Transmission Line and Microwave Filters
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Transmission Line and Microwave Filters |
Filter Solutions supports a wide variety of transmission line filter designs. Filters may be single terminated, or double terminated with equal or unequal load and source resistances. Diplexers are supported for all filter types. Finite resistance and conductance analysis is supported for all transmission line filters. All pass section are supported to create delay equalizers. All synthesized filters are checked for a proper frequency response prior to being displayed. All filters are displayed in graphical easy to read formats with a net list selection that displays the filter net list in a textual format that is ready for an AC or transient analysis. Filter Solutions creates both balanced and unbalanced filters.
To generate single terminated filters, enter a source resistance of "0" in the source resistance entry box. To generate a equally terminated filter, enter the same number for source resistance and load resistance. If you enter a different source resistance and load resistance, Filter Solutions will create both single and double terminated filters that fit the filter characteristics selected in the Control Panel.
Filter Solutions computes up to
eight filters internally that attempt to meet your design specification. To
prevent multiple filters from being displayed, switch settings are provided to
narrow the number of displayed filters. You may select only first element shunt
filters, first element series filters, voltage source filters, or current source
filters.
Transmission line filters use transmission line theory to translate passive LC filters to passive filters composed of transmission line stubs. Inductors and parallel LC resonators may be replaced with shorted transmission line stubs, Capacitors and series LC resonators may be replaced with open transmission line stubs. Replacing LC resonators with a single stub is more efficient, but results in significantly more aliasing. Inductors may be replaced with 90 deg transmission line segments. Series resonators may be replaced by 180 deg transmission line segments. Checking the "Combine Stubs" box in Filter Solutions will cause filters to be synthesized with single stub resonators. Checking the "Use Segments" box will cause filters to be synthesized using transmission line segments instead of cascade stubs.
Below are inductor and capacitor components and resonators along with their transmission line replacement and defining equations.
All Filter Solutions graphical filter displays are user interactive. It is possible to change the values of any stub or segment, add new components, or delete stubs, and then generate a frequency, time reflection or impedance analysis on the modified filter. Simply pass the cursor over the stub or segment you desire to change. When it highlights, left click the mouse to change the stub or segment or right click to add or delete a stub as shown: Changeable parameters include impedance, length, resistance, conductance, or propagation speed.
After a stub or segment is changed, it appears in blue for easy visual reference. If a frequency value changes as a result of the new element values, it also is displayed in blue.
Changing, Adding, or Deleting a Filter Solutions Component
Adding stubs is useful when modeling parasitics or evaluating the effect of other attached circuits. resonant stub pairs have the option to automatically update the other stub in the pair such that resonant frequency is maintained. All pass sections may be added by right clicking a stub adjacent to the load or source resistor, or by adding all pass poles and zeros to the pole zero plot.
Changing transmission line values is useful to evaluate the effect of real transmission lines in the filter
Filter Solutions offers you the flexibility to create your filters with a mixture of lumped and transmission line stubs. This is a flexible method of substituting only the low Q lumped elements with transmission line stubs, and using lumped elements when high Q parts are available.
A coupled resonator band pass filter is shown below with open stubs replaced with lumped capacitors. The shorted stubs remain as substitutions for inductors. The impedance of the shorted stubs was manually set to 100 Ohms with the use of the change control panel.
Lumped Element Substitution
Frequency, Reflection, Impedance, and Time Analysis
Each filter generated by Filter Solutions may have a frequency, reflection, impedance, or time analysis performed by selecting the appropriate control on the circuit window. Frequency, reflection, and impedance analysis include magnitude, phase, and group delay. Time analysis includes step, ramp, and impulse response. Depressing the left mouse key at any location brings up a cursor tracer with the frequency and trace information in the cursor window. These analysis include all user modifications made to the filter. When a filter has been modified by changing, adding, or deleting a stub, or if any elements or segments containing nonzero resistance or conductance, the "Ideal" analysis trace appears in dark blue for quick easy comparison purposes. The attenuation due to the source resistor may be included or removed as desired by checking or unchecking the "Inc Gen Bias" box in the passive control panel. Examples are below:
Frequency Analysis
Time Analysis
Reflection Analysis
Finite Resistance and Conductance
Filter Solutions allows you to simulate nonzero resistance and conductance in your transmission line filters. The specific filter frequency, reflection, impedance, and time analysis will use the resistance and conductance you have provided in the analysis, and will use a dark blue background trace to show the ideal filter with zero resistance and conductance for quick and easy comparison purposes. For single terminated and unequally terminated filters, the degradation effects of nonzero resistance and conductance may be compensated for manually by moving the pole locations in the pole/zero plot. The compensation is done in real time if the RTC box on top of the pole/zero plot is checked. The poles may be "Stretched" along the real axis, and flattened slightly along the imaginary axis. This works reasonably well for single terminated filters and largely unequal terminated filters. For filters whose source to load ratio is greater than 0.2 and less than 5.0, nonzero resistance and conductance compensation is marginal. Equally terminated filters may not be compensated for in this manner.
Since the effect of nonzero resistance and conductance is unique to each individual transmission line filter, the effects of nonzero resistance and conductance are only included in the specific filter being analyzed. The control panel analysis functions assume an ideal filter.
To display the nonzero resistance and conductance in ohms and mhos per unit length of each transmission line stub, check the "Other Info" checkbox in the upper right of the transmission line filter display. This checkbox will also display the stub inductance and capacitance in henries and farads per unit length.
Nonzero Resistance and Conductance
Coupled resonator band pass filters are narrow band approximations of band pass filters. The advantages to using coupled resonators over classical band pass filters are more desirable lumped element values at high frequencies and flexible element value selections. See the passive filter section on coupled resonator band pass filters for more information.
Filter Solutions supports coupled resonator band pass filters with transmission lines. Stub values may be selected based upon equivalent capacitance or inductance of one of the resonator legs. Lumped elements may be substituted for transmission line stubs where practical to do so. Resonators may be constructed with separate L and C equivalent stubs or one LC resonator stub.
Coupled Resonator Example:
Below are example of 1GHz capacitor coupled band pass filter. Only the first stage resonator and coupling elements are shown.
Lumped Coupled Resonator Band Bass Filter
Below is the transmission line equivalent of the same coupled resonator band pass filter. The first two stubs replace the LC resonator. The third element replaces the coupling capacitor. This filter aliases at 5GHz.
Transmission Line Coupled Series Resonator Filter
Below is the same coupled resonator filter with a single stub resonator. The price paid for using one stub instead of two is aliasing at 2GHz instead of 5GHz.
Filter With Single Stub Resonator
Below is the same filter with only the inductors replaced by transmission lines. This results in minimal aliasing, and fewer stubs.
Filter With Inductors Replaced With Stubs.
Parallel Coupled and Shunt Stub Filters
Parallel Edge Coupled and Shunt Stub band pass filters are available. Both offer superior geometries over classical designs and lumped coupled resonator equivalent designs. Parallel coupled filters support both open and shorted ends, as shown below. The outer sections may be replaced with narrow band single line approximations to remove narrow gaps.
Shunt stub band pass filters may be produced with all identical stubs when designing Chebyshev I and Butterworth filters, as shown below.
Interdigital, Hairpin, and Combline filters are available. Interdigital and Hairpin filters may be calculated with and without tapped and hairpin resonator end-couplings, and with and without ground end couplers. Combline filters are available with and without tapped end-couplings. The grounded end couplers generally produce more practical geometry than without, but are more costly. Tapped and hairpin coupled ends frequently eliminate impractically small outer gap geometries.
Below are examples of the various multi-conductor filter options.
Filter Solutions supports both balanced and unbalanced transmission line filters. Many applications require balanced circuits due to the better noise immunity characteristics. To translate an unbalanced circuit to a balanced circuit, cut the series stub impedances in half and place an identical stub in the bottom. All parallel elements should be left alone. All pass elements are always balanced.
The entire passive circuit may be balanced by checking the "Balance" box above each passive filter schematic. Individual elements, LC tank pairs, or all pass sections may be balanced or unbalanced with the use of the right mouse key.
Example:
Balanced and Unbalanced Transmission Line Filters
When "Net List" is selected in the transmission line control bar, the filter net list is shown in a textual window. The net list is setup for an AC and a transient analysis on the load resistance, and is ready to plug into any application that uses net lists. When finite Q is selected, the parasitic resistances are included in the net list. Resistance values used are based upon the resonant frequency of LC pairs, and the cutoff or center frequency for all other components. The pulse source is comments out to prevent source conflicts with the AC source. Select "Netlist" again to remove the net list window.
The net lists support transmission line segments between stubs, ideal transmission lines, and real LCRG transmission lines. Ideal transmission lines output the quarter wavelength of the transmission lines stubs and segments. Dummy resistors are inserted to allow the net list to execute in spice programs.
The net list may be printed, copied to the windows clipboard, or saved to a text file. Individual stub values may be selected and copied to the windows clipboard for ease in retrieving component values for other applications. Select nothing to copy the entire contents to the clipboard.
Below is the Filter Solutions net list for the filter shown in "Graphical Displays" above and shown again to the right:
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MULTIPLE ANALYSES |
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MULTIPLE ANALYSES |
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Transmission line 1st order all pass stubs are created with four transmission line stubs. 2nd order all pass sections may be created with four or eight stubs. The eight stub solution substitutes each passive element to a transmission line stub. The four stub solution translates each passive resonator to a transmission line stub. The 4 stub solution is more efficient, but results in significantly more aliasing. Since it is difficult to draw eight stubs in one location, dotted lines are used to indicate points that are electrically connected. All pass sections are derived from passive balanced all pass sections. The example below shows a second order passive all pass section translated over to eight stub and four stub transmission line all pass stages.
All Pass Sections |
A Monte Carlo statistical analysis may easily be performed visually with Filter Solutions. After creating and displaying a transmission line filter and filter frequency, reflection, impedance, or time response, left click a stub and select the feature(s) you would like to study. In the Change Control Panel, select "Random", and enter the maximum tolerance or standard deviation in percent of the desired random change. Monte Carlos may be done manually by repetitious clicks of "Apply", or automatically by entering the desired number of simulations. Graphical traces may be overwritten or retained as desired. Both Uniform and Gaussian distributions are provided for inserting errors.
Below is an example of the effect of random error from 5% stub length accuracy has on the group delay of a 5th order Bessel Filter.
Random Error Due to 5% Stub Length Accuracy
Microstrip and stripline filters are most easily visualized with good geometry layouts. Filter Solutions offers a layout view to aid in such purposes and to augment the schematic view. Schematic views include distance scale and overall width and length information.
Transmission line filters, just as in digital filters, produce aliasing in the frequency axis, which in turn causes warping in the frequency range of interest. This warpage causes a reduction in the bandwidths of pass band and band stop filters. Just as in digital bilinear filters, the bandwidths of these filters may be preserved by prewarping the filter prior to synthesis. When possible, Filter Solutions automatically applies this prewarping to transmission line pass band and band stop filters so that the bandwidths are properly maintained.
Below is an illustration of the effect of prewarping on the pass band of a transmission line band pass filter.
 No Prewarping |
 With Prewarping |
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Effect of Prewarping on a Transmission Line Band Pass Filter The Pass Band is Designed for 6GHz to 9 GHz. The Null Frequency is Set to 20GHz. |
Filter Solutions quickly calculates conductor widths of microstrips and striplines to implement transmission line filters. Simply select the option, and enter the dielectric parameters. For microstrips, Filter Solutions will calculate the new line lengths to compensate for the effective dielectric constant due to the absence of dielectric material above the line.
All pass functions and balanced filters are not implementable as microstrips and striplines, so filters requiring these features are disabled when microstrips or stripline filters are selected.
Filter Solutions supports coupled striplines and microstrip high pass and band pass filters, including coupled line resonator filters. The graphical syntax is shown in Filter 1, below, along with the uncoupled line models. Strip line and micro strip widths and gaps are calculated and displayed, provided the width and gap calculations are of reasonable dimensions. High pass filters are implements as coupled line band pass filters with a wide band, such that the upper band edge notch is very narrow.
Conductor and Dielectric Losses
Transmission line losses are modeled for accurate filter simulations. For RGLC lines, standard modeling techniques to compute complex impedance Beta are used with the calculated L and C values and user entered R and G values. For stripline and microstrips, attenuation is calculated with the calculated impedance and conductor dimensions, and the user entered conductor resistivity, dielectric dimensions, and dielectric loss tangent. Attenuation in dB/length at the center frequency is displayed on the schematic. For coupled lines, both the even and odd mode attenuation is calculated, modeled, and displayed at the center frequency.
Smith charts, Jones charts, and polar plots are provided for frequency and reflection responses for easy to read informative graphical feedback. Left and right mouse keys provide easy to read curser data from the impedance grid.
Smith Chart Display
