# ANN Based Modeling of High Speed IC Interconnects. Q.J. Zhang, Carleton University

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1 ANN Based Modeling of High Speed IC Interconnects

2 Needs for Repeated Simulation Signal integrity optimization Iterative design and re-optimization Monte-Carlo analysis Yield optimization Iterative design and yield re-optimization

3 Applications and Numerical Examples: A typical interconnect network example (Veluswami, Zhang & Nakhla, 1995) dr1 dr2 rec 1 rec 4 dr3 rec 2 rec 3

4 Electrical Equivalent of the Interconnect Configuration l1 t1 l2 t2 l3 t3 R3 C3 Source R1 C1 R2 C2 l4 t4 R4 C4

5 Different Network Topologies for 4 Interconnects

6 Neural Network Model for 4 Interconnect Network t1 t2 t3 t4... L1 L2 L3 L4 R1 R2 R3 R4 C1 C2 C3 C4 Rs Vp Tr Topology Vertices

7 Input Variables and Their Range Variable Name Symbol Range of Values Interconnect Length L i 1 15 cm Termination Resistance Ri ,000 Ohms Termination Capacitance Ci nf Source Resistance Rs Ohms Input risetime Tr ns Peak Voltage Vp V Termination Vertices v 2 6

8 CPU Time Needed for Simulation of 20,000 Circuit Configurations Method NILT AWE Neural Network CPU time for delay hours 9.56 hours 6.67 minutes

9

10 Performance Comparison for NILT, AWE and Neural Network Model: NILT AWE NNet Number of configurations simulated per minute Factor of increase if Neural Network models are used

11 Three Parallel Coupled Interconnects Cross-section of three parallel interconnects: s s w w w t h Ground plane Conductors Substrate

12 Neural Model: Inputs: where [ w, t, s, h f ] x =, w width of interconnects t thickness of interconnects s separation between conductors h height of substrate f frequency of operation Outputs: The elements of the L and C matrices L L= L L L L L L L L C C = C C C C C C C C

13 Neural Network Input Parameters and Their Range: Parameter Symbol Minimum Maximum Conductor width w 5 mil 11 mil Conductor thickness t 0.7 mil 2.8 mil Separation s 1 mil 16 mil Substrate height h 5 mil 10 mil Frequency f 1 MHz 8 GHz

14 Features of Neural Network Model: Feature Value Number of inputs 5 Number of outputs in the overall model 18 Number of output nodes in neural network 6 Number of neurons in the hidden layer 10 Size of model (in floating point numbers) 126 Size of training set 500 Size of test set 500 Data Generation Technique SALI Training time (in hours) 6 Average training error Average test error

15 Average Training Error as Training Proceeded:

16 Test Error for 100 Random Inputs From the Test Set: rms error (normalized) over all six outputs sample number

17 C 13 as a Function of Separation, Keeping Other Parameters Constant:

18 An 8-bit Digital Bus Configuration 8-bit bus on a PCB, showing region of high crosstalk and signal noise: Area of high noise and crosstalk I / O Pad To different destination ICs Line of cross section

19 Cross-section of an 8-bit Digital Bus: w s conductors Substrate Ground plane

20 Test Error For 100 Random Inputs From the Test Set:

21 Mutual Capacitance:

22 Transmission Line Circuit with Nonlinear Terminations (Zaabab, Zhang and Nakhla, 1995) Use neural networks to model the response of a circuit. This figure represents a high-speed VLSI interconnect network modeled by 7 transmission lines and 5 nonlinear driver/receivers.

23 Signal delay through interconnect network is an important criteria in high-speed VLSI system design. The percentage error between the four delays predicted by the neural model and those obtained from Hspice for 350 training samples is shown as:

24 A comparison of the four integrity responses (delays of Vout1 throughvout4) predicted by the neural network with those from Hspice was also made for 100 sets of randomly generated termination parameters not used for training. The result is shown as:

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