Understanding capacitors, ripple and self-heating
Ripple is often evaluated in terms of its two components: ripple voltage and ripple current. In most applications, it’s a circuit condition that you want to minimize. For example, in an AC–DC converter, which takes power from an AC source and converts it to a steady DC output, you want to avoid any of the source AC power appearing as a small, frequency dependent variation on top of the DC supply. However, in other cases, ripple can be a necessary design function, such as a clocking signal or a digital signal capable of using changes in voltage level to switch the state of the device.
In the latter case, ripple considerations can be quite straightforward: don’t let the peak voltage exceed the voltage rating of the capacitor. Although, it’s important to bear in mind that the peak voltage will be the sum of the maximum ripple voltage plus any DC bias in the circuit. Additionally, there is a second caveat for electrolytic capacitors – such as tantalum, aluminum, and niobium oxide technologies – due to their polarity: don’t let the minimum voltage of the ripple drop below zero, as this will cause the capacitor to operate under reverse bias conditions. This caveat also applies to Class II ceramic capacitors in low-frequency applications, but more on that below.
Since capacitors act as charge reservoirs, they charge as the incoming voltage increases and discharge into the load as it decreases, essentially smoothing out the signal. Capacitors will see varying voltage and, depending on the power applied, varying current, as well as both continuous and intermittently pulsed power. Regardless of the incoming form, the resultant changes in the capacitor’s electric field cause the dipoles in the dielectric material to oscillate, which creates heat. This reaction, known as self-heating, is one of the primary reasons that dielectric properties are important, as any parasitic resistance (ESR) or inductance (ESL) will add to the energy dissipation.
A dielectric with low losses (i.e., low ESR / DF and low ESL) will heat less than a dielectric with high ESR and DF; however, these parameters also vary with frequency, as different dielectric materials provide optimum performance (i.e., generate the least heat) over different frequency ranges.
Next: Heating effects
Capacitor dielectrics are thin, and may only constitute a small amount of the capacitor’s overall mass, so the other materials used in their construction need to be considered when evaluating ripple as well. For example, the capacitor plates in a non-polar device (e.g., ceramic or film capacitors) are metallic, while polar devices, such as tantalum or aluminum, have a metallic anode (or, in the case of niobium oxide technology, a conductive oxide anode) and a semiconducting cathode, such as manganese dioxide or conductive polymer. There are also a variety of conductive contacts, including metals (e.g., copper, nickel, silver palladium, solder, etc.) and conductive epoxies, on the external terminations or leads, and all of these materials heat to some degree when passing an AC signal or current.
To see how these factors come into play, let’s use a solid tantalum capacitor employed to smooth residual AC ripple current in the output stage of a DC power supply as an example. Firstly, since this is a polar technology, it will need a positive voltage bias to prevent an AC component from causing reverse bias to occur. This voltage will typically be the nominal output voltage of the supply.
Figure 1: Ripple Voltage superimposed on Bias Voltage.
Before we consider any ripple, we will have to note the heat resulting from the DC bias applied. Capacitors are not ideal, and one parasitic will be a parallel resistance across the dielectric, which will give rise to a leakage current (DCL). This small DC current causes some heating, but – unlike other typical application ripple conditions – can usually be ignored. A 100uF/10V tantalum chip capacitor has a room temperature DCL limit of 10uA (and 100uA at 85oC), so the maximum power dissipation is 1mW.
Next, let’s look at the power dissipated by the ripple value (equal to I2R where “I” is the root mean square [rms]) of the current at a given frequency (which is equal to “R”, the capacitor ESR at that same frequency).
Next: Setting limits
As a starting point, let’s consider a sinusoidal ripple current and its rms equivalent. If, at a certain frequency, we have a 1A Irms applied to a 100mOhms ESR capacitor, the power dissipated is 100mW. Supplied continuously, this power will internally heat the capacitor until it reaches equilibrium with its surroundings, based on the heat capacity of the materials used in both the capacitor element and packaging, and taking into account any method of heat dissipation to the surroundings (e.g., combinations of convection, conduction, and radiation). In this case, the heat generated by ripple is 100x that generated by DC leakage, so the latter (as previously mentioned) can be ignored. However, it’s always an idea to check this first when evaluating a new family of capacitors.
Having defined the factors that contribute to self-heating from applied ripple, we can now set about defining a limit. Although, the question, “How much ripple is too much ripple?” is almost as open-ended as, “How long is a piece of string?” Consequently, the standard methodology is to just set an arbitrary temperature change and use this as a reference point to back-calculate how much ripple it would take to cause this change in a given capacitor.
In general, depending on the capacitor technology, it’s recommended that you stay within a maximum temperature delta allowance of +10oC or +20oC. The ripple required to generate this is calculated using the following reference conditions:
1) An ambient temperature of 25oC;
2) Ripple that is continuous, sinusoidal, and at a frequency corresponding to the ESR test frequency for the capacitor;
3) A capacitor in “free space” (i.e., with no thermal heat sink or forced cooling, and free to radiate on at least five sides [as one side could be soldered to the test board]);
4) And, in the case of polar capacitors, applied DC bias to ensure that the associated ripple voltage does not cause any reverse voltage on the capacitor.
The ripple current is then increased, and the temperature of the device monitored, until it reaches equilibrium at its recommended delta T allowance above ambient.
The resultant Irms measured is often referenced as the ripple current limit, but is not an actual limit in the sense of a maximum voltage rating or maximum ESR limit; rather, it’s a best-practice condition that can be used as a basis for application evaluation.
This measurement also allows the power dissipation and thermal resistance to be calculated for the capacitor. The power dissipation, “P”, is given by the equation
in which “R” is the ESR for the part at the ripple frequency, and the thermal impedance is the amount of heat generated per unit time and temperature, expressed in oC/W.
From the above, we can see that, for a given capacitor, the power dissipation will be a function of frequency due to the dependence on ESR. The thermal impedance, in this case measured empirically, can also be calculated based on the mass of the capacitor and the heat capacities of its constituent materials. However, a capacitor’s environmental conditions (i.e., the system’s thermal management) also have an equal role in how a capacitor heats in an application.
For capacitors of the same size and material content, the thermal impedance will be the same. Therefore, if the ESR is known, the amount of power dissipation per unit time can be calculated for various ratings from the same family, and the expected increase in temperature can be calculated by multiplying the power dissipation by the thermal resistance.
Going back to the ripple current measurement, this number will give an immediate indication as to whether the rating selected can be considered for a given application. To enable the fine-tuning of this number for actual ripple conditions, manufacturers share typical ESR vs. frequency and ESR versus temperature data so the ESR can be matched to the application conditions. This information is typically available in datasheet ratings tables or in software programs that allow users to vary frequency and temperature. If the ripple is non-sinusoidal, non-continuous, or intermittent (e.g., pulse discharges), then the designer will need to use an appropriate transformation method to calculate the rms equivalent or use the peak value as the worst-case scenario.
Next: Thermal modeling
Next, thermal modeling of the system can be done to take into account any forced cooling or heat-sinking that may reduce the capacitor temperature or, if the capacitor is in the proximity of other heat generating components, may increase it.
If there is insufficient data available for either of these methods, then an empirical approach, which is often the most accurate, can be taken. To execute, just run the circuit under worst-case conditions and measure the component temperature rise above ambient by thermocouple or pyrometer.
The first things to check will be that the equilibrium temperature does not exceed the maximum operational temperature for the part, and that the associated peak ripple voltage (plus any bias voltage applied) does not exceed the maximum operation voltage limit. For many capacitor technologies, ESR will decrease as temperature increases, so the contribution to ripple heating will be lower. However, this will either already be factored into the supplier’s data or not required if the part is actually measured in the application.
Figure 2: Thermal dissipation model for tantalum chip.
f the part is still being operated within its allowable envelope for all parameters, there will be no problem; and, for critical applications, the actual reliability of the capacitor can always be recalculated based on its actual maximum temperature rather than the ambient temperature for the circuit. If the calculated or measured temperature rise comes out above the recommended range, then the part may still be fine in the application (if the aforementioned conditions are met), but this should always be checked with the supplier in case any other stresses need to be taken into account.
Next: Practical applications.
Having established what parameters affect heating, let’s take a look at some practical applications.
For low voltage DC applications, such as 1.8V–5.5V power lines, high capacitance MLCCs and solid tantalum electrolytics are a first choice for DC power supply filtering capacitors in the 10kHz to 10MHz range. These technologies are capable of providing hundreds of microfarads of capacitance in small outline, low voltage ratings. The X5R temperature characteristic for MLCCs achieves especially high capacitance, with typical ESR in the 1–10 milliohm range, but has an upper temperature limit of 85°C. Although the capacitance of X5R devices is maximized for low voltage ratings, one characteristic of these capacitors is that their capacitance decreases with applied voltage (voltage coefficient) while the capacitance value decreases as operating temperatures increase (temperature coefficient).
However, their ESR remains low, so the ripple current capability will not be affected. In applications where less bulk capacitance loss is preferred, an X7R temperature characteristic can be used. For a given size and voltage rating, these will have lower nominal capacitance than X5R MLCCs, but the voltage coefficient effect will be lower (and can be further reduced if voltage derating is used), and the temperature coefficient will also be tighter, extending to 125oC operation.
Solid tantalum electrolytic capacitors are polar devices, which require a DC bias applied in ripple applications, and offer very high capacitance in the 100uF to 1mF range; although, typical ESR is an order higher than with MLCCs. Consequently, it is often worth considering a niobium oxide capacitor in place of a tantalum capacitor. Solid tantalum electrolytic capacitors use tantalum metal as the base anode material (i.e., the positive capacitor plate), are coated with tantalum pentoxide dielectric, and use manganese dioxide or a polymer film as the counter electrode material (i.e., the negative capacitor plate).
Niobium oxide capacitors have conductive NbO anodes with niobium pentoxide dielectric. Niobium is a sister element to tantalum, but with lower density. It is processed in a similar way and achieves similar electrical properties; however, for any given voltage rating, the niobium dielectric will be thicker. This translates into niobium ratings operating with less electrical field stress and higher reliability than their tantalum equivalents, but limits their maximum voltage ratings and slightly increases their ESR. In ripple applications, though, minor differences in ESR are compensated by the higher specific heat and lower thermal impedance of the niobium material. This means that similar ratings of tantalum and niobium oxide have similar ripple performance.
Next: Lower ripple frequencies
At lower ripple frequencies, the typical ESR for X5R or X7R (Class II dielectric) MLCCs increases more steeply than tantalum or niobium. As such, the latter are favored for audio applications, but neither should be used for low frequency applications (e.g., line applications below 100Hz) due to excessive self-heating. When using larger stacked ceramics for switch mode applications, the manufacturers’ software will usually provide an alert when the self-heating or ripple voltage itself becomes excessive at low frequencies, and may also give a caveat about using Class II ceramics without an additional DC voltage bias.
The dielectric structure of a Class II ceramic capacitor can be envisaged as a collection of domains having internal dipoles that change alignment in response to an applied AC voltage. However, if there is no offsetting DC bias, when in reverse voltage, the individual domains will flip, increasing the internal heating. So, for low frequency applications, Class I dielectrics, such as NP0/C0G are preferred since a lower dielectric constant (i.e., lower capacitance yield for a given size and voltage/rating combination), larger outline, or the stacking of multiple capacitor elements (such as in stacked switch mode ceramic capacitors) may be required.
In DC link applications for large film capacitors in the 500uF to 1mF / 450V to 1kV range (which is typical of automotive inverters for electric vehicles), the ripple current will heat the parts, but their high mass means that their thermal time constant needs to be taken into consideration. In fact, in some cases, it may take an hour or so for the capacitor to achieve an equilibrium temperature in a ripple application. Polypropylene is typically the dielectric of choice due to its extremely low power loss and resultant low self-heating for high levels of ripple current. Such capacitors typically have a custom specification tailored to a single vehicle and/or inverter application.
For example, all film capacitors have an intrinsic self-healing mechanism, but this can be enhanced by using special patterning within the metal electrode system, such that the total capacitor surface area is divided into parallel microelements that prevent short-circuit failure. Exposure to prolonged high temperatures and applied voltages will reduce the capacitance value over time, but if the application duty cycle is known, the expected divergence from nominal can be accurately calculated and factored into the initial design.
In conclusion, ripple is typically a circuit condition that you want to minimize. However, in certain applications, it can also be an effective design function, and software tools that allow design engineers to model capacitor performance and ensure safe operation are readily available.
Chris Reynolds holds a B.Sc. in physics from Birmingham University, UK and has more than 30 years’ experience working with passive component technologies in both an R&D and applications engineering capacity.
This article first appeared on EE Times’ Planet Analog website.
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