Georgia Institute of Technology. simulating the performance of a 32-bit interconnect bus. referenced to non-ideal planes. A transient simulation

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1 Power ntegrity/signa ntegrity Co-Simuation for Fast Design Cosure Krishna Srinivasan1, Rohan Mandrekar2, Ege Engin3 and Madhavan Swaminathan4 Georgia nstitute of Technoogy 85 5th St NW, Atanta GA Te: (404) {krishna1, rohan2, engin3, madhavan.swaminathan4}(ece.gatech.edu Abstract There is a growing need to reduce the design cyce time of eectronic packages to meet the consumer needs quicker. A design methodoogy to achieve this is to integrate signa and power-deivery anaysis. n this paper, a transient simuation technique using S-parameters that does not vioate causaity is presented. Eye-diagram resuts are shown, with and without expicit deay extraction. Scaabiity of this technique has been demonstrated by soving a arge sized probem. 1. ntroduction As the compexity of interconnects and packages increases, and the rise and fa time of the signa decreases, the eectromagnetic effects in distributed passive structures become an important factor in determining the system performance. Hence there is a need for a methodoogy to accuratey simuate these parasitic eectromagnetic effects that are observed in the signa distribution (SDN) and the power deivery (PDN) networks of an eectronic system. This paper presents a methodoogy that can efficienty and accuratey simuate these effects for arge sized systems. The methodoogy enforces causaity on the transient simuations and is scaabe for soving arge sized probems. Traditionay, athough the SDN is referenced to non-idea PDN, they are anayzed separatey in the time and frequency domains respectivey. This approach fais to account for the parasitic effects due to the non-idea nature of the PDN, which cause signa degradation in the SDN. Hence, severa techniques ike macro-modeing [1] have been pubished that invove co-simuation of the SDN and the PDN. Transient simuations conducted using such techniques suffer from two major drawbacks: 1) the integration of the PDN effects in the SDN transient simuation carried out using macro-modeing, imits the size of the simuation being performed, and 2) the resuting transient simuation vioates causaity causing an artificia cosure of the eye opening. This paper proposes a methodoogy that addresses both the above-mentioned drawbacks. The methodoogy incorporates an approach that uses the Noda Admittance Matrix method aong with the stamp-rue and the moda decomposition technique to obtain the frequency domain parameters of a passive system [2][3]. This approach enabes the integration of the SDN and the PDN such that a parasitic eectromagnetic effects in the passive system are accuratey captured in the frequency domain network parameters. The approach works very efficienty for mutiayered power deivery structures aong with a variety of interconnect geometries ike microstrip, stripine, via transitions etc. This paper demonstrates the appication of the proposed methodoogy on a variety of passive structures incuding simpe microstrip and stripine interconnects referenced to non-idea power/ground panes, interconnects with via transitions etc. The paper aso demonstrates the scaabiity of the proposed methodoogy by simuating the performance of a 32-bit interconnect bus referenced to non-idea panes. A transient simuation methodoogy that does not vioate causaity is given in Section. The extraction of frequency domain port-port behavior is presented in Section. Deay extraction from S- parameters and transient simuation using signa fow graphs are expained in Sections V and V, respectivey. Eyediagram resuts are shown in Section V, foowed by concusions in Section V. 2. Causa Transient Simuation Methodoogy The method proposed in this paper for causa transient simuation of muti-port passive networks is shown in the fow diagram in Figure 1. Figure 1: Obtain frequencyresponses of the SDN and the PDN ntegrate the frequency responses ofsdn and PDN and obtain reduced muti-port mode Perform deay extraction on mutiport frequency data Perform transient simuation using signa fow graphs Fow chart of the proposed method The method begins with obtaining the frequency domain admittance responses (Y-parameters) of the signa deivery and power distribution networks separatey. These can be obtained through simuation or measurement based techniques. The frequency responses thus obtained are integrated using the Noda Admittance Method (NAM), the stamp-rue [3], and moda decomposition techniques [4]. The integration of the SDN and the PDN responses ensures that a parasitic eectromagnetic effects due to the non-idea nature of the PDN are accuratey accounted for in the transient simuation. Once the SDN and the PDN responses have been integrated, port ocations are defined to obtain a reduced muti-port representation of the entire system. The procedure to obtain the port-port frequency behavior wi be /05/$ EEE Eectronics Packaging Technoogy Conference

2 outined in detai in Section. The reduced muti-port Y- parameters are then converted to S-parameters for deay extraction, causaity enforcement and transient simuation using signa fow graphs. 3. Extraction of Port-Port Behavior Extraction of port-port behavior for most circuits can be obtained through the Noda Admittance Matrix method by using the stamp-rue. The stamp-rue is outined in detai in [3]. n this technique, every node is assigned a unique number and the admittance vaue between the nodes is stamped to the Y-matrix. To extract the port-port behavior, the Y-matrix of the overa circuit is reordered such that the Y-matrix of the output ports, Ypp, appears on the top-eft of the matrix as shown in (1). wer YCP Y~1[VP = [other [ Lcp cc[ other] ( Setting th, to the zero-vector and soving for pp, the Y- matrix of the output-ports can be obtained from (2). Y. t = Y'P + Y, (- YC' Yc) (2) n (2), Yc is the inverse of the YCC matrix given in Eq.. Another approach where the port-port behavior is obtained using the Z-parameters and the S-parameters is outined in [4]. However, computing the Y-matrix is easier when Y- parameters are used. Furthermore, Y-parameters are convenient to extract port-port behavior for panar circuits, e.g. a non-idea power-pane (see Figure 2), as we as mutiayered circuits, e.g. transmission ines referenced to non-idea power-panes (see Figure 3). n addition, passive terminations can be easiy incorporated. Computing the port-port behavior of a muti-ayered circuit foows a simiar approach as outined in the previous paragraph. The ony modification is that when an M-port network is referenced to a non-idea ground node, the M-port network is repaced with its equivaent mode. For exampe, in Figure 3, the two-port transmission ine network is repaced with the mode shown in Figure 4. The stamp-rue can then be used to obtain the Y-matrix. The mode for an arbitrary M-port network is shown in Figure 5. 11!.M L, 2 3 2!21 Figure 3: A muti-ayered circuit: Two-port transmission ine network referenced to an N-port power-pane network. Figure 4: The two-port transmission ine network in Figure 3 is repaced with its equivaent circuit mode. The Y-parameters cacuated between the ports can then be converted to any other parameters such as S-parameters, Z- parameters, etc. using the appropriate conversion formua. 4. Deay Extraction A nove technique for extracting port-to-port deay from the frequency response of a passive structure is proposed in [2]. The technique makes use of the minimum-phase property of passive systems in conjunction with the Hibert Transform and invoves the separation of the transfer responses of a system into minimum phase and a-pass components. Based on the theory described in [2], if Td is the port-toport deay for a 2-port passive network described by its S- parameters, the deay extraction process can be described as foows: N S12min(jt) = S12(jiw) (3) arg[s2.i (iw)] = 2P fos 2(iJ)J cot 2 )d (4) S12p(jw) = S12(jws) = e-jtd AP =_arg(s12,,,(jo) Td =- arg(s12,4a, (jw)) a) (5) (6) Figure 2: A panar circuit: A non-idea power-pane mode where S12 is the transfer response of the network under consideration, and S 2n,,n and S12Ap are its minimum phase and a-pass components respectivey such that Eectronics Packaging Technoogy Conference

3 S12 = S12,nn*S12Ap. transient response of the circuit. These equations are given as Por 1t Yii Port 2 Y22 PortM YMM (,21v1 2V3 YmVM Y2MVM V(t) = Vs(t) + V3(t)0J7S V2 (t) = V (t) V3 (t) = V2 (t) 0 s1 (t) + V5 (t) 0 S12 (t) V4 (t) = V2 (t) 0 s21 (t) + V5(t) 0 s22 (t) (7) (8) (9) (10) V5 (t) = V4 (t) 0 FL (1 1) where si 1(t), s12(t), s21(t) and s22(t) are the respective impuse responses of the transmission ine structure. From the deay extraction technique it is evident that s12(t) and s21(t) are each composed of a minimum phase component and an a-pass component where the a-pass component determines the port-to-port deay. This indicates that a votage change at V2 does not reach V4 for a time period YM - \/hx 1 given by the deay. A simiar case can be made for the votage change at V5 affecting the votage V3. These conditions can be used to rewrite (9) and (10) as, V3 (t) = V2 (t) 0 s1 (t) + V5(t - Td) s 12min (t) (12) Figure 5: An equivaent mode for an arbitrary M-port network characterized by Y-parameters. (3) foows from the unity magnitude property of the apass component whie (4) is obtained using the Hibert Transform for minimum phase systems. The method proposed in this paper uses the deay thus extracted to obtain causa signa fow graph equations for transient simuation of passive networks. 5. Transient Simuation Using Signa Fow Graphs Signa fow graphs (SFGs) have been previousy used in the transient simuation of passive systems [6]. One of the key advantages they provide is that it is possibe to perform transient simuation without any kind of approximation/interpoation of the frequency response data. Since this approximation step is a key botteneck for the scaabiity of macro-modeing techniques, signa fow graphs are capabe of handing arger sized simuation probems. n order to demonstrate the enforcement of causaity on transient simuation using signa fow graphs, consider a SFG of a transmission ine circuit. ik. P, U1, V.: = ti B. V Figure 6: SFG of the transmission ine circuit. The SFG shown in Figure 6 resuts in a system of equations which need to be soved in order to generate the V4(t) = V2(t-Td)Os21min (t) + V5(t) s22(t) (13) where s2mi (t) and s21,m,(t) are the transfer impuse responses of the transmission ine after the deay portion has been removed. This new system of equations expicity enforces the deay and the resuting transient simuation satisfies the causaity conditions. 6. Resuts The method proposed in this paper was tested on a number of passive structures. n each of the cases, a simuation was performed using SFGs with and without enforcing causaity. The transient resuts were compared using an eye-diagram observed at a particuar output ocation. The first case was a simpe stripine structure referenced to non-idea power ground panes. The ine was 20 inches in ength with characteristic impedance of 22Q.. The termination at the far-end of the stripine is 442 connected to the Vdd-pane and the ground-pane. The simuation setup is shown in Figure 7. The frequency responses of the stripine interconnect and the power/ground panes (simuated up to 2.5 GHz) were obtained separatey and then integrated using the moda decomposition technique described in [4]. Terminations were incorporated using the stamp-rue and from Equation 2 the system was reduced to a 4-port network. This network was simuated using the SFG approach described in Section V. A random bit pattem source time of 1 50ps was used to excite the ine at the near end and the output was observed at the far end. The comparison of the non-causa and the causaity enforced transient simuations is shown in Figures 8 and 9. t can be seen that the non-causa transient simuation resuts in an artificia eye-cosure of about 50 mv Eectronics Packaging Technoogy Conference

4 0.3 in. 4, 20 in. Figure 7: Stripine referenced to a power-ground pane The fina test case was a 32 bit bus running over a non-idea power distribution network. The simuation setup is shown in Figure 13. The bus was driven using 32 different random bit pattern drivers and the resuts of the noise couping were observed at the output of one of the ines. The PDN was modeed using the Transmission Matrix method as a 64-port passive network [7]. b.5 o n. Tme Figure 11: Non-causa T-ine and via simuation Figure 8: Non-causa stripine simuation. -1S a 05.,m Figure 12: Causa T-ine and via simuation Figure 9: Causa stripine simuation The second test case was a microstrip ine passing through a via discontinuity. The microstrip ine was 20 inches in ength with a 34 mi via ocated at the midpoint. The termination at the far-end of the microstrip is 44Q connected to the Vdd-pane and the ground-pane. The simuation setup is shown in Figure 10. A transient simuation was performed using a 400 ps source and the resuts obtained are shown in Figures 11 and 12. n this case, the non-causa transient simuation resuts in an artificia eye-cosure of about 100 mv. in. Thirty-two22S 2 Lines i.4 t 5 in. - 13: Top-view of the 32-bit ine simuation setup - 10 in. Vdd Gnd 10 in. Figure 10: Side-view of the microstrip with via configuration. tgure 14: (ausa i3-bit bus simuation Eectronics Packaging Technoogy Conference

5 ntegrating the interconnect modes using the stamp-rue and adding the ine terminations to the structure resuted in a consoidated system circuit represented by a 128-port network. Using Equation 2 this network matrix was reduced to a 66-port network. Macro-modeing techniques ike the one described in [1] can hande ony about ports. Using the SFG approach described in this paper, the 66-port network coud be effectivey simuated. The comparison between the non-causa and causaity enforced transient responses is shown in Figures 14 and 15. n this case the non-causa simuation resuted in a 160 mv eye-cosure. 7. Concusion A causa transient simuation methodoogy has been outined in this paper. t has been demonstrated that a simuation performed without expicit deay enforcement resuts in artificia eye-cosure. Extraction of port-port behavior for muti-ayered circuits that aso incudes passive terminations has been outined in detai. References. S. Min and M. Swaminathan, "Construction ofbroadband passive macro-modes from frequency data for distributed interconnect networks", EEE Transactions on EMC, vo. 46, no. 4, pp , Nov R. Mandrekar et a., "Causaity Enforcement in Transient Simuation of Passive Networks through Deay Extraction", Proceedings of SP J. Dobrowoski, ntroduction to Computer Methods for Microwave Circuit Anaysis and Design, Norwood, MA: Artech House, K. C. Gupta, R. Garg, R. Chadha, Computer-Aided Design of Microwave Circuits, Artech House, E. Engin et a, "Modeing of non-idea panes in stripine structures", Proceedings of Eectrica Performance of Eectronic Packaging, pp , J. Schutt-Aine et a., "Noninear transient anaysis of couped transmission ines", EEE Tran. on C&S, vo. 36, , Ju J. Kim and M. Swaminathan, "Modeing of Muti- Layered Power Distribution Panes Using Transmission Matrix Method," EEE Trans. Advanced Packaging, vo. 25, pp , May Eectronics Packaging Technoogy Conference