Modeling and Characterization

of On-Chip Transformers

Sunderarajan S. Mohan, C. Patrick Yue,

Maria del Mar Hershenson,

S. Simon Wong, and Thomas H. Lee

Center for Integrated Systems

Stanford University

OUTLINE

Motivation

Background

On-chip transformer realizations

Models

Experimental verification

Summary

MOTIVATION FOR TRANSFORMER MODELING

Essential for Radio Frequency Integrated Circuits (RFICs)

3-D field solvers are inconvenient

– Numerically expensive and cumbersome

– Good for verification but not for design

Scalable, analytical models

– Design guidelines and explore trade-offs

– Circuit design and optimization

SELF-INDUCTANCE

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Quantity Units

A

V

s

H

nH typical in RFOn-chip environ-ment

MUTUAL INDUCTANCE

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TRANSFORMERPSfrag replacements

Mutual coupling coefficient,

NON-IDEAL TRANSFORMER

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.

Series resistance.

Port-to-port & port-to-substrate capacitances

CONFIGURATIONS

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Three or four terminal device

Grounded terminals

TAPPED TRANSFORMER

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Inner

spiral

Outer spiral

Low

High ,

Top metal layer

Asymmetric

Low port-to-portcapacitance

INTERLEAVED TRANSFORMER

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Primary Secondary

Medium

Low ,

Top metal layer

Symmetric

Medium port-to-portcapacitance

STACKED TRANSFORMER

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Top View

Side Viewtop spiral

bottom spiral

High

High ,

Multiple metal layers

Area efficient

High port-to-port &port-to-substratecapacitances

STACKED TRANSFORMER VARIATIONS

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Bottom spiral Top spiral

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Shift top and bottom spirals laterally or diagonally

Trade-off lower for reduced port-to-port capacitance

COMPARISON OF TRANSFORMER REALIZATIONS

Transformer Area Coupling Self- Self-resonant

type coefficient, inductance frequency

Tapped High Low Mid High

Interleaved High Mid Low High

Stacked Low High High Low

Non-idealities result in trade-offs

Optimal choice determined by circuit application

Transformer models needed for comparison

SELF-INDUCTANCE CALCULATIONPSfrag replacements

Absolute error

Indu

ctor

sex

ceed

ing

abs.

erro

r

modified Wheeler expression

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Verified by measurements (75) and 3-D field solver simulations (17,000)

TAPPED TRANSFORMER MODEL

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Port1

Port2

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(outer)

Evaluate , , ,& by extending

previous work

Use modified Wheelerexpression for ,

Calculate

MUTUAL INDUCTANCE CALCULATION

Single inductor.

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Interleaved transformer.

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(primary) (secondary)

Tapped transformer.

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(outer)

FOR TAPPED AND INTERLEAVED TRANSFORMERS

1. Find , and

2. Determine from

3. Evaluate

STACKED TRANSFORMER MODEL

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Port1

Port2

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Evaluate , , ,, & by extending

previous work

Use modified Wheelerexpression for ,

Calculate

CURRENT SHEET APPROACH FOR

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Reduce complexity by

Use symmetry

Derive simple expression using electromagnetic theory

FOR STACKED TRANSFORMERSPSfrag replacements

predicted kmeasured k

Mut

ualC

oupl

ing

Coe

ffici

ent(

)

(for )PSfrag replacements

Metal and oxide thicknesses have only 2nd order effects on

FOR STACKED TRANSFORMERS

1. Find and

2. Determine

3. Evaluate

ACCURACY OF MODELS

Lumped model of distributed structure

Substrate not modeled

Patterned Ground Shield (PGS)

– Eliminates resistive and capacitive coupling to substrate

– Inductive coupling to substrate may degrade performanceat high frequencies

EXPERIMENTAL SET-UP

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S parameters

DUT

Coplanar GSG probes

HP8720Bnetwork analyzer

environment

port 1 port 2

port 3

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port 1

port 2

port 2

port 3

port 3

DIE PHOTO

EXPERIMENTAL VERIFICATION: TAPPED

,

,

,

0.8 1.2 1.6 2.0 2.4Frequency (GHz)

-1.0

-0.5

0.0

0.5

1.0

S 21

real(S21) measimag(S21) measreal(S21) calcimag(S21) calc

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Frequency(GHz)

0.8 1.2 1.6 2.0 2.4Frequency (GHz)

-1.0

-0.5

0.0

0.5

1.0

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real(S11) measimag(S11) measreal(S11) calcimag(S11) calc

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Frequency(GHz)

0.8 1.2 1.6 2.0 2.4Frequency (GHz)

-1.0

-0.5

0.0

0.5

1.0

S 22 real(S22) measimag(S22) measreal(S22) calcimag(S22) calc

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Frequency(GHz)

Frequency(GHz)

EXPERIMENTAL VERIFICATION: STACKED 1Stacked transformer withtop spiral overlapping bot-tom one

, ,,

, ,

0.0 0.5 1.0 1.5Frequency (GHz)

-1.0

-0.5

0.0

0.5

1.0

S 21

real(S21) measimag(S21) measreal(S21) calcimag(S21) calc

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Frequency(GHz)

0.0 0.5 1.0 1.5Frequency (GHz)

-1.0

-0.5

0.0

0.5

1.0

S 11

real(S11) measimag(S11) measreal(S11) calcimag(S11) calc

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Frequency(GHz)

0.0 0.5 1.0 1.5Frequency (GHz)

-1.0

-0.5

0.0

0.5

1.0

S 22

real(S22) measimag(S22) measreal(S22) calcimag(S22) calc

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Frequency(GHz)

Frequency(GHz)

CONTRIBUTIONS

On-chip transformer models

Expressions for mutual inductance andmutual coupling coefficient

Models verified by measurements

Basis for design and optimization oftransformer circuits

ACKNOWLEDGMENTS

IBM fellowship support

NSF contract MIP-9313701

Rockwell InternationalDr. Christopher HullDr. Paramjit Singh

Staff of the Stanford Nanofabrication Facility

Industrial Sponsors of the Center for Integrated Systems