Difference between revisions of "RF Tutorial Lesson 7: Designing Distributed Bandpass Filters Using Coupled Transmission Line Segments"
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− | Run a Network Analysis Test of your circuit with start and stop sweep frequencies set to 1GHz and 3GHz, respectively, and a linear frequency step size of 1GHz. Check only the "Table" checkbox and uncheck the "Graph" checkbox. In the "Output" tab of Network Analysis Test Panel, choose "Z" [[Parameters]] options with "Real/Imag" format. Make sure to uncheck the "Decibels" checkbox. The simulated Z-parameter results are compared to their analytical values in the table below: | + | Run a Network Analysis Test of your circuit with start and stop sweep frequencies set to 1GHz and 3GHz, respectively, and a linear frequency step size of 1GHz. Check only the "Table" checkbox and uncheck the "Graph" checkbox. In the "Output" tab of Network Analysis Test Panel, choose "Z" [[Parameters]] options with "Real/Imag" format. Make sure to uncheck the "Decibels" checkbox. |
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+ | | valign="top"| | ||
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+ | ! scope="row"| Start Frequency | ||
+ | | 1G | ||
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+ | ! scope="row"| Stop Frequency | ||
+ | | 3G | ||
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+ | ! scope="row"| Steps/Interval | ||
+ | | 1G | ||
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+ | ! scope="row"| Interval Type | ||
+ | | Linear | ||
+ | |- | ||
+ | ! scope="row"| Parameter Set | ||
+ | | Z | ||
+ | |- | ||
+ | ! scope="row"| Graph Type | ||
+ | | Cartesian (Amplitude Only) with Decibels | ||
+ | |} | ||
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+ | The simulated Z-parameter results are compared to their analytical values in the table below: | ||
Revision as of 22:09, 24 September 2015
Contents
What You Will Learn
In this tutorial first you will cascade several sections of generic coupled T-Lines to design a distributed bandpas filter. Then, you will realize a microstrip version of your distributed filter.
Examining the Filter Building Block
A two-port network can be formed by terminating two of the four ports of a Generic Coupled T-Lines device in either short or open circuits. Several configurations are possible. You can then build narrowband bandpass filters by cascading several of such terminated coupled transmission line segments. For this project, you will open-circuit Ports 2 and 3 of the Generic Coupled T-Lines device and will use Port 1 and Port 4 as the input and output ports of the resulting two-port network, respectively. This is shown in the figure below:
In this case, the 4×4 Z matrix is reduced to a 2×2 matrix with the following elements:
[math]Z_{11} = Z_{22} = -\frac{j}{2} \left( Z_{0e} + Z_{0o} \right) cot \left( \frac{2\pi f}{c} L \sqrt{\epsilon_{eff}} \right) [/math]
[math]Z_{21} = Z_{12} = -\frac{j}{2} \left( Z_{0e} - Z_{0o} \right) csc \left( \frac{2\pi f}{c} L \sqrt{\epsilon_{eff}} \right) [/math]
The following is a list of parts needed for this part of the tutorial lesson:
Part Name | Part Type | Part Value |
---|---|---|
VS1 - VS2 | AC Voltage Source | 1V |
X1 | Generic Coupled T-Lines | Z0e = 70, Z0o = 30, len = 37.5 |
IN | Net Marker | N/A |
OUT | Net Marker | N/A |
Build a new circuit using a Generic Coupled T-Lines device with Z0e = 70Ω, Z0o =30Ω and len = 37.5mm. Use two Net Markers to designate the input and output ports.
Run a Network Analysis Test of your circuit with start and stop sweep frequencies set to 1GHz and 3GHz, respectively, and a linear frequency step size of 1GHz. Check only the "Table" checkbox and uncheck the "Graph" checkbox. In the "Output" tab of Network Analysis Test Panel, choose "Z" Parameters options with "Real/Imag" format. Make sure to uncheck the "Decibels" checkbox.
Start Frequency | 1G |
---|---|
Stop Frequency | 3G |
Steps/Interval | 1G |
Interval Type | Linear |
Parameter Set | Z |
Graph Type | Cartesian (Amplitude Only) with Decibels |
The simulated Z-parameter results are compared to their analytical values in the table below:
f | βL | Analytical Z11 [Ω] | Simulated Z11 [Ω] | Analytical Z21 [Ω] | Simulated Z21 [Ω] |
---|---|---|---|---|---|
1GHz | π/4 | -j50 | 0.009 - j50 | -j28.284 | 0.003 - j28.284 |
2GHz | π/2 | 0.003 | 0 | -j20 | - j20 |
3GHz | 3π/4 | j50 | 0.009 + j50 | -j28.284 | -0.003 - j28.284 |
Before closing this section, run another Network Analysis Test of your circuit with the same port assignments. But this time you will calculate the S-parameters over a wider frequency range from 500MHz to 3.5GHz with a linear frequency step size of 10MHz. Choose the "S" Parameters option with Amplitude-Only Cartesian graph type. Check the "Decibels" checkbox once again. The insertion loss (|s21|) and return loss (|s11|) results are shown in the figure below:
Designing a Coupled Line Bandpass Filter
In this part of the tutorial lesson you will cascade four quarter-wavelength Generic Coupled T-Line segments to build a distributed bandpass filter as shown in the opposite figure. Port 1 of the first segment and Port 4 of the last segment are designated as the input and output ports. Port 4 of each segment is fed into Port 1 of the next segment. Ports 2 and 3 of all coupled line devices are left open-circuited. Proper grounding is done for all the negative pins.
The following table gives the parameters of each segment:
Coupled Line Segment | Z0e | Z0o | eeff | len |
---|---|---|---|---|
L1 | 70.61Ω | 39.24Ω | 1 | 37.5mm |
L2 | 56.64Ω | 44.77Ω | 1 | 37.5mm |
L3 | 56.64Ω | 44.77Ω | 1 | 37.5mm |
L4 | 70.61Ω | 39.24Ω | 1 | 37.5mm |
All the segment lengths are chose to be len = 37.5mm, which is a quarter wavelength at the center frequency of the filter fo = 2GHz. TEM transmission lines with εeff = 1 are assumed. The impedances have been chosen to achieve an equal-ripple bandpass filter design.
Run a network analysis of this two-port circuit. Set the start and stop frequency of the sweep to 1GHz and 3GHz, respectively, with a linear step of 10MHz. Generate an amplitude-only, Cartesian graph of the S-parameters. The figure below shows the graph of s11- and s21 parameters. Note that a linear scale is used for frequency. The filter has a center frequency of fo = 2GHz with a 3dB bandwidth of about 235MHz. The response drops to -45dB at 1.5GHz and 2.5GHz.
Realizing a Microstrip Version of the Coupled Line Bandpass Filter
In the last part of this tutorial lesson, you will design and test a microstrip realization of the coupled line bandpass filter you simulated in the previous part. For this purpose, you will use a substrate of thickness h = 1.6mm with εeff = 3.4. You will assume a lossless substrate (tand = 0). Remember that in the previous section, TEM line segments with εeff = 1 were assumed and the length of the coupled line segments were set to be a quarter free-space wavelength at 2GHz. For this part, first you need to design couple microstrip lines with the given even and odd mode impedances. Then, you have to calculate the guide wavelengths of the couple microstrips at 2GHz. You will do these using RF.Spice's Device Editor.
Open the "Coupled Microstrips Designer" dialog from the RF Menu of Device Editor. Enter the substrate parameters: h = 1.6mm and er = 3.4. Enter the Z0e and Z0o values for the two types of coupled line segments from the previous section and calculate width and spacing of the coupled microstrip lines for each case. Then, open the "Coupled Microstrips Calculator" dialog from the RF Menu of Device Editor. Enter the calculated microstrip width and spacing values to verify your design and also find the corresponding guide wavelengths λg at 2GHz. The lengths of the coupled microstrip segments are chosen to be a quarter of the corresponding guide wavelength at 2GHz. The following table summarizes the parameters of the coupled microstrip segments L1, L2, L3 and L4.
Coupled Microstrip Segment | Z0e | Z0o | w | s | Average εeff | λg at 2GHz | len |
---|---|---|---|---|---|---|---|
L1 | 70.61Ω | 39.24Ω | 2.96mm | 0.4mm | 2.57 | 93.52mm | 23.38mm |
L2 | 56.64Ω | 44.77Ω | 3.6mm | 1.68mm | 2.66 | 91.97mm | 23mm |
L3 | 56.64Ω | 44.77Ω | 3.6mm | 1.68mm | 2.66 | 91.97mm | 23mm |
L4 | 70.61Ω | 39.24Ω | 2.96mm | 0.4mm | 2.57 | 93.52mm | 23.38mm |
Build your microstrip circuit using four "Coupled Mirostrips" parts with the parameters specified in the above table. Connect them in a cascade fashion as shown in the opposite figure. Run a network analysis of this two-port circuit. Set the start and stop frequency of the sweep to 1GHz and 3GHz, respectively, with a linear step of 10MHz. Generate an amplitude-only, Cartesian graph of the S-parameters. The graphs of s11- and s21 parameters are shown in the figure below and agree perfectly with the results of the previous section.