Co-simulation ofSignal andPowerDelivery Networks withCausality

Thispaperdiscusses atransient simulation methodthat enforces causality onthesimulated waveform. Themethodintegrates thefrequency responses ofthesignal andpowerdistribution networks, performs delay extraction, andsimulates thetransient response oftheintegrated network. Thepaperdemonstrates the application ofthemethodtoaccount forEM parasitics andcross-talk, andshowsthescalability ofthemethodfor performing large sized transient simulations. IIntroduction: Causality, whichdeals withtheprecise timing ofsignal propagation through passive structures like interconnects, isanimportant problem inthetimedomain simulation ofdistributed passive structures. Current macro- modeling techniques (1) usebandlimited frequency response data ofpassive structures toconstruct macro-models. Such macro-models areunable toaccurately capture distributed effects likedelay leading tocausality violations inthe transient simulation. A noveldelay extraction technique thatenables theenforcement ofcausality onatransient simulation hasbeenproposed in(2). Thetechnique isshowntoresult inacausal transient simulation ofasimple transmission line structure. Thispaper demonstrates theapplication ofcausality enforcement onlarge sized transient simulations. Thisincludes integration ofthefrequency domain responses ofthesignal andpowerdelivery networks, performing delay extraction onthemulti-port data, andconducting thesystem level simulation using signal flowgraphs. Thepaper also showstheapplication ofthecausal transient simulation method onavariety ofpassive structures to demonstrate thesimulation ofpowerdistribution parasitics, viatransitions andcrosstalk. Section IIdescribes the causality conditions indistributed passive systems andtheproblems withcurrent macro-modeling techniques in enforcing causality. Section IIIdescribes indetail thevarious steps involved inperforming acausal transient co- simulation ofthesignal andpowerdelivery networks inasystem. Section IVlists theresults oftheapplication onthe above method onavariety ofstructures including stripline interconnect, viastructure, coupled lines anda64-bit busall referenced tonon-ideal power/ground planes. Theconclusion andsomeconsiderations onthetransient simulation method arepresented insection V. II Causality violations in bandlimited