`Microwave ElectronicsAn Introduction to the Notion of Equivalent Circuit Starting from Maxwell's Equationsin six lecturesMaxwell's Equations &amp; Modes in a Guide Ë Equivalent Circuit for Waveguide Modes Ë Modes of a Cavity Ë Cavity with a Port &amp; External Q Ë Microwave Networks Ë Slater's Perturbation TheoremMicrowave Electronics IMaxwell's EquationsandWaveguide Modesx Lorentz Force Law y Maxwell's Equations z Skin Depth { Orthogonal Modes | Phase &amp; Group Velocity ¶ QuizxLorentz Force Lawr r r r F = q (E + v × B )r Er BNewtons per Coulomb=V/m &quot;electric field strength&quot;Newtons per Ampere-meter=T=Wb/m2 &quot;magnetic flux density&quot;or &quot;magnetic induction&quot;defines the fields &amp; abstracts them from the sources qdescribes &quot;test particle&quot; motion qdescribes response of mediaqHendrik Antoon Lorentz b. July 18, 1853, Arnhem, Netherlands d. Feb. 4, 1928, HaarlemExample: Conductivityr r r dv v m = qE - m  dtr q r v = E mr J = nqv+ + + ++ + + ++ + + ++ + + +nq  r = E m r = E2 =&quot;  DC &quot;  5.8 × 107 mho / m for CuGeorg 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 EquationsElectricity &amp; Magnetism before Maxwell...q q qCharges repel or attract Current carrying wires repel or attract Time-varying currents can induce currents in surrounding mediaAfter Maxwell...qq qq qLight 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...&quot;Ordinary&quot; 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 &quot;lumped&quot; ·unique notion of impedance of an element ·bring a multimeterMicrowave Electronics·circuit size appreciable compared to a wavelength ·voltage between two points depends on path ·elements are &quot;distributed&quot;, spatial phase-shifts occur between them ·if the word &quot;impedance&quot; is used, you may always ask how it was defined... ·if any result of test &amp; 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HistoryHenry Cavendish(b. Oct. 10, 1731, Nice, France--d. Feb. 24, 1810, London, Eng.)Charles-Augustin de Coulomb(b. June 14, 1736, Angoulême, Fr.--d. Aug. 23, 1806, Paris)André-Marie Ampere(b. Jan. 22, 1775, Lyon, France--d. June 10, 1836, Marseille)Karl Friedrich Gauss(b. April 30, 1777, Brunswick--d. 1855)Hans Christian Ørsted(b. Aug. 14, 1777, Rudkøbing, Den.--d. March 9, 1851, Copenhagen)Siméon-Denis 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, Edinburgh--d. Nov. 5, 1879, Glenlair )Heinrich (Rudolf) Hertz(b. Feb. 22, 1857, Hamburg--d. Jan. 1, 1894, Bonn)Guglielmo Marconi(b. April 25, 1874, Bologna, Italy--d. July 20, 1937, Rome)(r r ^ D2 - D1 · nA = AVGauss's Law r r  D · dS =  dV^ nMedium 2)V+ +++++++++++++++ Medium 1 pillbox area AD    C / m2electric displacementor electric flux densitysurface charge density Ampere's Law before Maxwellr r r r  H · dl =  J · dSSl^^ nMedium 2Medium 1 contour side L r surface current densityKS(r r r ^ H 2 - H1 · l^ = K × n · l^)r r r ^ n × H 2 - H1 = K()H  K  A /mmagnetic field strengthor magnetic fluxIn Vacuum... r r r r H = B / µ0 D = 0 E 0  8.85 × 10 -12 farad per meterµ0 = 4 × 10 -7 henry per meteror1 = 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 mFiner Points: ·These are really frequency domain expressions ·In general ,µ are tensors · µ may be non-linear &amp; biased by a DC field ·H,D depend on your point of viewFaraday's Lawr r r B r  E · dl = -  · dS S S tMaxwell, 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 mindqBeforeCharge Conservationr  + ·J = 0 tr r   dV = -  J · dS t V VAmpere's Law (before Maxwell's addition of Displacement Current) impliedorr 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 tMaxwell's Displacement Currentr r r B Faraday's Law  ×E = - t r No Magnetic Charge  · B = 0James Clerk Maxwellb. June 13 or Nov. 13, 1831, Edinburgh d. Nov. 5, 1879, GlenlairBoundary Conditionsapply Maxwell's equations in integral form...( (r r ^ D2 - D1 · n =  r r ^ B2 - B1 · n = 0) )^ nMedium 2+ +++++++++++++++ Medium 1 pillbox area Asurface charge density r r r ^ n × H 2 - H1 = K r r ^ n × E 2 - E1 = 0( () )l^^ nMedium 2Medium 1 contour side L r surface current densityKExample to Illustrate : Unmagnetized Plasma r r r dv v m = qE - m  dtr ~ 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 &amp; 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     02 pnq 2 2 with  p = m 0Evidently...·electric displacement depends on what you consider to be the &quot;external&quot; circuit, electric field does notView #1~ ~  ·  0E = plasma + other ~ ~ ~ D =  0EView #2~ ~  ·  E = other ~ ~ D = E·electric permittivity is a frequency-domain concept...1  DC  = 0 + =  ( ) j (1 + j )Polarization in the time domain...+ d r ~ P (t ) =  e jt P ( ) - 2d 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 is1 + 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&gt;0, contour may be closed at Im+ with contributions from two poles-planepole at =j/ pole at =0contour for t&lt;0, contour may be closed at Im- so that G=0Susceptibility in the High Frequency Limitwhen the Green's function is analytic near t&gt;0,e ( ) =  dt e - jt G (t )-+=  dt e- +- jtG (n ) (0) n H (t )  t n! n =0G (n ) (0)   n + - jt =  j  dt e n!    0 n =0 G (n ) (0)   n 1 =  j    j n! n =0G (0) G (1) (0) G (2) (0) - +j K = -j 2 3   Example: unmagnetized plasmae ( ) = -2 p2-j2 p 3+KKramers-Kronig Relations Since G is causal e must be analytic in the Im&lt;0 half-plane, so that1 e ( ) e ( ) =  2j   - for points ,' and contour in the lower half-plane. Let the contour lie just below the real axis and use1 1  + j (  -  ) P =  -     0   -  - j limthen1 + e (  ) e ( ) = P  j -   - 1 + e (  ) e ( ) = P   -   -  1 + e (  ) e ( ) = - P   -   - relates dispersion &amp; absorptionScalar &amp; Vector Potentials r r r r v A r B = ×A E =- -  tMaxwell'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 Invariancer r r A  A -    + tleaves E,B unchanged Lorentz Gauge2r r r  A  2 2 2  A - µ 2 = - µJ   - µ 2 = -  /  t tevidently the characteristic speed of propagation in the medium is Coulomb Gauge2r   · A + µ =0 tv = ( µ )-1/ 2r r ·A = 0r r r r   A 2  A - µ 2 = - µJ + µ t t2 = -  / related to the Lorentz Gauge potentials via     = - µ  t  Lorentz Gauge2Hertzian Potentialsin a homogeneous, isotropic source-free region...r r ~ ~  ·E =  ·H = 0Magnetic Hertzian potentialr ~ E = - jµ × mr 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 gauger 2  =  ·  m   2 + k 0  = 022 m + k 0 m=0rr 2 ~ H =  · m + k 0 mElectric Hertzian potentialr ~ H = j × err 2 ~ E =  · e + k 0 e22 e + k 0 e=0Energy Conservationr 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:µr r r r u -J · E =  · S + twherer 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 that1 ~ ~ S =  E × H 2(r r D r B r r= ·E + ·H t tsomewhat more challenging is the calculation of the rate of change of field energy densityQuestions arise...is this integrable?r=u =? tand if so, what is the average stored energy densityu?To address this problem we first compute taker ~ ~ ~ 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 )ejt~ ~ =  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 )ejt ~ ~ =  0E 0 ( )  e ( )e jt +  0E 1( )  e ( )e jt jor   ~ ~ ~ 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   thenfinallyr ~ 2 D r 1   ( ) E ( ,t ) ~  ~ · E =  · E ( ,t ) + j E ( ,t )  t 2   t Finallyr ~ 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 twhere the field energy density is2  (µ ) 1  ( ) ~ ~ ( ,t ) 2  u=  E ( ,t ) + H  4    Energy conservation takes the formr r u -J · E =  · S + twith time-averaged Poynting flux1 ~ ~ S =  E × H 2()zSkin DepthStart from Maxwells Equationsr ~ ~ = D + J  J = E ~ ~ ~  ×H t r ~ B ~ ~  ×E = - = - jB t r r ~ ~  ·E =  ·B = 0Fields  exp(jt)Reduce to an equation for Hr r r r ~ ~ ~ ~  ×  × H =   · H - 2H = -2H r ~ ~ ~ =  × E = - jB = - jµH()() ( )~ - j sgn  2 H = 0 ~  H 22=2 =&quot; skin - depth &quot; µ  2 µm at 1GHz in CuLet's solve for fields in conductor...VACUUMt angent ial H normal HCONDUCTORselect coordinate along outward normald2 ~ 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   &quot;impedance boundary condition&quot;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 zr r ~ ~  ·E =  ·B = 0 r ~ ~  × E = - jB r ~ ~  × H = jDwe can see that E &amp; H satisfy the wave equation,r r ~ ~  ×  × H = -2H r ~ ~ = j × D = j - jB()()~ =  2µHand similarly for E, so that( ) 2 ~ 2 + k c )E = 0 ( where2 k 0 =  2µ2 ~ 2 + k c H = 0 2 2 2 kc = k 0 - k zThe divergence conditions take the form1 ~ ~ Ez =  · E  jk z1 ~ ~ Hz =  · H  jk z1 r ~ ~ E=  × Z 0H jk 0so that the longitudinal field components may be determined from the transverse components. In addition,we may write the curl equations1 r ~ ~ Z 0H = -  ×E jk 0Z0 =µ r ~ ~ - jk 0Z 0H  = - z ×  E z - jk z z × E  ^ ^ ~ r ~ ~ ~ jk 0E  = - z ×   Z 0H z - jk z z × Z 0H  ^ ^orto express the transverse components in terms of the longitudinalr 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=0kz r ~ ~ Z 0H  = 2   Z 0H z jk c r k0 ~ = - ~ z = - k 0 z × Z 0H  ~ E z ×   Z 0H ^ ^ 2 kz jk clongitudinal field satisfiestransverse fields may be determined from Hz(2 ~ 2 + k c H z = 0 )with boundary conditionr kz ~ ~ ^ ^ 0 = n · Z 0H  = 2 n ·   Z 0H z jk c~ H z =0 i .e. nTM Modes Hz=0transverse fields may be determined from Ezkz r ~ ~ E  = 2  E z jk cr k0 k ~ ~ Z 0H  = 2 z ×  E z = 0 z × E  ^ ^ ~ kz jk c2 ~ 2 + k c E z = 0 longitudinal field satisfies()with boundary condition~ Ez = 0Cut-Off &amp; Characteristic Impedance ZcBoundary conditions restrict the permissible values of cut-off wavenumber kc to a discrete set. Each mode has a corresponding minimum wavelength c beyond which it is &quot;cut-off&quot; in the waveguide.c = 2 / k cThe guide wavelength isg = 2 / k z = 0 / 1 - 2 / 2 0 c0 = 2 / k 0In general for a given mode we have~ Z cH  = z × E  ^ ~whereg  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 DecompositionA general solution for a given geometry may be represented as a sum over modesr ~t =  E a (r ) a (z , ) E Va ar ~ t =  H a (r )I a (z , )Z ca ( ) HwhereZ caH a = z × E a ^and we adopt the normalizationr r  d rE a (r ) · E a (r ) = 12where the integral is over the waveguide cross-section. We choose the sign of Z for positive kz. The coefficients V,I take the formsVa (z , ) = Va+e - jk za z + Va-e jk za z Z caI a (z , ) = Va+e - jk za z - Va-e jk za zRelation between Power, V &amp; IOne can also show, for non-degenerate modes, thatr r  d rE a (r ) · E b (r ) =  ab r r 2 Z ca Z cb  d rH a (r ) · H b (r ) =  ab2 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 &amp; Ez As a result, one may express the power flow in the waveguide, in terms of V &amp; I according to1 ~ ~ P =  d 2r  Et × Ht 2 1  =   VaI a a 2()( )Meaning of V,IGiven the orthogonality relations, one can determine V,I from the transverse fields at a point zr 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 rH2and this is enough to determine the solution everywhere in the uniform guide, since this fixes the right &amp; left-going 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 &amp; 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 &amp; I can often be related to these more conventional concepts|Phase &amp; Group Velocityconsider a narrow-band drive at z=0V (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 ( - 2compute the voltage down-range V (t , z ) = -d ~ V ( , 0)e jt - jk z z 2j ( - 0 )t - jk z ( 0 )z - j dk z ( )( - 0 )z d 0d ~   V ( , 0)e - 2=e =ej 0t - jk z ( 0 )z j 0t - jk z ( 0 )zd ~ V ( , 0)e  - 2 t - dk z z  f  d dk j ( - 0 ) t - z z   d can see that constant phase-fronts travel atv = = phase - velocity kzwhile the modulation f travels atvg =d = group - velocity dk zFor a mode in uniform guide,v =2 2 k 0 - kc=1 c c &gt; 2 2 µ 1- k c / k 0 µc kz c c 2 2 1- kc / k 0 &lt; vg = = µ k 0 µ µSummaryLorentz Force Law  Maxwell's Equations  Skin Depth   Modes in a Waveguide  Phase Velocity v &amp; Group Velocity vgAcknowledgementsEncyclopedia Brittanica http://www.eb.com100 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 subjectqDept.of Physics and Astronomy, Michigan State University qUniversity of GuelphVocabularyq q q q q q q q qElectric 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 &amp; H Fields, Charged Particles Behavior of Fields in MediaFor More Information...http://beam.slac.stanford.edu/W3 Virtual Library of Beam Physicslinks to all accelerator labs on the planet ...conferences...schools...news...jobs... companies...vendors...databases... researchers...preprints...Recommended ReadingqRF Engineering for Accelerators, Turner, (CERN 92-03) An introduction to RF as applied to accelerators. Microwave Electronics, Slater The classic introduction to microwave electronics.qRelated TextsqClassicalElectrodynamics, Jackson A graduate level electrodynamics text.qFieldTheory of Guided Waves, Collin A modern introduction to microwave electronics. for Microwave Engineering, Collin An overview of the elements of microwave electronics.qFoundationsMeasurements, Ginzton An introduction to practical microwave work. qPrinciples of Microwave Circuits, Montgomery, Dicke, Purcell An introduction to common network elements.qMicrowave qWaveguideHandbook, Marcuvitz Analysis of the circuit parameters for network elements.SI UnitsHandy Numbers10 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 SchoolRF Engineering for Particle AcceleratorsTo¶Understand ¶Invent ¶Design ¶Build ¶OperateRF SystemsOutline for Morning Lectures1 Microwave Electronics 1 -Maxwell's Equations &amp; 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 &amp; External Q 6 M.E. 5 - Microwave Networks 7 M.E. 6 - Slater's Perturbation Theorem 8 Superconducting Cavities 9 Beam-Cavity Interaction, Beam-Loading 10 Klystron 1 - Space-Charge Limited Flow, Guns 11 Structure 1-Standing-Wave 12 SLED Pulse Compression 13 Wakefields 1 - Fundamentals 14 Klystron 2 - Bunching, Space-Charge 15 Structure 2-Travelling Wave 16 Ferrite Loaded Cavity 1 17 Wakefields 2 - in SW &amp; TW Structures 18 Klystron 3 - Simulation 19 Structure 3-Fabrication 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 &amp; High-Power Transmission 25 Ferrite Loaded Cavity 2 26 Design for System Stability - Heavy Beam LoadingOutline for Morning Lectures1 Microwave Electronics 1 -Maxwell's Equations &amp; 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 &amp; External Q 6 M.E. 5 - Microwave Networks 7 M.E. 6 - Slater's Perturbation Theorem 8 Superconducting Cavities 9 Beam-Cavity Interaction, Beam-Loading 10 Klystron 1 - Space-Charge Limited Flow, Guns 11 Structure 1-Standing-Wave 12 SLED Pulse Compression 13 Wakefields 1 - Fundamentals 14 Klystron 2 - Bunching, Space-Charge 15 Structure 2-Travelling Wave 16 Ferrite Loaded Cavity 1 17 Wakefields 2 - in SW &amp; TW Structures 18 Klystron 3 - Simulation 19 Structure 3-Fabrication 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 &amp; High-Power Transmission 25 Ferrite Loaded Cavity 2 26 Design for System Stability - Heavy Beam LoadingMicrowave ElectronicsAn Introduction to the Equivalent Circuit Starting from Maxwell's Equationsin six lecturesMaxwell's Equations &amp; Modes in a Guide t Equivalent Circuit for Waveguide Modes Ë Modes of a Cavity Ë Cavity with a Port &amp; External Q Ë Microwave Networks Ë Slater's Perturbation TheoremMicrowave ElectronicsAn Introduction to the Equivalent Circuit Starting from Maxwell's Equationsin six lecturesMaxwell's Equations &amp; Modes in a Guide Equivalent Circuit for Waveguide Modes Ë Modes of a Cavity Ë Cavity with a Port &amp; External Q Ë Microwave Networks Ë Slater's Perturbation TheoremMicrowave ElectronicsAn Introduction to the Equivalent Circuit Starting from Maxwell's Equationsin six lecturesMaxwell's Equations &amp; Modes in a Guide Equivalent Circuit for Waveguide Modes Modes of a Cavity Ë Cavity with a Port &amp; 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 &amp; Voltage ·Transit Time &amp; 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 &amp; tune my cavity? ·What is the right power source to use? ·My system isn't working, what to do?`

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