High-Level Time-Accurate Model for the Design of Self-timed Ring Oscillators ASYNC 2008 - Newcastle Jérémie Hamon 1 , 2 , Laurent Fesquet 1 , Benoît Miscopein 2 and Marc Renaudin 3 1 TIMA Laboratory - 2 Orange Labs - 3 TIEMPO SAS Grenoble, FRANCE April 2008
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects Context of the Study On-chip digital oscillators are very useful in a great variety of communication systems: Radio Frequency systems Intra-chip communication systems ... A lot of advantages: Standard CMOS design flow Frequency range Configurability ... And a major constraint: robustness to PVT Self-timed rings should be a promising solution for such digital oscillators... ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 2/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects State of the Art Structure of a self-timed ring: 5-stage self-timed ring It exists different stable propagation modes: Example of a burst propagation Example of an evenly-spaced propagation Previous works have been focused on the stage timing properties to analyse or control these propagation modes. ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 3/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects Contributions A model based on the combination of two different abstraction level models: The 3D Charlie Model: timing properties of a ring stage A behavioural model: ring structure and initialisation A high-level time-accurate model for self-timed rings: Evenly-spaced or burst propagation modes Oscillating period and phases analytical expression Robustness to the process variability Validated by electrical simulations on CMOS 65nm STMicroelectronics technology. ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 4/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects 3D Charlie Model 1 Timed Behavioural Model 2 3 Numerical Simulations Electrical Simulations 4 Conclusions and Prospects 5 ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 5/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects 3D Charlie Model 1 The Charlie and the Drafting Effects The Analytical 3D Charlie Model Timed Behavioural Model 2 Numerical Simulations 3 Electrical Simulations 4 5 Conclusions and Prospects ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 6/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects The Charlie and the Drafting Effects The Charlie effect: the closer the input events, the longer the propagation delay The Drafting effect: the shorter the time between two successive output commutations, the shorter the propagation delay A Q C B A possible Muller gate implementation ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 7/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects The Charlie and the Drafting Effects The Charlie effect: the closer the input events, the longer the propagation delay The Drafting effect: the shorter the time between two successive output commutations, the shorter the propagation delay 1 A 0 A t Q 1 C B 0 B t 1 C 0 t A possible Muller gate implementation ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 7/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects The Charlie and the Drafting Effects The Charlie effect: the closer the input events, the longer the propagation delay The Drafting effect: the shorter the time between two successive output commutations, the shorter the propagation delay 1 A 0 A t Q 1 C B 0 B t 1 C 0 t A possible Muller gate implementation ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 7/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects The Charlie and the Drafting Effects The Charlie effect: the closer the input events, the longer the propagation delay The Drafting effect: the shorter the time between two successive output commutations, the shorter the propagation delay 1 A 0 A 1 t C Q 0 1 C t B 0 B t 1 C 1 C 0 t 0 t A possible Muller gate implementation ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 7/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects The Analytical 3D Charlie Model 1 F 0 t F 1 s s C R 0 t R 1 charlie(s,y) y C 0 t −1 t t R t mean t F t Ring stage structure C C Timing diagram of a stage Output commutation instant: t C = t F + t R + charlie ( s , y ) 2 Analytical 3D Charlie Model: � charlie +( s − s min ) 2 − Be − y D 2 charlie ( s , y ) = D mean + A Drr + Dff Drr − Dff With: D mean = and s min = 2 2 3D Charlie Model diagram ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 8/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects 3D Charlie Model 1 Timed Behavioural Model 2 Notations and Definitions Behavioural Model Time Annotation Propagation Modes Period and Phases Numerical Simulations 3 Electrical Simulations 4 Conclusions and Prospects 5 ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 9/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects Notations and Definitions [0] [1] [2] [L−1] F 0 F 1 F F L−1 2 C 0 C 1 C C L−1 2 R R 1 R 2 R L−1 0 Structure of an L-stage asynchronous ring Definitions: Tokens and bubbles: L the number of stages stage i ⊂ token ⇔ C i � = C i + 1 i the stage index N T the number of tokens stage i �⊂ token ⇔ C i = C i + 1 N B the number of bubbles Ring structure: Propagation rules: C i = F ( i + 1 )% L = R ( i − 1 )% L C i − 1 � = C i = C i + 1 ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 10/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects Notations and Definitions [0] [1] [2] [L−1] 0 1 1 T B ? Structure of an L-stage asynchronous ring Definitions: Tokens and bubbles: L the number of stages stage i ⊂ token ⇔ C i � = C i + 1 i the stage index N T the number of tokens stage i �⊂ token ⇔ C i = C i + 1 N B the number of bubbles Ring structure: Propagation rules: C i = F ( i + 1 )% L = R ( i − 1 )% L C i − 1 � = C i = C i + 1 ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 10/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects Notations and Definitions [0] [1] [2] [L−1] 0 0 1 B T ? Structure of an L-stage asynchronous ring Definitions: Tokens and bubbles: L the number of stages stage i ⊂ token ⇔ C i � = C i + 1 i the stage index N T the number of tokens stage i �⊂ token ⇔ C i = C i + 1 N B the number of bubbles Ring structure: Propagation rules: C i = F ( i + 1 )% L = R ( i − 1 )% L C i − 1 � = C i = C i + 1 ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 10/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects Behavioural Model Example of 5-stage ring with 2 tokens Ring state representation: At logical abstraction level: C = { C 0 , C 1 , C 2 ,..., C L − 1 } C i ∈ { 0 , 1 } At token/bubble abstraction level: X = { X 0 , X 1 , X 2 ,..., X L − 1 } X i ∈ { T , B } State graph model: A node represents a possible state of the ring. An edge represents a possible transition from one state to another. Without any temporal assumption on the propagation delays of the stages. State graph of a 5-stage ring with 2 tokens ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 11/26
3D Charlie Model Timed Behavioural Model Numerical Simulations Electrical Simulations Conclusions and Prospects Behavioural Model Example of 5-stage ring with 2 tokens Ring state representation: At logical abstraction level: C = { C 0 , C 1 , C 2 ,..., C L − 1 } C i ∈ { 0 , 1 } At token/bubble abstraction level: X = { X 0 , X 1 , X 2 ,..., X L − 1 } X i ∈ { T , B } State graph model: A node represents a possible state of the ring. An edge represents a possible transition from one state to another. Without any temporal assumption on the propagation delays of the stages. State graph of a 5-stage ring with 2 tokens ASYNC 2008 High-Level Time-Accurate Model for the Design of Self-Timed Ring Oscillators 11/26
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