Chapter 5 - Passive Components

Wanting to learn more about passive components? Here is an excerpt from our AC/DC Book of Knowledge covering various types of capacitors complete with diagrams, images, and equations.

Capacitors play an important part in AC power supplies because the input voltage drops to zero twice during every AC mains cycle. An energy storage element is usually needed to keep the power supply running (although there are AC powered LED drivers that allow the output to fail at every zero crossing as a 100Hz or 120Hz LED flicker is not perceptible to most people).

An inductor can be used to effectively store current in the form of its magnetic field, but capacitors are needed to store DC voltage in the form of the electric field between its electrodes. In addition, AC filter capacitors are needed between the line inputs and between line and ground for EMC and surge protection. As such, they are classed as safety critical components.

AC filter capacitors are typically ceramic disc or metallized film. Both of these constructions are symmetric and work equally well with either voltage polarity. A ceramic disc capacitor consists of two metal electrodes separated by a ceramic dielectric substrate. This gives a very stable capacitance value over a wide operating temperature range, but limited capacitance in the range of picofarads to tens of nanofarads. Multiple layers can be used to increase the insulation, so withstand voltages in the range of 1kV up to 15kV are available, as are SMD versions.


Metalized film capacitors use multiple layer plastic film insulators which are coated on one or both sides with a metal film to make the electrodes. There are many different plastic films that can be used but PTFE, polypropylene and polyester are the most common. As many layers can be interleaved, high capacitance values are possible (nanofarads to tens of microfarads), but they can become very bulky with both high rated voltage and high capacitance values. Film capacitors also have inherently low ESR and ESL values which makes them also suitable for snubber and filtering applications. Film capacitors are almost exclusively available as through-hole mounting only.


A class X capacitor is designed to go across a mains input (from line to neutral or from phase to phase). It is assumed that there is some form of current limiting in the supply, such as a fuse or over-current trip, so if the capacitor fails short circuit the protection device will open. Therefore, X class capacitors are designed to fail short circuit because as long as the capacitor does not catch fire or ignite any other adjacent components, it will then fail safe.

A class Y capacitor is designed to go from line to ground (Class 1 power supplies), line to a zero potential (Class II power supplies) or across the isolation barrier from primary to the secondary side. A short circuit would lead to hazardous voltages appearing on the zero potential or secondary side connections, so they are designed to fail open circuit. For many applications, a double fault must not cause an unacceptable hazard, so for medical and household applications, two Y-class capacitors in series are specified across the isolation barrier or from line to ground/zero potential.

You might wonder how you can design the failure mode of a capacitor? The answer is in the internal construction. If an arc-over occurs due to an over-voltage event or a mechanical failure such as a pinhole in the insulation, X-class capacitors tend to fuse together, shorting the electrodes, while a Y-class capacitor has thinner conductors that will locally evaporate away and break the conduction path. They are thus said to be self-healing. A Y-class capacitor can be used in place of an X-class capacitor, but not the other way around. However, there are socalled safety capacitors that are rated for both X-class and Y-class applications. The marking will indicate the appropriate voltage ratings for each type of application class.

Both X-class and Y-class capacitors are classified according to their peak or rated operating voltage and over-voltage withstand ability as defined by IEC 60384-14:



Another use of film capacitors is in tuned filter and resonance circuits, phase shifters and power factor correction circuits. The inherently low parasitic inductance and low ESR makes the frequency response very stable and the capacitance value remains linear over a wide range of operating temperatures, simplifying the design process.

As mentioned previously, the other main function of capacitors is to store energy. Electrolytic capacitors are almost exclusively used as the bulk storage elements in AC/DC converters due to their high volumetric efficiency, high voltage and temperature rating and cost effective. The downside is that electrolytics are polarized (DC only), so they can only be used after the rectification stage, and they can explosively fail if the electrolyte overheats and starts to evaporate.

The internal construction is similar to the foil capacitor, except with a liquid or solid (polymer) dielectric, so that they have much in common with a battery cell construction. For example, Supercapacitors are low voltage capacitors with very high capacitance (several Farads) which are a cross-over between a rechargeable battery and a capacitor. The most common electrolytic capacitor is the aluminium type that uses aluminium oxide (AL2O3) as the liquid electrolyte between foil electrodes which have an etched surface to increase their effective surface area. This allows a high capacitance-volume (CV) product with low ESR (equivalent series resistance), both important factors for bulk storage capacitors.

Question: When is a low-ESR 100μF electrolytic not a low-ESR 100μF capacitor?
Answer: When it is operated with a high frequency ripple current. As the frequency increases beyond around 1 kHz, the effective capacitance decays. If the capacitor is used to smooth rectified mains frequency, then the datasheet capacitance value can be reliably used. However, if the capacitor is used in a PFC circuit operating at a higher switching frequency (typically 100kHz), then a 450VDC 100μF capacitor might act like a 60μF capacitor.


Question: When is a low-ESR 100μF electrolytic not a low-ESR 100μF capacitor?
Answer: When the ambient temperature is not 25°C. At low temperatures, the liquid electrolyte becomes viscous and less conductive, so the ESR increases and the capacitance decreases. At high ambient temperatures, the capacitor core expands, effectively decreasing the separation between the foil electrodes, so the capacitance increases. A 100μF capacitor at 25°C could be a 62μF capacitor at -40°C and a 110μF capacitor at 105°C.
(Note: polymer electrolytics do not exhibit this effect)


The equivalent series resistance, ESR, has three main components: the ohmic resistance of the connections (≈10milliohm) plus the frequency dependent resistance of the dielectric oxide layer, called the dissipation factor, Dox, plus the temperature dependent resistance of the electrolyte, Re[T] which is typically:


The combination of the first two factors (ohmic resistance and frequency dependent resistance) gives the blue line in the right hand image on the diagram above that will also change with temperature according to the third factor (dissipation factor). The equivalent series inductance, ESL will also vary, but this effect is minor and can usually be ignored.

Question: When is a low-ESR 100μF electrolytic not a low-ESR 100μF capacitor?
Answer: When the capacitor is old. As an electrolytic capacitor ages, the liquid electrolyte dries out and the ESR and equivalent series inductance, ESL, increases while the capacitance decreases. The definition of the end of useful life is when the ESR, ESL or capacitance fall outside of their respective limits. This does not mean that the capacitor will immediately fail, but the higher dissipation will gradually increase the internal temperature until failure is inevitable.


The tan-delta figure is thus an important indicator of capacitor reliability:



From figure 6 it can be seen that after around 6800 operating hours, a typical 100μF capacitor operated at its limits will have become a 75μF capacitor and the ESR/ESZ ratio (tan δ) will have increased by a factor of 3.5.

Bearing in mind these aging effects with electrolytic capacitors, it is vital to ensure reliability-by-design by derating the operating conditions to give an increased lifetime. Despite the graphs shown above, it is easily possible to have a 20-year lifetime of an electrolytic capacitor when it is not overstressed.

The electrolytic capacitor manufacturer’s datasheet will specify a lifetime under maximum stress conditions (maximum voltage and temperature), therefore any reduction in the operating stress will increase the lifetime according to various multiplication factors:


Where:
L is the service lifetime in hours.
L0 is the datasheet lifetime at maximum ripple current and full temperature limit and voltage stress.

KT is the temperature factor,, where T0 is the temperature limit and TA is the temperature in the application.
For example, if the T0 temperature is 105°C and the TA temperature is 70°C, then the KT lifetime multiplier is x11.3.

KR is the ripple current factor,, where Ia is the ripple current in the application, IR is the maximum ripple limit, ΔT0 is the internal temperature rise and Ki is an empirical safety factor in the range of 2 to 4.

For example, if the ripple current is kept to half of the maximum ripple limit, the internal temperature rise kept below 5°C and the safety factor is chosen to be 2, then the KR lifetime multiplication factor is x1.3
KV is the voltage factor, where VA is the operating voltage, VR is the maximum rated voltage and n is an exponent that is either:
n= 2.5 (VA to VR ratio more than 50%)
n= 5 (VA to VR ratio more than 80%).

For example, if the operating voltage is 0.9 of the rated voltage, then n=5 and the KV lifetime multiplication factor is x 1.7.

Thus, the calculated service lifetime, L = 7000 x 32 x 1.3 x 0.6 = 174,000 hours or nearly 20 years when all of the lifetime multipliers are taken into account.

To simplify such electrolytic capacitor lifetime calculations, RECOM offers an on-line calculator tool on its website (www.recom-power.com)

It is useful to play around with the data in the lifetime calculator to see how small changes in the operating conditions can affect the lifetime:

For the example given above:


However:
Changing the maximum voltage from 90% rated to 80% rated increases the lifetime to nearly 36 years. Changing the maximum ambient temperature from 70°C to 85°C reduces the lifetime from 20 years down to only 7 years. Changing the ripple current from 50% rated to 60% rated reduces the lifetime by only 6% (from 174 khrs down to 167.5 khours), but changing it to 100% rated current loses nearly 4 years off the lifetime.

Component selection is often a compromise between performance and cost, so by careful design, the optimal price/specification benefit can be realized.

It is also often very difficult to find out the capacitor ripple current. Adding even a 10milliohm shunt resistor to measure the current can seriously affect the measured result if the ESR of the capacitors is also around 10milliohm. An alternate method is to derive the ripple current based on the temperature rise and volumetric thermal conductivity of the capacitor.


Heat generated inside a capacitor can be dissipated to the surroundings by radiation, convection or conduction. Black body radiation contributes only a small amount to the overall thermal performance of the capacitor at sea level air pressure and can be ignored in most practical cases. Free air convection cooling is dependent on the surface area and ambient temperature difference. Conduction cooling is via the pins into the PCB which then acts a large flat area heatsink to transfer the heat to the surroundings via convection. Due to the construction of a typical electrolytic capacitor, the thermal path between the foil electrode layers and the connection pins is less than ideal and conduction cooling from the core through the pins can also be largely ignored.

This leaves convection cooling as the primary mechanism for heat dissipation.

Step 1. Calculate the free surface area: A cylinder has a side surface area of 2πrh, where r is the radius and h is the height of the cylinder. The top of the cylinder has an area of πr². Together they give the exposed surface area as:


Where SA_cap is the surface area of a capacitor in cm² with diameter D in mm and height h in mm.

Step 2. Calculate the internal power dissipation
The ripple current dissipates energy in the equivalent series resistance, ESR, of the capacitor. This value can be found from the capacitor datasheet. The dissipated energy will cause a temperature rise in the core of the capacitor.


Where P_diss is the power dissipated in the capacitor core, Fe is the emissions factor (typically 0.95 for free air convection), KSB is the Stefan Boltzmann’s Constant (5.56x10-8 Wm²K4) and Trise is the temperature difference between ambient and the top centre point of the capacitor. The ripple current that causes this temperature rise is:


Practical Tip: In the introduction to this section, it was stated that heat transfer from the capacitor through the pins into the PCB can largely be ignored. This is valid for heat transfer from the capacitor core out into the PCB copper tracks as the thermal impedance is higher from the core through the pins to the PCB than directly from the core to the capacitor case. However, if there is an external source of heat, for example a power diode placed close to a capacitor, then the low thermal impedance copper PCB tracks can transfer sufficient heat back into the capacitor via the pins to significantly add to the thermal load inside the capacitor and reduce its lifetime. Another “unexpected” source of internal heat generation can be varying external magnetic fields. Both electrolytic and foil capacitors are often placed very close to inductors, chokes and transformers. Any stray AC magnetic fields can generate eddy currents in the metallized foil conductors which will increase the core temperature and reduce lifetime.

Inductors are specified with a maximum continuous RMS current, I_RMS, and a maximum peak current, I_SAT. The I_RMS current is usually defined as that causing a 40°C rise in the core temperature. Two losses contribute to the temperature rise: the copper loss in the windings = DCR x I_RMS² and the magnetic core loss which is frequency and duty cycle dependent. In a common mode choke (CMC) input filter configuration, the flux from the two windings cancels out, making the I_SAT figure largely irrelevant.


The rated operating voltage is also important if the inductor is used as a common mode choke on the input side of an AC/DC converter as the two windings carry the full mains input voltage across them. The rated voltage must be sufficient over the entire operating temperature range. It is often necessary to insulate the conductive ferrite core and put a separator between the two windings to guarantee the creepage and clearances so that there is no flash-over.


The impedance of a CMC increases with increasing frequency until it reaches a peak at the self-resonant frequency (SRF), then it declines due to the effect of the interwinding capacitance. The SRF should be chosen to be close to the frequency of the maximum noise interference (usually the switching frequency or a multiple thereof) to give the largest attenuation.


Where SRF is the self-resonant frequency (assuming DCR is low and R_MAG is high)

Power supply specification: 100W, 115 – 230V supply, 45 kHz switching frequency, 85% efficient flyback design.

Step 1. Determine the probable noise level
The circuit switches at 45kHz with a 50% duty cycle at full load. This will generate a fundamental noise peak at 45kHz with harmonics at higher frequency intervals of nf0, where n = 1,3,5,… decreasing in intensity with -20dBμV/decade. Frequencies below 150kHz are ignored by the industrial EMC standards, so we need only concern ourselves from the fifth harmonic at 5f0 or 225kHz and above. If we assume a 1V drop across the diode bridge, then the fundamental frequency will have an amplitude:


And the 5th harmonic will have an amplitude of:


Step 2. Determine the filter attenuation:
The required attenuation is equal to the noise amplitude (first odd harmonic above 150kHz) minus the EN55011 EMI Quasi peak limit (65dBμV) plus a 3dB safety margin. For our example, the attenuation, A, at the fifth harmonic needs to be 108 – 65 + 3 = 46dBμV.

Step 3. Find the filter corner frequency:
The filter should attenuate the noise from the fifth harmonic at 225kHz with a +40dB/decade attenuation. This gives a corner frequency of:



Step 4: Determine the maximum AC current:
The maximum input current occurs at full load with the minimum input voltage (115VAC -10% ≈ 103VAC). Assuming power factor is corrected, the input current will then be (100/0.85)/103 = 1.14A

Step 5: Select a suitable common mode choke and the X and Y capacitors to make up the filter as shown below:


As the application is a universal mains filter, the choke needs to be rated for 250VAC operation. From step 4, we need a current rating of 1.14A or higher. From step 3, it should have a peak attenuation close to 225kHz.

We could choose a 5mH choke rated at 250VAC, 2A @ Tamb + 40°C for example. The high common mode inductance will give an attenuation curve that peaks at around 0.2MHz, which is ideal. The stray inductance is typically 1%, i.e. 47μH.
The X-capacitor reacts with the stray inductance to make a differential mode filter:



The Y-capacitors react with the common mode inductance to make a common mode filter:




It must be stressed that the above calculation is not sufficient to guarantee an EMC test pass. It is just a first step to allow a test set-up to be made.

Practical Tip: It is often quite difficult to find a common mode choke with enough stray leakage inductance to keep the size of the X-capacitor reasonable. It is often worth using either using a differential mode choke in series with the common mode choke or using a hybrid choke which incorporates elements of both DM and CM types in one body.