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==Description== |
==Description== |
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| − | A '''branchline coupler''' (see <xr id="fig:branch"/>) is a microwave semiconductor device, which is simulated by the time-harmonic Maxwell's equation. |
+ | A '''branchline coupler''' (see <xr id="fig:branch"/>) is a microwave semiconductor device, which is simulated by the [http://www.maxwells-equations.com/forms.php#harmonic time-harmonic Maxwell's equation]. |
A 2-section '''branchline coupler''' consists of four strip line ports, coupled to each other by two transversal bridges. |
A 2-section '''branchline coupler''' consists of four strip line ports, coupled to each other by two transversal bridges. |
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The energy excited at one port is coupled almost in equal shares to the two opposite ports, when considered as a [[List_of_abbreviations#MIMO|MIMO]]-system. |
The energy excited at one port is coupled almost in equal shares to the two opposite ports, when considered as a [[List_of_abbreviations#MIMO|MIMO]]-system. |
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<figure id="fig:branch"> |
<figure id="fig:branch"> |
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| − | [[File:BranchlineCoupler.png|frame|<caption>Branchline Coupler Model<ref |
+ | [[File:BranchlineCoupler.png|frame|<caption>Branchline Coupler Model<ref name="hess13"/></caption>]] |
</figure> |
</figure> |
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The affine form <math> a(u, v; \omega, \mu_r) = \sum_{q=1}^Q \Theta^q(\omega, \mu_r) a^q(u, v) </math> can be established using <math> Q = 2 </math> affine terms. |
The affine form <math> a(u, v; \omega, \mu_r) = \sum_{q=1}^Q \Theta^q(\omega, \mu_r) a^q(u, v) </math> can be established using <math> Q = 2 </math> affine terms. |
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The matrices corresponding to the bilinear forms <math> a^q( \cdot , \cdot ) </math> as well as the input and output forms and the H(curl) inner product matrix have been assembled |
The matrices corresponding to the bilinear forms <math> a^q( \cdot , \cdot ) </math> as well as the input and output forms and the H(curl) inner product matrix have been assembled |
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| − | using the Finite Element Method, resulting in <math>27679</math> degrees of freedom, after removal of boundary conditions. |
+ | using the [[wikipedia:Finite_Element_Method|Finite Element Method]], resulting in <math>27679</math> degrees of freedom, after removal of boundary conditions. |
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The coefficient functions are given by: |
The coefficient functions are given by: |
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while assembling the matrices, while the material variation occurs between <math> \mu_r \in [0.5, 2.0] </math>. The input functional also has a factor of <math> \omega </math>. |
while assembling the matrices, while the material variation occurs between <math> \mu_r \in [0.5, 2.0] </math>. The input functional also has a factor of <math> \omega </math>. |
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==Origin== |
==Origin== |
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==References== |
==References== |
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| − | <references |
+ | <references> |
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| + | <ref name="hess13">M. W. Hess, P. Benner, "<span class="plainlinks">[https://doi.org/10.1109/TMTT.2013.2258167 Fast Evaluation of Time-Harmonic Maxwell's Equations Using the Reduced Basis Method]</span>", IEEE Transactions on Microwave Theory and Techniques, 61(6): 2265--2274, 2013.</ref> |
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| + | </references> |
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==Contact== |
==Contact== |
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Revision as of 11:42, 26 February 2018
Description
A branchline coupler (see xx--CrossReference--dft--fig:branch--xx) is a microwave semiconductor device, which is simulated by the time-harmonic Maxwell's equation.
A 2-section branchline coupler consists of four strip line ports, coupled to each other by two transversal bridges.
The energy excited at one port is coupled almost in equal shares to the two opposite ports, when considered as a MIMO-system.
Here, only the SISO case is considered.
The branchline coupler with 
thickness is placed on a substrate with 
thickness and relative permittivity
and zero-conductivity 
.
The simulation domain is confined to a 
box.
The metallic ground plane of the device is represented by the electric boundary condition. The magnetic boundary
condition is considered for the other sides of the structures. The discrete input port with source impedance 
imposes 
current as the input. The voltage along the coupled port at the end of the other side of the coupler is
read as the output.
Considered parameters are the frequency 
and the relative permeability 
.
The affine form 
can be established using 
affine terms.
The discretized bilinear form is 
, with matrices 
.
The matrices corresponding to the bilinear forms 
as well as the input and output forms and the H(curl) inner product matrix have been assembled
using the Finite Element Method, resulting in 
degrees of freedom, after removal of boundary conditions.
The coefficient functions are given by:
The parameter domain of interest is ![\omega \in [1.0, 10.0] * 10^9 Hz](/morwiki/images/math/b/f/8/bf8d49edc686adb6e6f829f3e4e53180.png)
, where the factor of 
has already been taken into account
while assembling the matrices, while the material variation occurs between ![\mu_r \in [0.5, 2.0]](/morwiki/images/math/2/9/2/29202560b62a3e37f907f997d40d342e.png)
. The input functional also has a factor of .
Data
The files are numbered according to their appearance in the summation and can be found here: Matrices.tar.gz
Origin
The models have been developed within the MoreSim4Nano project.
References
- ↑ M. W. Hess, P. Benner, "Fast Evaluation of Time-Harmonic Maxwell's Equations Using the Reduced Basis Method", IEEE Transactions on Microwave Theory and Techniques, 61(6): 2265--2274, 2013.