**Power/Alternative Energy??**

# Grasping capacitors, ripple and self-heating

**Keywords:Ripple?
converter?
capacitors?
parasitic resistance?
inductance?
**

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 C unlike other typical application ripple conditions C 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).

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.

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