**Matlab _{¨} Code and Algorithms of Eric J.
Lundquist**

1 1D FDTD RLGC Simulations/Code/FDTD_Matching.m

Description: This code was developed in order to test a signal along a constant line. This was used to develop boundary conditions for the end load, which, if matched properly, could be used to minimize reflections.

Input/Variables: surrounding medium, cable type/impedance, RLGC values

Output/Results: movie plot of signal propagation, voltage values

1 1D FDTD RLGC Simulations/Code/FDTD_Filter.m

Description: The RLGC method is used to simulate signal
propagation through a low-pss filter. Measures were taken in order to program
the filter design as a traditional RLGC element. This was necessary in order to
combine the inductors and capacitors which are connected in series in both the
matching sections and the *m*-derived
section of the filter.

Input/Variables: surrounding medium, cable type/impedance, RLGC values, filter RLGC lumped elements at wire center

Output/Results: movie plot of signal propagation, voltage values

1 1D FDTD RLGC Simulations/Code/FDTD_Refl.m

Description: Reflections are measured by first running the code for a longer length of line, and the re-running the simulation for a shorter length and allowing the signal to reflect from the load. Thus, the original signal could be subtracted from the second signal in order to attain the reflected signal. The amplitude of the reflections could then be obtained.

Input/Variables: surrounding medium, cable type/impedance, RLGC values

Output/Results: movie plot of signal propagation, voltage values, reflection coefficient values

4 FDFD Validation of Microstrip and Parallel Wire Configuration/Code/FDFD_Microstrip.m

Description: FDFD method is validated by programming microstrip parameters. Because the parameters of a microstrip are analytically solvable, the numerical solutions to the simulations were compared with expected results.

Input/Variables: microstrip dimensions, dielectric values, surrounding medium, voltage

Output/Results: charge, capacitance, characteristic impedance

4 FDFD Validation of Microstrip and Parallel Wire Configuration/Code/Parallel.m

Description: FDFD method is used to simulate parallel wire pair. Because the parameters of a parallel pair are analytically solvable, the numerical solutions to the simulations were compared with expected results.

Input/Variables: radius of wires, distance between wires, surrounding medium, voltage

Output/Results: charge, capacitance, characteristic impedance

5 FDTD Circuit Design and Validation/Code/FDTD_Filter_Freq.m

Description: The FDTD RLGC method is used to simulate a low-pass filter design for a range of frequencies, and the frequency response is compared to that which is expected analytically.

Input/Variables: surrounding medium, cable type/impedance, RLGC values, filter RLGC lumped elements at wire center

Output/Results: movie plot of signal propagation, voltage values, filtered signal magnitude vs. frequency

5 FDTD Circuit Design and Validation/Code/FDTD_Attenuation.m

Description: Validation the line attenuation. Using parameters from both measured lines and lossless lines, attenuation vs. distance was measured in FDTD by storing the maximum amplitudes of the waves as they propagated along the line.

Input/Variables: cable type, RLGC values, surrounding medium

Output/Results: calculated and simulated reflection coefficients, attenuation constants

5 FDTD Circuit Design and Validation/Code/FDTD_FreqDomain.m

Description: FDTD method used for a range of frequencies to test frequency response of line.

Input/Variables: surrounding medium, cable type/impedance, RLGC values

Output/Results: movie plot of signal propagation, voltage values, signal magnitude vs. frequency

6 FDFD-FDTD Simulation of Connector Impedances and Damaged Shielded Wire Pairs/Code/Shield.m

Description: Shielded pair case was modeled and simulated. Wire pair is surrounded by grounded shield. However, in order to simulate effects of damage on the shield, portions of the shield are removed and results compared. Contour/quiver plots are also generated in order to visualize direction of fields.

Input/Variables: shield and wire pair parameters

Output/Results: charge, capacitance, characteristic impedance, plots of field contour and direction

7 Integration of FDFD with FDTD for Wiring and Connector Modeling/Code/Connector_Pins.m

Description: In order to obtain an understanding of the reflections and changes in signal propagation due to shielded (grounded shell) connectors and their pins, pin properties can be varied and overall connector characteristic impedances measured. A noticeable difference can be observed in the capacitance and characteristic impedance when pin materials are varied, being filled with air or plastic dielectric, instead of containing wires.

Input/Variables: pin configurations, pin materials, voltages, distance between pins, pin radii

Output/Results: charge, capacitance, characteristic impedance

7 Integration of FDFD with FDTD for Wiring and Connector Modeling/Code/Connector_Shell_Damaged.m

Description: In order to simulate the effects of connector shell damage, portions of the grounded shell can be removed, including corners, holes, and entire side plates.

Input/Variables: pin configurations, voltages, distance between pins, pin radii, shell size, shell damage

Output/Results: charge, capacitance, characteristic impedance

7 Integration of FDFD with FDTD for Wiring and Connector Modeling/Code/Shield_Patterns.m

Description: In order to more realistically visualize the fields
and leakage of a damaged shielded pair, the shield was brought into closer
proximity of the wire pair, the surrounding medium within the shield was filled
with dielectric, and directional (quiver) and contour plots were produced. This
code is for visualization purposes and does not produce accurate Z_{0}
or C values.

Input/Variables: shield and wire pair parameters

Output/Results: charge, capacitance, characteristic impedance, plots of field contour and direction

8 Simulation and Measurement of Connector Effects on Wire Systems/Code/FDTD_Connector_Freq.m

Description: In order to determine the frequency response which results from changes in characteristic impedance as the signal passes through a connector, FDTD code was used and the signal magnitude was calculated as it emerged from the connector into the second cable. It was found that, for sufficiently high frequencies, the magnitude was attenuated, and that frequency response was resonant.

Input/Variables: connector parameters

Output/Results: frequency response

8 Simulation and Measurement of Connector Effects on Wire Systems/Code/FDTD_Connector3.m

Description: In order to implement and simulate measured and simulated values of changes in characteristic impedance between different wires and connectors, an FDTD connector script was programmed with the following features:

á
Three regions (cable+connector+cable) can be programmed
at the beginning of the code, according to their Z_{0} value.

á The multiple reflections are tracked as they propagate from the connector toward the left. A plot is produced.

á A PEC reflection originating from the left boundary, which is intended to emulate reflections measured in the TDR.

á The movie frame rate is adjustable for faster visualization of signal propagation.

á A status bar indicates the simulation progress.

Input/Variables: three region impedance values

Output/Results: Output/Results: movie plot of signal propagation, voltage values

8 Simulation and Measurement of Connector Effects on Wire Systems/Code/reconnectortdr/ConnectorTDR.m

Description: Analysis of physical TDR measurements with 3 sections, cable + connector + cable. Additional data files are needed in order to run this code.

Input/Variables: TDR data

Output/Results: plots of reflection coefficients

11 Pulse Analysis Using Integrated Fourier Transform and FDTD Methods/Code/PulseFFT.m

Description: Uses the Fourier transform method for analysis of voltage pulse after transmitted through a line using FDTD. By combining these two methods, the reflection coefficient of the signal reflections passing through varying mediums or wires is determined and compared to analytic expectations.

Input: pulse parameters and data, characteristic impedances of three regions

Output: simulated reflection coefficients, analytic solution

Description: ABCD parameters analyze series connection of multiple wires with varying RLGC properties, along with analytic validation of simulation using plane wave calculations.

Input: characteristic impedances, wire lengths, RLGC parameters, sample frequency

Output: simulated (ABCD) and analytic (plane wave) reflectometry data

13 Integration of FDFD with ABCD Methods for Analysis of Damage to Shielded Twin Wires/Code/Shield.m

Description: FDFD code integrated with ABCD code in order to survey parameter changes and detectability of damage to shielded twin wire configurations—a wire type of

special interest for use in space and air craft, and susceptible to chafing damage.

Input: shield properties

Output: reflectometry data

14 Statistical Variation/Code/ABCD_PW_rand.m

14 Statistical Variation/Code/FDTD_Connector3_rand.m

14 Statistical Variation/Code/STP_rand.m

Description: Simulates effects of statistical variation integrated with ABCD and FDTD simulation code. The analytical solution for wire pairs was also used to estimate the effects of statistical variation on wire pairs and shielded twisted pairs (STP).

Input: wire lengths and properties, randomness threshold, dimensional tolerances

Output: reflectometry data and characteristic impedances

**Corresponding Write-ups**

1 1D FDTD RLGC Simulations/1D FDTD RLGC Simulations.pdf

5 FDTD Circuit Design and Validation/FDTD Circuit Design and Validation.pdf

**Code and Write-ups from Shang Wu**

Shang Wu/ABCD/ABCD Method Manual.doc

Description: ABCD_method.m simulates cascaded setup of transmission lines. By default, it also loads a 5-section open-ended measured result for comparison purposes. Most of the lines in the Matlab code are commented, so the user can easily modify them as needed.

Shang Wu/Signal Flow Diagram/Signal Flow Diagram.doc

Description: The signal flow graph has long been used in many different applications (i.e. Feedback Control Systems). It is a way of describing transitions with block diagrams. In fact, the transmission line is a perfect feedback system with the signal flow point of view. The following examples illustrate the usage of the signal flow graph.

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*Last updated Nov. 20, 2009*