Study of a Defective Microstrip Line via Frequency-to-Time FFT Analysis

While transient analyses are useful for time domain reflectometry (TDR) to handle signal integrity (SI) problems, many RF and microwave examples are addressed using frequency domain simulations generating S-parameters. However, from the frequency domain data it is difficult to identify sources for this signal degradation.

This example simulates a microstrip line in frequency domain with a couple of line width discontinuities and performs frequency-to-time fast Fourier transform. The computed results help to identify the physical discontinuities and impedance mismatches on the transmission line, by analyzing the signal fluctuation in the time domain.

Figure 1: Microstrip line circuit board model using lumped ports. The surrounding air domain is not included for visualization purposes.

Model Definition

The model describes a 50 Ω microstrip line on a 60 mil substrate with the dielectric constant of εr = 3.38. A wider strip is placed in the middle of the microstrip line to represent a lower impedance line causing unwanted reflections. All metallic parts, including the patterned line on the top of the substrate and bottom ground plane, are set to perfect electric conductor (PEC) by ignoring the loss from a finite conductivity to simplify the modeling process. The small rectangular surfaces, bridging between each microstrip end and the ground plane, are used to add lumped ports. The lumped ports excite the microstrip line and terminate it with 50 Ω characteristic impedance. The material on top of the circuit board is air. The exterior surfaces of the air are finished by a scattering boundary condition that is an absorbing boundary to describe an open radiating space.

The study consists of two steps:

•

Frequency Domain

•

Frequency-to-Time FFT

The time domain results may vary with the input arguments in each study step.

Table 1: impact of the study step input arguments.
Study Step	Argument	Impact on Transformed time domain result
Frequency Domain	Start frequency	Low frequency envelope noise
	Stop frequency	Resolution and high frequency ripple noise
	Frequency step	Alias period
Frequency-to-Time FFT	Stop time	Alias visibility

The frequency step, Δf, is set to make the period of alias in the time domain response greater than the round trip travel time from the excitation, lumped port 1, to the line termination, lumped port 2:

1/Df = 1 ns > 65 mm/c_const*sqrt(3.38)*2 = 0.7.9723 ns

where 65 mm is the circuit board length and c_const is a predefined COMSOL constant for the speed of light in vacuum.

While performing FFT, a Gaussian window function is used. This helps to suppress the noise coming from the limited range of the frequency sweep. Each study step uses “Store fields in output” that defines the selections where the computed results are stored. By choosing only the lumped port boundaries for Store fields in output settings, it is possible to reduce the size of the model file a lot.

Results and Discussion

Figure 2 shows the electric field norm on the lumped port boundaries in the time domain. The boundaries include the solutions transformed from the frequency-domain data. Since the FFT only transforms the dependent variable, the electric field E, to the time domain, it is only possible to use postprocessing variables directly related to E in the time domain. The frequency domain response is still accessible through Solution Store 1 dataset.

Figure 2: Time domain field on the lumped port boundaries.

Figure 3: Time domain lumped port voltage. The overshoot and undershoot of the signal indicate the discontinuities of the microstrip line.

In Figure 3, the time domain results of the voltage bandpass impulse response at lumped port 1 is plotted. The voltage fluctuation times correspond to the propagation times for the incident pulse to be reflected from the two line discontinuities-the defective parts of the 50 Ω microstrip line. The round trip travel time from lumped port 1 to each discontinuity is described in Table 2 below. The estimated time agrees with the voltage fluctuation location in Figure 3.

Table 2: Round trip travel time from lumped port 1 to discontinuity.
Discontinuity	Expression	Time
Wider microstrip line start	31.5 mm/c_constsqrt(3.38)2	0.3864 ns
Wider microstrip line end	42.5 mm/c_constsqrt(3.38)2	0.5213 ns
Line termination	65 mm/c_constsqrt(3.38)2	0.7972 ns

The alias of the FFT is observed at 1 ns that is the inverse of the frequency step used in the frequency domain study step.

Notes About the COMSOL Implementation

The frequency-to-time fast Fourier transform (FFT) study step transforms the solution of dependent variables in frequency domain to time domain with a very small time step, ten samples per period, defined by the highest frequency in this model. Only the postprocessing variables that can be expressed with the dependent variables are valid for result analysis. Since the transformed solutions typically contain many time steps, it is recommended to use the option to reduce the size of the model.

RF_Module/EMI_EMC_Applications/microstrip_line_discontinuity

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
f0	15[GHz]	1.5E10 Hz	Center frequency
df	f0/15	1E9 Hz	Frequency resolution

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type range(0.001[GHz],df,2*f0).

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 20.

In the text field, type 65.

In the text field, type 1.524.

Locate the section. From the list, choose .

Create a block for the microstrip line trace and two lumped port boundaries.

Block 2 (blk2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 3.3.

In the text field, type 65.

In the text field, type 1.524.

Locate the section. From the list, choose .

Block 3 (blk3)

In the toolbar, click

In the window for , locate the section.

In the text field, type 30.

In the text field, type 70.

In the text field, type 10.

Locate the section. In the text field, type (10-1.524)/2.

From the list, choose .

Click

Click the

button in the toolbar.

Work Plane 1 (wp1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

On the object , select Boundary 4 only.

It might be easier to select the correct boundary by using the window. To open this window, in the toolbar click and choose . (If you are running the cross-platform desktop, you find in the main menu.)

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Work Plane 1 (wp1)>Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 6.

In the text field, type 11.

Locate the section. In the text field, type -3.

In the text field, type -10.

In the window, right-click and choose .

Electromagnetic Waves, Frequency Domain (emw)

Lumped Port 1

In the window, under right-click and choose .

Select Boundary 13 only.

In the window for , locate the section.

Click

In the dialog box, click .

Lumped Port 2

In the toolbar, click

and choose .

Select Boundary 18 only.

In the window for , locate the section.

Click

The added selection will be used to define where to store the results. The model evaluates only the lumped port voltage in time and frequency domain.

In the dialog box, click .

Perfect Electric Conductor 2

In the toolbar, click

and choose .

Select Boundaries 11, 15–17, and 23 only.

Scattering Boundary Condition 1

In the toolbar, click

and choose .

Select Boundaries 1, 2, 4, 5, and 26 only.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Material 2 (mat2)

In the window, under right-click and choose .

Select Domains 2–4 only.

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	3.38	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic

Mesh 1

In the window, under right-click and choose .

Click the

button in the toolbar.

Select Boundary 4 only.

Select Boundary 1 only.

Select Boundary 2 only.

Study 1

Step 1: Frequency Domain

The period of a ripple noise and alias after FFT are defined by the inverse of the maximum frequency and frequency step, respectively.

In the window, under click .

In the window for , click to expand the section.

Find the subsection. From the list, choose .

Under , click

In the dialog box, in the list, choose and .

Click .

By choosing only the port boundaries for settings, it is possible to reduce the size of a model file a lot. The lumped port boundaries are included for the voltage evaluation.

Frequency to Time FFT

In the toolbar, click