# Estimation of SMPS' Conducted Emission According to CISPR Standards
## 2 Materials and Methods
### The Layout of the SMPS
#### 2.3.2 ANSYS HFSS  
ANSYS HFSS [10] is a full-wave solver which considers mutual coupling between magnetic and electric fields. It considers all relevant magnetic phenomena connected to Maxwell equations, but the analysis can be more time-consuming than with Q3D. It uses the finite element method to generate an electromagnetic field solution. In this method, the area of the solution is divided into smaller regions called tetrahedra (finite element mesh). Then, fields in those subregions are estimated by local basis functions. Structures within the model are excited through ports, with field patterns that can originate from transmission lines of the same cross-section as the port. Finite element mesh is firstly created and refined for an adaptive solution frequency; also, the field solution is primarily computed for that frequency. Then, this mesh is used for the interpolating frequency sweep, which estimates solutions in the whole frequency range of interest. Frequency points at which field solutions are solved are chosen by HFSS software so that the entire interpolated solution is within the error tolerance specified by the user. During the solution process, S-parameters [11] are generated and saved for every frequency point. A driven terminal solution is used to calculate the S-parameters based on terminals. The S-parameters' matrix is then expressed in terms of voltages and currents on the terminals. The layout that the authors worked with was lacking any plane that could be used for reference plane purposes. To overcome this problem and extract parameters of the layout with a full-wave solver, the authors of this publication added the artificial REF plane to the model at a distance of 20 mm (Figure 15) from the layout. According to the equation 1 and equation 2 from [12; 13], a higher distance from the conductor to the reference plane means that the characteristic impedance is also rising. In order to replicate the lack of a reference plane in the real layout, the 20 mm distance of the reference plane to the layout traces were arbitrarily chosen so that the characteristic impedance of a 1 mm trace is 300 Ohm--which is considered to be a high enough value that all positive aspects of having a reference plane can be neglected. The transformer was modeled as a perfect conducting plane TR (Figure 15) with two ports. The shape of the plane is exactly the same as the shape of the real transformer. For simplicity of the analysis, it was assumed that secondary currents of the transformer flow to the reference plane REF (Figure 15).  
\[\in_{eff}=0.475\in_{r}+0.67, \tag{1}\]  
Figure 14: View of the Q3D model mesh.  
\[Z_{0}=\frac{60}{\sqrt{\varepsilon_{eff}}}\ln\frac{5.98h}{0.8w+t}, \tag{2}\]  
where:  
* \(w\) is the trace width,
* \(h\) is the trace height,
* \(t\) is the trace thickness,
* \(\varepsilon_{eff}\) is the effective dielectric constant,
* \(Z_{0}\) is the characteristic impedance,
* \(\varepsilon_{r}\) is the dielectric of the material.  
Next, the traces associated with the current loops of primary winding shown in Figure 5 were divided into sections with two ports on each section. This limitation comes from the methodology of how S-parameters are calculated. The view of the ports, layout, and reference plane model is shown in Figure 16.  
Figure 16: Overview of the ports assigned to the 3D model in HFSS.  
Figure 15: Overview of the 3D model used in HFSS.  
The simulation integration time was set to a fixed value of 10 ns, which allows having results up to 50 MHz.  
Figure 19: Electrical schematic for transient simulation—Q3D approach: (**a**) LISN and primary side; (**b**) secondary side.  
Figure 18: Electrical schematic for transient simulation—HFSS approach: (**a**) LISN and primary side; (**b**) secondary side.