*Simulation saves time, money, and effort in resolving EMI problems in any application.*

Chris Debraal

Curtis Industries

Milwaukee, WI

The insertion loss of a power line EMI filter can be accurately predicted over a wide range of frequencies through circuit simulation. While analyzing the circuit, it is important to consider test modes and impedances, basic component values, and a variety of parasitic elements representing each component, as well as construction and layout.

Formulas for determining equivalent series inductance and resistance of capacitors, as well as inter-winding capacitance and core roll-off, will help create component models. Other elements concerning lead length, proximity effects, and crosstalk will help define the system parasitics. These “modeled” components can then be combined into a single full schematic for simulation of constructed circuits.

Manipulation of the basic and parasitic component values will lead to performance enhancements and will suggest design improvements. A comparison of simulation and actual test data will demonstrate how accurate results can be. With complete circuit representations, performance of EMI filters can be correctly characterized and can be optimized for efficiency. Filter circuit simulations can be set up to “mimic” actual test results, saving time and money in research and prototyping.

**EMI
**

Electromagnetic interference (EMI) is a type of undesirable electromagnetic emission that causes various levels of noise response, malfunctioning, or degradation in the performance of electrical equipment. This noise is most often found in the frequency range of 10 kHz to 30 MHz. To reduce this noise, an EMI filter is often used. An EMI filter is a passive electronic device used to suppress conducted interference present on any power or signal line. The filter may be used to suppress noise generated by the device itself, as well as noise generated by other equipment, and to improve the functionality of the device within its electrical environment. EMI filters can include components to suppress both common-mode (line-to-ground) and differential-mode (line-to-line) interference.

**Selecting Components
**

The proper design of an EMI filter includes selecting the appropriate components needed to filter out any EMI noise. These components include inductors and capacitors. Assessing these components involves a variety of details that must be addressed to insure proper filtering, such as inter-winding capacitance within the inductor coil, effective series resistance (ESR), and effective series inductance (ESL or lead inductance) within the capacitors themselves.

**Schematic
**

EMI filters consist of common-mode coils that improve line-to-ground performance, but can also be used to help differential-mode (line-to-line) performance by utilizing the coil’s leakage inductance. Line-to-ground capacitors are used in conjunction with the inductors to boost common-mode performance, and line-to-line capacitors are used to obtain differential-mode performance. (The line-to-line resistor provides no help in performance. Its only function is to serve as a bleeder resistor for safety by discharging the L/L capacitors upon disconnecting the filter.)

With a basic understanding of the construction of an EMI filter, a designer is prepared to take the next step by simulating the filter circuit to determine how well the filter will perform over the desired frequency range. A number of software programs can be used to simulate circuits. In this instance, the author used a PSpice and SPICE-compatible analog and digital simulator for electronic design automation. The makers of this type of software often offer evaluation versions easily downloadable from the Internet. These programs are very user friendly and will allow for easy simulation of circuits using AC analysis tools, while setting the desired frequency range and nodes to be analyzed. The filter schematic used in this example is shown in (Figure 1).

**50/50 Circuit
**

In each of the schematics, the simulation will use a 50/50-Ohm circuit (50-Ohm impedance on both the line and load sides of the filters). These values are used as a standard insertion loss test method; therefore, it is necessary to represent these values in the schematic to simulate real insertion loss testing.

**Inductor Simulation
**

The first component to be considered is the inductor. Most inductors are made up of a toroid core wound with various gauges of magnet wire. The most common core materials used in filter applications are ferrite and iron powder. Depending on the core material and the number of turns, the performance of an inductor tends to have a “roll-off” property–f0, the frequency at which the inductor starts to lose its performance capabilities. This roll-off value is almost always specified within the specification of the core material. Simply find the f0 within the spec of the core material, and insert it into the formula shown in the circuit schematic. This step helps make the inductor model more “real.” For example, a 5k-permeability core material generally has an f0 value of approximately 300 kHz. That number is squared and is put into the inductor model formula, shown in Figure 3 as “1E11.”

When using a common-mode inductor, the filter will have a different performance level in common mode than it does in differential mode so it is important to simulate the two circuits separately. Inductors carry a standard inductance value (most effective in common-mode performance), as well as a leakage inductance value (most effective in differential-mode performance). Consequently, the common-mode circuit will have an inductor model that represents the standard inductance, and the differential-mode circuit will show an inductor model that includes the value of the leakage inductance. If not measured, leakage inductance can be assumed to be 1% to 2% of the common-mode inductance value. Both models will also include a roll-off frequency formula to help make the simulations as close as possible to the actual filter. Again, the differential-mode roll-off frequency is approximated at 30 times higher than the common. By using the given formula, a designer can “mimic” the actual performance of a real inductor coil, which will result in more accurate filter simulation results.

**Inter-Winding Capacitance
**

Inter-winding (parasitic) capacitance is created from the proximity of the winding to the core and to other windings. The space between each turn acts as a capacitor in parallel with the inductor. The higher the level of capacitance, the greater reduction there is in the impedance of the inductor at higher frequencies. This reduced impedance will allow unwanted noise to pass more freely through the system. Hence, more parasitic capacitance will lower the upper limit of useful frequency.

The number of turns on a coil is limited by the inner diameter of its core and just how tightly the turns have been packed together. For increased inductance, once the maximum number of turns has been reached to wind the coil within a single flat layer, the designer must then create more turns with overlapping windings, thus creating multiple layers. While the first layer has capacitance from adjacent turns, the subsequent layers have additional capacitance from the adjacent layers as well, thus vastly increasing the inter-winding capacitance of the inductor. Clearly, with this vast increase, it is vital to include this component value in filter simulations (in parallel with the inductor) to obtain a more realistic result indicating actual filter performance. Figure 2 shows capacitance, as well as a picture of a typical inductor coil and a cross-section of the spacings of each turn and layer of wire.

C = kεA/d

where

k = dielectric constant of insulation material (typically 5 for magnet wire insulation)

ε = permittivity of free space, 8.55 X 10^{-12} (F/m)

A = effective plate area, (m2)

d = separation between turns/layers, (m)

Within the formula, ‘A’ is normally calculated by taking approximately 1/4 of the diameter of the magnet wire and multiplying it by the length of a single turn and the number of turns, and ‘d’ is simply two times the thickness of the insulation of the magnet wire. This formula is a simple approximation and a good approach for finding a useable value of inter-winding capacitance for a circuit simulation.

Additionally, the designer should include the actual resistance of the inductor’s wire in the formula. However, in the case of this simulation, it is only .055 Ohms and has a minimal effect.

Now, all the parasitic information can be put into the schematic. Figure 3 shows both the schematic and a plot of a simulated inductor coil as compared to that of a real inductor coil. Clearly, the match in plots is very favorable.

**Capacitor Lead Inductance
**

Any length of wire carries a certain inductance. Therefore, capacitor leads will also have a small amount of inductance associated with them, which can be easily measured. Generally, a 1/4″ capacitor lead measures approximately 9 nH of inductance. It’s important to include this lead inductance in the filter simulation circuit to obtain accurate results. This inductance value will be shown in series with the capacitor within the simulation circuit (Figure 4). As the length of a capacitor lead varies, the lead inductance will also vary and so will the resonant frequency of the capacitor. Obviously, it’s best to have an accurate measurement of real lead inductance based on the lead length and to “plug” that value into the circuit simulation.

**ESR
**

Capacitors also have a resistance associated with them called ESR (Effective Series Resistance). This value is usually specified within the specification of the capacitor and will also appear in series with the components within the filter schematic. Generally, .05 Ohms is a reasonable assumption for the ESR of most capacitors, as shown in these circuits. Now, having included the capacitor with appropriate lead inductance and ESR in series, let’s analyze the capacitor simulation versus a real capacitor plot.

Figure 4 shows a picture of a line-to-line film capacitor used for differential-mode performance, as well as the plots of simulated results versus real results. Again, as with the inductor, the plots are very similar.

**Simulating Complete Filters
**

Having considered all of the components, let’s simulate the entire filter in both common- and differential-modes. Figures 5 and 6 are the simulated schematics for both modes, as well as the filter plots versus actual filter test results. Since the models do not address certain types of parasitics such as grounding, shielding and iron proximity, unrealistic results may be seen well above 100 dB within a software simulation. Normally, because of these specific parasitics, the best real performance one might expect out of most EMI filters is 80 dB at any given frequency (shown as a dashed line in the differential-mode plots (Figure 5)). Aside from that limitation, the differential plots match very closely and demonstrate that the models do approximate the insertion loss of the filter.

In the common-mode plots (Figure 6), the resonant frequency patterns match, but there is again a shift in magnitude because of the parasitics that were not included.

**Conclusion
**

As shown in the information above, EMI filters can be easily simulated to help save time, money, and effort in resolving electromagnetic interference problems in any application. Regardless of the design, these simulations will determine the exact type of filter needed and are ideal for custom designs where time and materials are limited. Rather than building countless prototypes and testing each design, these simulations create the designs on-screen rather than in the screen room.

**Chris Debraal** works as a Project Engineer for Curtis Industries in Milwaukee, WI. His primary job duties include the design, simulation, prototyping, and aid in construction of EMI/RFI filters.

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