Example40 Circular Patch Antenna


  • The transient analysis is performed for a circular patch antenna on a dielectric substrate.

  • Due to the resonant characteristics, it takes long time to obtain the S-parameters with high accuracy.

  • At the end of the analysis, result estimation is executed because the ratio of residual fields is higher than the threshold.

  • The result estimation is verified by the restart analysis.

  • Unless specified in the list below, the default conditions will be applied.

  • Electromagnetic-transient analysis is available in an optional package.

Analysis Condition

The condition setting for the transient analysis is as follows.





Electromagnetic analysis [Hertz]

Analysis Space


Analysis Type

Transient analysis

Select Input at each port





Setting Item



Frequency-Dependent Meshing

  • Select The conductor bodies thicker than the skin depth constitute the boundary condition

  • Select Determine the reference frequency automatically from the input waveform

Transient Analysis



Input wave setting

  • Waveform type: Broadband pulse
  • Minimum frequency: 3.0 × 109 [Hz]
  • Maximum frequency: 6.0 × 109 [Hz]

Finish time of calculation

  • 2.0×10-9[s]


Select Output Field




Antenna pattern is a circular sheet body. It is covered with a hemispherical air.

An open boundary is set on the hemisphere of the air domain as an outer boundary condition. To the plane of the air domain,

electric wall is set. A port is placed slightly off the center of the circular antenna pattern.


Body Attributes and Materials

Body Number/Type

Body Attribute Name

Material Name



006_Glass_epoxy *



000_Air *



008_Cu *

(*) Available from the material DB

Boundary Condition

Boundary Condition Name/Topology


Boundary Condition Type





Reference Impedance:

  • select Specify

  • 50 Ω


Integral Path:

  • Set Path1



Electric Wall


Outer Boundary Condition


Open Boundary

Select on the open boundary tab of the analysis condition setting.


The resonant characteristics of the circular patch antenna can be examined in the result table and field of the electromagnetic analysis (time domain).

Also the resonant characteristics can be examined in the S-parameters as well.


The electromagnetic waves entered from the port resonate on the circular patch antenna. At the finish time of calculation, many electromagnetic waves

(residual field) still remain in the model and its ratio is above the threshold. In such a case, analysis accuracy of the S-parameters which is a result of the frequency domain is not high.


If the residual field at the finish time of calculation is larger than the threshold, the output results of each timestep are automatically estimated

until when the residual field becomes small. The estimated S-parameters are output as well.


In this example, the result of the resonant characteristics is compared to the estimated result. Also, based on the estimated result,

the restart analysis is performed by resetting the finish time of analysis to verify the estimated result.


Note: The numerical values of the results below depend on the meshes used.

Examine Resonant Characteristics from the Result Table (Time Domain)

Fig. 1 shows the output voltage of the result table and the ratio of the residual electric field.

As shown in the graphs, the output voltage at the port and the ratio of the residual electric field do not attenuate very much after when the input is finished at around 450[ps].

The values remain large even at the finish time of analysis.

(The estimated data is not displayed on these graphs. On the graph of the ratio of residual electric field, Y axis is in logarithmic display)


This means that the input electromagnetic waves are stored as a resonant mode in the model for a long time. Due to conductor loss, dielectric loss,

and dissipation of the electromagnetic waves to the outside through open boundary and port, the residual electric field is gradually attenuated.

If resonant mode exists, the attenuation speed is very slow.


From the output voltage of Fig. 1, the period of the resonant mode is approximately 250[ps], and the resonant frequency is approximately 4GHz.


Fig. 1: Output Voltage at the Port and Ratio of the Residual Electric Field



Examine Resonant Characteristics from the Result Field

Fig. 2 shows the electric fields near the circular patch antenna at 1.5[ns] and 1.625[ns]. In the left figure (1.5[ns]), the electric field near the port

is in the positive Z direction. In the right figure (1.625[ns]), the magnitude of the electric field is almost the same but its direction is in the negative Z direction.


This means that resonance occurs on the circular patch antenna and the direction of the electric field is reversed in a cycle of about 125[ps].

It idicates that the period of the resonant mode is approximately 250[ps]. It matches with the resonant frequency in the result table above.

Fig. 2: Result Field of Electric Field (Left: 1.5[ns], Right: 1.625[ns])


Examine the Estimated Result

The estimated result is examined as below.

In this model, the result is estimated up to 5.0[ns] because it is judged that by 5.0[ns], the electromagnetic waves in the analysis model will disappear due to the dissipation or loss,

and that the residual electric field will be reduced. (Caution: Finish time of estimation depends on the meshing condition.

The estimation is not an accurate result. )


If the ratio of residual electric field exceeds the threshold and estimation is performed normally, the estimated result up to the time when the ratio of residual electric field becomes small is output.

Fig. 3 shows the result (red line) and the estimated result (red line) of the output voltage and the S-parameters.

In this model, the analysis finished at 2.0 [ns]. Based on the analysis result, the output is estimated until 5.0 [ns]. (Note: The field values are not estimated)


Compared to the actual analysis result up to 2.0 [ns], the S-parameters obtained by the estimated result until 5.0 [ns]

shows clearer resonant characteristics. The resonant frequency is approximately 4.3GHz which is close to the estimated value of 4GHz in the result above.


Fig. 3: Analysis Result and Estimated Result (Left: output voltage, Right: S-parameters)



Verify the Estimated Result by Restart Analysis

In order to verify the estimated result, restart analysis is performed.


From the estimated result, it is expected that the electromagnetic waves in the model will disappear if the analysis continues until 5.0[ns] because of dissipation or loss. It is also expected that the analysis accuracy of the S-parameters, which is the result of frequency domain,

will be sufficiently high. As shown in Fig. 4, the restart is set up on the transient analysis tab of the analysis condition for the model (Trans).


Select Continue from the last session and set 5.5[ns] for Finish Time of Calculation. By continuing from the last session, the meshes used in the last session

(analysis up to 2.0[ns]) are used starting at time of 2.0[ns]. For the finish time of calculation,

5.5[ns] is set which is longer than the estimated time of 5.0[ns] just in case.


Fig. 4: Restart Analysis Setup



The residual electric field of the model becomes small in the analysis up to 5.5[ns]. The analysis is automatically finished when the value becomes smaller than the threshold.


Fig. 5 shows the result of output voltage. The right figure is a comparison of the analysis result after 2.0[ns] and the estimated result.

As the figure shows, the result and the estimation match indicating the estimation is correct in this model.

Fig. 6 shows a comparison of S-parameters. The left figure is a comparison between the analysis result and the estimated result. The right figure is a comparison between the estimated result and the harmonic analysis result.

From these results, it can be confirmed that the estimated result is correct. On the contrary, the analysis result up to 2.0[ns] shows the low accuracy of the S-parameters.


In a model having resonant mode as in this example, the analysis accuracy of the frequency domain such as S-parameters may be low if the analysis is not carried on for a long time after the input of electromagnetic waves is finished.

For such model, the result estimation gives suggestions on


  • For how long the analysis is needed to be performed
  • Rough idea of S-parameters behavior


Fig. 5: Output Voltage (left: analysis result up to 5.0[ns], right: comparison with estimation)


Fig. 6: S-parameters (left: result comparison of restart analysis (blue line) and estimation (red line),

right: result comparison of harmonic analysis (blue line) and estimation (red line))