A Uniform Compact Model for Planar RF/MMIC Interconnect, Inductors - PowerPoint PPT Presentation

A Uniform Compact Model for Planar RF/MMIC Interconnect, Inductors and Transformers John R. Long and Mina Danesh * RF/MMIC Group Department of Electrical and Computer Engineering University of Toronto long@eecg.utoronto.ca *Harris Corporation, Montreal, Canada University of Toronto

RF/MMIC Group BCTM 2001 Outline • Distributed components and RF IC design • Parameter computation • Transmission line model • Inductor/Transformer modeling • Experimental verification • Summary University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Motivations and Objectives • Compact models are required for fast and efficient simulation of RF circuits • Model must be a lumped-element circuit for time- domain, large-signal simulation (e.g., SPICE) • Minimize number of component values to simplify building and maintaining CAD libraries • Physics-based model is desirable for optimization University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 RF IC Passives Presc Inductor Transformer Transmission Line RF IC distributed elements range from transmission line to transformer University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Differential Circuits Common Inductor1 node Inductor2 Cross-Coupled Oscillator 2-Inductor V CC Implementation L 1 L 2 Port 2 Port 1 Axis of symmetry V out − V out + Symmetric Q 1 Q 2 Common Inductor node V BB Port 1 Port 2 University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Uniform Compact Model C o r o r o r o C o C o A ’ L s r s (f) L s L s r s (f) r s (f) A C ox C ox C ox C ox C ox C ox C Si C Si C Si R Si R Si C Si C Si R Si R Si C Si R Si R Si Section 1 Section 2 Section N • Single section commonly used to model passives • Symmetry in differential circuits modeled by multiple, identical sections (uniform model) University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Conductor Resistance w=10 µ m, s=1 µ m, OD=200 µ m 943 Current Density at 3GHz, in A/m 660 Non-uniform current distribution 377 due to proximity effect 0 Current crowding at corners ( ) rconductor f rdc rsk rdc k f = + = + University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Substrate Effect on Series Loss 30 Series Resistance, r s , in Ω Uniform Model MoM Simulator1 25 MoM Simulator2 20 ρ Si = 1 Ω - cm 15 2   tSi 10   f 2 ( ) r δ f k 2 = - - - - - - - - -   ρ Si   5 ρ Si = 10 Ω - cm 0 2 4 6 8 10 12 14 16 18 20 Frequency, in GHz University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Self and Mutual Inductances • Based on formulae for rectangular conductors over ground plane, e.g., for self-inductance: I 1 I 2 Conductor   2h w s Lself = 0.2 ln ( ) + 1.5 nH/mm - - - - - - - - - - - - - t   w + t h I 1 Ground Plane • Inductances are computed for each pair of conductors in layout • More flexible than using closed-form expressions optimized for each component topology University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Wave Propagation on Silicon t ox = 5.8 µ m t Si = 200 µ m ρ Si = 10 Ω -cm 30 Effective Permittivity, ε eff w = 5 µ m Wave velocity is 25 w = 10 µ m proportional to w = 20 µ m Slow-Wave Mode frequency due to 20 variation in ε eff : 15 Quasi-TEM Mode 8 × 10 3 v - - - - - - - - - - - - - - - - = 10 ε eff 5 0 0 5 10 15 20 25 30 35 40 Frequency, in GHz University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Substrate Capacitance 250 Substrate Capacitance, in fF Uniform Model Measurement Step 1: C ox 200 Simulation 150 Step 2: C Si 100 C ox and C Si computed from 2-D numerical 50 simulations in 2 steps 0 2 4 6 Frequency, in GHz University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Spiral Capacitances C 2 C 4 Underpass group of 4 group of 2 C 1 group of 1 C 3 group of 3 C 5 group of 5 • Substrate capacitances C ox C si α (C5, C4, C3, C2, C1; w+s) Total capacitance for the spiral averaged over compact model sections University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Interwinding Capacitance C u • C o Underpass parallel-plate Line-to-line interwinding C m2 C m2 C u C m6 C u C m1 C m6 C m3 • r o dissipation C m5 Interwinding C m7 Port 2 C m9 C m7 C m9 C m3 C m5 C m8 C m8 C m1 C m4 C m4 Port 1 Capacitance computed between adjacent conductors only. Dissipation is significant when pitch is small University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Transmission Line Models Attenuation Constant 0.3 measured 0.25 0.2 L s r s (f) 0.15 C ox C ox 0.1 C Si C Si R Si R Si 0.05 0 2.5 1-section model Phase Constant 2.0 L s r s (f) L s r s (f) 1.5 C ox C ox C ox 1.0 C Si C Si C Si R Si R Si R Si 0.5 0 0 10 20 30 40 2-section model Frequency, in GHz University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Inductor Q-Factor 7 Uniform Model Z Pk Measurement 6 2.5D-MoM Sim. 0.707(Z Pk ) |Z1(s)| Quality Factor 5 ∆ω 4 ω Pk log( ω ) 0 3 - Q-factor from 1-port 2 input impedance is: ω pk 1 Q fpk - - - - - - - - - = ∆ω 0 1 2 3 4 5 6 Frequency, in GHz University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Transformer Model C si / 4 4R si C si / 4 C si / 4 4R si C si / 4 4R si 4R si C ox / 4 C ox / 4 C ox / 4 C ox / 4 Port 1 r / 2 L / 2 L / 2 r / 2 C o / 2 C o / 2 C o M/ 2 M/ 2 L / 2 r / 2 L / 2 r / 2 Port 2 C ox / 4 C ox / 4 C ox / 4 C ox / 4 C si / 4 4R si C si / 4 4R si C si / 4 4R si C si / 4 4R si University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 1:1 Frlan Transformer 0 400 Phase of S 21 , in degrees |S 21 |, in dB Uniform Model Measurement 200 -10 400 µ m N turns = 4 0 -20 w = 15 µ m 0 1 2 3 4 5 6 s = 3 µ m Frequency, in GHz University of Toronto long@eecg.utoronto.ca

RF/MMIC Group BCTM 2001 Summary • Uniform compact models for on-chip transmission lines, inductors and transformers demonstrated • Models are applicable to any planar RF technology (e.g., silicon, III-V, hybrid microcircuit) • Models are SPICE compatible • Parameter extraction based on physical layout and technology parameters University of Toronto long@eecg.utoronto.ca