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Microwave Electronics
An Introduction to the Notion of Equivalent Circuit Starting from Maxwell's Equations
in six lectures
Maxwell's Equations & Modes in a Guide Ë Equivalent Circuit for Waveguide Modes Ë Modes of a Cavity Ë Cavity with a Port & External Q Ë Microwave Networks Ë Slater's Perturbation Theorem
Microwave Electronics I
Maxwell's Equations
and
Waveguide Modes
x Lorentz Force Law y Maxwell's Equations z Skin Depth { Orthogonal Modes  Phase & Group Velocity ¶ Quiz
xLorentz Force Law
r r r r F = q (E + v × B )
r E
r B
Newtons per Coulomb=V/m "electric field strength"
Newtons per Amperemeter=T=Wb/m2 "magnetic flux density"
or "magnetic induction"
defines the fields & abstracts them from the sources qdescribes "test particle" motion qdescribes response of media
q
Hendrik Antoon Lorentz b. July 18, 1853, Arnhem, Netherlands d. Feb. 4, 1928, Haarlem
Example: Conductivity
r r r dv v m = qE  m dt
r q r v = E m
r J = nqv
+ + + +
+ + + +
+ + + +
+ + + +
nq r = E m r = E
2
=" DC " 5.8 × 107 mho / m for Cu
Georg Simon Ohm (b. March 16, 1789, Erlangen, Bavaria d. July 6, 1854, Munich) P. Drude, 1900
NB This is a simplified picture of a normal conductor...occasionally this picture breaks down...
and of course this model cannot be applied to all materials...
yMaxwell's Equations
Electricity & Magnetism before Maxwell...
q q q
Charges repel or attract Current carrying wires repel or attract Timevarying currents can induce currents in surrounding media
After Maxwell...
q
q q
q q
Light is an electromagnetic phenomenon Nature is not Galilean Thermodynamics applied to electromagnetic fields gives divergent results Matter appears not to be stable Questions arise concerning gravitation...
"Ordinary" Electronics
·voltages vary slowly on the scale of the transit time = circuit size / speed of light ·circuit size small compared to wavelength ·voltage between two points independent of path ·may treat elements as "lumped" ·unique notion of impedance of an element ·bring a multimeter
Microwave Electronics
·circuit size appreciable compared to a wavelength ·voltage between two points depends on path ·elements are "distributed", spatial phaseshifts occur between them ·if the word "impedance" is used, you may always ask how it was defined... ·if any result of test & measurement is quoted, you may always ask how the equipment was calibrated ·bring crystal detectors, filters, mixers, a signal generator, a spectrum analyzer, and, if you have them a network analyzer, calibration kit, vector voltmeter
History
Henry Cavendish
(b. Oct. 10, 1731, Nice, Franced. Feb. 24, 1810, London, Eng.)
CharlesAugustin de Coulomb
(b. June 14, 1736, Angoulême, Fr.d. Aug. 23, 1806, Paris)
AndréMarie Ampere
(b. Jan. 22, 1775, Lyon, Franced. June 10, 1836, Marseille)
Karl Friedrich Gauss
(b. April 30, 1777, Brunswickd. 1855)
Hans Christian Ørsted
(b. Aug. 14, 1777, Rudkøbing, Den.d. March 9, 1851, Copenhagen)
SiméonDenis Poisson
(b. June 21, 1781, Pithiviers, Fr.d. April 25, 1840, Sceaux)
Michael Faraday
(b. Sept. 22, 1791, Newington, Surrey d. August 25, 1867, Hampton Court)
James Clerk Maxwell
(b. June 13 or Nov. 13, 1831, Edinburghd. Nov. 5, 1879, Glenlair )
Heinrich (Rudolf) Hertz
(b. Feb. 22, 1857, Hamburgd. Jan. 1, 1894, Bonn)
Guglielmo Marconi
(b. April 25, 1874, Bologna, Italyd. July 20, 1937, Rome)
(
r r ^ D2  D1 · nA = A
V
Gauss's Law r r D · dS = dV
^ n
Medium 2
)
V
+ +++++++++++++++ Medium 1 pillbox area A
D C / m2
electric displacement
or electric flux density
surface charge density
Ampere's Law before Maxwell
r r r r H · dl = J · dS
S
l^
^ n
Medium 2
Medium 1 contour side L r surface current densityK
S
(
r r r ^ H 2  H1 · l^ = K × n · l^
)
r r r ^ n × H 2  H1 = K
(
)
H K A /m
magnetic field strength
or magnetic flux
In Vacuum... r r r r H = B / µ0 D = 0 E
0 8.85 × 10 12 farad per meter
µ0 = 4 × 10 7 henry per meter
or
1 = c = 2.9979 × 108 m / s 0 µ0 µ0 = 377 0
In Media...
r r r r D = 0E + P = E r r electric dipole moment density P = e 0E r r r r H = B / µ0  M = B / µ r r magnetic dipole moment density M = H m
Finer Points: ·These are really frequency domain expressions ·In general ,µ are tensors · µ may be nonlinear & biased by a DC field ·H,D depend on your point of view
Faraday's Law
r r r B r E · dl =  · dS S S t
Maxwell, Ampere's Law was inconsistent with conservation of charge qAfter Maxwell, the fields didn't need charge to support them, they could propagate on their own qOf course no one believed Maxwell, but the fields didn't mind
qBefore
Charge Conservation
r + ·J = 0 t
r r dV =  J · dS t V V
Ampere's Law (before Maxwell's addition of Displacement Current) implied
or
r r =  · J =  · × H = 0 t
...actually not a bad approximation in conductors, or a dense plasma.. excellent for electrostatics, magnetostatics
Maxwell's Equations r r Gauss's Law ·D = r r r r D Ampere's Law ×H = J + with t
Maxwell's Displacement Current
r r r B Faraday's Law ×E =  t r No Magnetic Charge · B = 0
James Clerk Maxwell
b. June 13 or Nov. 13, 1831, Edinburgh d. Nov. 5, 1879, Glenlair
Boundary Conditions
apply Maxwell's equations in integral form...
( (
r r ^ D2  D1 · n = r r ^ B2  B1 · n = 0
) )
^ n
Medium 2
+ +++++++++++++++ Medium 1 pillbox area A
surface charge density
r r r ^ n × H 2  H1 = K r r ^ n × E 2  E1 = 0
( (
) )
l^
^ n
Medium 2
Medium 1 contour side L r surface current densityK
Example to Illustrate : Unmagnetized Plasma r r r dv v m = qE  m dt
r ~ jt = 1 Ee jt + E *e  jt ~ ~ E = Ee 2
(
) (
)
q ~ 1 ~ = nqv = DC E ~ v= E J ~ ~ (1+ j ) m (1+ j )
Apply charge conservation & Gauss's Law...
r ~ + · J = 0 j + · J = 0 ~ t ~ = =  1 · J =  1 · DC E ~ ~ · 0E ~ j j (1+ j ) 1 DC ~ 1 DC · 0 + E = 0 = 0 + j (1+ j ) j (1 + j )
N .B .
= 1 2 lim 0
2 p
nq 2 2 with p = m 0
Evidently...
·electric displacement depends on what you consider to be the "external" circuit, electric field does not
View #1
~ ~ · 0E = plasma + other ~ ~ ~ D = 0E
View #2
~ ~ · E = other ~ ~ D = E
·electric permittivity is a frequencydomain concept...
1 DC = 0 + = ( ) j (1 + j )
Polarization in the time domain...
+ d r ~ P (t ) = e jt P ( )  2
d jt ~ e 0 e ( )E ( ) =  2
+ dt r d jt  jt e 0 e ( ) e E (t ) =  2  2 + r = 0 dt G (t  t )E (t ) + 
+
where the Green's function is
1 + jt G (t ) = d e e ( ) 2 
e ( ) = dt e  jt G (t )

+
Example...unmagnetized plasma...
1 + G (t ) = d e jt e ( ) 2 
2 p 1 + = d e jt j (1+ j ) 2  2 = p 1  e t / H (t )
(
)
for t>0, contour may be closed at Im+ with contributions from two poles
plane
pole at =j/ pole at =0
contour for t<0, contour may be closed at Im so that G=0
Susceptibility in the High Frequency Limit
when the Green's function is analytic near t>0,
e ( ) = dt e  jt G (t )

+
= dt e

+
 jt
G (n ) (0) n H (t ) t n! n =0
G (n ) (0) n +  jt = j dt e n! 0 n =0 G (n ) (0) n 1 = j j n! n =0
G (0) G (1) (0) G (2) (0)  +j K = j 2 3
Example: unmagnetized plasma
e ( ) = 
2 p
2
j
2 p
3
+K
KramersKronig Relations Since G is causal e must be analytic in the Im<0 halfplane, so that
1 e ( ) e ( ) = 2j 
for points ,' and contour in the lower halfplane. Let the contour lie just below the real axis and use
1 1 + j (  ) P =  0   j lim
then
1 + e ( ) e ( ) = P j  
1 + e ( ) e ( ) = P   1 + e ( ) e ( ) =  P  
relates dispersion & absorption
Scalar & Vector Potentials r r r r v A r B = ×A E =  t
Maxwell's Equations...
r r r r r ·B = · × A = 0 r r r v r A r r r B × E = ×   =  × A =  t t t
r r r r r r r 2 × µH = × × A = · A  A r r r r E = µ × H = µ + µJ t r r A r = µ   + µJ t t
(
)
(
)
r r r r r r A r · D = · E = ·   = t
Gauge Invariance
r r r A A 
+ t
leaves E,B unchanged Lorentz Gauge
2
r r r A 2 2 2 A  µ 2 =  µJ  µ 2 =  / t t
evidently the characteristic speed of propagation in the medium is Coulomb Gauge
2
r · A + µ =0 t
v = ( µ )1/ 2
r r ·A = 0
r r r r A 2 A  µ 2 =  µJ + µ t t
2 =  /
related to the Lorentz Gauge potentials via
=  µ t Lorentz Gauge
2
Hertzian Potentials
in a homogeneous, isotropic sourcefree region...
r r ~ ~ ·E = ·H = 0
Magnetic Hertzian potential
r ~ E =  jµ × m
r 2 2 ~ ~ × H = jE = k 0 × m with k 0 = µ 2 r 2 ~ H = k 0 m + rr ~ × E =  jµ · m  2 m r 2 ~ =  jµH =  jµ k 0 m +
(
(
)
)
choice of gauge
r 2 = · m 2 + k 0 = 0
2
2 m + k 0 m
=0
rr 2 ~ H = · m + k 0 m
Electric Hertzian potential
r ~ H = j × e
rr 2 ~ E = · e + k 0 e
2
2 e + k 0 e
=0
Energy Conservation
r r J · E = rate of work done on fields r D r r r =  × H ·E t r D r r r r r r r r r r = · E  × H ·4 +4444  × E · H E H 1444 2 × E ·3 r r r t r r D r r r r B r ·H = ·E + · E × H + t t r r r S = E × H = Poynting Flux
· E ×H
(
)
(
)
In a linear medium, with and independent of frequency:
µ
r r r r u J · E = · S + t
where
r r r r u = E · D + B · H = field energy density
When and µ are not independent of frequency we should work in the frequency domain...
r ~ jt = 1 Ee jt + E *e  jt ~ ~ E = Ee 2
(
) ( )
)
and similarly for J, H, etc...let us compute averages over the rapid rf oscillation...can show that
1 ~ ~ S = E × H 2
(
r r D r B r r= ·E + ·H t t
somewhat more challenging is the calculation of the rate of change of field energy density
Questions arise...is this integrable?
r=
u =? t
and if so, what is the average stored energy density
u
?
To address this problem we first compute take
r ~ ~ ~ E (t ) = E ( ,t )e jt = E 0 ( ) + E 1( )t e jt r r ~ D (t ) = 0E (t ) + P ( ,t )e jt
{
{
}
{(
r D r ·E t
}
) }
and compute P...
~ P ( ,t )e
jt
~ ~ = 0 dt G (t  t ) E 0 ( ) + E 1( )t e jt
 +
+
(
)
~ ~ = 0E 0 ( ) dt G (t  t )e jt + 0E 1( ) j

+

dt G(t  t )e
jt
~ ~ = 0E 0 ( ) e ( )e jt + 0E 1( )
e ( )e jt j
or
~ ~ ~ P ( ,t ) = 0E 0 ( ) e ( ) + 0E 1( ) et  j e ~ ~ = 0 e ( )E ( ,t )  0 j e E 1( )
r r ~ D E P ~ = 0 + 0 jP ( ,t )e jt + e jt t t t r ~ ~ E E ( ,t ) ~ = 0 + 0 j e ( )E ( ,t )  j e E 1( ) e jt + e jt e ( ) t t ~ E ( ,t ) ~ ~ = e jt + jE ( ,t ) + 0E 1( ) e t ~ E ( ,t ) ( ) ~ = e jt + jE ( ,t ) t
then
finally
r ~ 2 D r 1 ( ) E ( ,t ) ~ ~ · E = · E ( ,t ) + j E ( ,t ) t 2 t
Finally
r ~ 2 2 ( i ) E ( ,t ) ~ D r 1 ( r ) ~ ~ ·E = · E ( ,t ) E ( ,t )  i E ( ,t )  2 t 4 t t
so that, in the absence of losses,
r r D r B r u r= ·E + ·H = t t t
where the field energy density is
2 (µ ) 1 ( ) ~ ~ ( ,t ) 2 u= E ( ,t ) + H 4
Energy conservation takes the form
r r u J · E = · S + t
with timeaveraged Poynting flux
1 ~ ~ S = E × H 2
(
)
zSkin Depth
Start from Maxwells Equations
r ~ ~ = D + J J = E ~ ~ ~ ×H t r ~ B ~ ~ ×E =  =  jB t r r ~ ~ ·E = ·B = 0
Fields exp(jt)
Reduce to an equation for H
r r r r ~ ~ ~ ~ × × H = · H  2H = 2H r ~ ~ ~ = × E =  jB =  jµH
(
)
(
) ( )
~  j sgn 2 H = 0 ~ H 2
2
=
2 =" skin  depth " µ
2 µm at 1GHz in Cu
Let's solve for fields in conductor...
VACUUM
t angent ial H normal H
CONDUCTOR
select coordinate along outward normal
d2 ~ 2 ~ H  j sgn 2 Ht = 0 2 t d
~ ~ Ht ( ) = Ht (0) exp  (1 + j sgn ) ~ H 1r ~ 1 ~ ^ ^ ~ E = ×H n × =  Z s n × Ht
"impedance boundary condition"
1 + j sgn Zs = = Rs (1 + j sgn ) 1 Rs = = surface resistance 8.3m at 1GHz in Cu
Power per m2 into the conductor...
^ S ·n = = = = 1 ~ ~ ^ E × H ·n 2 1 ~ ^ ~ ^  Z s n × Ht × H · n 2 1 ~t 2 ^ Z s n × H 2 1 ~ 2 = 1 Rs K 2 ~ Rs n × H 2 2
(
)
( (
)
)
where in the last line we have made use of the result for surface current density,
~ ~ ^ ~ K = Jd = n × H (0)
0
{Orthogonal Modes
(Uniform Waveguide)
From Maxwell's Equations, with fields
e jt  jk z z
r r ~ ~ ·E = ·B = 0 r ~ ~ × E =  jB r ~ ~ × H = jD
we can see that E & H satisfy the wave equation,
r r ~ ~ × × H = 2H r ~ ~ = j × D = j  jB
(
)
(
)
~ = 2µH
and similarly for E, so that
( ) 2 ~ 2 + k c )E = 0 (
where
2 k 0 = 2µ
2 ~ 2 + k c H = 0
2 2 2 kc = k 0  k z
The divergence conditions take the form
1 ~ ~ Ez = · E jk z
1 ~ ~ Hz = · H jk z
1 r ~ ~ E= × Z 0H jk 0
so that the longitudinal field components may be determined from the transverse components. In addition,we may write the curl equations
1 r ~ ~ Z 0H =  ×E jk 0
Z0 =
µ
r ~ ~  jk 0Z 0H =  z × E z  jk z z × E ^ ^ ~ r ~ ~ ~ jk 0E =  z × Z 0H z  jk z z × Z 0H ^ ^
or
to express the transverse components in terms of the longitudinal
r k0 kz r ~ ~ ~ E =  2 z × Z 0H z  E z ^ k0 jk c r k0 kz r ~ =  ~ z  Z 0H z ~ Z 0H ^  z × E 2 k0 jk c
TE Modes Ez=0
kz r ~ ~ Z 0H = 2 Z 0H z jk c r k0 ~ =  ~ z =  k 0 z × Z 0H ~ E z × Z 0H ^ ^ 2 kz jk c
longitudinal field satisfies
transverse fields may be determined from Hz
(
2 ~ 2 + k c H z = 0
)
with boundary condition
r kz ~ ~ ^ ^ 0 = n · Z 0H = 2 n · Z 0H z jk c
~ H z =0 i .e. n
TM Modes Hz=0
transverse fields may be determined from Ez
kz r ~ ~ E = 2 E z jk c
r k0 k ~ ~ Z 0H = 2 z × E z = 0 z × E ^ ^ ~ kz jk c
2 ~ 2 + k c E z = 0
longitudinal field satisfies
(
)
with boundary condition
~ Ez = 0
CutOff & Characteristic Impedance Zc
Boundary conditions restrict the permissible values of cutoff wavenumber kc to a discrete set. Each mode has a corresponding minimum wavelength c beyond which it is "cutoff" in the waveguide.
c = 2 / k c
The guide wavelength is
g = 2 / k z = 0 / 1  2 / 2 0 c
0 = 2 / k 0
In general for a given mode we have
~ Z cH = z × E ^ ~
where
g k0 Z 0 k = Z 0 0 z Zc = Z 0 k z = Z 0 0 g k0
TE mod e TM mod e
Modal Decomposition
A general solution for a given geometry may be represented as a sum over modes
r ~t = E a (r ) a (z , ) E V
a a
r ~ t = H a (r )I a (z , )Z ca ( ) H
where
Z caH a = z × E a ^
and we adopt the normalization
r r d rE a (r ) · E a (r ) = 1
2
where the integral is over the waveguide crosssection. We choose the sign of Z for positive kz. The coefficients V,I take the forms
Va (z , ) = Va+e  jk za z + Vae jk za z Z caI a (z , ) = Va+e  jk za z  Vae jk za z
Relation between Power, V & I
One can also show, for nondegenerate modes, that
r r d rE a (r ) · E b (r ) = ab r r 2 Z ca Z cb d rH a (r ) · H b (r ) = ab
2 2 1 ^ d r z · E a × H b = ab Z ca
(
)
This requires Green's Theorem,
r r 2 2 dl 1 2 + 1 · 2 d r = 1 n
(
2
)
and the eigenvalue equations for Hz & Ez As a result, one may express the power flow in the waveguide, in terms of V & I according to
1 ~ ~ P = d 2r Et × Ht 2 1 = VaI a a 2
(
)
( )
Meaning of V,I
Given the orthogonality relations, one can determine V,I from the transverse fields at a point z
r r ~t (r , z ) · E a (r ) Va (z , ) = d rE r r 2 ~ t (r , z ) · H a (r ) I a (z , ) = Z ca d rH
2
and this is enough to determine the solution everywhere in the uniform guide, since this fixes the right & leftgoing amplitudes.
Given the uniqueness of V,I, their relation to power, and the units (volts, amperes) it is natural to refer to them as voltage & current. It is important to keep in mind however that they appear as complex mode amplitudes,not work done on a charge or time rate of change of charge.
at the same time, for particular geometries and applications, V & I can often be related to these more conventional concepts
Phase & Group Velocity
consider a narrowband drive at z=0
V (t , 0) = f (t )e j 0t dt j  t ~ f (t )e ( 0 ) V ( , 0) =  2 d ~ j  0 )t f (t ) = V ( , 0)e (  2
compute the voltage downrange
V (t , z ) =

d ~ V ( , 0)e jt  jk z z 2
j (  0 )t  jk z ( 0 )z  j dk z ( )(  0 )z d 0
d ~ V ( , 0)e  2
=e =e
j 0t  jk z ( 0 )z j 0t  jk z ( 0 )z
d ~ V ( , 0)e  2
t  dk z z f d
dk j (  0 ) t  z z d
can see that constant phasefronts travel at
v =
= phase  velocity kz
while the modulation f travels at
vg =
d = group  velocity dk z
For a mode in uniform guide,
v =
2 2 k 0  kc
=
1 c c > 2 2 µ 1 k c / k 0 µ
c kz c c 2 2 1 kc / k 0 < vg = = µ k 0 µ µ
Summary
Lorentz Force Law Maxwell's Equations Skin Depth Modes in a Waveguide Phase Velocity v & Group Velocity vg
Acknowledgements
Encyclopedia Brittanica http://www.eb.com
100 Years of Radio http://www.alpcom.it/hamradio/
Dept. Materials Science, MIT http://tantalum.mit.edu/
Varian Associates http://www.varian.com/
Nikola Tesla's Home Page http://www.neuronet.pitt.edu/~bogdan/tesla/
Special Thanks to Prof. Shigenori Hiramatsu, KEK and Prof. Perry Wilson, SLAC for introducing me to this subject
qDept.
of Physics and Astronomy, Michigan State University qUniversity of Guelph
Vocabulary
q q q q q q q q q
Electric Field E Magnetic Field H Energy U, Power P Frequency f, or Angular Frequency Conductivity, or Resistivity Phase Velocity v, Group Velocity vg Distributed vs Lumped Elements E & H Fields, Charged Particles Behavior of Fields in Media
For More Information...
http://beam.slac.stanford.edu/
W3 Virtual Library of Beam Physics
links to all accelerator labs on the planet ...conferences...schools...news...jobs... companies...vendors...databases... researchers...preprints...
Recommended Reading
q
RF Engineering for Accelerators, Turner, (CERN 9203) An introduction to RF as applied to accelerators. Microwave Electronics, Slater The classic introduction to microwave electronics.
q
Related Texts
qClassical
Electrodynamics, Jackson A graduate level electrodynamics text.
qField
Theory of Guided Waves, Collin A modern introduction to microwave electronics. for Microwave Engineering, Collin An overview of the elements of microwave electronics.
qFoundations
Measurements, Ginzton An introduction to practical microwave work. qPrinciples of Microwave Circuits, Montgomery, Dicke, Purcell An introduction to common network elements.
qMicrowave qWaveguide
Handbook, Marcuvitz Analysis of the circuit parameters for network elements.
SI Units
Handy Numbers
10 log10 (1 / 2) 3dB 10 log10 (1 / 3) 5dB 20 log10 (0.99) 0.1dB 1mW 0 dBm
401 W / ° K m C 385 J / ° K kG
1.7 × 10 5 / ° K 1.56 × 10 8  m
Copper
Joint Accelerator School
RF Engineering for Particle Accelerators
To
¶Understand ¶Invent ¶Design ¶Build ¶Operate
RF Systems
Outline for Morning Lectures
1 Microwave Electronics 1 Maxwell's Equations & Modes in a Guide 2 M.E. 2  Equivalent Circuit Representation for Modes in a Guide 3 M.E. 3  Modes of a Cavity 4 Cavity Design 5 M.E. 4  Cavity with a Port & External Q 6 M.E. 5  Microwave Networks 7 M.E. 6  Slater's Perturbation Theorem 8 Superconducting Cavities 9 BeamCavity Interaction, BeamLoading 10 Klystron 1  SpaceCharge Limited Flow, Guns 11 Structure 1StandingWave 12 SLED Pulse Compression 13 Wakefields 1  Fundamentals 14 Klystron 2  Bunching, SpaceCharge 15 Structure 2Travelling Wave 16 Ferrite Loaded Cavity 1 17 Wakefields 2  in SW & TW Structures 18 Klystron 3  Simulation 19 Structure 3Fabrication and Conditioning 20 Structure 4 Surface fields, Breakdown, Multipactor, Dark Current 20 Wakefields 3  Other Sources of Impedance 21 Other RF Sources 22 High Gradients in Superconducting Cavities 23 Modulators 24 Windows & HighPower Transmission 25 Ferrite Loaded Cavity 2 26 Design for System Stability  Heavy Beam Loading
Outline for Morning Lectures
1 Microwave Electronics 1 Maxwell's Equations & Modes in a Guide 2 M.E. 2  Equivalent Circuit Representation for Modes in a Guide 3 M.E. 3  Modes of a Cavity 4 Cavity Design 5 M.E. 4  Cavity with a Port & External Q 6 M.E. 5  Microwave Networks 7 M.E. 6  Slater's Perturbation Theorem 8 Superconducting Cavities 9 BeamCavity Interaction, BeamLoading 10 Klystron 1  SpaceCharge Limited Flow, Guns 11 Structure 1StandingWave 12 SLED Pulse Compression 13 Wakefields 1  Fundamentals 14 Klystron 2  Bunching, SpaceCharge 15 Structure 2Travelling Wave 16 Ferrite Loaded Cavity 1 17 Wakefields 2  in SW & TW Structures 18 Klystron 3  Simulation 19 Structure 3Fabrication and Conditioning 20 Structure 4 Surface fields, Breakdown, Multipactor, Dark Current 20 Wakefields 3  Other Sources of Impedance 21 Other RF Sources 22 High Gradients in Superconducting Cavities 23 Modulators 24 Windows & HighPower Transmission 25 Ferrite Loaded Cavity 2 26 Design for System Stability  Heavy Beam Loading
Microwave Electronics
An Introduction to the Equivalent Circuit Starting from Maxwell's Equations
in six lectures
Maxwell's Equations & Modes in a Guide t Equivalent Circuit for Waveguide Modes Ë Modes of a Cavity Ë Cavity with a Port & External Q Ë Microwave Networks Ë Slater's Perturbation Theorem
Microwave Electronics
An Introduction to the Equivalent Circuit Starting from Maxwell's Equations
in six lectures
Maxwell's Equations & Modes in a Guide Equivalent Circuit for Waveguide Modes Ë Modes of a Cavity Ë Cavity with a Port & External Q Ë Microwave Networks Ë Slater's Perturbation Theorem
Microwave Electronics
An Introduction to the Equivalent Circuit Starting from Maxwell's Equations
in six lectures
Maxwell's Equations & Modes in a Guide Equivalent Circuit for Waveguide Modes Modes of a Cavity Ë Cavity with a Port & External Q Ë Microwave Networks Ë Slater's Perturbation Theorem
Why are you here?
What do you want?
Understanding of fundamentals... ·Distributed vs. Lumped Elements ·The Meaning of Current & Voltage ·Transit Time & Retardation Familiarity with the language... ·V, I, Z, , Rs, Qw, Qe, R/Q... · mode, Travelling Wave,... ·Tee, Load, Circulator, 3dB Coupler... Ability to Solve Problems... ·How to design, build & tune my cavity? ·What is the right power source to use? ·My system isn't working, what to do?
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