being0.0008)corresponding to the6.8575GHz poles was less256IEEE TRANSACTIONS ON ADV ANCED PACKAGING,VOL.22,NO.3,AUGUST1999(a)(b)Fig.10.TDT measurement and simulation comparison of the transient response.(a)Diagonal ports.(b)Edge ports.than the magnitude of the residues(100ps time period whichrelates to thePANNALA et al.:CONTRIBUTION OF RESONANCE TO GROUND BOUNCE IN LOSSY THIN FILM PLANES257Fig.11.Simulation of the ground bounce for the lossless test case.TABLE IR ESONANT F REQUENCIES FOR THE V ARIOUS T EST C ASESstructure was assumed to be lossless.The position of the portswere the same as thefirst test case.A rational function modelfor this case required seven poles for a good approximationand was developed as before.Poles and residues of such astructure are shown in(10)258IEEE TRANSACTIONS ON ADV ANCED PACKAGING,VOL.22,NO.3,AUGUST1999A CKNOWLEDGMENTThe authors would like to thank P.Chahal for the fabrication of the thinfilm plane structure,L.Smith and M.Torres,Sun Microsystems,and X.Yuan and G.Fitzgerald,Cadence Design Systems,for many useful suggestions.R EFERENCES[1]L.Smith,“Decoupling capacitor calculations for CMOS circuits,”inProc.Elect.Performance Elect.Packag.Conf.,1994,pp.101–105. [2]J.C.Parker,“Via coupling within parallel rectangular planes,”IEEEpat.,vol.39,pp.17–23,Feb.1997.[3]J.-M.Jong,V.Tripathi,and B.Janko,“Modeling and simulation ofswitching noise with the associated package resonance for high speed digital circuits,”in Proc.45th p.Technol.Conf.,1995, pp.323–328.[4]P.Chahal,R.R.Tummala,M.G.Allen,and M.Swaminathan,“A novelintegrated decoupling capacitor for MCM-L technology,”in Proc.46th p.Technol.Conf.,1996,pp.125–132.[5]FastHenry User’s Guide.Cambridge,MA:MIT b.,Nov.1996,version3.[6]SONNET User’s Manual.Liverpool,NY:SONNET,vol.I-III,Sept.1996.[7]SIGNOISE Manual.San Jose,CA:CADENCE,1998.[8]K.L.Choi,N.Na,and M.Swaminathan,“Characterization of embed-ded passives using LTCC technology,”IEEE p.,Packag., Manufact.Technol.B,vol.21,pp.258–268,Aug.1998.[9]S.Lin and E.S.Kuh,“Transient simulation of lossy interconnects basedon the recursive convolution formulation,”IEEE Trans.Circuits Syst.I, vol.39,pp.879–892,Nov.1992.[10]W.T.Beyene and J.E.Schutt-Aine,“Interconnect simulation usingorder reduction and scattering parameters,”in Proc.48th Electron.Comp.Technol.Conf.,1998,pp.627–631.[11]J.Bandyopadhyay,P.Chahal,and M.Swaminathan,“Importance ofdamping and resonance in thin-film integrated decoupling capacitor design,”in Proc.Elect.Performance Elect.Packag.Conf.,1997,pp.31–34.[12]S.Corey and A.T.Yang,“Interconnect characterization using timedomain reflectometry,”in Proc.Elect.Performance Elect.Packag.Conf.,1994,pp.189–191.[13]M.E.Van V alkenburg,Network Analysis,3rd ed.Englewood Cliffs,NJ:Prentice-Hall,1986.Sreemala Pannala(S’97)received the B.E.degreein electronics and communication engineering fromJawaharlal Nehru Technological University,India,in1991,the M.E.degree in microwave engineeringfrom Osmania University,India,in1994,the M.S.degree from the Georgia Institute of Technology,Atlanta,in1997,and is currently pursuing the Ph.D.degree in electrical engineering.She worked for the National Remote SensingAgency,Hyderabad,India,from1994to1996.Shehas been a Graduate Research Assistant with the Packaging Research Center,Georgia Institute of Technology,since1996.Her research work is on development of time domain characterization methods for packaging structures.Ms.Pannala is a student member of IMAPS andSWE.Jaya Bandyopadhyay received the B.E.degree inelectronics and communication engineering fromBengal Engineering College,Shibpur,India,in1995and the M.S.E.E.degree from the Georgia Instituteof Technology,Atlanta,in1998.She joined the Future Technology Group,Somer-set Design Center,Austin,TX,as a Package DesignEngineer.She is now a a Signal Integrity Engineerwith the IBM Corporation,Austin,TX. Madhavan Swaminathan(A’91–M’95),for a photograph and biography, see this issue,p.239.。