152

1.3.4 Temperature dependence of dissipation factor

Dissipation factor varies with temperature as the typical

curves show to the right. For maximum limits please refer to

ratings tables.

Typical Curves-Dissipation Factor vs. Temperature

100 F/6V

1 F/35V

10

5

0

-55 -40 -20

0

20 40 60 80 100 125

Temperature C

1.4 IMPEDANCE, (Z) AND EQUIVALENT SERIES RESISTANCE (ESR)

1.4.1 Impedance, Z

This is the ratio of voltage to current at a specified frequency.

Three factors contribute to the impedance of a tantalum

capacitor; the resistance of the semiconducting layer,

the capacitance, and the inductance of the electrodes and

leads.

At high frequencies the inductance of the leads becomes a

limiting factor. The temperature and frequency behavior of

these three factors of impedance determine the behavior of

the impedance Z. The impedance is measured at 25°C and

100 kHz.

1.4.2 Equivalent series resistance, ESR

Resistance losses occur in all practical forms of capacitors.

These are made up from several different mechanisms,

including resistance in components and contacts, viscous

forces within the dielectric, and defects producing bypass

current paths. To express the effect of these losses they are

considered as the ESR of the capacitor. The ESR is frequency

dependent. The ESR can be found by using the relationship:

ESR =

Tan

2πfC

where f is the frequency in Hz, and C is the capacitance in

farads. The ESR is measured at 25°C and 100 kHz.

ESR is one of the contributing factors to impedance, and at

high frequencies (100 kHz and above) is the dominant factor,

so that ESR and impedance become almost identical,

impedance being marginally higher.

1.4.3 Frequency dependence of impedance and ESR

ESR and impedance both increase with decreasing frequency.

At lower frequencies the values diverge as the extra contri-

butions to impedance (resistance of the semiconducting

layer, etc.) become more significant. Beyond 1 MHz (and

beyond the resonant point of the capacitor) impedance again

increases due to induction.

1k

100

10

1

0.1

0.01

0.1

μF

0.33

μF

1

μF

10

μF

33

μF

100

μF

330

μF

100

1k

10k

100k

1M

Frequency f (Hz)

Impedance (Z)

ESR

Frequency Dependence of Impedance and ESR

TAP/TEP Technical Summary and

Application Guidelines