In order to choose the right components for EMI filters, the behavior of passive components at high-frequencies is important to understand. Therefore, we discuss here the high-frequency behavior of passive electronic components.
There are, roughly said, three basic classes of resistors. All of them are designed for different applications and have their own advantages and drawbacks when it comes to high frequency:
Wirewound. For high-power applications. High inductance L [H].
Film type. General-purpose low-power resistors. Low inductance L [H].
Carbon composition. High energy surge applications. Low inductance L [H].
Below is the high-frequency equivalent circuit of a resistor with the parasitic elements Cp [F] (between the solder pads and internally) and Ls [H] (series lead inductance) [9.1][9.2].
Be aware that the equivalent circuit model in Fig. 11.9 does not include the parasitic effects of the resistor’s mounting parts (PCB pads). The impedance Z [Ω] of a non-ideal resistor can be written as:
where R [Ω] is the resistance, Ls [H] is the parasitic series inductance, and Cp [F] is the parallel (shunt) capacitance.
Besides the parasitic elements of Ls [H] and Cp [F], the frequency response of a resistor
also depends on the resistor’s nominal value itself. The figures below show the simplified frequency response for resistors with small nominal values (e.g. <100Ω, the upper graph) and for large resistor values (e.g. >1kΩ, the lower graph).
Nowadays, film resistors are widely used because they are inexpensive and accurate. The pictures below compare the frequency behavior of a 50Ω resistor (upper graph) vs. a 1kΩ resistor (lower graph) of the same technology and size (axial, 0603 thick film, 0603 thin film). With increasing frequency, the parasitic parallel (shunt) capacitance Cp [F] and the parasitic series inductance Ls [H] lead to non-ideal frequency response. The plots show that for frequencies f>100MHz, only surface-mount technology (SMT) resistors should be used (axial leaded resistors are not suitable for high-frequency applications due to the wired terminals). Above 1GHz, dedicated high-frequency thin-film resistors show acceptable performance, whereas thick-film resistors often fail because they have higher parasitic inductance and capacitance compared to thin-film resistors.
Capacitors can be categorized by its dielectric material:
Ceramic. Multilayer ceramic capacitors (MLCCs) are the most widely used capacitors
today. They have relatively low equivalent series inductance (ESL) and low equivalent series resistance (ESR). They are used up to several GHz (dielectric
material C0G, NP0).
Electrolytic. Electrolytic aluminum and tantalum capacitor have a high capacitance-to-volume ratio and they have relatively high ESRs. They are usually used up to 25 kHz or 100 kHz.
Film and Paper. Film and paper capacitors have considerably lower ESR than electrolytic capacitors but still moderately large inductance. They are usually used up to several MHz.
Moreover, capacitors can be categorized according to their application:
Decoupling. Decoupling or bypass capacitors are placed close to the power supply pins of integrated circuits (IC) to provide a stable supply voltage to the ICs. In addition, decoupling capacitors help prevent voltage drops or spikes on the power supply line in case of a sudden change of current drawn by the integrated circuit. Usually, MLCCs with X7R or X5R dielectric are used as decoupling capacitors.
Low-voltage signal filters. Signal filters with a defined cut-off frequency in the low-voltage range (< 50V) are usually performed with stable class I MLCCs (C0G, NP0).
AC mains power filters. AC mains power filters require capacitors with a sufficient safety rating (IEC 60384-14, USA: UL 1414 and UL 1283, Canada: CAN/CSA C22.2 and CAN/CSA 384-14, China: GB/T 14472) because a failure of a mains power filter capacitor could either result in fire (short circuit of an X-capacitor) or in electric shock (short circuit of a Y-capacitor). The safety classifications for X- and Y-capacitors according to IEC 60384-14 [9.4] are presented below.
An actual capacitor is not a pure capacitance C [F]. The series inductance Ls [H] (ESL) is caused by the leads and by the internal structure. The series resistor Rs [Ω] (ESR) is also caused by the leads as well as from internal losses. The parallel resistor Rp [Ω] represents the non-ideal dielectric material (leakage current) and has typically a value of 10GΩ or more.
The impedance Z [Ω] of a non-ideal capacitor can be written as (with neglected Rp [Ω]):
The following graph shows a simplified frequency behavior (impedance vs. frequency) of an actual capacitor. From DC up to the serial resonant frequency of L [H] and C [F]: the capacitance dominates. However, for frequencies higher than the resonant frequency, the inductance L [H] dominates and the capacitor becomes an inductor.
For EMC filter applications with C<100µF, Multilayer Ceramic Capacitors (MLCCs) are in most cases the best option. MLCCs have excellent small ESR and ESL, are inexpensive, accurate, robust, long-term stable, and available in small packages (e.g., in the SMT packages 0201, 0402). However, MLCCs have also drawbacks that must be considered [9.5]:
Temperature derating. The capacitance of MLCCs varies with temperature T [C].
Class I. Dielectrics like C0G (NP0) and U2J are ultra-stable across a wide temperature range from 55°C to +125°C.
Class II. Dielectrics like X7R and X5R have a much higher dielectric constant εr than Class I dielectrics, but the capacitance can vary as much as 15% over the range of 55°C to +85°C (X5R) or to 125°C.
Class III. Dielectrics like Y5V and Z5V have the largest dielectric constants εr, but the capacitance can vary as much as +22% to 56% for Z5U (10°C to +85°C) or even +22% to 82% for Y5V (30°C to +85°C).
Voltage derating. Class I dielectrics show no voltage derating effect (meaning, the capacitance of the C0G (NP0) or U2J capacitor does not change with the applied DC voltage). However, class II and class III show a significant drop (up to 90%) in their rated capacitance with applied DC voltage. It looks different for applied AC voltages. The capacitance of a capacitor is usually specified at 1 Vrms. Class II and class III MLCCs show an increase in capacitance when an AC voltage within a reasonable range is applied and a decrease for small AC voltage amplitudes (e.g., 10% at 10mV). If a high enough AC voltage is applied, eventually, it will reduce capacitance just as a DC voltage. The capacitance decreases more quickly with smaller case sizes.
Aging. Class I dielectrics show very little to no aging effect. Whereas class II and class III dielectrics have an aging effect (see Fig. 11.18). E.g. X7R and X5R have a typical aging-rate A = 2%=decadehours, Z5U A=3%/decade-hours, and Y5V A=5%/decade-hours (a decade-hour is e.g. from 1h to 10h or from 100h to 1000h).
Frequency. Class I dielectrics do not show a frequency-dependent capacitance. On the other hand, class II and class III dielectric materials show a frequency-dependent capacitance.
Some drawbacks of MLCCs are illustrated in the graphs below.
The conclusion from the points above is that whenever a stable capacitance C [F] is needed: use a class I MLCC capacitor (e.g., NP0, C0G for filter applications). Another important point to remember is that the capacitance C [F] of class II and class III MLCCs is a function of temperature T [C], DC voltage V [V], time (aging) t [h] and frequency f [Hz]. Nonetheless, class II and class III MLCCs have their use cases. E.g., X7R capacitors are commonly used for decoupling on PCB designs because X7R capacitors provide a higher nominal capacitance C [F] than class I capacitors for the same package size.
Inductors can be categorized in:
Non-magnetic core. E.g., air-core inductors. They are often used for high-frequency applications because air-core inductors are free from core losses that occur in ferromagnetic cores at increasing frequency.
Magnetic core. E.g. ferrite beads (open-loop magnetic core) and toroidal inductors (closed-loop magnetic core inductors).
Non-ideal inductors have not only inductance L [H] but also a series resistance Rs [Ω] (wire resistance) and a distributed capacitance Cp [F] between the windings. In addition, inductors with a magnetic core do also show magnetic core losses, which can be modeled with a parallel resistor Rp [Ω].
Here is the equivalent circuit of an air core inductor:
Here is the equivalent circuit of an inductor with a ferromagnetic core:
The impedance Z [Ω] of a non-ideal inductor can be written as [9.3]:
where L [H] is the nominal self-inductance, Cp [F] is the parasitic parallel (shunt) capacitance, Rs [Ω] is the series resistance of the windings and Rp [Ω] is the parallel resistance representing the magnetic losses.
The following graph shows a simplified frequency behavior (impedance vs. frequency) of an air inductor. At DC and low frequencies, the impedance is purely resistive (Z = Rs). With increasing frequency, the impedance changes and the inductance dominates up to the parallel resonant frequency of L and Cp. For frequencies higher than the parallel resonant frequency, the capacitance dominates and the inductor becomes a capacitor.
The self-inductance L [H] is proportional to the core material’s relative magnetic permeability μr. It is important to note that μr and the self-inductance L [H] are a function of:
Current. The higher the current I [A], the lower the μr(I) becomes. This means that the inductance L [H] decreases with increasing current I [A] through an inductor. Therefore, care must be taken that an inductor is used below its defined saturation current Isat [A].
Frequency. Typical core materials are manganese zinc (MnZn) and nickel-zinc (NiZn). MnZn cores tend to have high initial magnetic permeability μri, but their μr(f) deteriorates more rapidly with increasing frequency f [Hz] than that of NiZn cores. The frequency behavior of an inductor is usually presented in its datasheet.
Temperature. The relative magnetic permeability μr(T) of any ferromagnetic material changes with temperature T [C]. Usually, the permeability μr peaks out just before the material reaches its Curie temperature [9.3]. At the Curie temperature, the magnetic material loses all its permanent magnetic properties.
Inductors and ferrite beads are both inductive components. However, there are some differences:
Inductors. Inductors consist of a coiled electrical conductor around a magnetic or non-magnetic core material. They typically have a much higher quality factor Q than ferrite beads and lower losses. Typical applications: filters, DCDC-converters.
Ferrite beads. Ferrite beads consist of an electrical conductor surrounded by a ferrite material. They typically have a lower quality factor Q than inductors and higher losses. Typical application: noise suppression (converting noise signals into heat).
The behavior of ferrite beads is often described as frequency-dependent resistance because, in the frequency range of interest, the impedance Z [Ω] of ferrite beads is dominated by its resistive part. Different types of ferrite beads can be found on the market. The two most common form factors are:
Cable mount ferrite beads. Cable mount ferrite beads are wrapped around a cable, wire, or a group of conductors. They can be flexibly installed and are usually used to lower radiated emissions by suppressing common-mode currents.
Chip ferrite beads. Chip ferrite beads are mounted on a PCB as SMD parts. Chip ferrite beads are compact, inexpensive, and often used to lower radiated emissions or increase immunity to radiated disturbances.
Cable Mount Ferrite Beads. With cable-mount ferrite beads, the ferrite material is placed around a cable, a wire, or a group of conductors. The picture below shows the simplified high-frequency equivalent circuit of a cable mount ferrite bead. The self-inductance L [H] and the magnetic losses depend on the signal frequency f [Hz]. The losses are modeled as resistance R [Ω].
Typical cable mount ferrite beads can be expected to give impedances of order 100Ω for frequencies >100MHz. The impedance |Z| [Ω] of a cable-mount ferrite depends on:
Frequency. The graph below shows a typical frequency response of a cable-mount snap ferrite.
Temperature. The impedance |Z| [Ω] of ferrite beads reduces with increasing temperature T [°C]. Above the Curie temperature (≈120...220°C), the magnetic permeability µr of the ferrite becomes equal to 1.0 (paramagnetic). The ferrite regains its previous permeability when the temperature gets back below the Curie
temperature (the effect is reversible).
DC bias current. The impedance |Z| [Ω]of ferrite beads reduces with increasing DC bias current I [A] because the ferrite bead core material moves towards saturation, causing a drop in inductance L [H]. The larger the volume of a ferrite core, the higher the DC bias currents can be without causing much impedance loss.
PCB Mount Ferrite Beads. Chip ferrite beads consist of a conductor surrounded by a ferromagnetic material (typical NiZn). The simplified high-frequency equivalent circuit of a chip ferrite bead is shown below. RDC [Ω] represents the DC series resistance, L [H] represents the inductance, Cp [F] represents the parasitic capacitance, and RAC [Ω] represents the intended losses at high frequencies.
The non-ideal behavior of PCB mount ferrite beads comprises the following points:
Frequency dependence. As shown below, the chip ferrite bead behaves capacitive for frequencies >fr and the noise suppression for this frequency range is reduced.
Temperature influence. The impedance |Z| [Ω] of ferrite beads reduces with increasing temperature T [°C] (see below). Above the Curie temperature (≈120...220°C), the magnetic permeability µr of the ferrite becomes equal 1.0 (paramagnetic). The ferrite regains its previous permeability when the temperature
gets back below the Curie temperature (the effect is reversible).
DC bias current influence. The impedance |Z| [Ω] of ferrite beads reduces with increasing DC bias current I [A], because the ferrite bead core material moves towards saturation, causing a drop in inductance L [H].
A common-mode choke consists of two coils wound around a common ferromagnetic core (sometimes even more than two coils). The differential signal current flows through one coil and back through the second one. Common-mode chokes in EMC are primarily used to block common-mode currents and, therefore, to eliminate unintended radiated electromagnetic emissions. The symbol of common-mode chokes is shown here:
The picture below presents the high-frequency equivalent circuit of a common-mode choke, where Rs [Ω] represents the ohmic losses, L [H] represents the self-inductance of each coil, M [H] represents the mutual inductance of the coils, Rp [W] represents the magnetic core losses, Cp [F] represents the parasitic capacitance between the turns of the coils and C12 [F] represents the parasitic capacitance between the two coils.
In the following, we will calculate the common-mode impedances Z1CM, Z2CM [Ω] and differential-mode impedance Z1DM, Z2DM [Ω] of a common-mode choke. These impedances can be modeled like this:
If we assume that the common-mode current ICM [A] splits up equally through both coils of the common-mode choke (I1CM = I2CM = ICM/2) and that the self-inductance of the coils is equal to the mutual inductance (L1 = L2 = M12 = M21), the common-mode impedance of each coil is [9.3]:
where Z1CM [Ω] is the ideal common-mode impedance of common-mode choke coil 1, Z2CM [Ω] is the ideal common-mode impedance of common-mode choke coil 2, L [H] is the self-inductance of a single coil of the common-mode choke, M [H] is the mutual inductance between the coils of the common-mode choke and ω [rad/sec] is the signal frequency.
The equations above for Z1CM [Ω] and Z2CM [Ω] show why common-mode chokes have a high impedance for common-mode currents. On the other hand, an ideal common-mode choke (L1 = L2 = M12 = M21) would not influence the differential-mode current at all:
where Z1DM [Ω] is the ideal impedance of common-mode choke coil 1 for differential-mode currents, Z2DM [Ω] is the ideal impedance of common-mode choke coil 2 for differential-mode currents, L [H] is the self-inductance of a single coil of the common-mode choke, M [H] is the mutual inductance between the coils of the common-mode choke and ω [rad/sec] is the signal frequency.
The non-ideal (and therefore unintended) behavior of common-mode chokes is summarized here:
Frequency dependence. As the figure below shows: the common-mode choke influences differential signals at higher frequencies and the common-mode impedance starts dropping with higher frequencies. Therefore, it is necessary to check the datasheet of the common-mode choke.
Temperature influence. The impedance |ZCM| [Ω] of a common-mode choke reduces with increasing temperature T [°C] until it suddenly drops when the Curie temperature of the magnetic core material is reached. The temperature of common-mode chokes should usually not exceed 125°C or 150°C.
Amperage of the differential current. It has to be checked that the coils can carry the differential-mode current from a thermal standpoint (heating due to ohmic losses).
Voltage clamping devices like varistors and TVS diodes have in common that they block the current flow up to a specified voltage. Once the voltage reaches that clamping voltage, the voltage across the voltage clamping device does not increase anymore. In other words: the voltage is clamped. Voltage clamping devices are commonly used to protect circuits from transient pulses like:
ESD. IEC 61000-4-2, 1/60 nsec-pulses of 1nsec rise-time by 60nsec duration.
Bursts (EFTs). IEC 61000-4-4, 5/50 nsec-pulses of 5nsec rise-time by 50nsec duration.
Surges. IEC 61000-4-5, 8/20 μsec-pulses of 8 μsec rise-time by 20μsec duration.
The figure below shows the different responses of clamping and crowbar devices on a voltage transient pulse [9.6].
Transient-voltage-suppression diodes (TVS diodes) are typically used as overvoltage protection devices against ESD pulses, bursts (EFTs), and surges (if the current through the diode is limited). TVS diodes belong to the category of clamping devices. Compared to varistors, TVS diodes have a shorter response time and a lower clamping voltage Vclmap [V] (for the same breakdown voltage VBR [V]). On the other side, TVS diodes do endure less pulse current IPP [A] compared to varistors.
TVS diodes are available in two configurations:
Unidirectional. Forward operation: normal silicon diode with Vf ≈ 0.7V. Reverse operation: transient protection with defined breakdown voltage VBR [V].
Bidirectional. Both directions can be used for transient protection with defined breakdown voltage VBR [V].
The figure below shows the current I [A] vs. voltage V [V] diagram of a bidirectional TVS diode [9.8].
The most essential parameters of TVS a diode are:
Reverse standoff voltage, reverse working voltage. Up to the reverse working voltage VRWM [V], the suppressor diode does not conduct any significant amount. VRWM [V] must always be greater than the maximum operating voltage (consider all the tolerances of the signal’s amplitude).
Breakdown voltage. At the breakdown voltage VBR [V], the TVS diode starts to
conduct and the diode changes to the conductive state.
Clamping voltage. At the clamping voltage Vclamp [V], the suppressor diode carries the maximum current IPP [A]. Therefore, care must be taken that the circuit to be protected can withstand Vclamp [V] without any damage.
Peak pulse current. At the peak pulse current IPP [A], the TVS diode gets the maximum energy that a short electrical pulse can convert into heat in the suppressor diode without damaging it.
Leakage current. The leakage current is the current that flows in the reverse direction through the suppressor diode at a given voltage.
Parasitic parallel capacitance. The parasitic parallel capacitance of the diode could lead to bad signal integrity in the case of high-speed signal interfaces.
Insertion loss IL. TVS diodes designed for high-speed interfaces often specify the insertion loss IL [dB] of the TVS diodes in their datasheets.
Varistors are voltage-dependent resistors (VDR), and they are typically used as overvoltage protection devices against bursts (EFTs) and surges, which arrive at the victim via the public mains supply or the DC supply port.
We do not live in an ideal world, and VDRs have some points to be considered when using them in a design:
Operating voltage. Up to this voltage, the varistor does not conduct. The operating voltage in the datasheet specifies the maximum operating voltage (consider power supply tolerances when calculating the maximum operating voltage).
Breakdown voltage. The breakdown voltage VBR [V] specifies typically the voltage where the DC current through the varistor is 1mA. When a voltage is applied, which exceeds VBR [V], the junctions experience an avalanche breakdown, and a large current can flow.
Energy absorption. Depending on the case size, the energy absorption varies from 0.01J (SMT 0402) up to 10kJ (chassis mount). Most varistors can absorb 5/50 nsec-burst-pulses and/or 8/20 μsec-surge-pulses (take care of which immunity level you need for your product: 1, 2, 3, or 4).
Response time. Most varistors have a response time that exceeds >25nsec, which makes them too slow for ESD protection (IEC 61000-4-2, 1/60 nsec-pulses). VDRs with a fast response time of <1nsec — which is fast enough to protect against ESD-pulses — usually have the downside that they cannot absorb enough energy for surge pulses.
Clamping voltage. The clamping voltage Vclamp [V] describes the voltage across the VDR for a certain pulse (rise-time) and current. Unfortunately, Vclamp is usually much higher than the breakdown voltage VBR [V]. Therefore, care must be taken that the circuit to be protected can withstand Vclamp [V] without any damage.
Capacitance. The parallel capacitance Cp [F] of varistors is much higher than the capacitance of TVS diodes or gas discharge tubes. Cp [F] is usually in the range of 10pF up to 10nF and, therefore, too high for high-speed signal interfaces. However, in the case of the protection of AC or DC power inputs, the parallel capacitance Cp [F] is very welcome and can be used to replace filter capacitors.
Leakage current. The leakage current depends on the voltage applied across the VDR, and it is usually in the range of 1μA to <1mA. The leakage current can be extracted from the current-to-voltage characteristic curve for any given voltage.
Aging. VDRs show an aging effect based on the number of current pulses they experience.
The graphic below shows the current I [A] vs. voltage V [V] curve of ZnO and SiC varistors [9.7]. ZnO VDRs belong to the category of metal oxide varistors (MOV) and are the most common.
Crowbar devices commonly block the current flow up to a specific voltage. Once that voltage is exceeded, the crowbar device changes suddenly into a low impedance state, the voltage across the crowbar device gets low, and the current through the crowbar device increases and is only limited by the external circuit. After that, when the current through the crowbar device falls below a certain threshold, the crowbar device resets itself.
Examples of crowbar devices are:
Gas discharge tubes
Crowbar devices are mainly used to protect circuits from high-energy transient pulses like:
Surges. IEC 61000-4-5, 8/20 μsec-pulses of 8 μsec rise-time by 20 μsec duration.
EMP transients. Electromagnetic pulse (EMP) transients are transients generated
by EMPs that are produced, e.g., by detonations of a nuclear explosive.
Compared to voltage-clamping devices (TVS diodes, varistors) crowbar devices can handle much more energy, but the downside is that they do not turn on as fast as voltage-clamping devices. We do not go further into detail about crowbar devices because for many products on the market, the presented clamping devices — like varistors and TVS diodes, in combination with other passive filter components like capacitors, — are the most practical and economical to use. However, gas discharge tubes are very popular for lightning protection of antennas and telecommunication products.
The figure below compares the principles of "voltage clamping devices" vs. "crowbar devices" [9.6].
[9.1] Eric Bogatin. Signal and Power Integrity - Simplified. 3rd edition. Prentice
Hall Signal Integrity Library, 2018, p. 124
[9.2] Chris Bowick. RF Circuit Design. Newens, 1982, p. 10
[9.3] Reto B. Keller, Design for electromagnetic compatibility - In a nutshell, Springer, 1st Edition, 2023, pp. 148-180
[9.4] Fixed capacitors for use in electronic equipment - Part 14: Sectional specification
- Fixed capacitors for electromagnetic interference suppression and connection to the supply mains. International Electrotechnical Commission (IEC). 2013.
[9.5] KEMET. Here’s What Makes MLCC Dielectrics Different. June 4, 2021.
[9.6] Reto B. Keller, Design for electromagnetic compatibility - In a nutshell, Springer, 1st Edition, 2023, p. 185
[9.7] Reto B. Keller, Design for electromagnetic compatibility - In a nutshell, Springer, 1st Edition, 2023, p. 181
[9.8] Reto B. Keller, Design for electromagnetic compatibility - In a nutshell, Springer, 1st Edition, 2023, p. 183