2Review Impedance matching to minimize power reflection from load Lumped-element tunersSingle-stub tunersMicrostrip linesThe most popular transmission lineKnowing the characteristic impedance and the relative dielectric constant of the material helps determine the strip line configuration and vice versa.Attenuationconduction lossdielectric lossradiation loss
3A pair of conductors is used to guide TEM wave MicrostripParallel plateTwo-wire TLCoaxial cable
4The use of waveguideWaveguide refers to the structure that does not support TEM mode, bring up “the cutoff frequency”
5General wave behaviors along uniform guiding structures (1) The wave characteristics are examined along straight guiding structures with a uniform cross section such as rectangular waveguidesWe can write in the instantaneous form asWe begin with Helmholz’s equations:assume WG is filled in with a charge-freelossless dielectric
6General wave behaviors along uniform guiding structures (2) We can write and in phasor forms asand
7Use Maxwell’s equations to show and in terms of z components (1) Fromwe have
8Use Maxwell’s equations to show and in terms of z components (2) We can express Ex, Ey, Hx, and Hy in terms of z-componentby substitution so we get for lossless media = j,
9Propagating waves in a uniform waveguide Transverse ElectroMagnetic (TEM) waves, no Ez or HzTransverse Magnetic (TM), non-zero Ez but Hz = 0Transverse Electric (TE), non-zero Hz but Ez = 0
10Transverse ElectroMagnetic wave (TEM) Since Ez and Hz are 0, TEM wave exists only whenA single conductor cannot support TEM
11Transverse Magnetic wave (TM) FromWe can solve for Ez and then solve for other components from (1)-(4) by setting Hz = 0, then we haveNotice that or j for TM is not equal to that for TEM .
12Eigen valuesWe defineSolutions for several WG problems will exist only for realnumbers of h or “eigen values” of the boundary value problems, each eigen value determines the characteristic ofthe particular TM mode.
13Cutoff frequency From The cutoff frequency exists when = 0 or or We can write
14a) Propagating mode (1) or and is imaginary Then This is a propagating mode with a phase constant :
15a) Propagating mode (2) Wavelength in the guide, where u is the wavelength of a plane wave with a frequencyf in an unbounded dielectric medium (, )
16a) Propagating mode (3)The phase velocity of the propagating wave in the guide isThe wave impedance is then
17b) Evanescent mode or Then Wave diminishes rapidly with distance z. ZTM is imaginary, purely reactive so there is no power flow.
18Transverse Electric wave (TE) FromWe can solve for Hz and then solve for other components from (1)-(4) by setting Ez = 0, then we haveNotice that or j for TE is not equal to that for TEM .
19TE characteristicsCutoff frequency fc,, g, and up are similar to those in TM mode.ButPropagating mode f > fcEvanescent mode f < fc
20Ex1 Determine wave impedance and guide wavelength (in terms of their values for the TEM mode) at a frequency equal to twice the cutoff frequency in a WG for TM and TE modes.