# 2.1. Introduction

Because EMI produced by switch mode power supplies usually exceeds acceptable levels, the emissions must be reduced. In most practical cases, noise suppression is accomplished by using lowpass filters. For instance, a typical L-type lowpass filter, as shown in Fig. 2-1; used to attenuate high frequency noise, Z1 (in the series path), which requires high impedance; is normally implemented by inductor. Meanwhile, low impedance characteristics are required for Z2 (in the shunt path), which is normally implemented by capacitors. To obtain desirable high-frequency (HF) attenuation, the HF characteristics of the filter elements are critical.

# 2.2. Parasitic parameters of EMI filter components

EMI filter elements are subject to two basic requirements: they have to safely tolerate the nominal operating voltage and current of the electrical equipment, and their HF characteristics must not vary with frequency. It is necessary to understand the HF characteristics of filter elements in order to design EMI filters. EMI filter elements cannot be simply considered ideal within their frequency reduction bands. In the frequency range of 150 kHz to 30 MHz, the equivalent circuit of EMI filter elements becomes a two- or four-terminal network containing several components. Characterization of EMI filter elements at HF should be based on analysis of the entire equivalent circuit.

# 2.2.1. Parasitic parameters of filter capacitors

A real capacitor is not pure capacitance (even at low frequencies), since the leakage resistance of the isolation and equivalent series resistance (ESR) cannot be neglected in either case. In addition, at higher frequencies, the effect of stray inductances should also

be taken into account. The characteristics of a real capacitor can be described by the equivalent circuit shown in Fig. 2-2. The impedance of the capacitor, ZC, is stated as follows:

Neglecting Rp, eqn. 2-1 is simplified to the form :Neglecting Rp, eqn. 2-1 is simplified to the form :

With the frequency increasing, the impedance of real capacitors will be determined more and more by the parasitic inductance L instead of the capacitance, which means the real capacitors behave more like an inductor than a capacitor at high frequencies. For real capacitors, a resonant frequency can be defined as:

The impedance of a real capacitor is RS (ESR) at resonance frequency. The impedance as a function of frequency, defined by eqn. (2-1), is shown in Fig. 2-3. As seen from the curve, the capacitor can be regarded as capacitance only in the frequency range labeled ωc. As the frequency and the applied voltage increase, the value of the dielectric constant and associated capacitance C may decrease. Sometimes this fluctuation is significant and cannot be neglected.

# 2.2.2. Parasitic parameters of inductors

Noise-suppression inductors can be well characterized in a wide frequency range by the equivalent circuit shown in Fig. 2-4. The resistance in the equivalent circuit represents the losses of the coil. Parasitic effects on higher frequencies, resulting from the stray capacitances between turns and layers, cannot be neglected. Although the parasitic capacitance is distributed, a parallel-connected concentrated capacitor provides a suitable approximation. The impedance of the inductor according to the equivalent circuit is:

At low frequencies, impedance ZL is dominated by inductance, and at DC it is equal to RS. At a certain frequency (defined as self-resonance frequency ω0=1/\sqrt((1)/(LC) , the inductor L resonates with the parallel capacitor C, and the impedance ZL reaches its maximum, as shown in Fig. 2-5. At higher frequencies, the impedance of the choke

decreases because the parallel capacitor dominates; i.e., the inductor acts like a capacitor.

# 2.3. Discrete EMI filter structure and equivalent circuit

The schematic of a typical EMI filter is shown in Fig. 2-6 (a). The photograph of a prototype is shown in Fig. 2-6 (b). The EMI filter consists of a common mode (CM) choke, a differential mode (DM) inductor, two CM capacitors (so-called Y-caps) and two DM capacitors (so-called X-caps).

To prevent a threat of electrical shock for personnel handling the equipment, the safety standards relating to the use of Y-caps are much stricter than those applied to Xcaps. The capacitance of Y-caps is limited by the leakage current according to different safety standards for different applications, normally within a range from 1 nF to10 nF. Therefore, Y-caps are normally single layer ceramic disk capacitors. X-caps do not pose a threat of electrical shock to personnel. However, the input power factor can be greatly reduced if the X-cap is too large. Therefore the X-cap capacitance is usually within a range from 0.1 µF to 1 µF. Normally, multi-layer ceramic capacitors (MLC) or polypropylene film capacitors are used for X-caps.

Since the DM power current also passes through the filter, EMI filters are required to exhibit high impedance for CM signals but low impedance for DM signals. This is accomplished by using a CM choke. A CM choke consists of identical windings placed in a closed core. For DM excitation (i1 = -i2), the flux generated by the currents in the two

windings is cancelled in the core; hence, only the leakage inductance is observed. For CM excitation (i1=i2), the equivalent circuit is reduced to two coupled inductors in parallel, which exhibits high impedance for CM noise. Because the amplitude of CM noise current is usually very low, the magnetic core can be made without an air gap, using high permeability ferrite materials. The CM inductance ranges from 1 mH to 5 mH. In practice, the inductance of the DM inductor cannot be very large because the DM power current will excite the ferrite core, and high inductance will cause core saturation or require a large core size. The DM inductance is usually within a range from 10 µH to 20 µH. Normally the DM inductance can be implemented by utilizing the leakage inductance of the CM choke; hence, a separated DM inductor is not necessary.

Under CM and DM excitations, the equivalent circuits are different, as shown in Fig. 2-7 (a-b), respectively. It is found that the CM equivalent circuit is an L-type lowpass filter, while the DM equivalent circuit is a π-type lowpass filter.

2.4. Measuring HF characteristics of EMI filters

In widely accepted practices, EMI filters can be evaluated by transfer gain (TG) or insertion loss (IL).

Fig. 2-6 (a) Schematic of EMI filter (b) Photo Photograph of a discrete EMI filter prototype

The CM or DM equivalent circuits of EMI filters can be represented by a fourterminal network, shown in Fig. 2-8. Its transfer gain is defined as:

TG = 20log(U2/U1) (2-5)

The insertion loss is expressed by the ratio of two powers:

IL=10log(P1/P2) (2-6)

# 2.5. Impacts of parasitic parameters on characteristics of EMI filters

As mentioned before, inevitably every EMI filter element has parasitics, such as EPC of the inductors and ESL of the capacitors. When mounting the filter components on a board and connecting them with wires and traces, ESL and EPC will change, caused by the electromagnetic coupling between the filter components and interconnection wires and traces. As far as these parasitics are considered, the first order approximation equivalent circuit of EMI filters is shown in Fig. 2-9.

To illustrate the impacts of parasitics on HF characteristics of EMI filters, the CM and DM transfer gains of a discrete EMI filter prototype are measured, as shown in Fig. 2-10 and Fig. 2-11.

On the measured CM transfer gain curve shown in Fig. 2-10, f0 is the corner frequency of the filter, determined by the CM inductance and the Y-caps capacitance. At f1, the measured gain curve diverts from the ideal curve, caused by the self-resonance of the CM choke, resulting in reduced HF attenuation. The HF attenuation is further reduced starting from frequency f2, where the Y-cap resonates with its ESLs. Similar phenomena can be observed in the measured TG curve shown in Fig. 2-11, except that f1’ is determined by the self-resonance frequency of the X-caps, and f2’ is determined by the self-resonance of the DM inductor. From the above observations, it can be concluded that HF characteristic of EMI filters is actually determined by parasitics.

## 2.6. Other issues of discrete

EMI filters In addition to the major issue of the inherent parasitics of the discrete EMI filters, there are some other concerns. Firstly, a discrete EMI filter is composed of separate components with different sizes and form factors. When putting them together, a large interconnection space is required because of the unmatched form factors. Poor space utilization and large overall filter size is expected. Secondly, as low-profile switch mode power supplies (SMPSs) become more and more common in the current power supply industry, low-profile EMI filters are also required in order to be compliant with other components in the circuit. Consequently, the conventional high-profile toroidal CM choke has to be replaced by planar magnetics. Lastly, the different types of filter elements are manufactured through different processing, fabrication and packaging technologies, and are physically separated at point of assembly. Some of the elements, such as the wire-wound toroidal inductors, require labor-intensive processing steps, resulting in a long manufacturing time and high cost.

## 2.7. Summary

In this chapter, high frequency characteristics and parasitics of EMI filter elements are discussed. Their impacts on HF characteristics of EMI filters are studied. Because of the parasitics of the elements and the interconnection of wires and traces, attenuation of discrete EMI filters reduces appreciably at high frequencies. Also, different form factors, sizes, structures, processing technologies, and packaging technologies of different components contribute to a large size, high profile, and high cost. These issues are difficult to solve by using the current discrete-component approach. Passive integration technologies are developed to integrate EMI filter components into a single module and to attempt to solve these problems. Details will be presented in the following chapters.