Extension of the BLT Equation to Incorporate Electromagnetic Field Propagation

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USA This research was supported by the U.S. Department of Defense under MURI grant F4962-1-1-436 to University of Illinois at

1 Extension of the BLT Equation to Incorporate Electromagnetic Field Propagation Fredrick M. Tesche Chalmers M. Butler Holcombe Department of Electrical and Computer Engineering 336 Fluor Daniel EIB Clemson University, Clemson, SC USA This research was supported by the U.S. Department of Defense under MURI grant F to University of Illinois at Chicago and Clemson University University of Houston University of Illinois at Urbana-Champaign University of Michigan June 8, 22 CLEMSON UNIVERSITY

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3 Outline of Presentation Introduction Review of the Derivation of the BLT Equation Extension of the BLT Equation Summary Extension of the BLT Equation - Slide 2/17,EMSON L S I V E R S I T Y

of the BLT equation to take into account the following: -EM field propagation and coupling to the network -EM penetration through

4 Overview The BLT equation for analyzing transmission line networks permits a system-level analysis of the EM effects on large systems -This is the basis of the CRIPTE code, and its predecessor, QV7TA In this MURI effort, we wish to extend the formulation of the BLT equation to take into account the following: -EM field propagation and coupling to the network -EM penetration through apertures -EM scattering from nearby bodies (including cavities) Extension of the BLT Equation - Slide 3/17 EMSON L S I V E R S I T Y

Illustration of BLT Equation Extension We wish to

sequence diagram -To model aperture or diffusive

path Conventional BLT conducting interaction path

5 Illustration of BLT Equation Extension We wish to include non-conducting paths in the interaction sequence diagram -To model aperture or diffusive penetrations New, non-conductive BLT interaction path Conventional BLT conducting interaction path Extension of the BLT Equation - Slide 4/17 CLEMSON l s I h t I T V

6 Outline of Presentation Motivation Review of the BLTEquation Extension of the BLT Equation Summary Extension of the BLT Equation - Slide 5/17,EMSON L S I V E R S I T Y

The BLT Equation for a Single Line Network Consider a single transmission line "network" The

Transmission Line This is done b^ incident and n Linear Graph And including the excitation

$z Vi V1 Node #1 ref XX Excitation Forward traveling wave -w> V + (x) <^- \T(x) Backward$

7 The BLT Equation for a Single Line Network Consider a single transmission line "network" The BLT Equation provides the voltage or current responses at the ends (junctions) of the line Transmission Line This is done b^ incident and n Linear Graph And including the excitation of forward and backward traveling wave components on the line by the excitation sources. z Vi V1 Node #1 ref XX Excitation Forward traveling wave -w> V + (x) <^- \T(x) Backward traveling wave v 2 ref X) Node #2 Extension of the BLT Equation - Slide 6/17 CLEMSON L S I V I R S I T Y

$form as Z Load voltages at each end of the line 1 + A A \ + p 2 l Matrix involving load reflection coefficients i fi A$ Inverse matrix involving line propagation -i r- 5, i Excitation vector -where the excitation vector for the lumped

Inverse matrix involving line propagation -i r- 5, i Excitation vector -where the excitation vector for the lumped

8 The BLT Equation for the Load Voltages The BLT equation for the load voltage responses is written in a simple matrix form as Z Load voltages at each end of the line 1 + A A \ + p 2 l Matrix involving load reflection coefficients i fi A Inverse matrix involving line propagation -i r- 5, i Excitation vector -where the excitation vector for the lumped sources is given as S, ±(v 8 +z e i 8 y- -±(v s -z c i s y^s) Extension of the BLT Equation - Slide 7/17 CLEMSON L S I V I R S I T Y

The BLT Equation for Incident Field Excitation» The BLT equation for a lumped voltage source can be viewed as a Green 's function -The response is found by integrating over the line to incorporate

9 The BLT Equation for Incident Field Excitation» The BLT equation for a lumped voltage source can be viewed as a Green 's function -The response is found by integrating over the line to incorporate the tangential E-field excitation of the line..incjfc %- inc EL,() j± incident Field Excitation t d I <v < Distributed Voltage Sources inc 2 \ The same functional form of the BLT equation is valid for incident field (plane-wave) excitation: l + A l + A A J L A S, S^ Only a change in the source vector is necessary: E inc d ( e JkL(l-cosy/) _ A eßl -jkl(\+cosi//) "l)j = E inc Extension of the BLT Equation - Slide 8/17 F 2 {Y) Note the field coupling functions Fj and F 2 CLEMSON l s I h t I T V

10 Outline of Presentation Motivation Review of the Derivation of the BLT Equation Extension of the BLT Equation Summary Extension of the BLT Equation - Slide 9/17,EMSON L S I V E R S I T Y

Extension of the BLT Equation to Include EM Field Propagation Consider the

"conventional" BLT problem) -And EM field propagation from the source to the

Observation Point Induced line current Responses: E- fields and load voltages

11 Extension of the BLT Equation to Include EM Field Propagation Consider the following simple problem -Involving transmission line responses (the "conventional" BLT problem) -And EM field propagation from the source to the line Primary source Incident E-fields EM Field Source(s) Load #1 Field Observation Point Induced line current Responses: E- fields and load voltages Load #2 Transmission Line Extension of the BLT Equation - Slide 1/17,EMSON l S I V l R S 1 T V

"Regular" nodes where the incident and reflected waves are n coefficient.

Node 3 Node 2 ransmission line "tube" Node 4 Tubel i.

12 Extension of the BLT Equation (con't.) We define a signal flow granh including both the transmiss ing paths "Regular" nodes where the incident and reflected waves are n coefficient. Incident and reflected voltage waves at the transmission line ends < riofle Node 3 Node 2 ransmission line "tube" Node 4 Tubel i... Incident and reflected E- fields at the ends of the EM field propagation path Node 1 Extension of the BLT Equation -Slide 11/17 CLEMSON L S I V I R S I T Y

The Extended BLT Propagation Equation As in the case.

reflected matrix lized E-: tubes: Field coupling terms between the incident E- field on the line and the

and a 4, which are typical dimensions of the that both the coupling ai incident voltage nodes ition terms

13 The Extended BLT Propagation Equation As in the case.^f thp trqngmk^ion line BLT equation, we Transmission line can define a p propagation sub onship betweei and reflected matrix lized E-: tubes: Field coupling terms between the incident E- field on the line and the traveling voltage waves,ß( r o- r s) Note that the E-fields are normalized by suitable 4-vector of lengths a 3 and a 4, which are typical dimensions of the that both the coupling ai incident voltage nodes ition terms contain the sa waves on the "I ^rr^^rr^r^vna^ji^ nmctions Fj and F 2 a const tubes of reciprocity ith the source functions Extension of the BLT Equation - Slide 12/17 CLEMSON l s I h $ I T V

The Extended BLT Reflection Coefficient Matrix Similarly, we define an extended

transmission line: T/ref *A (n T/ref vo '1,2 Py a 3 h 23 a F ref / Ground plane

reflection at node 4, in the absence of the transmission line.

14 The Extended BLT Reflection Coefficient Matrix Similarly, we define an extended reflection coefficient matrix, which is similar to the 2x2 matrix for the simple transmission line: T/ref *A (n T/ref vo '1,2 Py a 3 h 23 a F ref / Ground plane (cavity wall) P3 re us p 4 (which = in this example) corresponds to E-field reflection at node 4, in the absence of the transmission line. The line has already been taken into account in the propagation and coupling matrix. Node 4 Tubel CLENISON l N I V E R S I T Y

The Extended Voltage BLT Equation The BLT reflection and propagation matrix equations can be combined just like the single transmission line

$rl o jk z -Ffoo) 2na A Z c \+p 3 1 + A "1 + A \ + p 2 -Pi A jk z 2n;a A Z -F 2( o ) ^e^ o -A etr fne^mmevpßl/r voltage equation 1 -<p 2 W F$

15 The Extended Voltage BLT Equation The BLT reflection and propagation matrix equations can be combined just like the single transmission line case to yield the extended BLT equation for the load voltages and normalized E-fields: v t 1,1 a 3 h 23 Cl^-L-i /T BLT voltage equation for a sing?rl o jk z -Ffoo) 2na A Z c \+p A "1 + A \ + p 2 -Pi A jk z 2n;a A Z -F 2( o ) ^e^ o -A etr fne^mmevpßl/r voltage equation 1 -<p 2 W F 2 ( ) a A a. J kr o A o re s,k)^ jk(r-rs) s 2 W r oe ß(r -n) Extension of the BLT Equation - Slide 14/17 CLEMSON l s I h $ I T V

16 Outline of Presentation Motivation Review of the Derivation of the BLT Equation Extension of the BLT Equation Summary Extension of the BLT Equation - Slide 15/17,EMSON L S I V E R S I T Y

Summary A modified BLT equation, taking into account EM field propagation paths in addition to the usual transmission line propagation mechanisms, has been developed.

17 Summary A modified BLT equation, taking into account EM field propagation paths in addition to the usual transmission line propagation mechanisms, has been developed. -This required modifying the BLT propagation matrix to include the field coupling to the transmission line and the EM scattering from the line. -These features have been illustrated with a very simple example. The next step in this development will be to include the more general case of EM shields with apertures, and multiple field paths, as shown in the next slide Extension of the BLT Equation - Slide 16/17 EMSON L S I V E R S I T Y

P&M Induced Load Responses Transmission line within a simple shielded region with an

Node 2 Interaction diagram, showing both field propagation and transmission line

18 Work Currently Underway... Excitation Region "outside" Shielded Region "inside" v^n Load #1 EM Field Source(s) 4> P&M Induced Load Responses Transmission line within a simple shielded region with an aperture -^J Load #2 EM Field Source Shield and Aperture Transmission Line Outside Inside Node 2 Interaction diagram, showing both field propagation and transmission line propagation paths Node 3 Source Tube 2 Tube 1 Node 4 Node 5 Tube 3 Tube 4 Node 6 Node 1../' Extension of the BLT Equation - Slide 17/17 Tube 5 CLEMSON l s I h t I T V

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