Ensure AC Film Capacitor Reliability with Thermal Analysis

When employing electrolytic, ceramic, and film capacitors in various configurations for high ripple current applications, you run the risk of stressing the capacitor, which leads to premature failure. Although each type of capacitor has its own limitations, advantages, and disadvantages, the film capacitor has the blend of properties that make it well suited for these applications. So, how can you avoid premature failure? You must pay attention to the operating conditions — in particular, the thermal characteristics of the capacitor, including operating ambient, cooling abilities of the package, and self-generated heat. Often the self-generated heat can overshadow the ambient temperature considerations — leading to degeneration and early failure.

Several items are responsible for heat generation and the flow of heat from the capacitor, including:

• Dielectric material and its inherent power losses,
• Electrode systems and their ohmic losses,
• Interfacial spray (schooping) materials, and
• Termination (wire, tabs, or terminals).

Dielectric material selected for use in the capacitor winding is usually based on operating temperature capability, voltage stress capability, cost, dielectric constant, and dissipation factor (tan δ). Certainly, the temperature capability and tan δ are the primary concerns. Of the suitable dielectrics, polypropylene is the best for low tan δ. In limited applications, polycarbonate is the best for temperature and polyester as a low-cost dielectric. However, polycarbonate has become increasingly expensive and difficult to obtain since the end of 2000. It's no longer a viable contender — except under special circumstances where temperature is most important and cost is a minor concern. Figs. 1 and 2 show the temperature and frequency performance of these three dielectrics.

Note: You should study the tan δ vs. frequency curve at the frequency of concern. Consider those frequencies for high harmonic content as well. Remember that the temperature in the capacitor core causes losses. Normally, the core temperature is the ambient, plus the skin rise, plus the rise from the skin to the core.

The electrode system is another source of heat within the capacitor. Film-foil, metallized film, and metallized-carrier constructions are typical. Fig. 3 shows examples of these structures. Film-foil construction has the advantage of higher current handling, whereas the metallized structure has self-healing features and smaller size. The metallized carrier is a construction style that brings better current handling than a metallized type. The film foil and metallized carrier are large when compared with a metallized style. The metallized-carrier electrode has one-half the ohmic losses and twice the thermal conductivity of a single metallized electrode.

Because the current passing through the electrode produces I²R losses, each construction behaves differently. The film foil sees little I²R heating. However, resistivity of metallized types can vary from 1 ohm/sq to 10 ohms/sq. Even higher resistivities are sometimes applicable. The actual value chosen depends on the application. In addition, thermal conductivity aspects of metallization affect cooling. Typically, the higher resistivities used for 60 Hz ac-rated capacitors achieve good life performance. Parts with light metallization do not cool as effectively.

With electrode termination, film-foil parts are soldered or sprayed. The heavy foil electrode carries the most current and is good for heat removal. Spray termination of metallized electrode capacitors is the only practical method of interfacing from the electrode to external termination.

Even though ESR is normally specified at 100 kHz to accurately depict the loss picture, you should measure ESR at the frequency of use.

Heat Generation

You can calculate heat generated within the capacitor from any one of three formulas:

P=2πFCV²tanδ (1)

P=I_rmstanδ/2πFC (2)

P=I_rms² ESR (3)

Where:

P=Power dissipated in watts

F=Frequency of waveform

C=Capacitance in farads

V=rms voltage of waveform

tan δ=Dissipation Factor of the capacitor at frequency F

I=rms Current

ESR=Equivalent Series Resistance in ohms

When the waveform is sinusoidal, the above equations apply directly. For non-sinusoidal waveforms, you must first analyze the waveform to determine V_rms and I_rms. If evaluating waveforms with harmonic content, apply the equations for each harmonic frequency for voltage or current and the loss factor tan δ at the harmonic frequency. The power for all harmonics is then summed. Also, non-sinusoidal waveforms may induce high peak currents, which may stress the termination and cause localized end heating.

Size and Shape Effects

The size and shape of a capacitor has a direct relationship to its ability to dissipate heat and handle current. Its size directly relates to its capacitance value and its voltage rating. Voltage stress on the capacitor dielectric and the reliability considerations of the application dictate what dielectric thickness to use for that voltage rating. Advances in metallizing technology have improved the ability to pack more capacitance in a smaller volume at a given voltage rating. However, this concentrates the heat into a smaller volume and reduces the ability to dissipate the generated heat. For a capacitor design that has evolved for the needed stress ratings, the size directly relates to the capacitance value.

Current path length is critical when considering current handling and capacitor package inductance. Current path length includes the point where the circuit current enters the terminal execution, flows through the termination and electrode, couples through the dielectric via the electric field, and continues out through the other set of electrode, termination, and terminal execution. The user controls the external leads, circuit board paths, and items related to packaging. The electrode width (material width) is the primary influence of current path length. Selecting material width requires a blend of packaging, manufacturing, and cost considerations.

Circuit current entering through the termination spreads via the endspray connection to the entire length of the winding. In the broad sense, it doesn't matter if you have a wound or stacked capacitor; the current path length is the same. In some cases the stacked construction may provide a more intimate contact between the endspray and the electrode, and hence a better dv/dt, but the current path length is still critical. As a general rule, the shorter the current path length, the lower the inductance of the capacitor and the lower the I²R losses in the electrode.

For a given material width, the use of multiple leads lowers the inductance, lowers the ESR somewhat, and provides improved heat conduction out of the capacitor. The best winding designs for current are short and fat, whereas long and thin is least favorable. You'll have little ability to control the design, unless you use custom windings. Often the economics of a situation dictate a standard design solution. However, when evaluating intrinsic performance between product sources, keep this general rule in mind.

Capacitor Cooling

Removal of generated heat is the broad subject of capacitor cooling. Generally, the higher the power level the more exotic the removal methods. Large welders, motor drives, and other systems use heat pipes, water cooling, and similar techniques to cool the semiconductors. These can be very effective for the capacitors and may be necessary, depending on the power involved. In typical switchmode power supplies, UPS systems, small motor drives, and inverters, cooling is left to convective means.

Fig. 4 illustrates a simple convective cooling scheme. The surface of the capacitor, be it an axial or radial package, heats the cooler ambient air. As the air heats, its temperature increases, and it rises from the surface. From basic thermodynamics, we know that to get heat flow we must have a temperature differential. Normally, we assume the capacitor skin is warmer than the fluid (air) in which it's immersed. If the air were warmer, the capacitor would be a heat sink for the air. This is not desirable, and it may be destructive.

The basic formula for heat flow in convective cooling is:

Where:

ΔT=Temperature difference

Q=Heat flow

A=Surface area immersed in the fluid.

You can reduce this equation to the form:

Where:

ΔT=temperature difference of the skin and the fluid in which it is immersed

P=Power being dissipated as derived by Equations 1, 2, 3

A=Surface area being cooled by the fluid

K=Convection coefficient

The convection coefficient can be derived empirically from test data and is affected by airflow velocity.

Typical values for K are:

K=176 empirically derived for still air and area in square inches, power in watts.

K=113,550 for still air and area in square millimeters, power in watts

K=125 from MIL-Std-198 for still air and area in square inches, power in watts.

K=35 for forced air (about 200 cfm) and area in square inches, power in watts.

Variance for the K value seems large, but many factors affect heat flow. Thus, Equation (5) is an easy one to use to get into the ballpark. If the fluid is other than air, you should expect different values for K. High altitude operation, at reduced density, will also have a different set of numbers. View the value for K in the light of trying to be conservative in ratings. If the application is one in which it's best to err on the side of running cooler than calculated, then the higher value of K is more appropriate. On the other hand, if the application is short-term and you want to push the performance envelope, then the lower values of K are more appropriate. These equations are only valid for long-term steady-state conditions. Cyclic operation with long “off” periods is more tolerant of using the lower values of K.

Radiation cooling is largely ignored in this analysis. Regard radiation cooling as a benefit that allows a larger safety margin. On the other hand, radiation heating from a nearby transformer or other device may cause one side of a device to operate at a higher temperature than the other. In such cases, you may need empirical testing to determine if product limitations are exceeded.

Occasionally, the capacitor may be immersed in oil that may or may not be cooler than the ambient of the surrounding medium. Even though the liquid may be near the maximum operating temperature of the capacitor; the thermal capacity of the liquid and its ability to absorb heat may be several orders of magnitude better than that of a gas. Consequently, the liquid acts like an infinite heat sink that can absorb so much heat that the capacitor surface stays at the liquid temperature and does not rise. This keeps the thermal differential from the core to the skin high and allows more heat to flow.

Heat Removal

The flow of heat from the core of the capacitor to outer skin is a conductive process and requires a temperature difference (ΔT) for heat to flow and cool the capacitor. Without this ΔT, the temperature of the capacitor will continue to rise until it exceeds the thermal limits of the capacitor dielectric.

You can solve an exact analysis of the temperature within the capacitor using differential equations and/or finite element analysis, which is beyond the scope of this article. However, it is beneficial to identify the conductive paths and gain knowledge of how the heat flows within the winding.

You can break down dielectric and electrode ohmic losses into a per-turn basis. You can apply Equation (1), on page 58, to the capacitance created by the first active turn around the winding arbor. The amount of capacitance in this turn is a function of the dielectric constant, the spacing between the electrodes (dielectric thickness) some constants and the common area between the electrodes.

As each turn is wound, the area increases slightly because the diameter increases slightly and the circumference by the term πD, where D is the diameter of each turn. This means the amount of losses incurred by each turn increases with the area. Thus, the turns in the center generate the least amount of heat and the turns on the outside produce the most heat.

To consider the heat flow from the core to the skin, look at the two modes of heat conduction. Axial heat flow is that along the axis of the winding. Radial heat flow is that perpendicular to the winding axis (see Fig. 5).

The flow of heat in each of these modes, can be found by reviewing the flow of heat through a solid block, as shown in Fig. 6. The formula for conduction through a block is:

Where:

Q=Heat flowing

L=Path length

A=Area of block side

K_T=Thermal conductivity

Typical values for K_T are listed in Table 1.

In Fig. 6, the heat “Q” flows from t₁ (higher) to t₂ (lower) through area “A” along a path length “L,” depending upon the thermal conductivity “K_T.” Note that the values of K_T are vastly different. The metals are about four orders of magnitude better than the plastics. Within the groups, they may vary two to three times. This shows that the metals conduct heat much better than plastics.

Fig. 7, on page 65, represents one layer of a winding. Only the left half is shown. It is assumed that the right half is the same and an equal amount of heat is flowing in that direction. This layer is made of a dielectric and an electrode. The electrode is terminated in all edge spray material, typically Zinc.

For Fig. 7, we know from physics that the heat entering (Q₁) and heat leaving (Q₂) is the same and that it splits into electrode (Q_M) and dielectric (Q_D), or: Q₁=Q_M+Q_D=Q₂. Values of Q_M and Q_D are a function of the thickness and the length of the electrode. Rearranging Equation (6), on page 64, gives:

Equation (7) yields some important ideas. The amount of heat flow is inversely proportional to the path length, L, so that shorter values of L (i.e., narrow winding materials) increase the amount of heat that can flow with a given ΔT. The amount of heat flow is directly proportional to the area, which is the width (in this case, the circumference at whatever turn is being considered) of the dielectric times the thickness of the electrode. Q is also proportional to the thermal conductivity of the materials being used.

For example, consider a 10 μF capacitor made with 6-micron polypropylene. The capacitor design is compared with a 20-mm active material width and a 50-mm active material width. This means the one-half width is 10 mm and 25 mm, respectively. Table 2 compares the (K×A/L) value transferred through the electrode (Aluminum or Zinc at 3Ω/sq) or 6 micron aluminum foil and the dielectric. Note that the Q/ΔT term is the same as (K×A/L). This term can be considered two ways. We know the heat flow being generated, so we can determine the rise of the core for axial mode flow. We also can use it to determine how much heat can flow for a given ΔT. Note: To get actual heat values multiply by ΔT, then double to get the total heat flow.

Table 2, on page 65, shows several interesting details.

• Heat flow for the metallization is 2.8 to 3.1 times better than the accompanying dielectric flow — even though the dielectric is more than 600 times thicker.
• There's not much difference between Aluminum or Zinc metallization.
• The heat flow in the aluminum foil is 1783 times greater than the dielectric, and 757 times better than the metallization.
• Heat flow is proportional to the path length. The longer path is 2.5 times longer, but has 6.2 times poorer heat flow.
• The diameter increase can be substantial for using the shorter heat paths.
• Aluminum foil has much better heat conduction and lower ESR, but film-foil will not self heal. Thus, the voltage ratings may not be as high as for the same thickness of metallized dielectric.
• 1/Q_T/ΔT=θ_A. This is actually the term for thermal impedance.

Fig. 8 examines heat flow in the radial mode. Notice the successive layers of dielectric and metallization (shown detached for clarity). Applying Equation (6), on page 64, to these layers provides the ΔT for a heat flow Q for the metallized layers and the dielectric layers.

ΔT_Alum Q×1.882×10^-6

ΔT_Zinc Q×4.93×10^-6

ΔT_{Polypropylene}=Q×3571

These numbers show that the ΔT needed to push heat flow, Q, through the metallization layers is more than nine orders of magnitude less than to push it through the plastic. Therefore, in the radial mode, the plastic is the biggest thermal impedance and the metallization is insignificant.

Fig. 9 represents radial heat flow in a round capacitor section. Here, r₁ is the winding arbor radius, r₂ is the outside radius (½ di) and r is the radius at the point of interest. For most parts, if r=r₁, then ΔT is the core temperature — the skin temperature. The formula for determining the AT for the core to the skin for radial flow only, is:

Where:

A=4×K/g×r₁²

g=Uniform heat generation term, i.e., Power (I²×ESR in cal/sec) divided by winding active volume in cm³.

K=Thermal conductivity

When applying Equation (8) to the first two examples of the metallized capacitor outlined in Table 2, the radial heat rise is 13.6°C for the 10 mm example and 5.45°C for the 25 mm example. The axial temperature rise for these same two examples is 8.1°C and 50.7°C, respectively. These examples show that for fat and short designs, the axial flow and the radial flow are similar. There's probably an ideal design that gives the same rise in both modes. It also shows that for the long and skinny design the radial flow mode is greater than the axial mode. In actual operation, there is a blending of these two flow modes. The overall skin temperature rise will also be affected by the removal of heat from that surface. Thus, the overall hot spot will move depending on the part's geometry.

The solution to the axial and radial flow combination is complex with many variables. Sometimes, empirical data is the best way to determine where that spot is located. These equations also show that for increasing power levels, the rise of the core above the skin temperature diverges.

Empirical Test Data

Tests conducted on a short fat winding excited under sinusoidal high current show the radial skin temperature was higher than the axial exit point. Differentials and overall variance of core to skin was about as expected.

Testing of a similar part at increased power levels showed a divergence of core to skin rise as power increased (Fig. 10, on page 66). Therefore, increasing current loads would result in a spreading of surface and core temperatures.

Ultimately, we must keep the core of the capacitor within the temperature limitations of the dielectric material used. This is critical information when selecting a capacitor. (See the sidebar for some thermal rules for selecting a capacitor.)

Paying attention to thermal characteristics of capacitor systems, as described above, can help you to avoid premature capacitor failure.

Thermal Rules for Capacitors

When selecting capacitors, keep the following “rules for the road” in mind.

1. Observe the operating temperature limits for the capacitor, which generally means the limit applies to the core of the winding. You must adjust the temperature by considering core-to-skin and skin-to-ambient differentials.

2. Reliability essentially doubles for every 10°C drop — so even small improvements in cooling help. High-power operation requires planning for reliability.

3. Capacitor size reductions decrease the surface area for heat removal. In turn, this increases the skin temperature for a given set of operating conditions. Although size reductions are desirable, you must balance them against reliability.

4. Forced air-cooling helps. Even small amounts can increase the heat removal from the capacitor surface.

5. Use the capacitor manufacturer's resources to discuss these issues. If the manufacturer doesn't understand your questions, think twice about using that product.

6. When considering careful analysis of performance and reliability, film capacitors come out better than most other types of capacitors for these applications.