EE 201C Homework 1 Fang Gong gongfang@ucla.edu

Email Response Time HomeWork Email Response Time for Fang Gong: Monday: 3-4pm Wednesday: 3-4pm Saturday: 9-10pm Online Office Hour (Elluminate Live! Meetings) for Fang Gong Wednesday 9-10pm Please send emails about homework during these time slots for quick response. The schedule for Wei Yao will be announced by Wei soon. HomeWork HW1: CL extraction (Fang) HW2: Elmore delay & moment calculation (Fang) HW3: MOR (Wei) HW4: crosstalk noise calculation (Wei) HW5: Yield Estimation (Fang) HW6: Temporal correlation estimation for switching currents (Fang) HW7: PDN (Wei) Fang Gong: gongfang@ucla.edu Wei Yao: weiyao@ee.ucla.edu

Homework (due Jan 22) [1] Given three wires, each modeled by at least 2 filaments, find the 3x3 matrix for (frequency-independent) inductance between the 3 wires. We assume that the ground plane has infinite size for the purpose of capacitance calculation. l l T l W W W S S H wire width: W=10um, wire thickness: T=6um, wire length: l=6000um, wire spacing: S = 5um, distance to ground: H=5um, Copper electrical resistivity 0.0175e-6 Ωm2/m (room temperature), µ =1.256×10−6H/m, free space 0=8.85×10 -12F/m

Discretization and L calculation Discretize 3 wires into 6 filaments. Step 1.1 Filament 6 Filament 1 T l S W Discretization and L calculation Discretize 3 wires into 6 filaments. For each filament, calculate its self-inductance with (e.g.) For each pair of filament, calculate the mutual inductance with (e.g.) Different filaments and formulae may be used for better accuracy.

Step 1.2 Calculate inductance matrix of three wires Mutual Inductance Self Inductance If k=m, Lpkm is the self Lp for one conductor T l S W Lpkm is the mutual inductance between conductor Tk and Tm Lpij is the mutual inductance between filament i of Tk and filament j of Tm Lpij can be negative to denote the inverse current direction. L matrix from FastHenry =[ 8.0133e-09 6.8039e-09 6.1751 e-09 6.8039e-09 8.0133e-09 6.8039e-09 6.1751e-09 6.8039e-09 8.0133e-09]

Capacitance Calculation Step 1.3 Capacitance Calculation Cap. from FastCap: C3=312.86e-15 F C1=C5=251.54e-15 F C2=C4=112.98e-15 F

Step 1.4 Resistance Calculation Copper electrical resistivity 0.0175e-6 Ωm2/m (room temperature), l is length of wire A is area of wire’s cross section time

[2] Build the RC and RCL circuit models in SPICE netlist for the above wires. (suggest to use matlab script to generate matrix and thus SPICE netlist)

[3] Assume a step function applied at end-end, compare the waveforms at the far-end for the central wire using SPICE transient analysis for (a) RC and RLC models and (b) rising times (e.g., 20ns). Suggested Input: VDD 1 0 PULSE(0 1 0 20ns) Output volt 1 20ns 50ns time Input

RC model RLC model