Modes Planar transmission line

1 modes

1.1 tem mode
1.2 quasi-tem modes
1.3 transverse modes
1.4 longitudinal-section modes

modes

an important parameter transmission lines mode of transmission employed. mode describes electromagnetic field patterns caused geometry of transmission structure.

tem mode

the mode found on ordinary conductive wires , cables transverse electromagnetic mode (tem mode). dominant mode on planar transmission lines. in tem mode field strength vectors electric , magnetic field both transverse direction of travel of wave , orthogonal each other. important property of tem mode can used @ low frequencies; way down 0 (dc).

another feature of tem mode on ideal transmission line (one meets heaviside condition) there no change of line transmission parameters (characteristic impedance , signal group velocity) frequency of transmission. because of this, ideal tem transmission lines not suffer form of distortion called dispersion. dispersion different frequency components travel @ different velocities resulting in wave shape (which may represent transmitted information) becoming smeared out in direction of line length. other modes suffer dispersion puts limit on bandwidth achievable.

quasi-tem modes

some planar formats, notably microstrip, not have homogeneous dielectric; different above , below line. such geometries cannot support pure tem mode, there component of electromagnetic field parallel direction of line. however, transmission can tem. such mode referred quasi-tem. discontinuities placed on line of tem line, such gaps , posts, used construct filters , other devices, have impedance purely reactive. is, can store energy, not dissipate it. in quasi-tem, these structures additionally have resistive component impedance. causes structure radiate , circuit lossy. same problem occurs @ bends , corners of line. these problems can mitigated using high permittivity material substrate. causes higher proportion of wave contained in dielectric, making more homogeneous transmission medium , mode closer pure tem.

transverse modes

in hollow metal waveguides , optical waveguides there unlimited number of other transverse modes can occur. however, tem mode cannot supported since requires conductors propagate. transverse modes classified either transverse electric (te) or transverse magnetic (tm) (also called respectively h , e modes) according whether, respectively, of electric field, or of magnetic field transverse. there longitudinal component of 1 field or other. exact mode identified pair of indices counting number of wavelengths or half-wavelengths along specified transverse dimensions (for instance te10). exact definition depends on whether waveguide rectangular, circular, or elliptical. waveguide resonators third index introduced mode wavelengths in longitudinal direction.

a feature of te , tm modes there definite cutoff frequency below transmission not take place. cutoff frequency depends on mode , mode lowest cutoff frequency called dominant mode. multi-mode propagation undesirable. because of this, circuits designed operate in dominant mode @ frequencies below cutoff of next highest mode. 1 mode, dominant mode, can exist in band.

some planar formats designed operate tem devices can support te , tm modes unless steps taken suppress them. ground planes or shielding enclosures can behave hollow waveguides , propagate these modes. suppression can take form of shorting screws between ground planes or designing enclosure small support frequencies low operational frequencies of circuit. similar issue found in coaxial cable can support circular te , tm modes not require centre conductor propagate.

longitudinal-section modes

longitudinal-section electric (lse) modes , longitudinal-section magnetic (lsm) modes hybrid modes can occur in planar formats non-homogeneous transmission media. when determining whether structure can support particular te mode, 1 sets electric field in z direction (the longitudinal direction of line) 0 , solves maxwell s equations boundary conditions set physical structure of line. 1 can set electric field in x direction 0 , ask modes gives rise to. such modes designated lse modes. there can lse modes and, analogously magnetic field, lsm , lsm modes. turns out lse modes linear superposition of corresponding te , tm modes. in other words, in general, have longitudinal component of both electric , magnetic field. likewise lsm modes found setting 1 of transverse components of magnetic field 0 analogous results.

when dealing longitudinal-section modes, te , tm modes written lse , lsm consistent set of notations. alternatively, tse etc. can written te etc. achieve same result. lse , lsm modes subsets of hybrid electromagnetic (hem) modes. there structures unable support pure te or tm mode , consequently transmission mode must hybrid.

^ oliner, pp. 557–559


^ connor, pp. 52–53, 100–101
^ flaviis, pp. 539–542
^ rao, p. 227


^ zhang & li, pp. 294–299
^ zhang & li, pp. 188, 294, 332