Spehro said:
thats the professional comic; I meant the journal
The guts of his model is this:
Michael Gaspari wrote a great paper in IEE trans. Industry applications,
vol.41 no.6 nov/dec 2005, pp1430-1435.
his cap model is:
---[Ro]---[R1]---+----[R2]----+----[C1]----
| |
+----[C2]----+
R0 = resistance of foil, tabs & terminals
R1 = resistance of electrolyte
R2 = dielectric loss resistance
C1 = terminal capacitance
C2 = dielectric loss capacitance
R2 and C2 give a large variation in ESR with frequency. typically the
effect of R2,C2 peters out above 10kHz, so you can take the ESR at
100kHz as the combined value of R0 and R1. this can be seen from the
ripple current multiplier tables a decent cap data sheet has.
R0+R1 = ESR @ 100kHz
R2 = ESR @ 100Hz - (Ro + R1)
and pick C2 to get the right values for ESRs in the 100H - 10kHz range
the reason the ripple current varies with temperature is the loss in the
cap is kept constant (for a given lifetime) so lower ESR means more
current. you can thus translate a ripple-current multiplier table (eg
see LXZ cap datasheet) into an ESR multiplier.
ESR_multiplier = 1/(ripple_multiplier)2
the LXZ table for 220uF - 560uF caps is:
120Hz 1kHz 10kHz 100kHz
0.5 0.85 0.94 1.00
so the ESR multiplier is:
4 1.4 1.13 1
the ESR of these caps have at 100Hz is 4x th 100kHz value....
ESR variation with temperature is due to the increased conductivity of
the electrolyte.
R1(T) = R1o*exp[(To-Tcore)/E]
R1o = ESR at temperature To
E = temperature sensitivity factor
R1 is usually 5x Ro, and you can calculate E from the two ESR
measurements (-10C, 20C) for a given cap family.
Cheers
Terry