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13.6. iFilter Synthesis Wizard

iFilter Synthesis is a filter synthesis capability embedded within the Cadence® AWR® iFilter™ filter synthesis wizard that allows designers to:

Standard iFilter uses known topologies for its filter solutions with explicit formulations where element values are often realizable. Many filters used in RF and microwaves are in the form of a fixed topology, so iFilter is suitable for most applications.

iFilter, however, does not have built-in solutions in design constraints such as the following, when:

In this case, the iFilter Synthesis presents various options and offers considerable flexibility.

13.6.1. Running the iFilter Synthesis Wizard

To run the iFilter Synthesis Wizard, open the Wizards node in the Project Browser and double-click iFilter Filter Synthesis, then click Synthesis.

13.6.2. Synthesis Specific Dialog Boxes

The following dialog boxes and toolbars are used in filter synthesis.

13.6.2.1. Advanced Synthesis Dialog Box

The Advanced Synthesis dialog box is used in manual or semi-automatic synthesis design mode.

This dialog box is laid out vertically in the order of synthesis steps with the following sections:

  • Transmission Zero Placement - manual

  • Element Extraction - manual/automatic

  • Circuit Transformations - manual/automatic

  • Automatic Extraction Solutions - automatic

The "solutions" are a combination of the extraction sequence and circuit transformations. So, for a given list of transmission zeros, there can be several ways to extract the elements, and a suitable set of transformations for each extraction sequence. If there is an applicable solution, they are listed at the bottom of the dialog box, for example "1 of 5" shown in the figure.

Automatic actions are triggered as a result of two conditions:

  • when an appropriate control is selected

  • when the specification or topology is suitable to perform the action

In the previous figure, solution 1 is selected out of 5 potential solutions. Since the Auto check box is selected, the elements are extracted using the pre-stored extraction sequence for this solution. Since the Apply Transformations check box is also selected, the transformations given in Solution #1 are also applied to the filter.

The annotated Advanced Synthesis dialog box is shown in the following figure.

The toolbar buttons at the bottom of the dialog box are provided for convenience and are optional.

13.6.2.2. Transmission Zero Templates Toolbar

iFilter Synthesis has pre-stored solution templates for various sets of transmission zeros. The Transmission Zero Templates toolbar provides easy access to those templates. To display this toolbar, click the Show TZ Templates Toolbar button at the bottom of the Advanced Synthesis dialog box.

The available templates are listed in the drop-down list. If you select a new item, the corresponding TZs are displayed in the Advanced Synthesis dialog box. The templates can be filtered by degree or number of finite TZ.

13.6.2.3. Element Extraction Toolbar

The Element Extraction toolbar is another way of extracting circuit elements from the synthesis function. To display this toolbar, click the Show Extraction Toolbar button at the bottom of the Advanced Synthesis dialog box.

The three left buttons in the top row are used to extract TZ from f=0, f=infinity and a Unit element. The fourth button is used to extract the selected FTZ from the list. These buttons replicate the buttons in the Advanced Synthesis dialog box. The left button in the bottom row undoes the last transformations and replicates the Undo Last button in the Advanced Synthesis dialog and the Reset Element Extraction button replicates the Reset Extraction button.

13.6.2.4. Transformations Toolbar

The Transformations toolbar provides shortcuts to the common transformations that are normally listed in the Circuit Transformations dialog box. To display this toolbar, click the Show Transformation Toolbar button at the bottom of the Advanced Synthesis dialog box.

Most of the transformations in the toolbar work immediately. Pi-Tee-L transformations are slightly different. Since there are many different combinations of these transformations, and not all of them can be displayed, only the symmetric impedances cases are shown. In order to apply Pi-Tee-L transformations, you must first select the source topology and then the target topology. For example, to apply “LLeft to Pi – Symmetric Imp”, first select the LLeft from the source topology group, and then select Pi from the target topology group.

13.6.2.5. Root Finder Toolbar

The filter synthesis process requires many math operations, including complex number root finding. There is no single root finding algorithm that works for all combinations of transmission zeros. iFilter Synthesis provides several root finding algorithms to choose: SSP-POLRT, Newton, Bairstow, and Jenkins. SSP-POLRT is suitable for most of the cases so it is the default algorithm. You can change the selected algorithm by clicking the arrow buttons (Select Prev. Root Finder Method or Select Next Root Finder Method) on the Root Finder toolbar.

13.6.2.6. Circuit Transformations Dialog Box

To access the transformations of the current filter, click the Edit button in the Advanced Synthesis dialog box to display the Circuit Transformations dialog box.

The Current Transformation List displays the transformations applied to the extracted filter circuit. If the filter is in Auto-Transformation mode (Auto is selected in the Advanced Synthesis dialog box), the transformations display but are not editable. To allow editing in Custom-Transformation mode, select Custom in the Advanced Synthesis dialog box.

This dialog box includes the following options:

  • Clear List deletes all the transformations in the Current Transformation List.

  • Add adds the selected transformation in the Available Transformations list to the Current Transformation List.

  • Insert inserts the selected transformation in the Available Transformations list to the Current Transformation List above the selected item.

  • Replace replaces the selected transformation in the Current Transformation List with the selection in the Available Transformations list.

  • Delete deletes the selected transformation in the Current Transformation List.

  • Enable/Disable toggles the selected transformation in the Current Transformation List as enabled or disabled without deleting it.

  • Run List all runs all the transformations in the Current Transformation List.

  • Run List upto runs transformations up to the selected one in the Current Transformation List.

  • Copy Auto-List copies the transformations from the pre-stored Auto list into the Current Transformation List.

  • Available Transformations lists all the available transformations in the iFilter library. When there are too many to choose from, you can display a subset of transformations by selecting the desired option in Show Transformations.

The Options section of the dialog box lists options that are complementary to the selected transformation. In the previous figure, the setting for applying the transformation to the “1st shunt capacitor” is shown.

The software applies the transformations in the order shown in the Current Transformation List. If the software cannot find the element to apply the transformation, it may either abort the whole list or continue. To stop if a required element is not found, select Must find element (else abort macro).

If you want the software to stop upon a transformation fail because the following transformations depend on its success, select Must succeed this step to continue.

Some transformations result in an extra transformer. To simplify automatically after the transformation, select Simplify after transformation. This option is equivalent to adding an extra Collect Transformers command to the Current Transformation List.

Some transformations require you to enter a value with the command. For example, for Split Element you need to specify one value. To specify a value, select Use value and enter a value in the text box. If Tuning Mode is selected, you can change the value while the full transformation list is continuously applied to the filter.

13.6.2.7. Auto Synthesis Dialog Box

The Auto Synthesis dialog box presents simple controls for synthesizing in the automatic mode.

This dialog box includes the following options:

  • Order specifies the filter order.

  • The drop-down list below Order lists templates that change depending on the order specified. In the previous figure, N=6, Z=3, I=1, F=1 (0 ls, 1us) indicates the 6th order filter with 3 TZ at f=0, 1 TZ at f=infinity, and 1 finite TZ (1 at upper stopband). If the drop-down list changes the wizard resets the TZ list and creates finite TZs in the right side of the passband. In this example, 1us places the single FTZ at 610MHz, which is above upper frequency corner of the bandpass filter.

  • Finite lists the finite TZs. You can tune the FTZ selected in the list higher and lower in frequency.

  • Sym. FTZ is rarely used. The most appropriate case is when designing topologies with CQ-sections which require FTZ pairs which are symmetric around filter passband.

  • Apply Transformations is selected for all automatic synthesis. It is provided as a test option to check on the raw extraction circuit process.

  • Prev Solution and Next Solution buttons are used to select from pre-stored solutions that are suitable for the selected TZ template.

13.6.2.8. Coupling Coefficients

Most narrowband bandpass filters are realized using cavity combline resonators. These filters are normally realized by first selecting a suitable resonator impedance and then placing resonators by coupling them through irises. The relation between the iris dimensions and coupling coefficients are established through measurements. The coupling coefficients are found from the equivalent filter circuit. iFilter Synthesis displays coupling coefficients in a separate window.

To display the Coupling Coefficients window, click the button in the main iFilter dialog box.

13.6.2.9. Transformation Guide Dialog Box

The Transformation Guide dialog box provides quick information for transformations. To display this dialog box, click the button in the Circuit Transformations dialog box.

While this dialog box displays, you can select any transformation from the Available Transformations list in the Circuit Transformations dialog box to view its information. The schematic in the Before Transformation pane shows a typical topology for the transformation to be applied. The After Transformation pane shows the schematic after transformation. If the transformation requires you to select an element to apply, the element is marked in the schematic. To apply the transformation, you must select that element in the filter.

13.6.2.10. Synthesis Information Window

iFilter Synthesis provides a summary of synthesis actions in an information window. To display this window, click the button in the main iFilter dialog box.

13.6.3. Lumped Bandpass Filter Example

The following examples explain iFilter Synthesis functionality. Here, you design a 5th-order bandpass filter, centered at 500MHz, with a 40MHz bandwidth and a Chebyshev response with a 0.01dB passband ripple.

13.6.3.1. Solution 1 - Standard Textbook Solution from iFilter

A well-known passive filter design technique starts by constructing a lowpass prototype that is normalized to 1 ohm terminations and a 1Hz cut-off frequency. Next, a frequency transformation is applied for the required passband, and finally an impedance scaling is applied to the circuit elements, and all impedances are multiplied by the value of source impedance, which is usually 50 or 75 ohms in RF and microwave systems.

A transmission zero (TZ) is defined as a frequency where there is no transmission (that is, the input signal is fully reflected,|S11|=1 and |S21|= 0. An Nth order lowpass prototype contains N transmission zeros at f = ∞. When a frequency transformation is performed on the lowpass prototype, transmission zeros are also moved to new frequencies. An Nth order lowpass prototype results in the following after transformation:

  • For lowpass: There are N TZs f = ∞

  • For highpass: There are N TZs at f = 0

  • For bandpass: There are N TZs at f = 0 and N TZs at f =∞ because prototype TZs are mapped to both sides of the passband. Therefore, bandpass filters have 2N transmission zeros shared between upper and lower stopbands.

The following figure shows a standard textbook bandpass filter obtained by selecting Bandpass > Lumped > Lumped Element Filter in the Select Filter Type dialog box.

13.6.3.2. Solution 2 - Narrowband Microwave Filter solution from iFilter

A lesser-known passive filter design technique targets narrowband microwave filters, which is a significant portion of all filters used in high-frequency electronics. The design process starts by selecting an inverter-prototype, then applies frequency transformations to the shunt capacitors and replaces inverters by capacitive/inductive sections at the passband centre frequency, and finally applies impedance transformation. Although replacing inverters is an approximation, it invariably results in well-matched designs for narrowband filters.

The following design uses a Bandpass > Lumped > Narrowband Lumped Filter with an Inductively Coupled option. As the filter topology is a set of inductively coupled shunt resonator, the selectivity on the upper stopband is more pronounced than the lower stopband (see markers).

Various inductive/capacitive replacements are possible. The following graph illustrates a filter that employs only capacitive coupling between resonators and illustrates the improvement in lower sideband selectivity.

13.6.3.3. Solution 3 - Synthesis Solution from iFilter Synthesis

Using iFilter, solution 1 is an exact filter (the return loss behavior is exactly as prescribed in the original specification). Conversely, solution 2 (again using iFilter) is an approximate filter, yet close enough to the original specification, and one that possesses a topology that is realizable.

Solution 3, shown in the following design, uses iFilter Synthesis methods: TZ placement followed by Element Extraction. While the method yields an exact solution, it is not a design that is easily realized. iFilter Synthesis, however, also introduces equivalent circuit transformations that overcome this realizability issue.

In solution 1, the bandpass filter has 5 TZs at f=∞ and 5 TZs at f=0. This results in perfect symmetry in the behavior of both sides of the passband for frequencies near the passband corners. As the frequency extends to zero and infinity, the symmetry is still maintained, although it is a geometric symmetry, which is difficult to visualize on a linear frequency plot of S21.

iFilter Synthesis allows the 10 TZs for this bandpass filter to be distributed unevenly. The following design uses a Bandpass > Lumped > Syn. Lumped Filter where 9 TZs are placed at f=0 and 1 TZ is placed at f=∞. Since there are more TZs at f=0, the filter is more selective in the lower stopband than in the upper stopband. This filter is exact, but the element values vary over a large range and there is a voltage transformer present at the load end with a 1:100024 turns ratio, so the filter is not particularly practical.

At this stage in the design flow, you can use Norton transformations to remove the unwanted transformer by canceling it with a transformer possessing an inverse turns ratio. To do so, create a new transformer one from within the elements by 1:1/1.00024 turns ratio using the Norton transformation. The series capacitor 9338.49nH and the shunt capacitor 2.98496*106 nH form a capacitive L-Left section. You can replace this L-Left section with an L-Right section by using a specific transformation. iFilter Synthesis uses the terms L-Left, L-Right, Pi-, and Tee- to identify the circuit sections where successive Norton transformations can be applied.

The following circuit is obtained when the transformer is canceled after an L-Left to L-Right transformation is applied. It is important to note that the Norton transformations are exact, so the filter response does not change after applying them.

Although the transformer is removed by being absorbed by an inverse transformer, the filter is still not readily realizable given the large range of element values. The following variant, however, addresses this issue by applying an "All Equal Shunt Inductors" transformation. This results in a superior capacitively coupled bandpass topology, with a single inductance value (1.686nH) for the shunt inductors. With this realization, both the shunt and series capacitors possess a small range of values, which raises the possibility of simple tuning using printed elements. The final design has a practical topology where the passband return loss is exactly as initially prescribed.

As noted, there are many circuit solutions to a single filter specification. While standard iFilter provides several practical solutions, iFilter Synthesis provides more flexibility in the design process by being able to distribute the transmission zeros between DC and infinity and subsequently allowing the designer to apply various network transformations after element extraction to yield a more satisfactory solution.

13.6.4. Synthesis Process Flow

To use iFilter Synthesis effectively, you should know the filter synthesis process flow. The synthesis takes place in the following order:

  • Place transmission zeros

  • Extract circuit elements

  • Apply circuit transformations

iFilter Synthesis provides manual or automatic control in any or all of these steps.

13.6.5. Designing in Manual or Semi-Automatic Mode

iFilter Synthesis has two main synthesis and design modes.

The first mode is manual or semi-automatic, and the second mode is fully automatic. You access these modes in the Select Filter Type dialog box at the beginning of the synthesis process.

To run in manual or semi-automatic mode, select the option listed first under Main Filter Type. For lumped element filters, the filter type is named "Syn. Lumped Element Filter". For distributed element filters, the filter type is named "Syn. Distributed Element Filter". In both cases, there is a pre-selected single option listed under Options named "Generic Synthesis".

In manual or semi-automatic mode when you click OK the Advanced Synthesis dialog box displays.

13.6.6. Designing in Fully Manual Mode

To help understand the synthesis steps that are available, the bandpass filter described in the previous example is designed here using the fully manual mode. To constrain the example, the filter specification has a sideband attenuation of 30dB at 380MHz and 40dB at 595MHz.

Ensure that the units are set to MHz before defining the filter specification, then click the Analyze Ideal button . The behavior of the filter when lossy and real elements are used is discussed in a later section.

The specification of the bandpass filter is

PB Ripple       0.01
Fo [MHz]        500 
BW [MHz]        40
RSource/RLoad   50 

Add two markers, the first at 380 MHz and the second at 595 MHz.

If the iFilter is not already in synthesis mode, click the Select Design Mode button and select the Synthesis option to display the Select Filter Type dialog box. Alternatively, click the Change Filter Type button (at the top left; labeled with the current filter type) in the main iFilter dialog box.

In the Select Filter Type dialog box, select Bandpass > Lumped > Syn. Lumped Element Filter as a suitable manually synthesized filter for this example. Next you specify passband corners and passband ripple and then add markers to the insertion loss at this point by clicking the Edit Chart Settings button .

To place iFilter Synthesis in the fully-manual mode, in the Advanced Synthesis dialog box:

  1. Clear the Auto check box under Element Extraction.

  2. Select the Apply Transformations check box and Custom option under Circuit Transformations.

  3. Do not use the Prev or Next solution buttons under Automatic Extraction Solutions.

  4. Click the Reset Extract button under Element Extraction to clear any stored extractions.

  5. Select Type-B under Element Extraction to start with series element.

The filter parameters are already specified in the main iFilter dialog box. The rest of the synthesis is completed by specifying and extracting transmission zeros:

  1. Click the Clear Transmission Zeros button to start with a clean list.

  2. Add 3 TZs at f=0 by clicking 3 times on the "+" button in the ZERO row.

  3. Add 1 TZ at f=∞ by clicking once on the "+" button in the INF row.

  4. Add 1 Finite TZ (FTZ) by clicking the "+" button next to the Finite listbox.

  5. In the Add Finite TZ dialog box that displays, specify 610 MHz and then click OK.

Check the response and see that it satisfies the 30dB and 40dB rejection points.

To extract the filter:

  • Click the "E" button in the ZERO row to extract an element at f=0.

  • Click the "E" button in the ZERO row to extract an element at f=0.

  • Click the "E" button next to the Finite list to extract the element at f=610 MHz.

  • Click the "E" button in the INF row to extract an element at f=∞.

  • Click the "E" button in the ZERO row to extract an element at f=0.

You could extract elements in a different order. Although all of these filters have the response shown here, the resulting topologies and element values may differ considerably. The following circuit is obtained as a result of the defined extractions.

After defining the initial filter topology, you can now apply one or more Circuit Transformations. To do so, click the Edit button under Circuit Transformations to display the Circuit Transformations dialog box.

  1. Select the first shunt capacitor (from the left), 1560.37pF.

  2. Under Available Transformations, select the "LLeft to Pi - Symmetric Imp" transformation, then under Apply Transformation To select "CAP" and "Shunt" and enter "1" as the Element Index.

  3. Under Options, select the Simplify after transformation check box.

  4. Click the Add button, and then click the Run List all button to apply the selected transformation and change the circuit.

  5. Select the second shunt capacitor, 41.8487pF.

  6. Under Available Transformations, select the "LLeft to Tee - Equal Inductors" transformation, then under Apply Transformation To select "CAP" and "Shunt" and enter "2" as the Element Index (representing the 2nd shunt CAP).

  7. Under Options, select the Simplify after transformation check box.

  8. Click the Add button, and then click the Run List all button to apply the selected transformation and change the circuit.

  9. Select the third shunt capacitor, 476.601pF.

  10. Under Available Transformations, select the "LLeft to Pi - Equal Inductors" transformation, then under Apply Transformation To select "CAP" and "Shunt" and enter "3" as the Element Index (representing the 3rd shunt CAP).

  11. Under Options, select the Simplify after transformation check box.

  12. Click the Add button, and then click the Run List all button to apply the selected transformation and change the circuit.

The following figure shows the list of applied transformations.

You can see that this filter design is a realizable filter. Most notably all the inductors have a single value, that is 2.027nH. A 2nH quality RF inductor in 0402 or 0603 sizes can be selected or the inductors can be wound by hand. Capacitors range from 9.2 to 43.1pF and they are readily found in MLCC capacitor toolkits.

13.6.6.1. Tuning the Finite TZ

Any time during the synthesis, even after all the transformations are applied, you can tune the Finite TZ at 610MHz to move the rejection point along the frequency axis, perhaps to improve a passband slope or accommodate a late change in the filter specification. To do so, first select the FTZ from the list, then click in the FTZ text box and move the mouse wheel up and down to change the value. All the design steps that are integrated into the filter design up to this point in the design flow are repeated with the new FTZ value.

13.6.7. Designing in Semi-Automatic Mode

To design the bandpass filter in the previous example in the semi-automatic mode, you specify the passband center and bandwidth, and the TZs in the same way as the manual mode. Next you click the Next and Prev buttons under Automatic Extraction Solutions until you see solution 1 of 5. This solution is programmed as a built-in Ladder solution for this particular set of TZs. The result is the same circuit that was obtained by the tedious method in the fully-manual mode. Bandpass filters are commonly used, so 450 solutions are programmed into the iFilter Synthesis. Overall, there are about 1500 solutions in the wizard.

13.6.8. Designing in Fully Automatic Mode

About 1500 variations of TZ placements, extraction sequences, and transformations are programmed into iFilter Synthesis for designers. You can access them from the Advanced Synthesis dialog box as well as the Auto Synthesis dialog box.

To access the Auto Synthesis dialog box, in the Select Filter Type dialog box under Main Filter Type select any filter type other than the first option and then click OK. For example, selecting the filter described in the previous examples (Bandpass > Lumped > Syn. Lumped Ladder Bandpass Filter) displays this dialog box.

  1. To design the same example filter, specify "6" as the Order.

  2. Select "N=6, Z=3, I=1, F=1 (0 ls, 1 us)" from the drop-down box.

  3. Select and change the somewhat-arbitrary FTZ to 610.

  4. Select the Apply Transformations check box.

Since there is only one solution for the Syn. Lumped Ladder Bandpass Filter type, the Prev and Next buttons are disabled.

The following figure shows the resulting filter.

Note that this is the same filter obtained in the Manual mode because the transformations stored in the Syn. Lumped Ladder Bandpass Filter is in the same order that was manually specified.

Most common topologies are accessible through this semi-automatic mode. Other than the first filter type in the list, all other filter types listed in the Select Filter Type dialog box have predefined topologies. The lumped versions are shown in the following figure.

The distributed filters with pre-programmed topologies are shown in the following figure.

As new topologies become available, they will be added to the list. Note that the first filter type in these lists are manually extracted filters for the Advanced Mode.

13.6.9. iFilter Synthesis Features

The following list highlights some of the important capabilities available within iFilter Synthesis. This list is not comprehensive.

  • Lumped Bandpass filters contain a CT/CQ option. These are cascaded triplets and quadruplets which provide cross-coupling within a ladder structure. While there are exact CT/CQ sections, there are also approximate sections available for selection for "filters having linear phase response in the passband".

  • Lumped Bandpass Coupled Resonator filters feature all-equal shunt inductors which can be specified directly from the main iFilter dialog box. For example, the following filter only has 3.3nH shunt inductors. Having identical inductors means a reduced Bill of Materials.

  • In distributed filters, you can add and extract contributing unit elements in iFilter Synthesis. In a non-contributing UE filter, 50-ohm transmission lines are inserted from source and load ends and moved in towards the mid-circuit by applying Kuroda transformations. In the contributing unit element case, the same topology can be obtained by synthesizing unit elements directly within structure. This feature is used in “Open Circuit Stubs with Non-redundant Transmission Lines” design, which you select by choosing the Lowpass > Microstrip > Syn. Dist. LPF - OC stubs + Nonrdn. TL filter in the Select Filter Type dialog box.

13.6.10. Distributed Element Lowpass Filter Example

This example shows the design of 7th order 10 GHz microstrip lowpass filter in iFilter Synthesis.

  1. In the Select Filter Type dialog box, select the Lowpass > Microstrip > Syn. Distributed Element Filter, then click OK.

  2. Enter the following filter parameters in the main iFilter dialog box.

  3. Finish the design setup by clicking the Design Options button and on the Technology tab of the Distributed Model Options dialog box that displays, enter the substrate parameters. Use "0.010” (0.254mm) Rogers RO4350B substrate for this design.

  4. In the Advanced Synthesis dialog box under Element Extraction, clear the Auto check box to enable manual extraction, then click the Clear Transmission Zeros button above it to do a clean start.

13.6.10.1. Lowpass Filter with Monotonic Stopband

Filters with no finite transmission zeros have a monotonically increasing attenuation in their stopband. At the far away frequency from the passband, f=INF, no transmission occurs, i.e. S21=0.

For lumped lowpass filters, INF occurs at f=infinity Hz. For distributed filters, INF occurs at multiples of quarter wavelength frequency, Fq. For lowpass filters, Fq is related to Fp in the following equation: Fq = Fp * 90/EL

So for EL=45 deg, and Fp=10 GHz, Fq is found as 20 GHz.

13.6.10.2. Solution #1 – All Transmission Zeros located at Fq

As the first variation, you design with 7 TZ all located at infinite frequency. Each TZ at infinite frequency adds 1 order to the filter.

To place 7 TZ, click the "+" button in the INF row.

Next extract the element values. Since you only have all the TZs at f=INF, the only way to extract TZs is to click the "E" button in the INF row 7 times.

Note for future reference that the topology is symmetric around the middle shunt stub (30.62ohms).

Initially, this looks like a lumped element filter, where the series inductors are replaced with short-circuited stubs, and the shunt capacitors are replaced with open-circuited stubs. Instead of having inductances and capacitances, the stubs have impedance and lengths, which are quite reasonable. However, there is a fundamental problem with the structure: Series short-circuited stubs cannot be realized on microstrip, so an equivalent circuit that is realizable must be found.

Kuroda transformations are the most common way of converting series short-circuited stubs into shunt open-circuited stubs. To do so, you apply a series of Kuroda transformations until all stubs are replaced:

  1. Under Circuit Transformations, select the Apply Transformations check box, click the Custom button, and then click the Edit button to display the Circuit Transformations dialog box.

  2. In the Available Transformations list, select "Add Transmission Line to Source Side" and click the Add button to add it to the transformation list. Adding 50-ohm transmission lines to source and load sides does not change the response.

  3. Click the Run List all button.

  4. In the modified circuit, select the transmission line on the left.

  5. In the Available Transformations list, select "Kuroda Right – Full Stub" and click the Add button to add it to the transformation list.

  6. Click the Run List all button.

Note that the options related to the selected commands must be set correctly while adding to the list. Each command has a different options setting. For the software to apply the Kuroda transformation, it should know which transmission line is intended. You should specify the FIRST transmission line for this transformation by entering "1" in the Element Index box as shown in the following figure.

The following circuit results:

Kuroda transformation turned a "Transmission Line + Series SC Stub" into "Shunt OC Stub + Transmission Line" section. These two filter sections have identical frequency response. Similarly, all Kuroda transformations yield identical equivalent circuits; they are exact transformations.

By continuing to insert transmission lines and applying Kuroda transformations, all series SC stubs can be transformed into shunt OC stubs, although it is a tedious process. You should move the first transmission line towards the right by 3 successive "Kuroda-Right - Full Stub" transformations. You then add an "Add Transmission Line to Source Side", and apply 2 successive "Kuroda-Right - Full Stub" transformations as well. Finally, you add one more "Add Transmission Line to Source Side" and a "Kuroda-Right - Full Stub" transformation.

You can now continue to add transmission lines and do Kuroda transformations, however, it is tedious to do it from the left-hand (Source) side. You can also add transmission lines to the Load side and apply "Kuroda-Left - Full Stub" to them, however you must add 9 more transformations.

Short Cut 1

Alternatively, there is an easy way of converting the stubs on the right-hand side. As previously noted, 30.62-ohm shunt stub is the original center (pivot) of the original symmetric filter. You can now mirror the circuit around that stub, which is the same as repeating all the transformations on the right-hand side. Note that you should set the Element Index to "4" before adding the command to the list. If the command is selected first and stub is selected after, the wizard already places the correct index into the box.

After adding "Mirror Circuit" to the Current Transformation List and running the whole list, the following all-shunt-OC filter results:

Short Cut 2

The schematic in Short Cut 1 is an almost-realizable topology on microstrip. The only exception is the first shunt stub, whose impedance is 212.74 ohms. It’s difficult to realize impedances above 150 ohms, as the line widths become too small. The rest of the topology is suitable for construction, so at this stage for realization you can only replace the high impedance lines with lumped inductors, or try another solution.

13.6.10.3. Solution #2 – Filter with Non-redundant Transmission Lines

In Solution 1, you ended with series transmission lines which were not there in the original extracted circuit. These transmission lines are inserted and shifted through Kuroda transformations, so they are redundant elements (they don’t directly contribute to the filter selectivity) and do not count towards the filter order.

In this solution, you use transmission lines that contribute to the filter selectivity by adding a set of TZs in the following form:

  • 4 INF

  • 3 UE

Each UE practically adds 1 TZ effect to the filter response, so effectively you now have a 7th order filter. To extract the element values click the "E" buttons in the following order: INF-UEL-INF-UEL-INF-UEL-INF

Without performing any circuit transformations, you have a realizable topology and reasonable element values, as shown in the following figure.

The layout for this filter is shown in the following figure.

As an alternative extraction, under Element Extraction you can select the Auto check box. iFilter Synthesis matches the transmission zero list with pre-stored templates and uses the corresponding extraction sequence for this common template, (n+1) INF + n UE.

At this stage, you can investigate how the stopband can still be manipulated without touching the transmission zeros. As noted previously, the electrical length parameter specifies the length at the passband corner. When it is 45-degrees, f=INF=Fq occurs at 2*Fp. You can set it to a smaller value, like 30-degrees, and Fq is pushed higher in frequency to 30 GHz. The effect of changing EL from 45- to 30-degrees is shown in the following figure.

13.6.10.4. Solutions with Finite TZs

When finite TZs (FTZ) are considered, stopband attenuation can be formed to provide infinite attenuation at selected frequencies. Every FTZ adds 2 orders to the filter, so 2 INF can be replaced with a single FTZ. This swap changes the slope of attenuation near f=INF and (pull) S21 around the finite TZ to zero. Placing a FTZ is similar to pressing the middle of a balloon that is fixed between two points: when pressed, it bubbles up more on two sides further up.

For a 7th order filter, the following sets of transmission zeros are possible:

  • 7 INF

  • 6 INF, 1 UE

  • 5 INF, 2 UE

  • ...

  • 1 INF, 6 UE

  • 7 UE

  • 5 INF, 1 FTZ

  • 4 INF, 1 UE, 1 FTZ

  • 3 INF, 2 UE, 1 FTZ

  • ...

  • 3 INF, 2 FTZ

  • 2 INF, 1 UE, 2 FTZ

  • ...

  • 1 INF, 3 FTZ

Each of these TZ sets can be investigated to see if they are realizable, although with the number of combinations it would be very time consuming.

In iFilter Synthesis, some of the most realizable topologies are pre-stored as solution templates. Each solution has its own TZ extraction sequence and list of transformations that are applied after extraction. The following sections include solutions found among those pre-stored templates.

Solution #3 – Filter with 1 TZ at Inf, 4 UE and 1 FTZ

To access this solution, in the Select Filter Type dialog box select the Lowpass > Microstrip > Syn.Dist.LPF/OC stubs + Step.Res. filter type and click OK to display the Auto Synthesis dialog box.

Specify "7" as the Order, then click in the drop-down box to view three 7th order filter options. Select the first option with 1 TZ at INF, 4 UE and 1 FTZ.

You can tune the location of finite TZ by selecting it from the Finite list and entering a new FTZ value (alternatively, scroll the mouse-wheel up and down). The following figure shows FTZ specified as 15 GHz.

Note that the middle element is a step resonator. It consists of two cascaded transmission lines connected to the main filter arm as a shunt element. The final end of 133.72 ohms is left open.

To see the extraction sequence and transformations applied to obtain this circuit, click the "S" button in the main iFilter dialog box to display the Synthesis Information window. The first few lines from the window summarize the actions performed:

Extraction Order:

Type A: U U F1 I U U
Solution: 1 / 1 
					
Transformations:
# 1: Kuroda to All Series SST (1 at 1)  [OK]
# 2: All Series Stub Res to 2-step Resonator (1 at 1)  [OK]

If the steps are followed manually in the Advanced Synthesis dialog box, the same filter is obtained, however the Auto Synthesis mode makes it much easier by doing everything automatically.

Solution #4 – Filter with 3 TZ at Inf, 2 UE and 1 FTZ

Select the second option of the three 7th order filter options in the drop-down box, with 3 TZ at INF, 2 UE and 1 FTZ. The procedure is almost the same as solution #3, however the end topology is slightly different as there are two extra shunt stubs at the termination ends.

Solution #5 – Filter with 1 TZ at Inf, 2 UE and 2 FTZ

The third option of the three 7th order filter options in the drop-down box gives the following topology (FTZ1 tuned to 13.4 GHz, FTZ2 tuned to 15.9 GHz for equiripple-like stopband).

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