Modeling and Characterization of On-ChipTransformerssmirc.stanford.edu/papers/IEDM98s-mohan.pdf ·...
Transcript of Modeling and Characterization of On-ChipTransformerssmirc.stanford.edu/papers/IEDM98s-mohan.pdf ·...
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
NON-IDEAL TRANSFORMER
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.
Series resistance.
Port-to-port & port-to-substrate capacitances
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)
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
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
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
S 11
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