## 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 * f_{DF} * 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.

f_{DF} 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 * f_{DF} * 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

You can download a spread-sheet with these calculations here.

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 )

[1] | Illinois Capacitor "Impedance, Dissipation Factor and ESR" |

[2] | Cornell Dubilier "Aluminum Electrolytic Capacitor Application Guide" |

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