power integrity/signalintegrity co-simulationforfast...

Power Integrity/Signal Integrity Co-Simulation for Fast Design ClosureKrishna Srinivasan1, Rohan Mandrekar2, Ege Engin3 and Madhavan Swaminathan4

Georgia Institute of Technology85 5th St NW, Atlanta GA 30308

Tel: (404)-385 6417 {krishna1, rohan2, engin3, madhavan.swaminathan4}(ece.gatech.edu

AbstractThere is a growing need to reduce the design cycle time

of electronic packages to meet the consumer needs quicker.A design methodology to achieve this is to integrate signaland power-delivery analysis. In this paper, a transientsimulation technique using S-parameters that does notviolate causality is presented. Eye-diagram results areshown, with and without explicit delay extraction. Scalabilityof this technique has been demonstrated by solving a largesized problem.

1. IntroductionAs the complexity of interconnects and packages

increases, and the rise and fall time of the signal decreases,the electromagnetic effects in distributed passive structuresbecome an important factor in determining the systemperformance. Hence there is a need for a methodology toaccurately simulate these parasitic electromagnetic effectsthat are observed in the signal distribution (SDN) and thepower delivery (PDN) networks of an electronic system.This paper presents a methodology that can efficiently andaccurately simulate these effects for large sized systems. Themethodology enforces causality on the transient simulationsand is scalable for solving large sized problems.Traditionally, although the SDN is referenced to non-idealPDN, they are analyzed separately in the time and frequencydomains respectively. This approach fails to account for theparasitic effects due to the non-ideal nature of the PDN,which cause signal degradation in the SDN. Hence, severaltechniques like macro-modeling [1] have been published thatinvolve co-simulation of the SDN and the PDN. Transientsimulations conducted using such techniques suffer from twomajor drawbacks: 1) the integration of the PDN effects in theSDN transient simulation carried out using macro-modeling,limits the size of the simulation being performed, and 2) theresulting transient simulation violates causality causing anartificial closure of the eye opening. This paper proposes amethodology that addresses both the above-mentioneddrawbacks. The methodology incorporates an approach thatuses the Nodal Admittance Matrix method along with thestamp-rule and the modal decomposition technique to obtainthe frequency domain parameters of a passive system [2][3].This approach enables the integration of the SDN and thePDN such that all parasitic electromagnetic effects in thepassive system are accurately captured in the frequencydomain network parameters. The approach works veryefficiently for multilayered power delivery structures alongwith a variety of interconnect geometries like microstrip,stripline, via transitions etc. This paper demonstrates theapplication of the proposed methodology on a variety ofpassive structures including simple microstrip and striplineinterconnects referenced to non-ideal power/ground planes,

interconnects with via transitions etc. The paper alsodemonstrates the scalability of the proposed methodology bysimulating the performance of a 32-bit interconnect busreferenced to non-ideal planes. A transient simulationmethodology that does not violate causality is given inSection II. The extraction of frequency domain port-portbehavior is presented in Section III. Delay extraction from S-parameters and transient simulation using signal flow graphsare explained in Sections IV and V, respectively. Eye-diagram results are shown in Section VI, followed byconclusions in Section VII.

2. Causal Transient Simulation MethodologyThe method proposed in this paper for causal transient

simulation of multi-port passive networks is shown in theflow diagram in Figure 1.

Perform delay extraction on multi-port frequency data

Perform transient simulation usingsigna flow graphs

Figure 1: Flow chart of the proposed method

The method begins with obtaining the frequency domainadmittance responses (Y-parameters) of the signal deliveryand power distribution networks separately. These can beobtained through simulation or measurement basedtechniques. The frequency responses thus obtained areintegrated using the Nodal Admittance Method (NAM), thestamp-rule [3], and modal decomposition techniques [4].The integration of the SDN and the PDN responses ensuresthat all parasitic electromagnetic effects due to the non-idealnature of the PDN are accurately accounted for in thetransient simulation. Once the SDN and the PDN responses

have been integrated, port locations are defined to obtain a

reduced multi-port representation of the entire system. Theprocedure to obtain the port-port frequency behavior will be

49 2005 Electronics Packaging Technology Conference

Obtain frequencyresponses oftheSDN and the PDN

I

Integrate the frequency responsesofSDN andPDN and obtainreduced multi-port model

0-7803-9578-6/05/$20.00 .2005 IEEE

outlined in detail in Section III. The reduced multi-port Y-parameters are then converted to S-parameters for delayextraction, causality enforcement and transient simulationusing signal flow graphs.3. Extraction of Port-Port Behavior

Extraction of port-port behavior for most circuits can beobtained through the Nodal Admittance Matrix method byusing the stamp-rule. The stamp-rule is outlined in detail in[3]. In this technique, every node is assigned a uniquenumber and the admittance value between the nodes isstamped to the Y-matrix. To extract the port-port behavior,the Y-matrix of the overall circuit is reordered such that theY-matrix of the output ports, Ypp, appears on the top-left ofthe matrix as shown in (1).

lIwIer= YCP Y~1[VP I[other [Lcp ccl[ other] (I

Setting Ith, to the zero-vector and solving for Ipp, the Y-matrix of the output-ports can be obtained from (2).

Y. t = Y'P + Y, (- YC' Yc) (2)In (2), Yc is the inverse of the YCC matrix given in Eq.l.Another approach where the port-port behavior is obtainedusing the Z-parameters and the S-parameters is outlined in[4]. However, computing the Y-matrix is easier when Y-parameters are used. Furthermore, Y-parameters areconvenient to extract port-port behavior for planar circuits,e.g. a non-ideal power-plane (see Figure 2), as well asmultilayered circuits, e.g. transmission lines referenced tonon-ideal power-planes (see Figure 3). In addition, passiveterminations can be easily incorporated.

Computing the port-port behavior of a multi-layeredcircuit follows a similar approach as outlined in the previousparagraph. The only modification is that when an M-portnetwork is referenced to a non-ideal ground node, the M-portnetwork is replaced with its equivalent model. For example,in Figure 3, the two-port transmission line network isreplaced with the model shown in Figure 4. The stamp-rulecan then be used to obtain the Y-matrix. The model for anarbitrary M-port network is shown in Figure 5.

2!21N

Figure 3: A multi-layered circuit: Two-port transmission linenetwork referenced to an N-port power-plane network.

Figure 4: The two-port transmission line network in Figure 3 isreplaced with its equivalent circuit model.

The Y-parameters calculated between the ports can then beconverted to any other parameters such as S-parameters, Z-parameters, etc. using the appropriate conversion formula.

4. Delay ExtractionA novel technique for extracting port-to-port delay from thefrequency response of a passive structure is proposed in [2].The technique makes use of the minimum-phase property ofpassive systems in conjunction with the Hilbert Transformand involves the separation of the transfer responses of asystem into minimum phase and all-pass components.

Based on the theory described in [2], if Td is the port-to-port delay for a 2-port passive network described by its S-parameters, the delay extraction process can be described asfollows:

IS12min(jt)| = IS12(jiw)I (3)

arg[Sl2 .i (iw)] = 2P floSI 2(iJ)J cot 2 )d (4)

S12p(jw) = S12(jws) = e-jTdAP=_arg(S12,,,(jo)Td =- arg(S12,4A, (jw))

a)

(5)

(6)

Figure 2: A planar circuit: A non-ideal power-plane model

where S12 is the transfer response of the network underconsideration, and SI 2n,,n and S12Ap are its minimum phaseand all-pass components respectively such that


11!.ML,

2

3

S12 = S12,nn*S12Ap. transient response of the circuit. These equations are givenas

YImVM

Por 1t Yii

Port2 Y22

PortM YMM (

,21v1 2V3

VI(t) = Vs(t) + V3(t)0J7SV2 (t) = V (t)V3 (t) = V2 (t) 0 sl1 (t) + V5 (t) 0S12 (t)

V4 (t) = V2 (t) 0 s21 (t) + V5(t) 0 s22 (t)

V5(t) = V4(t) 0 FLwhere si 1(t), s12(t), s21(t) and s22(t) are the respective

impulse responses of the transmission line structure. Fromthe delay extraction technique it is evident that s12(t) ands21(t) are each composed of a minimum phase componentand an all-pass component where the all-pass componentdetermines the port-to-port delay. This indicates that avoltage change at V2 does not reach V4 for a time period

YM - \/hX 1 given by the delay. A similar case can be made for the

voltage change at V5 affecting the voltage V3. Theseconditions can be used to rewrite (9) and (10) as,

V3 (t) = V2 (t) 0 s1 l(t) + V5(t - Td) s l12min (t) (12)

Figure 5: An equivalent model for an arbitrary M-portnetwork characterized by Y-parameters.

(3) follows from the unity magnitude property of the all-pass component while (4) is obtained using the HilbertTransform for minimum phase systems. The methodproposed in this paper uses the delay thus extracted to obtaincausal signal flow graph equations for transient simulation ofpassive networks.

5. Transient Simulation Using Signal Flow GraphsSignal flow graphs (SFGs) have been previously used in

the transient simulation of passive systems [6]. One of thekey advantages they provide is that it is possible to performtransient simulation without any kind ofapproximation/interpolation of the frequency response data.Since this approximation step is a key bottleneck for thescalability of macro-modeling techniques, signal flow graphsare capable of handling larger sized simulation problems.

In order to demonstrate the enforcement of causality ontransient simulation using signal flow graphs, consider aSFG of a transmission line circuit.

iK.

U1,

8.1 V.:= ti

B. V

Figure 6: SFG of the transmission line circuit.

The SFG shown in Figure 6 results in a system ofequations which need to be solved in order to generate the

V4(t) = V2(t-Td)Os21min (t) + V5(t) s22(t) (13)

where sl2mi (t) and s21,m,(t) are the transfer impulseresponses of the transmission line after the delay portion hasbeen removed. This new system of equations explicitlyenforces the delay and the resulting transient simulationsatisfies the causality conditions.

6. ResultsThe method proposed in this paper was tested on a

number of passive structures. In each of the cases, asimulation was performed using SFGs with and withoutenforcing causality. The transient results were comparedusing an eye-diagram observed at a particular outputlocation. The first case was a simple stripline structurereferenced to non-ideal power ground planes. The line was20 inches in length with characteristic impedance of 22Q..The termination at the far-end of the stripline is 442connected to the Vdd-plane and the ground-plane. Thesimulation setup is shown in Figure 7. The frequencyresponses of the stripline interconnect and the power/groundplanes (simulated up to 2.5 GHz) were obtained separatelyand then integrated using the modal decompositiontechnique described in [4]. Terminations were incorporatedusing the stamp-rule and from Equation 2 the system wasreduced to a 4-port network. This network was simulatedusing the SFG approach described in Section V. A randombit pattem source time of 1 50ps was used to excite the line atthe near end and the output was observed at the far end. Thecomparison of the non-causal and the causality enforcedtransient simulations is shown in Figures 8 and 9. It can beseen that the non-causal transient simulation results in an

artificial eye-closure ofabout 50 mV.


(7)(8)

(9)

(10)

(1 1)

P,-.00-

Y2MVM

0.3 in.

4 , 20 in.

Figure 7: Stripline referenced to a power-ground plane

Figure 8: Non-causal stripline simulation.

Figure 9: Causal stripline simulation

The second test case was a microstrip line passing througha via discontinuity. The microstrip line was 20 inches inlength with a 34 mil via located at the midpoint. Thetermination at the far-end of the microstrip is 44Q connectedto the Vdd-plane and the ground-plane. The simulation setupis shown in Figure 10. A transient simulation was performedusing a 400 ps source and the results obtained are shown inFigures 11 and 12. In this case, the non-causal transientsimulation results in an artificial eye-closure of about 100mV.

l l

10 in.

The final test case was a 32 bit bus running over a non-idealpower distribution network. The simulation setup is shown inFigure 13. The bus was driven using 32 different random bitpattern drivers and the results of the noise coupling wereobserved at the output of one of the lines. The PDN wasmodeled using the Transmission Matrix method as a 64-portpassive network [7].

b.5 o n.Tme

Figure 11: Non-causal T-line and via simulation

-1SI

-1 5

20 5 a 05l.,m

Figure 12: Causal T-line and via simulation

in. Thirty-two22S 2 Lines

i.4 t 5 in. - -

13: Top-view of the 32-bit line simulation setup

10 in.

l Vdd

I Gnd

Figure 10: Side-view of the microstrip with viaconfiguration. tlgure 14: (ausal i3-bit bus simulation


Integrating the interconnect models using the stamp-rule andadding the line terminations to the structure resulted in aconsolidated system circuit represented by a 128-portnetwork. Using Equation 2 this network matrix was reducedto a 66-port network. Macro-modeling techniques like theone described in [1] can handle only about 20-30 ports.Using the SFG approach described in this paper, the 66-portnetwork could be effectively simulated. The comparisonbetween the non-causal and causality enforced transientresponses is shown in Figures 14 and 15. In this case thenon-causal simulation resulted in a 160 mV eye-closure.

7. ConclusionA causal transient simulation methodology has been

outlined in this paper. It has been demonstrated that asimulation performed without explicit delay enforcementresults in artificial eye-closure. Extraction of port-portbehavior for multi-layered circuits that also includes passiveterminations has been outlined in detail.

ReferencesI. S. Min and M. Swaminathan, "Construction ofbroadband

passive macro-models from frequency data for distributedinterconnect networks", IEEE Transactions on EMC, vol.46, no. 4, pp. 544-558, Nov. 2004.

2. R. Mandrekar et al., "Causality Enforcement in TransientSimulation of Passive Networks through DelayExtraction", Proceedings of SPI 2005.

3. J. Dobrowolski, Introduction to Computer Methods forMicrowave Circuit Analysis and Design, Norwood, MA:Artech House, 1991.

4. K. C. Gupta, R. Garg, R. Chadha, Computer-AidedDesign of Microwave Circuits, Artech House, 1981.

5. E. Engin et al, "Modeling of non-ideal planes in striplinestructures", Proceedings of Electrical Performance ofElectronic Packaging, pp 247-250, 2003.

6. J. Schutt-Aine et al., "Nonlinear transient analysis ofcoupled transmission lines", IEEE Tran. on C&S, vol.36, 959-967, Jul. 1989.

7. J. Kim and M. Swaminathan, "Modeling of Multi-Layered Power Distribution Planes Using TransmissionMatrix Method," IEEE Trans. Advanced Packaging, vol.25, pp. 189-199, May 2002.


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