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Example 38: TDR Analysis with Transient Analysis

General

The inputs of impulse wave and stepped wave are used for the TDR analysis.
Unless specified in the list below, the default conditions will be applied.

Electromagnetic-transient analysis is available in an optional package.

Analysis Condition

Item	Settings
Solver	Electromagnetic Analysis [Hertz]
Analysis Space	3D
Analysis Type	Transient Analysis Select Input at each port
Unit	mm

Tab	Setting Item	Settings
Mesh	General Mesh Size	0.5 [mm] *1
Mesh	Frequency-Dependent Meshing	Select [The conductor bodies thicker than the skin depth constitute the boundary condition]. Select Determine the reference frequency automatically from the input waveform
Transient Analysis	Input Waveform	Impulse Model Waveform Type: Impulse Pulse Width: 60.0×10-12 [s] Step Model *2 Waveform Type: Pulse Wave Rise Tme: 30.0×10-12 [s] Duration: 1.0×10-9 [s] Pulse Interval: 60.0×10-12 [s]
Transient Analysis	Finish Time of Calculation	1.0×10-9 [s]

*1 Small general mesh size is set because fine meshes are needed for the entire transmission line.

*2 To reproduce the stepped waveform in the Step model, the same time is set for the duration and the finish time of calculation.

Model

A coaxial cable consists of two insulators with different permittivity. For the outer boundary condition, electric wall is applied to the inside and outside of the cable.

The relative permittivity values for MAT1 and MAT2 are set so as to give them an impedance of about 50 [Ω] and 30 [Ω], respectively.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
Body10/Solid	MAT1	MAT1
Body11/Solid	MAT1	MAT1
Body12/Solid	MAT2	MAT2

Material Name	Tab	Properties
MAT1	Permittivity	Relative Permittivity: 1.0
MAT2	Permittivity	Relative Permittivity: 2.8

Boundary Condition

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
PORT1/Face	Electric	Port	Integral Path: Set Path1 Reference Impedance: select Select Specify 50 Ω
PORT2/Face	Electric	Port	Integral Path: Set Path1 Reference Impedance: select Select Specify 50 Ω
Outer Boundary Condition	Electric	Electric Wall

Results

The input/output voltage and TDR of the ports are confirmed in the result table of electromagnetic analysis (time domain).

Impulse model

The input voltage and the output voltage at PORT1 are as in the Fig. 1.

Fig. 1: The input and output voltage at PORT1

For the input of 1 [V], the reflection is -0.247 [V] at about 230[ps]. As the peak of the input wave is at 30[ps], it can be said that the input electromagnetic wave is reflected at the border of MAT1 and MAT2 where the impedances are unmatched.

The reflected wave take 200 [ps] to return.

These values can be estimated and verified in the following way.

The traveling distance until coming back to PORT1 after reflected at the unmatched portion is 60mm.
The propagation speed of the electromagnetic wave in MAT1 is 3.0 x 108 [m/s].
The time until the reflected wave returns to PORT1 is 60 mm / 30 x 10 8 [m/s] = 200 [ps].
Characteristic impedance of PORT1 and coaxial cable of MAT2 are about 50 [Ω] and 30[Ω], respectively.
The reflectance is (30 - 50) / (30 + 50) = -0.25. Therefore, the reflection of the input of 1V will be -0.25 V.

From TDR of the result table (Fig. 2), it is confirmed that the characteristic impedance of the coaxial cable of MAT2 is 30 [Ω].

Fig. 2: TDR of PORT1 (Impulse model)

Step model

The similar result is obtained with the step model. The stepped wave rises more rapidly than the impulse wave and its TDR changes faster than that of the impulse.

It can be confirmed as shown in Fig. 3.

Fig. 3: TDR of PORT1 (Step model)