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

University of Toronto

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

long@eecg.utoronto.ca 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

long@eecg.utoronto.ca University of Toronto

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

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

RF IC Passives

Presc Inductor Transmission Line Transformer RF IC distributed elements range from transmission line to transformer

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Differential Circuits

Common Port 1 Port 2 node Common node Port 1 Port 2

Inductor1 Inductor2

Axis of symmetry Cross-Coupled Oscillator Q1 Q2 Vout + Vout − L1 L2 VBB VCC

2-Inductor Implementation Symmetric Inductor

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Uniform Compact Model

• Single section commonly used to model passives
• Symmetry in differential circuits modeled by

multiple, identical sections (uniform model)

Ls rs(f) Co Cox CSi RSi Cox RSi CSi A ro Ls rs(f) Co Cox CSi RSi Cox RSi CSi ro Ls rs(f) Co Cox CSi RSi Cox RSi CSi A’ ro Section 1 Section 2 Section N

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Conductor Resistance

Current crowding at corners

Current Density at 3GHz, in A/m 377 660 943 w=10µm, s=1µm, OD=200µm

Non-uniform current distribution due to proximity effect rconductor f ( ) rdc rsk + rdc k f + = =

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Substrate Effect on Series Loss

MoM Simulator1 Uniform Model

2 4 6 8 10 12 14 16 18 20 Frequency, in GHz Series Resistance, rs, in Ω 5 10 15 20 25 30

MoM Simulator2

ρSi = 1 Ω-cm ρSi = 10 Ω-cm rδ f ( ) k2 tSi 2 ρSi

• 

       f2 =

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Self and Mutual Inductances

• Based on formulae for rectangular conductors over

ground plane, e.g., for self-inductance:

nH/mm

• Inductances are computed for each pair of

conductors in layout

• More flexible than using closed-form expressions
• ptimized for each component topology

Lself 0.2 ln 2h w t +

• (

) 1.5 +     =

Ground Plane w Conductor s t I2 I1 I1 h

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Wave Propagation on Silicon

w = 20µm w = 10µm w = 5µm

5 10 15 20 25 30 35 40 Frequency, in GHz 25 15 5 20 10 Effective Permittivity, εeff 30

tox = 5.8µm tSi = 200µm Wave velocity is proportional to frequency due to variation in εeff:

v 3

8

×10 εeff

• =

ρSi = 10Ω-cm Quasi-TEM Mode Slow-Wave Mode

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Substrate Capacitance

2 4 6 50 100 150 200 250 Substrate Capacitance, in fF Frequency, in GHz

Uniform Model Simulation Measurement

Step 1: Cox Step 2: CSi Cox and CSi computed from 2-D numerical simulations in 2 steps

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Spiral Capacitances

group of 5 group of 4 group of 3 group of 2 Underpass

• Substrate capacitances

C5 C3 C4 C2

Cox Csi α (C5, C4, C3, C2, C1; w+s)

group of 1 C1

Total capacitance for the spiral averaged over compact model sections

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Interwinding Capacitance

• Co Underpass parallel-plate

Line-to-line interwinding

Cu Cu Cu Cm1 Cm1 Cm5 Cm5 Cm9 Cm9 Cm2 Cm6 Cm6 Cm7 Cm7 Cm3 Cm2 Cm3 Cm8 Cm4 Cm8 Cm4 Port 2 Port 1

• ro dissipation

Interwinding

Capacitance computed between adjacent conductors

• nly. Dissipation is significant when pitch is small

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Transmission Line Models

1-section model measured 2-section model

10 20 30 40

Frequency, in GHz

0.5 1.0 1.5 2.0 2.5 Phase Constant 0.05 0.1 0.15 0.2 0.25 0.3 Attenuation Constant

Ls rs(f) Cox CSi RSi Cox RSi CSi Ls rs(f) Cox CSi RSi Ls rs(f) Cox CSi RSi Cox RSi CSi

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Inductor Q-Factor

1 2 3 4 5 6 1 2 3 4 5 6 7 Frequency, in GHz Quality Factor

Uniform Model 2.5D-MoM Sim. Measurement log(ω) ZPk ωPk |Z1(s)| ∆ω 0.707(ZPk)

• Q-factor from 1-port

input impedance is:

Qfpk ωpk ∆ω

• =

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

Transformer Model

L / 2 r / 2 Co Cox / 4 Csi / 4 4Rsi Port 1 Port 2 M/ 2 L / 2 r / 2 Co / 2 Co / 2 Csi / 4 Cox / 4 4Rsi L / 2 r / 2 M/ 2 L / 2 r / 2 Cox / 4 Csi / 4 4Rsi Csi / 4 Cox / 4 4Rsi Cox / 4 Csi / 4 4Rsi Csi / 4 Cox / 4 4Rsi Cox / 4 Csi / 4 4Rsi Csi / 4 Cox / 4 4Rsi

long@eecg.utoronto.ca University of Toronto

RF/MMIC Group BCTM 2001

1:1 Frlan Transformer

6

• 20
• 10

200 400 1 2 3 4 5 Frequency, in GHz |S21|, in dB Phase of S21, in degrees

Uniform Model Measurement

w = 15µm s = 3µm 400µm Nturns = 4

long@eecg.utoronto.ca University of Toronto

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