Difference between revisions of "RF Tutorial Lesson 5: Designing Lumped and Distributed Microstrip Lowpass Filters"

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{{projectinfo|Tutorial| Designing Lumped and Distributed Microstrip Lowpass Filters |RF57.png|In this project, the basic concepts of RF.Spice A/D are demonstrated, and a simple voltage divider is modeled and examined.|
+
{{projectinfo|Tutorial| Designing Lumped and Distributed Microstrip Lowpass Filters |RF57.png|In this project, you will use a classic lumped LC filter design to realize an equivalent distributed microstrip filter.|
  
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*Physical Transmission Line
+
*Lumped Element Filter
 +
*Distributed Filter
 
*Microstrip Line
 
*Microstrip Line
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*Device Manager
 
−
*Line Designer
 
−
*Line Calculator
 
 
*Microstrip Discontinuity
 
*Microstrip Discontinuity
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|All versions|{{download|http://www.emagtech.com/content/project-file-download-repository|RF Tutorial Lesson 5|[[RF.Spice A/D]] R15}} }}
+
*Network Analysis
 +
|All versions|{{download|http://www.emagtech.com/downloads/ProjectRepo/RFLesson5.zip RF Lesson 5}} }}
  
−
=== What You Will Learn ===
+
== What You Will Learn ==
  
 
In this tutorial you will build and analyze a stepped-impedance microstrip lowpass filter based on a standard lumped LC filter design.   
 
In this tutorial you will build and analyze a stepped-impedance microstrip lowpass filter based on a standard lumped LC filter design.   
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<tr>
 
<tr>
 
<td>
 
<td>
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[[File:RF52.png|thumb|540px|A lumped LC lowpass filter.]]
+
[[File:RF52.png|thumb|left|640px|A lumped LC lowpass filter.]]
 
</td>
 
</td>
 
</tr>
 
</tr>
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|}
 
|}
  
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The figure below shows the graph of S11- and S21 [[parameters]]. Note that a linear scale is used for frequency. The vertical axis is limited to -30dB and 0. Also note that the S21 response drops by 3dB at the cutoff frequency f<sub>o</sub> = 2GHz.  
+
The figure below shows the graph of S11- and S21-parameters. Note that a linear scale is used for frequency. The vertical axis is limited to -30dB and 0. Also note that the S21 response drops by 3dB at the cutoff frequency f<sub>o</sub> = 2GHz.  
  
 
<table>
 
<table>
 
<tr>
 
<tr>
 
<td>
 
<td>
−
[[File:RF53.png|thumb|720px|Graph of S11 and S21 parameters of the ladder LC filter over the frequency range 500MHz-3GHz.]]
+
[[File:RF53.png|thumb|left|720px|Graph of S11 and S21 parameters of the ladder LC filter over the frequency range 500MHz-3GHz.]]
 
</td>
 
</td>
 
</tr>
 
</tr>
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== Designing a Stepped Impedance Microstrip Lowpass Filter ==
 
== Designing a Stepped Impedance Microstrip Lowpass Filter ==
  
−
A distributed microstrip version of the above ladder LC filter can be realized using consecutive low- and high-impedance line segments. It is well known that short segments of low- and high-impedance [[Transmission Lines|transmission lines]] behave like capacitive and inductive elements, respectively. Therefore, you will need four low-Z0 microstrip segments to replace the capacitors C1, C2, C3 and C4, and three high-Z0 microstrip segments to replace the inductors L1, L2 and L3. The transformations are based on the following equations:   
+
A distributed microstrip version of the above ladder LC filter can be realized using consecutive low- and high-impedance line segments. It is well known that short segments of low- and high-impedance transmission lines behave like capacitive and inductive elements, respectively. Therefore, you will need four low-Z0 microstrip segments to replace the capacitors C1, C2, C3 and C4, and three high-Z0 microstrip segments to replace the inductors L1, L2 and L3. The transformations are based on the following equations:   
  
−
<math> \beta l = \frac{ L R_0} {Z_{high}} </math>
+
<math> \beta l = \frac{ \bar{L} R_0} {Z_{high}} </math>
  
 
for inductors and  
 
for inductors and  
  
−
<math> \beta l = \frac{ C Z_{low}} {Z_{R_0}} </math>
+
<math> \beta l = \frac{ \bar{C} Z_{low}} {R_0} </math>
  
 
for capacitors. Here Z<sub>high</sub> and Z<sub>low</sub> are the high and low characteristic impedances of the narrow and wide microstrip segments, respectively, and R<sub>0</sub> is the reference impedance of the filter.   
 
for capacitors. Here Z<sub>high</sub> and Z<sub>low</sub> are the high and low characteristic impedances of the narrow and wide microstrip segments, respectively, and R<sub>0</sub> is the reference impedance of the filter.   
  
−
[[File:RF54.png|thumb|600px|The schematic of a Stepped Impedance Microstrip Lowpass filter.]]
+
<table>
 +
<tr>
 +
<td>
 +
[[File:RF58.png|thumb|left|640px|The top view of layout of the Stepped Impedance Mirostrip Lowpass filter.]]
 +
</td>
 +
</tr>
 +
</table>
  
 
For this project, you will use 0.5mm-wide and 5mm-wide microstrip lines to realize Z<sub>high</sub> and Z<sub>low</sub>, respectively. As you found earlier, these lines provide approximately 102&Omega; and 30&Omega; impedances, respectively. Using the above transformations, the following table for the segment lengths is obtained:
 
For this project, you will use 0.5mm-wide and 5mm-wide microstrip lines to realize Z<sub>high</sub> and Z<sub>low</sub>, respectively. As you found earlier, these lines provide approximately 102&Omega; and 30&Omega; impedances, respectively. Using the above transformations, the following table for the segment lengths is obtained:
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! Line Segment !! w !! len !! Z<sub>0</sub>   
 
! Line Segment !! w !! len !! Z<sub>0</sub>   
 
|-
 
|-
−
| l1 || 3.3mm || 5mm || 29&Omega;  
+
| len1 || 3.3mm || 5mm || 29&Omega;  
 
|-
 
|-
−
| l2 || 8.4mm || 0.5mm || 102&Omega;  
+
| len2 || 8.4mm || 0.5mm || 102&Omega;  
 
|-
 
|-
−
| l3 || 13.4mm || 5mm || 29&Omega;  
+
| len3 || 13.4mm || 5mm || 29&Omega;  
 
|-
 
|-
−
| l4 || 13.5mm || 0.5mm || 102&Omega;  
+
| len4 || 13.5mm || 0.5mm || 102&Omega;  
 
|-
 
|-
−
| l5 || 13.4mm || 5mm || 29&Omega;  
+
| len5 || 13.4mm || 5mm || 29&Omega;  
 
|-
 
|-
−
| l6 || 8.4mm || 0.5mm || 102&Omega;  
+
| len6 || 8.4mm || 0.5mm || 102&Omega;  
 
|-
 
|-
−
| l7 || 3.3mm || 5mm || 29&Omega;  
+
| len7 || 3.3mm || 5mm || 29&Omega;  
 
|-
 
|-
 
|}
 
|}
 +
 +
Place and connect the above parts and mark the input and output of your circuit with two markers IN and OUT as shown in the figure below. Note how the negative pin (P1- and P2-) of all the parts have been grounded.
  
 
<table>
 
<table>
 
<tr>
 
<tr>
 
<td>
 
<td>
−
[[File:RF58.png|thumb|600px|The top view of layout of the Stepped Impedance Mirostrip Lowpass filter.]]
+
[[File:RF54.png|thumb|left|640px|The schematic of a Stepped Impedance Microstrip Lowpass filter.]]
 
</td>
 
</td>
 
</tr>
 
</tr>
 
</table>
 
</table>
  
−
Place and connect the above parts and mark the input and output of your circuit with two markers IN and OUT as shown in the above figure. Note how the negative pin (P1- and P2-) of all the parts have been grounded. Run a network analysis of your distributed filter circuit. Set the start and stop frequency of the sweep to 500MHz and 3GHz, respectively, with a linear step of 10MHz. Similar to the previous parts, generate a Cartesian, amplitude-only, graph of the S-[[parameters]]. The figure below shows the graph of s11- and s21 [[parameters]]. The horizontal and vertical axis scales have been set to match those of the lumped LC filter case for comparison. 
+
Run a network analysis of your distributed filter circuit with the following parameters:
  
 
{| border="0"
 
{| border="0"
 
|-
 
|-
−
| valign="bottom"|
+
| valign="top"|
−
[[File:RF55.png|thumb|800px|left|Graph of s11 and s21 parameters of the stepped-impedance microstrip filter over the frequency range 500MHz-3GHz.]]
+
 
|-
 
|-
 +
{| class="wikitable"
 +
|-
 +
! scope="row"| Start Frequency
 +
| 500Meg
 +
|-
 +
! scope="row"| Stop Frequency
 +
| 3G
 +
|-
 +
! scope="row"| Steps/Interval
 +
| 10Meg
 +
|-
 +
! scope="row"| Interval Type
 +
| Linear
 +
|-
 +
! scope="row"| Parameter Set
 +
| S
 +
|-
 +
! scope="row"| Graph Type
 +
| Cartesian (Amplitude Only) with Decibels
 
|}
 
|}
  
 +
The figure below shows the graph of S11 and S21 parameters. The horizontal and vertical axis scales have been set to match those of the lumped LC filter case for comparison. 
 +
 +
<table>
 +
<tr>
 +
<td>
 +
[[File:RF55.png|thumb|720px|left|Graph of S11 and S21 parameters of the stepped-impedance microstrip filter over the frequency range 500MHz-3GHz.]]
 +
</td>
 +
</tr>
 +
</table>
  
 
== Adding the Microstrip Step Discontinuity Models ==
 
== Adding the Microstrip Step Discontinuity Models ==
  
−
In the above analysis, you assumed that the high-Z0 and low-Z0 sections are directly connected to each other. Your circuit configuration ignored the effect of the step discontinuities between the segment junctions. Next, you will include the discontinuity models in your circuit similar to what you did in the previous part of this tutorial lesson. However, this time you need three 5mm-to-0.5mm and two 0.5mm-to-5mm "Microstrip Step" parts. Remember again that in [[RF.Spice]]'s microstrip model, w1 > w2. Therefore, you need to build the 0.5mm-to-5mm step by flipping the 5mm-to-0.5mm step horizontally. Similar to the microstrip line segment devices, you need to ground all the microstrip step devices, too. Forgetting to ground the RF parts properly may result in simulation failures. Run an AC Sweep Test of your new enhanced RF circuit and compare the results with the previous case. From the figures you can see that including the discontinuity models increase the slope of the roll-off part of the filter response. The previous circuit showed insertion loss values of -5dB and -17.5dB at 2GHz and 3GHz, respectively. After the inclusion of the five step discontinuity models, the new insertion loss values are -7dB and almost -20dB at 2GHz and 3GHz, respectively.     
+
In the above analysis, you assumed that the high-Z0 and low-Z0 sections are directly connected to each other. Your circuit configuration ignored the effect of the step discontinuities between the segment junctions. Next, you will include the discontinuity models in your circuit similar to what you did in the previous part of this tutorial lesson. However, this time you need three 5mm-to-0.5mm and two 0.5mm-to-5mm "Microstrip Step" parts. Remember again that in RF.Spice's microstrip model, w1 > w2. Therefore, you need to build the 0.5mm-to-5mm step by flipping the 5mm-to-0.5mm step horizontally. Similar to the microstrip line segment devices, you need to ground all the microstrip step devices, too.  
 +
 
 +
{{Note|Forgetting to ground the RF parts properly may result in simulation failure.}}
  
 
<table>
 
<table>
 
<tr>
 
<tr>
 
<td>
 
<td>
−
[[File:RF56.png|thumb|720px|The Stepped Impedance Mirostrip Lowpass filter including step discontinuity models.]]
+
[[File:RF56.png|thumb|left|720px|The Stepped Impedance Mirostrip Lowpass filter including step discontinuity models.]]
 
</td>
 
</td>
 
</tr>
 
</tr>
 
</table>
 
</table>
 +
 +
Run an Network Analysis of your new enhanced RF circuit with the same parameters as in the previous case:
  
 
{| border="0"
 
{| border="0"
 
|-
 
|-
−
| valign="bottom"|
+
| valign="top"|
−
[[File:RF57.png|thumb|800px|left|Graph of s11 and s21 parameters of the stepped-impedance microstrip filter including step discontinuity models over the frequency range 500MHz-3GHz.]]
+
 
|-
 
|-
 +
{| class="wikitable"
 +
|-
 +
! scope="row"| Start Frequency
 +
| 500Meg
 +
|-
 +
! scope="row"| Stop Frequency
 +
| 3G
 +
|-
 +
! scope="row"| Steps/Interval
 +
| 10Meg
 +
|-
 +
! scope="row"| Interval Type
 +
| Linear
 +
|-
 +
! scope="row"| Parameter Set
 +
| S
 +
|-
 +
! scope="row"| Graph Type
 +
| Cartesian (Amplitude Only) with Decibels
 
|}
 
|}
  
 +
Compare the resulting graphs with those of the previous part. From the figures you can see that including the discontinuity models increases the slope of the roll-off part of the filter response. The previous circuit showed insertion loss values of -5dB and -17.5dB at 2GHz and 3GHz, respectively. After the inclusion of the five step discontinuity models, the new insertion loss values are -7dB and almost -20dB at 2GHz and 3GHz, respectively.     
 +
 +
<table>
 +
<tr>
 +
<td>
 +
[[File:RF57.png|thumb|left|720px|Graph of S11 and S21 parameters of the stepped-impedance microstrip filter including step discontinuity models over the frequency range 500MHz-3GHz.]]
 +
</td>
 +
</tr>
 +
</table>
 
<p>&nbsp;</p>
 
<p>&nbsp;</p>
−
[[Image:Back_icon.png|40px]] '''[[RF.Spice_A/D#RF.Spice_A.2FD_Tutorial | Back to RF.Spice A/D Tutorial Gateway]]'''
+
[[Image:Back_icon.png|40px]] '''[[RF.Spice_A/D#RF.Spice_A.2FD_Tutorials | Back to RF.Spice A/D Tutorial Gateway]]'''

Latest revision as of 23:34, 8 November 2016

Tutorial Project: Designing Lumped and Distributed Microstrip Lowpass Filters
RF57.png

Objective: In this project, you will use a classic lumped LC filter design to realize an equivalent distributed microstrip filter.

Concepts/Features:

  • Lumped Element Filter
  • Distributed Filter
  • Microstrip Line
  • Microstrip Discontinuity
  • Network Analysis

Minimum Version Required: All versions

'Download2x.png Download Link: RF Lesson 5

What You Will Learn

In this tutorial you will build and analyze a stepped-impedance microstrip lowpass filter based on a standard lumped LC filter design.

Analyzing a Lumped Ladder LC Lowpass Filter

The following is a list of capacitors and inductors needed for this part of the tutorial lesson:

Part Value
C1 0.71pF
L1 4.96nH
C2 2.87pF
L2 7.96nH
C3 2.87pF
L3 4.96nH
C4 0.71pF

This is a classic Butterwoth LC lowpass filter with N = 7. The cutoff frequency of this filter is 2GHz and it attenuates to more than -20dB at 3GHz. Place the parts and connect them as a ladder filter. Mark the input and output of your lumped LC filter with two Net Markers: IN and OUT.

A lumped LC lowpass filter.

Run a network analysis of this two-port circuit according to the table below:

Start Frequency 500Meg
Stop Frequency 3G
Steps/Interval 10Meg
Interval Type Linear
Parameter Set S
Graph Type Cartesian (Amplitude Only) with Decibels

The figure below shows the graph of S11- and S21-parameters. Note that a linear scale is used for frequency. The vertical axis is limited to -30dB and 0. Also note that the S21 response drops by 3dB at the cutoff frequency fo = 2GHz.

Graph of S11 and S21 parameters of the ladder LC filter over the frequency range 500MHz-3GHz.

Designing a Stepped Impedance Microstrip Lowpass Filter

A distributed microstrip version of the above ladder LC filter can be realized using consecutive low- and high-impedance line segments. It is well known that short segments of low- and high-impedance transmission lines behave like capacitive and inductive elements, respectively. Therefore, you will need four low-Z0 microstrip segments to replace the capacitors C1, C2, C3 and C4, and three high-Z0 microstrip segments to replace the inductors L1, L2 and L3. The transformations are based on the following equations:

[math] \beta l = \frac{ \bar{L} R_0} {Z_{high}} [/math]

for inductors and

[math] \beta l = \frac{ \bar{C} Z_{low}} {R_0} [/math]

for capacitors. Here Zhigh and Zlow are the high and low characteristic impedances of the narrow and wide microstrip segments, respectively, and R0 is the reference impedance of the filter.

The top view of layout of the Stepped Impedance Mirostrip Lowpass filter.

For this project, you will use 0.5mm-wide and 5mm-wide microstrip lines to realize Zhigh and Zlow, respectively. As you found earlier, these lines provide approximately 102Ω and 30Ω impedances, respectively. Using the above transformations, the following table for the segment lengths is obtained:

Line Segment w len Z0
len1 3.3mm 5mm 29Ω
len2 8.4mm 0.5mm 102Ω
len3 13.4mm 5mm 29Ω
len4 13.5mm 0.5mm 102Ω
len5 13.4mm 5mm 29Ω
len6 8.4mm 0.5mm 102Ω
len7 3.3mm 5mm 29Ω

Place and connect the above parts and mark the input and output of your circuit with two markers IN and OUT as shown in the figure below. Note how the negative pin (P1- and P2-) of all the parts have been grounded.

The schematic of a Stepped Impedance Microstrip Lowpass filter.

Run a network analysis of your distributed filter circuit with the following parameters:

Start Frequency 500Meg
Stop Frequency 3G
Steps/Interval 10Meg
Interval Type Linear
Parameter Set S
Graph Type Cartesian (Amplitude Only) with Decibels

The figure below shows the graph of S11 and S21 parameters. The horizontal and vertical axis scales have been set to match those of the lumped LC filter case for comparison.

Graph of S11 and S21 parameters of the stepped-impedance microstrip filter over the frequency range 500MHz-3GHz.

Adding the Microstrip Step Discontinuity Models

In the above analysis, you assumed that the high-Z0 and low-Z0 sections are directly connected to each other. Your circuit configuration ignored the effect of the step discontinuities between the segment junctions. Next, you will include the discontinuity models in your circuit similar to what you did in the previous part of this tutorial lesson. However, this time you need three 5mm-to-0.5mm and two 0.5mm-to-5mm "Microstrip Step" parts. Remember again that in RF.Spice's microstrip model, w1 > w2. Therefore, you need to build the 0.5mm-to-5mm step by flipping the 5mm-to-0.5mm step horizontally. Similar to the microstrip line segment devices, you need to ground all the microstrip step devices, too.

Attention icon.png Forgetting to ground the RF parts properly may result in simulation failure.
The Stepped Impedance Mirostrip Lowpass filter including step discontinuity models.

Run an Network Analysis of your new enhanced RF circuit with the same parameters as in the previous case:

Start Frequency 500Meg
Stop Frequency 3G
Steps/Interval 10Meg
Interval Type Linear
Parameter Set S
Graph Type Cartesian (Amplitude Only) with Decibels

Compare the resulting graphs with those of the previous part. From the figures you can see that including the discontinuity models increases the slope of the roll-off part of the filter response. The previous circuit showed insertion loss values of -5dB and -17.5dB at 2GHz and 3GHz, respectively. After the inclusion of the five step discontinuity models, the new insertion loss values are -7dB and almost -20dB at 2GHz and 3GHz, respectively.

Graph of S11 and S21 parameters of the stepped-impedance microstrip filter including step discontinuity models over the frequency range 500MHz-3GHz.

 

Back icon.png Back to RF.Spice A/D Tutorial Gateway

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