ESR Frequency Characteristics
Like DF, the ESR varies with frequency. Rewriting the DF
equation above, ESR can be modeled as below:
ESR = 10,000(DF lf )/(2πfC) + ESR hf
Expressing the ideas in ESR terms, at low frequencies the
ESR declines steadily with increasing frequency and crosses
over to constant ESR at a frequency inversely proportional to
capacitance. This crossover is typically below 10 kHz. The ESR
of high-capacitance capacitors changes little with increasing
frequency because high-capacitance causes them to have low
crossover frequencies. The ESR hf ranges from 0.002 Ω for large,
screw-terminal capacitors to 10 Ω for miniature devices.
IMPEDANCE (Z)
For aluminum electrolytic capacitors impedance is actually
impedance magnitude. It is the ratio of voltage to current at
a given frequency and is related to the capacitor’s capacitance,
ESR and series inductance as follows:
Z = [(ESR)2 + (1/(2πfC) – 2πfLs)2] 1⁄2
Where Z is impedance in Ω, ESR is equivalent series resistance in
Ω, f is frequency in Hz, C is capacitance in F and Ls is equivalent
series inductance in H.