his is the third article of a three-article series devoted to the correlation between the insertion loss and input impedance of passive EMC filters. In the first article, [1], LC and CL filters were discussed, while the second article, [2], was devoted to the π and T filters. This article focuses on LCLC and CLCL, or cascaded LC and CL, filters. Analysis, simulation, and measurement results show that the frequencies at which the insertion losses of these filters are equal are the same frequencies at which the input impedances are equal. These frequencies define the regions where one filter configuration outperforms the other (with respect to the insertion loss). To determine these regions analytically, we compare the input impedances of the two filters.
or [3]
The magnitude of the input impedance is
or [3]
The magnitude of the input impedance is
Next, let’s calculate the frequencies at which the input impedances of the two filters are equal. Equating the expressions in equations (4) and (8) produces
This equation can be solved for ω [3] resulting in
These results are consistent with the values obtained from the simulation in Figure 4.
Note that up to the frequency of 561 kHz, the insertion loss of the CLCL filter is larger than that of the LCLC filter. Between the frequencies of 561 kHz and 1.04 MHz, the insertion loss of the LCLC filter is larger. Between the frequencies of 1.04 MHz and 1.36 MHz, the insertion loss of the CLCL filter is larger. Beyond the frequency of 1.36 MHz, the insertion loss of the LCLC filter is again larger.
Once again, [1,2], we have arrived at a very important observation: once the filter components values L and C are chosen, we can determine the frequencies at which the insertion losses of the two filters are equal. These are the frequencies at which the input impedances are equal, given by Equations (11).
To verify the simulation results of the insertion loss, the measurement setup shown in Figure 7 was used.
References
- Bogdan Adamczyk and Jake Timmerman, “Correlation Between Insertion Loss and Input Impedance of EMC Filters – Part 1: LC and CL Filters,” In Compliance Magazine, October 2023.
- Bogdan Adamczyk and Jake Timmerman, “Correlation Between Insertion Loss and Input Impedance of EMC Filters – Part 2: π and T Filters,” In Compliance Magazine, November 2023.
- Bogdan Adamczyk, Principles of Electromagnetic Compatibility: Laboratory Exercises and Lectures, Wiley, 2024.