CSE464 Coupling Calculations via Odd/Even Modes Spring, David M. Zar (Based on notes by Fred U. Rosenberger)

Transcription

1 SE464 ouping acuations ia Odd/Een Modes Spring, 009 aid M. Zar (Based on notes by Fred U. Rosenberger) - aid M. Zar - 3/4/009

2 ouped Lines Here are two couped ines I I ( )/ I ( I )/ I ( Odd, ifference ) ( )/ I ( I I )/ ( Een, ommon ) f r f r - aid M. Zar - 3/4/009

3 ouped Lines Een-mode impedance, Z OE impedance seen on each ine by a common-mode signa Odd-mode impedance, Z OO impedance seen on each ine by differentia mode signa ifferentia impedance, Z O Z OO impedance seen across a pair of ines by differentia mode signa ommon-mode impedance, Z O 0.5Z OE impedance seen between a pair of ines and a common return by a common-mode signa. Z OE L M d Z OO L M d tota ine apacitance (ine to GN d ) d ine to ine capacitance 3 - aid M. Zar - 3/4/009

4 ouped Lines Matched termination ( No refection ) Line Line R Z OE Z R Z OE OO Z Z OE OO ouped ine equiaent circuit ( T-ine ony, no externa components ) Line R * * R R Line Equiaent circuit at sending end Equiaent circuit at receiing end 0 r ; 0r ; f f 4 - aid M. Zar - 3/4/009

5 ouped Lines Matched termination (Wye) ( No refection ) Line R3 R3 Line R 3 Z OO R 4 Z OE Z OO R4 5 - aid M. Zar - 3/4/009

6 ouped Lines Procedure :( Assuming 0 t < 0 ). Soe for & at sending end ( 0 & 0. Find f & 0 f at sending end ( 0r 0 3. Find at 0 r t & 4. Find & 5. Find r r & r at receiing end (, at receiing end at receiing end f ; r 6. Find, ontinue ) f from EQ circuit unti exhaustion or sma changes ) 0 ) 6 - aid M. Zar - 3/4/009

7 Backward rosstak Next Boxes represent transmission ine impedances, Resistor symbos are physica resistors. R t is an externa termination resistor. 0 is the otage couped into Line at x0. c and d are zero in this case since the far end is matched. The otage on ine, and the couping coefficient is gien by the otage diider. x R R Line R Line 0 S * * R t x0 0 S R t t0 T r Line at x 0 : 0 R // Rt S R R // R t k rx R // Rt R R // R t (ay Eq 6-6) 7 - aid M. Zar - 3/4/009

8 Forward rosstak Next For inhomogeneous media, same procedure appies but now They do not arrie at same time so cacuation is a itte more tedious.. Matched Termination x 0.5 f x0 0.5 f 0 S / / t0 T r 8 - aid M. Zar - 3/4/009

9 9 - aid M. Zar - 3/4/009 Forward rosstak Next (cont.) r T r T Δ fx S x S r Ef k dt d t dt d T Eq 6-8) (ay, r T & for OR forward crosstak fx r T & for

10 onfigurations O > E Microstrip air dieectric O < E 300 Ohm T or Twisted Pair or fat cabe (ground aternate conductors, may hae gnd pane) onductors dieectric Fat cabe O E Ansey Back Magic fat cabe. Note wide ground, narrow signa to reduce backward crosstak P board stripine ground signa ε r ε r 0 - aid M. Zar - 3/4/009

11 Mutipe Aggressors We cacuate for singe aggressor, use superposition for mutipe aggressor ines Typica couping is a itte more than twice that for singe agressor ine Major rosstak ontributors ictim Sma ontribution - aid M. Zar - 3/4/009

12 What Ese? Simuation (SPIE) is widey used in eauating/cacuating transmission ine waeforms an easiy dea with ossy ines, non-inear termination, etc Time consuming to setup and eauate Has repaced measurement for the most part (sti want to get some confirmation from measurement (reaity)) You must know what questions to ask If you don t simuate critica cases, don t earn much Parameters are obtained by Fied Soer programs Maxwe, Mentor, ($50K or so) escribe geometry, get L,, etc (uniform cross-section) and 3 - aid M. Zar - 3/4/009

13 rosstak Wrapup Non-Linear terminations: Use Bergeron method (coered ater) Backward crosstak asts for round-trip propagation deay and ampitude is independent of couped ength (for t r < round-trip deay) Forward crosstak is proportiona to ength, zero for homogeneous dieectric, width equa to T r and ampitude inersey proportiona to T r. Typicay sma for moderate ength with inhomogeneous dieectric. Both forward and backward crosstak wi be refected from nonmatched terminations. Separate signas, pace signas cose to ground pane, use differentia signas, 3 - aid M. Zar - 3/4/009

14 Need to Mention Limits We hae not considered radiation or energy oss. When distance between conductor and return is sma with respect to rise/fa time our approximation is good. When rise/fa time becomes comparabe to signa-return spacing the system acts as antenna radiating energy. Our mode is no onger aid Loss of signa ampitude or energy EMI (eectromagnetic interference) which is frowned on by F and any one with radio or t receiers. Not usuay a probem of couping to digita signas, energy is too sma. More compicated probem than digita crosstak and not deat with in SE464. Howeer, keep atera dimensions and spacings sma! Eectromagnetic fieds and antennas 4 - aid M. Zar - 3/4/009