Signal Integrity and TDR Analysis of Adjacent Microstrip Lines

The signal integrity (SI) analysis gives an overview of the quality of an electrical signal transmitted through electrical circuits such as high-speed interconnects, cables, and printed circuit boards. The quality of the received signal can be distorted by noise from outside the circuit, and can be degraded by impedance mismatch, insertion loss, and crosstalk; in practice, EMC/EMI analyses are run to estimate the susceptibility of a device or a network to an undesired coupling. In this example model, we examine the crosstalk effect between two adjacent microstrip lines on a microwave substrate. The simulated results provide the time-domain reflectometry (TDR) response at the coupled ports and show increased distortion of a signal at higher data rates.

Figure 1: A microstrip line crosstalk model is composed of 20 mil microwave substrate with a ground plane and two adjacent microstrip lines 1.8 mm apart.

Model Definition

Two parallel 50 Ω microstrip lines are patterned on 20 mil substrate with a dielectric constant εr = 3.38. All metallic parts, including the patterned lines and bottom ground plane, are configured using perfect electric conductor (PEC) boundary conditions. The small rectangular surfaces, bridging between two parallel lines and the ground plane, are used to model lumped ports with which the microstrip lines are excited or terminated by 50 Ω. The air domain on top of the circuit board is defined using vacuum material properties. The exterior surfaces of the air are finished by a scattering boundary condition that is an absorbing boundary to describe an open space.

One bit of a single rectangular pulse is used to excite the circuit board. The widths of the two pulses are set to half of the 300 MHz and 600 MHz signals. The corresponding data rates for each frequency are 600 Mbit/s and 1.2 Gbit/s, respectively. A parametric sweep switches the frequency of the pulse during the simulation. It is necessary to apply smoothing to the transition zone of the pulse to remove undesirable high-frequency components from the signal.

The maximum simulation time is calculated using an approximated traveling time of a wave through a microstrip line based on the phase velocity. The effective dielectric constant for the phase velocity calculation is obtained using an equation in Ref. 1

(1)

where d is the thickness of the substrate and W is the width of the line.

It is assumed that a frequency about ten times greater than the input pulse signal frequency is enough to describe the highest frequency component in the smoothed rectangular pulse. The maximum mesh element size is set to 0.2 wavelengths in the dielectric substrate.

It is also important to define a time step that resolves the wave well in time as the mesh does in space. Any longer time steps would not optimally utilize the fine mesh, and any shorter time steps would unnecessarily lead to a longer simulation time without gaining significant accurate results. While running a simulation, the time step is continuously adjusted to meet the specified tolerances by the time-dependent solver. If there is an exact time step the solver needs to take, it can be manually set. In the Settings window of the Time-Dependent Solver node, the time step can be specified manually. See the step by step instructions to learn how to access this setting.

Results and Discussion

Figure 2 shows the input pulse signal as well as the voltage at lumped port 1 with a data rate of 600 Mbit/s (300 MHz) and 1.2 Gbit/s (600 MHz), respectively. Since the input signal is flowing through a straight 50 Ω line terminated with a 50 Ω resistor without discontinuity on the line, no distortion is evident on the port voltage.

Figure 2: The input pulse and the voltage at lumped port 1 (the excitation port) with a data rate of 600 Mbit/s and 1.2 Gbit/s.

Figure 3: The delayed input pulse and the voltage at lumped port 2 (the through port) with a data rate of 600 Mbit/s and 1.2 Gbit/s.

Figure 4: Voltage for the coupled signals at lumped ports 3 and 4. They are near-end crosstalk (NEXT) and far-end crosstalk (FEXT), respectively. The voltage of a coupled signal increases at a higher data rate.

Figure 5: The spectrum of input pulses up to 10 GHz. The signal strength decreases as frequency increases.

Figure 6: The impedance of lumped port 1 with data rates of 600 Mbit/s and 1.2 Gbit/s

Figure 3 shows the delayed input pulse and the received signals with two data rates at lumped port 2. The time domain response of the 1.2 Gbit/s signal is slightly distorted in the beginning when it reaches 1 V while that of the 600 Mbit/s signal seems to remain undistorted.

The crosstalk between two microstrip lines is observed in Figure 4. The coupled signal, near-end crosstalk (NEXT), level between two data rates is quite similar at lumped port 3, which is next to the excitation port. The time domain response at lumped port 4 next to the through port, far-end crosstalk (FEXT), shows that the higher data rate signal causes the stronger crosstalk on another signal path.

Figure 5 works as a reference to define the effective highest frequency component in the smoothed rectangular pulse since it provides the spectrum of results for 600 Mbit/s and 1.2 Gbit/s. A periodic rectangular pulse can be decomposed into a sum of sinusoidal functions. By estimating the level of a particular frequency, a proper frequency range can be defined for efficient simulations. The estimated highest frequency is used to choose the mesh size. With a finer mesh size, higher frequency components can be analyzed more accurately but it will increase the computation time. In this model, we set the maximum frequency component to 5 GHz that is two orders of magnitude smaller than the level of the DC component of each rectangular pulse.

In Figure 6, the TDR at lumped port 1 is presented in terms of impedance. The computed port impedance is around 50 Ω while the signal level is 1 V.

Notes About the COMSOL Implementation

Changing the number of output times in the node configures the output times for the results analysis but has a minimal effect on the time steps taken by the solver.

Reference

1. D.M. Pozar, Microwave Engineering, John Wiley & Sons, 1998.

RF_Module/EMI_EMC_Applications/microstrip_line_crosstalk

Modeling Instructions

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Global Definitions

Parameters 1

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Browse to the model’s Application Libraries folder and double-click the file microstrip_line_crosstalk_parameters.txt.

Geometry 1

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In the text field, type blength+0.5.

In the text field, type bwidth.

In the text field, type tsub*15.

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In the text field, type -bwidth/2.

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In the table, enter the following settings:


Layer name	Thickness (in)
Layer 1	0.25

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In the text field, type blength.

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In the text field, type rect1((t-Tb/8)/1[s]).

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Argument	Unit
t	s

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Locate the section. In the table, enter the following settings:


Argument	Lower limit	Upper limit	Unit
t	0	2*Tb	s

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Materials

Material 1 (mat1)

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In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	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

Material 2 (mat2)

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Select Domains 2 and 4–7 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	er_sub	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