Dk & Df ALGEBRAIC MODEL v2.04 (NOTE: only change from v2.03 is correction of Cu conductivity used in surface roughness [Hurray model] calculation)

Transcription

1 Joel Goergen Beth (Donnay) Kochuparambil Cisco Systems Inc. 5 January, 03 Dk & Df AGEBRAIC MODE v.04 (NOTE: only change from v.03 is correction of Cu conductivity used in surface roughness [Hurray model] calculation)

2 et s take a look WHAT YOU WI SEE

3 OOK & FEE NOTE: The Change Parameter window is a visual basic macro. If you save the file to your computer, be sure to select the Maco-Enabled file type. Quick preview of select frequencies Click to change the input parameters Fitted equation(s): Dk(f) = c*f + c*f + b See the connector. & channel loss at specific frequencies

4 OOK & FEE NOTE: The Change Parameter window is a visual basic macro. If you are having issues opening this window, consider Microsoft button > Excel Options > Trust Center > Trust Center Settings > Macro Settings You have 3 input options; Feel free to return and select a different option if you change your mind.

5 OOK & FEE Select your ) configuration Enter material ) & parameters Must have all entries 3) filled in, then click OK

6 OOK & FEE User input config. in comparison with 0-base-KR Max Attenuation & I Tab gives a graphical display.

7 Behind the Scenes EQUATIONS AND REFERENCES OF MODE

8 FREQUENCY DEPENDENCE 6 input frequency points for Dk and Df Fit Dk and Df to second order equations Coefficients shown on sheet Graphical representation shown on sheet Note that frequency dependence fit is only approximated to 0G, therefore, loss approximations should only be considered to 0G Z 0 is calculated with Dk (or ε r ) at a given frequency; a similar technique is used in loss calculations

9 DK & DF SECOND ORDER EQUATIONS Second order approximation is created using the INEST function. This function essentially fits a nd order polynomial to the 6 frequency points given; resulting in D k = c *f + c *f + b Function as implemented in the spreadsheet: INEST(C8:C3,B8:B3^[,]) Y Values (Dk entered points) X Values (Freq. associated w/ entered points) Exponents of X; Creating a second order equation. See Excel HEP for more details on INEST function. Methodology verified against add trend line within plot.

10 CHARACTERISTIC IMPEDANCE [, EQU 4-5] ohms c b t b w Z r f r ' t) - for w/(b ion goodapproximat infiniteplatebetween two infinitegroundplanes,but - * assumingsemi ' f/cm) capacitance ( fringing trace thickness (mil) trace width (mil) platespacing (mil) constant (at a given frequency) relative dielectric f r c t w b log log ' b t b t b t b t c e e r f

11 ATTENUATION IN OSSY INES Attenuation per length [, EQN 9-54] : n R G C C R G nepers/len gth Using a low-loss approximation [, EQN 9-55] : (surface roughness ignored) 0 n 0 db e for ease of R Z But we don t typically discuss in nepers [, EQN 9-57] n 0 G Z notation: 0 db nepers/length Y 0log ndb 0 e 0log 0 n e

12 CONDUCTOR OSS (per inch) cond Y ndb R Z 0 Y R Z cond ndb 0 attenuation of amplitude due to conductor loss, in db/length converstion from nepers to db resistance per length of conductor characteristic impedance Skin effect, ground resistance, and stripline effect are accounted for in resistance [3, EQNs 4.3a-4.0] : R - R of signal trace & return path (w/skin effect) f f signalcu skin effect RgroundCu skin effect 6H w [, EQN 9-59] - AC surface resistance for microstrip (or side of a stripline trace) R acmicrostrip R signal R ground

13 CONDUCTOR OSS (per inch) R - Stripline approximation assumes parallel resistance of top and bottom microstrip approximations f * w * f * w 6H 6H R striplinesurface resistance ( /inch) w width of trace (inch) H height dielectric from ground to signal (inch) -7 H permeability of Cu m resistivity of Cu m f frequency (hertz) Conductor loss per inch as entered in the model: cond 0log 0 e f * w 6H Z0

14 DIEECTRIC OSS (per inch) diel Yn dbg Z0 Y G Z cond ndb 0 attenuation of converstion from nepers to db shunt conductance per length from dielectric characteristic impedance As developed by Bogatin... G Z 0 tan( ) C cc r amplitude due to dielectric loss,in db/length Dielectric loss per inch as entered in the model: [, EQN 9-60] [, EQN 9-9,EQN 9-60] G equation [, EQN 9-67] Z0 equation is used to cancel the capacitance value, the Z0 value for a given frequency is NOT used c speed of light m/s converstion m in. is needed 0log e f diel 0 D f *39.37 r

15 k SURFACE ROUGHNESS (multiplier) Through the snowball method (Huray Model [4, CHAP 6] ), surface roughness is approximated as a collection of smaller spheres. *Note image shows non-uniform snowballs model approximates using uniform spheres. Applied to trace: Surface roughness multiplier as entered in the model: snowball 3 j i Ni 4a i Aflat ai ai total diel ksnowball cond(smooth) ai radius of spheres (m) Ni number of snowballs of size ai per Aflat Aflat total area containing stacked snowballs skin depth (m)... recall: f

16 CONNECTOR OSS & CHANNE OSS Attempting to base on 5G technology connectors Used connector models from multiple vendors to draw this max* connector loss used in model: I conn 6 9*0 * f.*0 * f.6*0 f * Max loss when ignoring majority of ID. Idea was to create equation that production connectors can beat. Note that this creates additional error in comparing model to measured, however, model should error in pessimistic direction. Connector implementation likely to be changed in future versions. Equation gives loss @4G A OVERA CHANNE OSS EQUATION: (simple enough, right?) total a CA_ total * CA Iconn abp _ total * BP Iconn CB _ total * CB

17 REFERENCES [] E. Bogatin. Signal Integrity Simplified. Pearson Education, Inc., 004. ISBN [] S. B. Cohn. Problems in Strop Transmission ines. IRE Trans. Microwave Theory and Techniques, Vol. MTT-3, March, 955, pp 9-6. [3] S. H. Hall, G.W.Hall, J. A. McCall. High-Speed Digital System Design: A Handbook of Interconnect Theory and Design Practices. John Wiley & Sons, Inc., 000. ISBN [4] P. G. Huray. The Foundations of Signal Integrity. John Wiley & Sons, Inc., 00. ISBN

18 TRACKING THE CHANGES Version Change.0 9/6/0 Initial release second order Dk & Df approximation, track user input channel along with Meg-6 & Improved FR-4 for given length/width/thickness, 3 materials compared to KR limit line..0 /5/0 surface resistance updated to include return path resistance and stripline approximation, Huray model for surface roughness added, worst-case connector added, partitioning option added (backplane w/ daughter cards), KR limit comparison made to attenuation max (instead of I).0 (a) /9/0 correction of error found in final multiplication/addition (A total ).03 //0 correction of error found in surface roughness multiplier (K snowball ) for line cards (matched equation given in the explanation slides), GUI clarified for Backplane w/ connectors, same material.