Distributed Nonlinearities in Microwave

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Distributed Nonlinearities in Microwave
Superconducting Devices

M. M. Assefzadeh



assefzadeh@ee.sharif.edu

Main Reference:
Analysis and Simulation of the Effects of Distributed
Nonlinearities in Microwave Superconducting Devices; C. Collado, J.
Mateu, and J. M. O’Callaghan; IEEE Transactions on Applied
Superconductivity, March 2005

Seminar for the Course:

Principles of Applied Superconductivity

Professor: Dr. Fardmanesh

June 2010



Outline


Introduction


High Tc Superconductive Devices


Nonlinearity Drawbacks


Nonlinearities in Superconductors


Analytical and Phenomenological


Superconductor Films


IMD and Third
-
Harmonic Generation in
SDevices


Nonlinear Transmission Line


Line Resonators


Superconductor Characterization with IMD Measurements


Harmonic Balance for Simulation of Superconducting Devices


Conclusion

2

Introduction

3


Motivations to use SC (esp. HTS) in electronics:


Low Surface Resistance


Reaching to High Currents


in Devices


Reduced Power Dissipation


and Delay


Unique Quantum Accuracy


Low Noise from Cryogenic


Operation


Taken from HTS Microwave Devices Lecture, Colorado University

Large
-
Area Double
-
Sided
YBCO Thin Films

Taken from The Web Page of
Semiconductor Physics Group of Leipzig
University

Introduction

4


HTS Microwave Devices such as:


Planar Filters


Resonators


Microstrip and
Stripline



Transmission lines


Benefits of SC Filters:


Low volume


Reduced insertion losses


High selectivity


Drawbacks

of High Powers:
Nonlinearities


Recognize Them


Simulate Them


Predict Them!




Taken from HTS Microwave Devices Colorado; Northrop Grumman

Nonlinearities in Superconductors

5


Intrinsic Concept of Nonlinearity in Superconductors


Assumptions


Microwave Frequencies (Low Surface Resistances)


Two Fluids Model (Nonlinearly)



Studying Intrinsic Nonlinearity


1. Nonlinear Conductance and Penetration Depth


Intrinsically:
Less Cooper Pairs when we have applied current.


Phenomenological
: Experimental works claiming the current
dependent penetration depth


2. Dependence of Electric Field on Surface Current

Nonlinear Conductance and
Penetration Depth

6


Analytical Approach


Basis:


Nonlinearity characterization function


Taylor expansion:



Approaching to:



Phenomenological Approach


Measuring current dependent
penetration depth and after fitting
Data:

Small Signal values (J~0):



Linear Conductance


Linear Penetration Depth


No Dependence On J



Large Current Magnitudes:



Increased


note that this is the resistive
conductance in the two fluid model





Increased



Time Domain Equation Between
E

and
J
s

:



assuming q
uasi exponential decay of



the electromagnetic fields:



Nonlinear inductive equation:



Assuming E

in two linear and NL components:







Deriving nonlinear parts of surface resistance and inductance:







Superconducting Films

From Nonlinear Electric Field to Nonlinear Surface Impedance

7

Talking
about
J
o

Talking
about
J
S

Nonlinear Distributed Parameters in
Transmission Lines

8


Intrinsic Nonlinearities in SC affecting Parameters in Transmission
Lines:



These nonlinearities follow the same nonlinear rules as the nonlinearity
function f(T,J).


Quadratic Nonlinearities:


Modulus Nonlinearities:



Nonlinear equivalent
circuit of a
superconducting
transmission line segment
with length
dz
; Taken from
the main reference.

IMD & Third Harmonic Generation

Derivation from intrinsic nonlinearities

9


Definitions:


Third Harmonic
: An effect of nonlinear devices creating freq. of
3f
.


IMD
: The unwanted amplitude modulation of signals containing different
frequencies.


In our work, we consider the products
f
12

= (2f
1



f
2
)
&

f
3

= 3f
1

for a
signal with two frequencies f
1

&

f
2

.

From Wikipedia

The spectrum
of an RF signal
containing two
fundamental
frequencies

IMD and 3rd Harmonic Generation in
Nonlinear Transmission Lines

10


Matched Transmission Line


Experimental use of
Transmission Lines:


1) Quadratic or modulus
nonlinearity?


Spurious powers against
sources powers slope:
3:1
and 2:1 for Quadratic and
Modulus



2) Resistive or inductive
nonlinearities?

From The Main Reference

IMD and 3rd Harmonic Generation in
Nonlinear Resonators

11


The Same Theory Analysis Applies for


Line Resonators


Disk Resonators and Cavities



Hairpin Resonator,


measurements fit theory (dots


are measured)


Quantitative results:


Taken From
The Main
Reference

In the Order of
J
c

Results of Harmonic Balance Simulation

12


Harmonic Balance:
A high performance method to simulate
nonlinear circuits


Linear part in Freq. domain


NL part in Time domain




Current Distribution


Along a SC Matched Line


Simulation (Dots) Versus Theory





Taken From the Main Reference

Results of Harmonic Balance Simulation

13


Matched SC Line: Powers
Delivered to the output


Dashed lines from the
theory, solid lines simulated



Inset chart: The error
between calculations and
simulations


10% Error for Input Power of
45dBm (=33W); The Effect of
Higher Order Nonlinearities.

Taken From the Main Reference

At the
fundamental
frequency

At the IMD 12
frequency

Conclusion

14


Nonlinearities due to high powers


Theory and phenomenological approaches


SC thin film devices: Theoretical solutions


Resulting intermodulation distortion and 3rd
harmonic generation


Simulations reveal the effects of extra high
powers; Higher order nonlinearities


References

15


[1]

Carlos
Collado
, J. M. (MARCH 2005). Analysis and Simulation of the Effects of
Distributed Nonlinearities in Microwave Superconducting Devices.
IEEE TRANSACTIONS ON
APPLIED SUPERCONDUCTIVITY

, 26
-
39.


[2]

T.
Dahm

and D.
Scalapino
, “Theory of intermodulation in superconducting
microstrip

resonator,” J. Appl. Phys. , vol. 81, no. 4, pp. 2002

2002, 1997.


[3]


T.
Dahm
, D.
Scalapino
, and B.
Willemsen
, “Phenomenological theory of intermodulation
in HTS resonators and filters,” J.
Supercond
., vol. 12, pp. 339

339, 1999.


[4]

B. A.
Willemsen
, T.
Dahm
, and D. J.
Scalapino
, “Microwave intermodulation in thin film
high
-
Tc superconducting
microstrip

hairpin resonators: Experiment and theory,” Appl. Phys.
Lett
., vol. 71, no. 29, pp. 3898

3898, 1997.


[5]

HTS Materials and Devices.

(
n.d
.). Retrieved from Colorado; Northrop Grumman:
http://boulder.research.yale.edu/Boulder
-
2000/transparencies/talvacchio
-
lecture1/colorado
-
rf.pdf

Thank You For Your Attention