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Tapered Microstrip Line Synthesized to Match (Klopfenstein, Exponential, Triangular): MTAPER2



MTAPER2 provides synthesis of three types of matching lines based on selected tapered distribution of characteristic impedance: Exponential, Triangular, and Klopfenstein. The width of microstrip tapers smoothly between ports. Synthesis of optimal taper shape is initiated by setting the initial value of synthesized parameter L (taper length) to zero.



Name Description Unit Type Default
ID Name   MT1
Fp Lower passband edge Frequency 1 GHz
Ro Input impedance @ node 1 Resistance 50 Ohm
RL Load impedance @ node 2 Resistance 100 Ohm
L Line length Length 0 (replaced by synthesized value)
Rmax Absolute value of maximum reflection coefficient (voltage)   0.1
Taper Switch between characteristic impedance distribution types (Klopfenstein, Exponential, Triangular)   Exponential
Nseg Number of straight microstrip segments per wavelength   30
W_min Minimal allowed conductor width Length 5 um
W_max Maximal allowed conductor width Length 5000 um
MSUB Substrate definition Text MSUB#[1]
W1 Width of line at Port#1 (synthesized value) Length Replaced by synthesized value
W2 Width of line at Port#2 (synthesized value) Length Replaced by synthesized value

[1] Modify only if schematic contains multiple substrates. See the “Using Elements With Model Blocks” for details.

* indicates a secondary parameter

Parameter Details

L. Input/output taper length. Any non-zero value of L is used as actual taper length. Input non-zero value does not provide optimal taper length. Setting L=0 provides immediate calculation of optimal taper length. MTAPER2 updates L on the schematic in-place with correct optimal value. See "Recommendations for Use" for details.

Fp. Desired lower frequency of matching passband.

Ro, RL. Desired input impedance (real) Ro and specified load impedance (real) RL.

Rmax. Desired absolute value of maximal reflection coefficient.

Taper. Provides three options: Exponential, Triangular, and Klopfenstein. These options specify the type of characteristic impedance distribution along the line (see [1], [2]).

W_min, W_max. Used to verify feasibility of specified values of parameters Ro and RL. W_min and W_max might be respectively minimal and maximal widths allowable by the device fabrication technology or any other user-specified values. MTAPER2 uses MSUB parameters to calculate characteristic impedances Zmin(W_max) and Zmax(W_min). If either Ro<Zmin or RL>Zmax then MTAPER2 interrupts the synthesis/simulation and issues an error message with recommendations for how to change Ro and/or RL.

W1, W2. Synthesized values of conductor widths at port #1 and port #2. You can use these to automatically match widths of connected microstrip lines (single or coupled). To provide this match width of microstrip line connected to taper, specify port #1 as W1@pin, where pin is the number of the connected line terminal. For line connected to taper port#2, width matching is provided if the connected line width is specified as W2@pin.

Parameter Restrictions and Recommendations

  1. Ro must be less than RL (Ro<RL). If Ro>RL then MTAPER2 interrupts the synthesis/simulation and issues an error message prompting you to review parameters Ro and RL.

  2. Ro should not be too close to RL. If RL>R0 and RL-R0<0.1 ohm then MTAPER2 interrupts the synthesis/simulation and issues an error message prompting you to review parameters Ro and RL.

  3. To build Klopfenstein taper for the specified reflection coefficient Rmax, Rmax should be less than 0.5log(RL/Ro). If this is not true, MTAPER2 interrupts the synthesis/simulation and issues an error message prompting you to review parameters Rmax, Ro, and RL.

Implementation Details

This model is constructed of a cascaded series of constant width microstrip transmission lines. It assumes a quasi-TEM mode of propagation and incorporates the effects of dielectric, conductive losses, and dispersion.


This element uses line types to determine its layout. By default, the layout uses the first line type defined in your Layout Process File (LPF). You can change the element to use any of the line types configured in your process:

  1. Select the item in the layout.

  2. Right-click and choose Shape Properties to display the Cell Options dialog box.

  3. Click the Layout tab and select a Line Type.

  4. Click OK to use the new line type in the layout.

See “Cell Options Dialog Box: Layout Tab ” for Cell Options dialog box Layout tab details.

See “The Layout Process File (LPF)” for more information on editing Layout Process Files (LPFs) and to learn about adding or editing line types.

Recommendations for Use

The first time you place MTAPER2 on a schematic, it is created with the set of default parameters. If MSUB is on the schematic, taper shape synthesis and taper layout pcell code run immediately and try to provide an initial optimal taper configuration. The optimal taper length displays as a value of parameter L. To simulate the synthesized configuration click the Analyze button on the toolbar.

Any forthcoming changes of any MTAPER2 parameter, particularly non-zero L and Rmax, initiate a new synthesis run and new layout cell generation. However, the resulting configuration is not optimal and does not warrant specified Rmax at minimum L.

The only way to obtain optimal configuration is to issue the special command: Manual setting parameter L to zero.

By setting L=0 you order MTAPER2 to calculate the minimal/optimal length of the taper line. The recalculated value of L replaces the zero value of the L parameter on the schematic, synthesizes the optimal taper shape, and updates the shape in the (previously) opened layout window. All of this occurs before simulation starts. Click the Analyze button on the toolbar to run the simulation. The simulation code uses the synthesized optimal taper line.

Remember to reset L=0 after switching the types of characteristic impedance distribution with the Taper parameter or after updating any parameter value.

The input value of Rmax is used only after you set L=0 to initiate synthesis and calculate optimal length. For a non-zero length MTAPER2 recalculates Rmax internally (the value of Rmax on the schematic stays unchanged) and uses the new Rmax value to create non-optimal taper configuration.

Note that synthesis of Klopfenstein taper does not provide start and end conductor widths that exactly correspond to the specified Ro and RL. This is by design (see [2]). Smaller ratios RL/Ro and smaller Rmax generate start and end widths that provide a better match to Ro and RL.


[1] R.W. Klopfenstein, "A transmission Line Taper of Improved Design," Proc. IRE, vol. 44, January 1956, pp. 31-35

[2] D.M. Pozar, Microwave Engineering, ch. 5, sect. 5.8, 4th ed. New York: Wiley, 2012

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