## Capacitor impedance.

### Electrolytic capacitor impedance.

Fig.1: Capacitor equivalent circuit and impedances.

 Type A B Capacitance 1000 µF 1000 µF Voltage 50 V 50 V Diameter 12.5 mm 16 mm Length 25 mm 25 mm Maximum ripple current @ 120 Hz 1.05 A @ 85 °C 1.8 A @ 105 °C Dissipation factor (=DF=tan φ) @ 120 Hz 0.12 0.1 Impedance @ 100 kHz No data 21 mΩ ESR (calculated) 1.6 mΩ 1.3 mΩ Self-inductance (calculated) No data 36 nH Self resonant frequency (calculated) No data 26.6 kHz

Xc = 1 / ( 2 * π * f * C ), where:
Xc is the capacitor reactance.
f is the frequency.
C is the capacitance.

Xl = 2 * π * f * L, where:
Xl is the inductor reactance.
f is the frequency.
L is the self-inductance.

ESR = ( DF / 100 ) / ( 2 * π * fDF * C ), where:
ESR is Equivalent Series Resistance
DF is dissipation factor. Note that this value is in % even if this is not stated in the data-sheet.
fDF is the frequency where DF is specified.
C is the capacitance.

Z = √ ESR² + ( Xl - Xc )², where:
Z is the total impedance
ESR is Equivalent Series Resistance
Xl is the inductor reactance.
Xc is the capacitor reactance.

Fr = 1 / ( 2 * π * √ L * C ), where:
Fr is self-resonant frequency
C is the capacitance.
L is the self-inductance.

L = ( Xc + √ Z² - ESR² ) / ( 2 * π * f ), where:
L is the self-inductance.
Xc is the capacitor reactance at the frequency where Z is specified.
Z is the total impedance at some high frequency.
ESR is Equivalent Series Resistance
f is the frequency where Z is specified.

Example ESL calculation (Type B in table 1):
ESR = ( DF / 100 ) / ( 2 * π * fDF * C ) = ( 0.1 / 100 ) / ( 2 * π * 120 * 1.00E-3 ) = 1.33E-3 = 1.33 mΩ

Example self-inductance calculation (Type B in table 1):
Z = 21 mΩ @ 100 kHz.
Xc = 1 / ( 2 * π * f * C ) = 1 / ( 2 * π * 1.00E5 * 1.00E-3 ) = 1.59E-3 = 1.59 mΩ
L = ( Xc + √ Z² - ESR² ) / ( 2 * π * f ) = ( 1.59e-3 + √ 2.10E-2² - 1.33E-3² ) / ( 2 * π * 1.00E5 ) = 3.59E-8 = 35.9 nH

Example self-resonant frequency calculation (Type B in table 1):
Fr = 1 / ( 2 * π * √ L * C ) = 1 / ( 2 * π * √ 3.59E-8 * 1.00E-3 ) = 2.66E4 = 26.6 kHz

If you need to measure a capacitor yourself, the easiest is to measure the self-resonant frequency.
The impedance at Fr is ESR.
L = 1 / ( 4 * π² * C * Fr² )

References.

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