1Basics of Microwave MeasurementsSteven Anlagehttp://www.cnam.umd.edu/anlage/AnlageMicrowaveMeasurements.htm2Electrical Signals at Low and High Freuencies3!ransmission Lines!ransmission lines carr" microwave signals from one point to another!he" are important #ecause the wavelength is much smaller than the length of t"pical !$linesused in the la#%ou have to loo& at them as distri#uted circuits' rather than lumped circuits!he wave euationsV4!ransmission Lines(ave Speed!a&e the ratio of the voltage and current wavesat an" given point in the transmission line:) *+!he characteristic impedance *+ of the !$line,eflections from a terminated transmission line*L*+00Z ZZ ZabVVLLrightleft+ ,eflectioncoefficientSome interesting special cases:-pen .ircuit *L ) /' ) 0 ei+Short .ircuit *L ) +' ) 0 ei1erfect Load *L ) *+' ) + ei?!hese are used in error correction measurements to characteri2e non$ideal !$lines5!ransmission Lines and !heir .haracteristic 3mpedances6!he power a#sor#ed in a termination is:!ransmission Lines' continuedModel of a realistic transmission line including loss!raveling(avesolutionswithShunt.onductance7How Much 1ower ,eaches the Load48(aveguides,ectangular metallic waveguideH95etwor& Anal"sisAssumes linearit"6105$1ort 7escription of an Ar#itrar" Enclosure5 8 1ort S"stem5 1orts 9oltages and .urrents' 3ncoming and -utgoing (aves* matri:11111111]1

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+++N N VVVSVVV2121] [1V+1VV0 ' I0VN ' INNV+NV) ( ) (010Z Z Z Z S + ) ( ), ( S Z Complicated Functions of frequency Detail Specific(Non!ni"ersal)11Linear vs. 5onlinear Behavior125etwor& vs. Spectrum Anal"sis13,esonator MeasurementsSample#icro$a"e%esonatorCa"ity&ertur'ationinput output!raditional Electrod"namics Measurements(rfrf currentsinhomogeneities) micro$a"e$a"elen*t+,+ese measurementsa"era*e t+e propertieso"er t+e entire samplefrequencytransmissionf0ff0-f-f . f0- / f0 (Stored 0ner*y)(1122) (Dissipated 0ner*y) 2uality Factor2 . 0stored10dissip32 . f0 1 f,1,24sample140lectric and #a*netic &ertur'ationsSampleE1i 2, 1t%s 5 i 6s7aryin* capacitance (1) and inductance (1) c+an*e t+e stored ener*y and resonant frequency ff . f0- / f0 (Stored 0ner*y)(1122) (Dissipated 0ner*y) 7aryin* sample losses (1t, tan 2/1, 2) c+an*e t+e qualityfactor (2) of t+e microscope#a*netic Field &ert31 5 i 2, /t%s 5 i 6sSampleE0lectric Field &ert3B B15!he 9aria#le$Spacing 1arallel 1late ,esonator1rinciple of -peration: Measure the resonant freuenc"' f0' and the ualit" factor' Q' of the 9S11, versus the continuousl" varia#le thic&ness of the dielectric spacer ;s0' ?0@A ;?+++> F0 20 40 60 80 10011.411.611.812.012.212.4 Dielectric Spacer Thickness ( m)Res

nant !re"#enc$ (%&')020040060080010001200;1?@>7S&&%, ,.;; A?N2 dielectric spacer()*act

r fit: ?G> H ?G nm,s fit: ?++ H ?+ I f* ) 0+ JH2L ) D.DK mm' w ) D.+0 mm' film thic&ness d ) >A+ H @+ nm' !c ) D?.L FMutual 3nductance Measurements;0M?