www.vishay.com For technical questions, contact: tantalum@vishay.com Document Number: 4003122 Revision: 03-Apr-06

AC Ripple Current CalculationsVishay Sprague

Application Notes AC Ripple Current Calculations Solid Tantalum Capacitors

INTRODUCTION

Solid tantalum capacitors are preferred for filteringapplications in small power supplies and DC/DC convertersin a broad range of military, industrial and commercialsystems including computers, telecommunications,instruments and controls and automotive equipment. Solidtantalum capacitors are preferred for their high reliability,long life, extended shelf life, exceptional stability withtemperature and their small size. Their voltage range is 4 to50 volts for the most common types. Tantalum chipcapacitors for surface mount applications are manufacturedin very small sizes and are compatible with standardpick-and-place equipment.

The electronics industry has moved to smaller and smallerpower supplies and higher switching frequencies, with anincreased requirement for capacitors with smaller size andoperating characteristics better suited to high frequencies.This application note briefly describes the construction ofsolid tantalum capacitors, the concept of Equivalent SeriesResistance (ESR) and presents calculations for powerdissipation and voltage limitations for both low and highfrequency applications.

CONSTRUCTION

The solid tantalum capacitor consists of a sintered tantalumpellet, the anode, on which a tantalum oxide dielectric isformed by electrolysis. The pellet is then coated withmanganese dioxide for the cathode. Positive and negativeterminations are attached to this pellet and the assemblymay be conformally-coated or molded.

Looking closely at the internal structure of the pellet, we seethat it is made of grains of tantalum powder sintered to eachother. A solid tantalum capacitor is equivalent to many smallcapacitors in parallel, one for each grain of powder. Thisconfiguration produces a very large surface area, therefore alarge capacitance in a relatively small volume.

CONFORMAL COATED SERIES

TANTALUM PELLET

MOLDED SERIES

Cathode Termination(Silver + Ni/Sn/Plating) Encapsulation

Anode Termination(Silver + Ni/Sn/Plating)

Red Epoxy Tower

Sintered Tantalum Pellet

MnO2/Carbon/SilverCoating

TANTAMOUNT®, Solid Electrolyte Tantalum Chip Capacitors.

Simplified View

Metallized OuterElectrode

Carbon

MnO2

Ta2O5

Tantalum

Tantalum Anode Lead

Anode Polarity BandTop Marking

Surface

Bottom

Side End

Silver Adhesive

Solderable CathodeTermination

Sintered TantalumPellet

Lead FrameSolderable

Anode Termination

Anode Polarity Bar

Epoxy Encapsulation

MnO2/Carbon/SilverCoating

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AC Ripple Current CalculationsApplication Notes AC Ripple Current

Calculations Solid Tantalum CapacitorsVishay Sprague

EQUIVALENT SERIES RESISTANCE (ESR)

A capacitor offers intemal resistance to AC current, calledthe Equivalent Series Resistance (ESR). At lowerfrequencies, this is mainly the resistance of the dielectric. Athigher frequencies, the resistance of the manganese dioxidein the voids between the grains is predominant. Because theresistivity of manganese dioxide is inversely proportional totemperature, the ESR of solid tantalum capacitors at highfrequencies decreases as temperature increases.

POWER DISSIPATION LIMITATION

When AC current is applied to a solid tantalum capacitor, theresistance (ESR) that opposes the flow of current results inheat generation, according to the formula:

(1)

The power (P) dissipated in the capacitor results in anelevation of temperature. The allowable temperature rise ofa capacitor due to power dissipation is determined byexperience. For example, this value is + 20 °C maximum formolded chip capacitors. This in turn limits the power that thecapacitor can dissipate.

VOLTAGE LIMITATION

The power a capacitor can dissipate is also limited by theapplied DC voltage. The operating voltage should not beallowed to rise above the rated voltage (nor should it dropbelow zero, since the solid tantalum capacitor is a polarizedcomponent). Assuming the capacitor is biased at half therated voltage, which is the optimum use condition, thelimiting value of the voltage is, for a sinusoidal waveform:

(2)

Vrms for each value of Rv (Rated voltage) are:

CURRENT LIMITATION (LOW FREQUENCY)

To find the limiting current Irms, we divide Vrms by theimpedance at the desired frequency.

(3)

using the formula:

(4)

where X is 1/Cw + Lw (w = 2pf)

Since inductance of a solid tantalum capacitor is usually inthe nanohenry range, the Lw factor becomes important onlywhen the frequency is higher than a few megahertz. Forfiltering applications at 100 kHz and lower, the inductancefactor will generally be ignored in the calculation. At 120 Hz,the impedance can be determined by calculation.

(5)

At 120 Hz, DF2 is relatively small compared with 1 and theformula can be simplified to:

(6)

More generally, DF values of less than 10 % will not affectthe final result by more than 1 %. It is important to use thelowest value for C, including the capacitance tolerance. At120 Hz, the formula can be simplified to:

(7)

where Irms is the maximum permissible rms current inmilliamperes, C the capacitance minus the capacitancetolerance in microfarads and V the rated voltage in volts. Allabove calculations assume the capacitor is properly biasedat half the rated voltage. If this is not the case, Vrmsbecomes

(8)

where Vp = V rated - V bias or V bias, whichever is lower.

RATED VOLTAGE Vrms MAXIMUM

4102025354050

1.425.307.078.84

12.3714.1417.68

P I2 ESR×=

Vrms Vpp 2 2⁄ Rv 2 2⁄= =

Irms Vrms Z⁄=

Z X2 ESR2+=

Z 1 2πfC⁄( )2 DF 2πfC⁄( )2+ 1 2πfC⁄( ) 1 DF2+( )= =

Z 1 2πfC⁄=

Irms 0.266 CV×=

Vp 2⁄

AC Ripple Current CalculationsVishay Sprague Application Notes AC Ripple Current

Calculations Solid Tantalum Capacitors

www.vishay.com For technical questions, contact: tantalum@vishay.com Document Number: 4003124 Revision: 03-Apr-06

CURRENT LIMITATION (HIGH FREQUENCY)

At frequencies in the 10 kHz to several hundred kilohertzrange, the power dissipation becomes the limiting factor. Thefollowing formula gives the maximum permissible ripplecurrent for a sinusoidal wave form:

(9)

Pmax is the maximum power dissipation the capacitor cantolerate. The ESR value in the formula is the maximum ESRof the capacitor at the required frequency. This can bedetermined by measuring capacitors and determining amaximum value by using the mean value and adding 3 ormore standard deviations. Some manufacturers specify themaximum impedance at 100 kHz or 1 MHz. Either value maybe used in ripple current calculations.

Power dissipation limits calculated for the most popularsurface mount types of solid tantalum capacitors are:

Molded Case Chip (293D):

ESR SCREENING

For parallel operation, the ESR spread can be minimized byscreening. This reduces the risk of excess ripple currentexposure to any one of the capacitors.

Some equipment will only measure impedance. Animpedance limit can be caluclated to insure that the ESRstays in the required range. Use the formula:

(10)

Impedance can be measured using an impedance meter anda fixture that is appropriate for the task. With the mostsophisticated fixtures, several capacitors may be tested atthe same time, reducing the test cycle time.

CORRECTIVE FACTORS

The calculations for high frequency ripple current are shownin formula (9) for a sinusoidal waveform and an ambienttemperature of + 25 °C. If the waveform is not sinusoidal, theripple current limitations may differ.

Generally speaking, the ripple current limit calculated byformula (9) can be divided by the duty cycle of the signal. Ifthe temperature is higher than + 25 °C, the ripple current limitshould also be multiplied by the factors shown:

RIPPLE CURRENT/VOLTAGE CALCULATIONS EXAMPLE

As an example, we will determine the ripple voltage andpower dissipation capability for a 1 µF, ± 20 % tolerance,35 volt, 293D capacitor.

At 120 Hz:

Irms = Vrms/Z

= 12.37 x 2 x 3.14 x 120 x 0.8 x 10-6

= 0.007 Amp.

If we used

With ESR = DF/2pfC= (04/2 x 3.14 x 120 x 0.8 x 10-6)

= 66 ohms

At 120 Hz, the voltage is the limiting factor.

At 100 kHz:

At 100 kHz, the typical ESR for a 1 µF/35 volts tantalum is:

Irms = 0.085/1.5 = 0.238 Amp.

If we now look at the maximum ripple voltage, the above

limitation translates into:

Vrms = Z x Irms = 3 x 0.231 = 0.71 volts.

At 100 kHz, the power dissipation is the limiting factor.

CASE SIZEMAXIMUM POWER AT + 25 °C

(WATTS)

ABCDE

0.0750.0850.1100.1500.165

Irms Pmax ESR⁄=

Zmax Xc2 ESR2+=

Xc 1 Cω⁄=

TEMPERATURE MULTIPLYING FACTOR

+ 85 °C+ 125 °C

0.90.4

Vrms Rv 2 2⁄ 12.37 volts= =

Irms Pmax ESR⁄=

Irms Pmax ESR⁄ 0.080/66= =

0.035 Amp=

Irms Pmax ESR⁄=

ESR 1.5 ohms Z 3 ohms=( )=

Document Number: 40031 For technical questions, contact: tantalum@vishay.com www.vishay.comRevision: 03-Apr-06 25

AC Ripple Current CalculationsApplication Notes AC Ripple Current

Calculations Solid Tantalum CapacitorsVishay Sprague

CONCLUSIONS

The industry is moving towards smaller and smaller powersupplies and DC/DC converters operating at higher

frequencies. The three factors shown become more and

more important in capacitor selection.

1. Higher Switching Frequencies: The switching frequencyof power supplies has increased from the 10 kHz range adecade ago to the 100 kHz range and up today. The ESR ofsolid tantalum capacitors is either the same or lower at higherfrequencies and impedance is at a minimum in the 100 kHzto megahertz range. Higher switching frequencies and theneed for smaller sizes will increase the use of solid tantalumcapacitors.

2. Surface Mount Technology: The application of surfacemount technology not only reduces the size of powersupplies and converters but also uses the substrate on whichthe components are mounted to dissipate some of the heatgenerated by the switching elements. Solid tantalum chipcapacitors are well suited for this application. They havesuperior operating characteristics, do not leak electrolyte andare compatible with common automated surface assemblyequipment.

3. Tighter High Frequency Parameters: The reduction ofthe maximum ESR of a solid tantalum capacitor mayproduce tradeoffs in size or DC characteristics. Rather thanlooking at lower ESR in terms of process average, it may beadvisable to try to reduce ESR variation, producing a lowermaximum ESR with a tighter distribution. This improvementmay be achieved by using statistical process control, anapproach already being implemented at Vishay SpragueSolid Tantalum manufacturing facilities.

TYPICAL CURVES OF IMPEDANCE AND ESR VS FREQUENCY

100

10

1

0.1

1 µF, 35 V, A CASE

4.7 µF, 35 V, C CASE

IMPEDANCEESR

100 1K 10K 100K 1M 10MFREQUENCY