Notch Filter Using a Split Ring Resonator
Introduction
A split ring resonator (SRR) has a band-stop frequency respon. In this model, a printed SRR on a dielectric substrate is coupled to a microstrip line. The entire circuit behaves as a notch (band-stop) filter, which can be ud to block a specific signal frequency range.
Figure 1: A split ring resonator coupled to a microstrip line.
Model Definition
Using the resonance characteristics of a split ring resonator, either a band-pass or band-stop filter can be realized on a microstrip line type structure. The band-pass or band-stop frequency respon depends on the coupling configuration between a microstrip line and a split ring resonator.
Numeric TEM port
Numeric TEM port
Dielectric substrate (εr =3.38)
Split resonator
Microstrip line
Ground on the bottom side
In this model, to get a band-stop filter respon, the split part of the resonator is adjacent and coupled to the straight microstrip line (Figure 1). On a ground plane, the printed split ring resonator, on a 1.524 mm thick dielectric (εr = 3.38) substrate, has multiple resonant modes. Although not included in this model, the resonant modes can be identified using an eigenfrequency analysis. Among tho resonant modes, the frequency clo to 2.4 GHz is of interest. The split ring resonator’s frequency respon is studied when it is coupled to the microstrip line.
All metal parts are modeled as perfect electric conductors (PEC). Scattering boundary conditions are assigned on all exterior boundaries of the model domain, except for the ground plane. The remaining part is characterized as a vacuum domain.
On the surfaces of each end of the microstrip line, including the air domain, a numeric port is added that calculates the electric mode field on the given structure, with an effective dielectric constant εr =
sqrt(3.38). This is done through a Boundary Mode analysis. In the numeric port tting, “Analyzed as a TEM field” is lected. To compute the voltage and current of the port, this tting requires defined electric and magnetic field integration lines, respectively. The port characteristic impedance is calculated using the voltage and current extracted from the integration lines. The port mode field is scaled by the ratio of the calculated impedance and the reference impedance, defined in the ttings window. The electric fields are guided between two conductors and the field component in the direction of propagation, the normal to the port boundary is negligible. Thus, it is reasonable to analyze the port mode as transver electromagnetic (TEM) field.
Results and Discussion
The default electric field norm on the xy-plane is plotted in Figure 2. The electric fields are confined symmetrically along the split ring resonator at 2.4 GHz. Figure 3 shows the frequency respon of the device. Around 2.4 GHz, its S11 is almost 0 dB, while its S21 is below −10 dB, so it behaves as band-stop (notch) filter.
Figure 3: The S-parameter plot showing a band-stop frequency respon.
咸丰皇帝Notes About the COMSOL Implementation
To learn more about how to define integration lines for calculating the voltage and the current of the numeric TEM port, review the following examples in the Model Library.
RF Module/Verification Models/coaxial_cable_impedance
RF Module/Verification Models/parallel_wires_impedance
Model Library path: RF_Module/Passive_Devices/notch_filter_srr
Modeling Instructions
烧烤From the File menu, choo New.
N E W
1In the New window, click Model Wizard.
M O D E L W I Z A R D
1In the Model Wizard window, click 3D.
2In the Select physics tree, lect Radio Frequency>Electromagnetic Waves, Frequency Domain (emw).
3Click Add.
4Click Done.
D E F I N I T I O N S
Parameters
1On the Model toolbar, click Parameters.
2In the Settings window for Parameters, locate the Parameters ction.
3In the table, enter the following ttings:
Name Expression Value Description
f0 2.4[GHz] 2.4000E9 Hz Frequency
lda0c_const/f00.12491 m Wavelength, free space
G E O M E T R Y1
1In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2In the Settings window for Geometry, locate the Units ction.
3From the Length unit list, choo mm.藕与莼菜
Plane Geometry
On the Geometry toolbar, click Work Plane.
Rectangle 1 (r1)
仙字成语1On the Work plane toolbar, click Primitives and choo Rectangle.
2In the Settings window for Rectangle, locate the Size ction.
3In the Width text field, type 60.
4In the Height text field, type 3.2.
5Locate the Position ction. From the Ba list, choo Center.
6In the yw text field, type 18.
Rectangle 2 (r2)
1On the Work plane toolbar, click Primitives and choo Rectangle. 2In the Settings window for Rectangle, locate the Size ction.
3In the Width text field, type 60.
4In the Height text field, type 70.
5Locate the Position ction. From the Ba list, choo Center.
6Click the Build Selected button.
7Click the Zoom Extents button on the Graphics toolbar.
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Rectangle 3 (r3)
1On the Work plane toolbar, click Primitives and choo Rectangle. 2In the Settings window for Rectangle, locate the Size ction.
3In the Width text field, type 32.
什么名字好听男生怪石嶙峋的意思4In the Height text field, type 32.
5Locate the Position ction. In the xw text field, type -16.
6In the yw text field, type -15.7.
Rectangle 4 (r4)
1On the Work plane toolbar, click Primitives and choo Rectangle. 2In the Settings window for Rectangle, locate the Size ction.
3In the Width text field, type 26.
4In the Height text field, type 26.
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