# Estimation of SMPS' Conducted Emission According to CISPR Standards
## 2 Materials and Methods
### The Layout of the SMPS
#### 2.3.1 ANSYS Q3D  
ANSYS Q3D [9] is a half-wave parasitic RLC extractor that can compute capacitance, inductance, and resistance matrices for AC or DC problems. It uses the finite element method to model current flow within conductors (DC resistance problems) and the method of moments to solve inductance and capacitance problems. Since Q3D uses [PERSON]'s equations simplification called quasi-static approximation, it assumes that the dimensions of the analyzed structures are small in comparison with the wavelength at the maximum frequency of analysis. Capacitance is extracted from the charge solution, DC resistance is extracted from DC conduction solution, and AC/DC inductance and AC resistance are extracted from the field solution. Afterwards, the ODB++ file was imported to the ANSYS Q3D software as a 3D model (shown in Figure 12). Then, nets were identified based on the previously chosen high-frequency current loop shown in Figure 5a,b. Nets are single pieces of conductors (whole traces or divided traces) for which parasitic RLC parameters were identified. The rest of the 3D model, not considered to be part of that loop, was removed from the analysis to prevent influence on the results and save the simulation time. Once the nets were identified, ports (sinks and sources) for each net were assigned based on the supposed current flow direction. Sinks and sources assignment is necessary to have full RLCG matrices calculation. For capacitance and conductance matrices, Q3D applies 1 volt to a single conductor and 0 volts to all other conductors. For resistance and inductance matrices, Q3D applies 1 amp to a single source and 0  
Figure 11: The electrical model of the LISN used in the time-domain simulation. Figure 12: The Q3D layout model. Resistance matrices are calculated based on ohmic losses (skin effect and mutual resistances are considered in the AC solution). The basic principle of Q3D simulation is the fact that the charge at infinity is assumed to be zero. This can be changed by \"float at infinity\" reduction which causes potential at infinity to float and enables the use of the local ground plane. Since there is no evident reference net in 3D SMPS layout model, it was decided to treat all the nets as signal nets and compute RLGC matrices for all of them, without indication of reference/GND net and use of \"float at infinity\" reduction. Since one path on the layout can be connected to multiple elements (e.g., the path between the ferrite core and upper MOSFET transistor is also connected to the filtering capacitor), original paths were divided into sections (Figure 13) to be able to extract parasitic RLCG for relevant traces. Then, those divided paths were assigned nets, sinks, and sources before being connected back to the time-domain electrical simulation. An interpolating sweep between 0 Hz and 100 MHz was chosen for analysis, while the solution frequency (solution for which the mesh is calculated) was chosen to be 1 GHz. It is worth noting that proper frequency range of the analysis should be chosen. In the case of the Q3D solver, for the low-frequency model, the starting point should be 0 Hz. The analysis end frequency--100 MHz--gives enough margin since the final emission analysis is done in the frequency range 9 kHz to 30 MHz. Error tolerance was set to 0.01%. The mesh size was set to default settings and is shown in Figure 14. An interpolating frequency sweep was used instead of a discrete frequency sweep because it estimates the solution for the entire frequency range and reduces the time required to calculate the parameters. The software uses frequency points in which the field solution is solved so that the entire interpolation solution is within the tolerance specified. It avoids solving solutions at each frequency point as it is done in a discrete sweep, which makes simulation converge in much less time. Full-field solution is saved only for the final point of the sweep, but RLGC matrices and S-parameters are saved for every solved point. Figure 13: An example of a path division.