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# Simulation of a Coupled Lines Filter

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## Description

Coupling between two transmission lines is introduced by their proximity to each other. Coupling effects are sometimes undesirable, such as crosstalk in printed circuits, and sometimes desirable, as in directional couplers where the objective is to transfer power from one line to the other.

Based on the coupled lines theory [1],  a filter was designed by utilizing  four microstrip resonators. In this example, we show a band pass filter operating around 2.54 GHz.

Figure 1 - Coupled microstrip filter

Figure 2 - All dimensions are in mm

## Simulation

The Scattering Parameter simulator was used. The frequency plan is precise with a small step and is uniformly distributed between 2 and 3 GHz.

## Solids and Materials

The microstrip lines were printed on a substrate with a relative permittivity of 3.3.  The layer beneath the substrate has a very small thickness and therefore is considered as a PEC surface. Since microstrips do not allow TEM propagation due to the air layer above the conductor, we should model an air box to create heterogeneity between the two mediums.

The ports are applied to small areas next to the microstrip line's beginning and end. The ground metal is considered as a Perfect Electric Conductor.

## Meshing

The mesh has to be fine enough on the port and RF carrier conductor. The gap between the conductor segments should be finely meshed as well.

Figure 3 - Mesh of the Microstrip Filter

## Results

Various 3D and 2D plots are available to exploit, depending on the nature of the task and on which parameter the user is interested in. As we are dealing with a filter simulation, we could plot the reflection coefficient alongside the insertion loss for matching purposes.

Figure 4 - Near Electric Field distribution at 2.54 GHz

Figure 5 - Variations of reflection coefficient at the filter's input port

The filter is best matched at 2.54 GHz : the return loss is very low. The plot might be smoother if we apply a smaller  frequency step and reduce the frequency interval. Plotting the input reflection coefficient on a Smith Chart is possible as well.

## References

[1] Electromagnetic Waves and Antennas, Sophocles J. Orfanidis ECE Department  Rutgers University