USPAS - Microwave Physics and Techniques [lecture slides]

903 Pages·2003·9.042 MB·English

Microwave Physics and Techniques
IU/USPAS P671D
University of California Santa Barbara
June 16 -20, 2003
Ali Nassiri
Argonne National Laboratory
Microwave Physics and Techniques UCSB –June 2003
Course Syllabus
Instructor: Ali Nassiri – Argonne National Laboratory
Class Time: M, T, W, TH ,F: 9:00 AM – Noon
&
2:00 PM – 5:00 PM
Prerequisites: College Physics, E&M and Calculus
Course Objectives: Provide essential background and training in
microwave physics and its applications in
synchrotron facilities
Grading: Homework 40%
Mid-week Exam (Take Home) 20%
Final Exam 40%
Textbook: Foundations For Microwave Engineering
Robert E. Collin
June 16, 2003 Microwave Physics and Techniques UCSB –June 2003
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Schedule
Monday 6/16 Tuesday 6/17 Wednesday 6/18 Thursday 6/19 Friday 6/20
9:00 – 10:30 AM 9:00 – 10:30 AM 9:00 – 10:30 AM 9:00 – 10:30 AM 9:00 – 10:30 AM
Lecture 1 Lecture 5 Lecture 9 Lecture 13 Lecture 17
10:30 -10:45 AM 10:30 -10:45 AM 10:30 -10:45 AM 10:30 -10:45 AM 10:30 -10:45 AM
Break Break Break Break Break
10:45 – Noon 10:45 – Noon 10:45 – Noon 10:45 – Noon 10:45 – Noon
Lecture 2 Lecture 6 Lecture 10 Lecture 14 Lecture 18
12:00 – 2:00 PM 12:00 – 2:00 PM 12:00 – 2:00 PM 12:00 – 2:00 PM 12:00 – 2:00 PM
Lunch Lunch Lunch Lunch Lunch
2:00 – 3:30 PM 2:00 – 3:30 PM 2:00 – 3:30 PM 2:00 – 3:30 PM 2:00 – 4:00 PM
Lecture 3 Lecture 7 Lecture 11 Lecture 15
FINAL EXAM
3:30 -3:45 PM 3:30 -3:45 PM 3:30 -3:45 PM 3:30 -3:45 PM
Break Break Break Break
3:45-5:00 PM 3:45-5:00 PM 3:45-5:00 PM 3:45-5:00 PM
Lecture 4 Lecture 8 Lecture 12 Lecture 16
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Topics
9:00 – 10:30 AM 10:45AM – 12:00 PM 2:00 -3:30 PM 3:45 – 5:00 PM
Mon Mathematics Math/E&M Review E&M Review Transmission Lines
Review
Tue Transmission Lines Waveguides Waveguides Microwave Network
Analysis
Wed Microwave Network Impedance Matching Impedance Matching Microwave
Analysis Resonator
Thu Power Dividers and RF Breakdown and Filters Measurements
Couplers
Ferrite Materials And
Simulations
Fri RF Systems for RF Systems for Final Exam
Synchrotron SR Synchrotron SR
2:00 – 4:00 PM
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Lecture 1
Review of Mathematics
June 16, 2003
A. Nassiri
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Vectors
Cartesian components of vectors
Let {e e e } be three mutually perpendicular unit vectors which form a
1, 2 , 3
right handed triad. Then {e e e } are said to form an orthonormal basis.
1, 2 , 3
The vectors satisfy:
e = e = e = 1
1 2 3
e × e = e , e × e = −e , e × e = e
1 2 3 1 3 2 2 3 1
e
3
a
3
a
2
a
e
1
2
e
1
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Vectors
We may express any vector a as a suitable combination of the unit
vectors {e e e }. For example, we may write
1, 2 , 3
3
a = a e +a e +a e = ∑a e
1 1 2 2 3 3 i i
i=1
{a ,a ,a }
where are scalars, called the components of a in the basis
1 2 3
{e e e }. The components of a have a simple physical interpretation.
1, 2 , 3
For example, if we calculate the dot product a. e , we find that
1
( )
a ⋅ e = a e + a e + a e ⋅ e = a
1 1 1 2 2 3 3 1 1
a ⋅ e = a e cosθ(a ⋅ e )
Recall that 1 1 1
a = a ⋅ e = a cosθ(a ⋅ e )
1 1 1
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Vectors
a
Thus, represent the projected length of the vector a in the direction
1
a , a
of e . This similarly applies to 2 3 .
1
Change of basis
Let a be a vector and let {e e e } be a Cartesian basis. Suppose that
1, 2 , 3
the components of a in the basis {e e e } are known to be {a ,a ,a }
1, 2 , 3 1 2 3
Now, suppose that we wish to compute the components of a in a second
Cartesian basis, {r r r }. This means we wish to find components
1, 2 , 3
a =αr +α r +αr
{α ,α ,α }
1 2 3 , such that 1 1 2 2 3 3 to do so, note that
α = a ⋅ r =α e ⋅ r +α e ⋅ r +α e ⋅ r
1 1 1 1 1 2 2 1 3 3 1
α = a ⋅ r =α e ⋅ r +α e ⋅ r +α e ⋅ r
2 2 1 1 2 2 2 2 3 3 2
α = a ⋅ r =α e ⋅ r +α e ⋅ r +α e ⋅ r
3 3 1 1 3 2 2 3 3 3 3
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Vectors
This transformation is conveniently written as a matrix operation
[ ][ ]
α= Q a
[ ]
α
where is a matrix consisting of the components of a in the basis
[ ]
a
{r r r }, is a matrix consisting of the components of a in the basis
1, 2 , 3
[ ]
{a ,a ,a } Q
, and is a “rotation matrix” as follows
1 2 3
α  a  r ⋅e r ⋅e r ⋅e 
1 1 1 1 1 2 1 3
     
[ ] [ ] [ ]
α = α a = a Q = r ⋅e r ⋅e r ⋅e
2 2 2 1 2 2 2 3
     
α  a  r ⋅e r ⋅e r ⋅e 
     
3 3 3 1 3 2 3 3
α = Q a , Q = r ⋅ e
Using index notation
i ij j ij i j
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Gradient of a Vector Field
Let v be a vector field in three dimensional space. The gradient of v is a
tensor field denoted by grad(v) or (cid:86)v , and is defined so that
v(r +εα) −v(r)
( )
∇v ⋅α= lim
ε
ε→0
for every position r in space and for every vector α.
Let { e , e , e } be a Cartesian basis with origin O in three dimensional space. Let
1 2 3
r = x e + x e + x e
denote the position vector of a point in space. The
1 1 2 2 3 3
gradient of v in this basis is given by  ∂v ∂v ∂v 
1 1 1
 
∂x ∂x ∂x
 1 2 3 
∂v ∂v ∂v
 2 2 2 
∇v =
 ∂x ∂x ∂x 
1 2 3
 
∂v ∂v ∂v
3 3 3
 
 ∂x ∂x ∂x 
 
1 2 3
∂v
[ ] i
∇v ≡
ij
∂x
j
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