Added: "Big" "Slow" compared to "Small" "Fast" is wrong. Capacitors are charged at different speeds because different time constants are used. T=R*C. Decrease R and the charge will be rapid.
Tomo,
By adding a small, insignificant film capacitor impedance doesn't matter enough to even spend the cash on the capacitor. i.e.
C2=Large electrolytic
C1=small film capacitor
Zc1+Zc2 = 1/((jw)^2*C1C2) / s(C1+C2)/((jw)^2*C1C2)=1/jw(C2+C1)
It helps a wee bit, but drowns in component tolerances, and wont change a thing. The model does not show any issues. The world is perfect and everything is acting ideal. But in these situations discussing capacitor types it will actually now be revealed that the impedance is still remarkably high at higher frequencies in real life, so the added capacitance won't help at all
Dizzyorange, What you read there to begin with is one of the dangers of the internet. A lot of people who believes in something, but can't prove anything with theory, but just excuses it all with less good sound signature and some jibber-jabber. I will be writing all this once - yes i'm bored - and people can use the search function later on, because this question pops up from time to time.
The trick with electrolytic capacitors is that in reality, they are a capacitor C1 in series with a resistance, the ESR, we call it R1. Film caps does not act like this, because of the physical differences (i.e. stack versus a roll, and depend on electrolytic as well)
The R1 of the electrolytics is also in series with a small inductance, L1, and the capacitance in parallel with another resistance R2.
Z(C1)=R2||(1/sC1) + sL1 + R1
Z(C1)=(R2 + (sL + R1)(sC1R2 + 1))
/ (sC1R2 + 1)
Z(C1)=(s^2L1C1R2 + s(L1+C1R1R2) + R1 + R2)
/ (sC1R2 + 1)
This is the impedance of the electrolytic capacitor with capacitance C1, measured at the frequency s=jw (w = omega, rad/sec)
According to
http://www.johansondielectrics.com/technicalnotes/dcd/ , typical values for L1~2nH, R1=15mOhm .... R2 is considered to be extremely high, because the current leakage typically is ~10 uA (!!). Thus assume R2=20 MOhm.
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Now, let's put a film capacitor, C2 in parallel with the electrolytic C1. Film capacitors have a much lower ESR and generally lower leakage current, thus I'll keep it at Z(C2)=1/sC2. This will still demonstrate the point.
Ztotal=Z(C1)||Z(C2)
= (S^2*L1C1R2 + s(L1 + C1R2) + R1 + R2)
/ (sC2(sC1R2 + 1))
/ (sC2(s^2*L1C1R2 + s(L1+C1R1R2) + R1 + R2) + sC1R2 + 1)
/ (sC2(sC1R2 + 1))
= (S^2*L1C1R2 + s(L1 + C1R2) + R1 + R2)
/ (s^2*L1C1R2 + s(L1+C1R1R2) + R1 + R2) + sC1R2 + 1)
= (S^2*L1C1R2 + s(L1 + C1R2) + R1 + R2)
/ (s^3*L1C1C2R2+S^2*C2(L1+C1R1R2) + sC2(R1+ (C1/C2)*R2) + 1)
Divide by R2, and i think it will become clearer:
= (S^2*L1C1 + s(L1/R2 + C1) + R1/R2 + 1)
/ (s^3*L1C1C2+S^2*C2(L1/R2+C1R1) + sC2((R1/R2) + (C1/C2)) + 1/R2)
Recall that C1 was your large capacitor. and C2 was the parallel small film cap, i.e. C2<<C1
L1 was in the 10^-12 henry area, so we might as well neglect it totally. Thus we achieve
Ztotal= 1/sC1 ... I.e. the same as the capacitance of the electrolytic when frequency->large. The small film cap will be significant because of the variable s=jw increasing. There's something else we don't like: The third order poles in the denominator of the function. One is introduced with L1.
Inserting typical values:
C1: 470uF
C2: 0.1nF
R1: 15 mOhm
R2: 10 MOhm
L1: 2 nH
We get:
Ztotal=(s^2*9.4e-13 + s0.00000705 +1)/(s^3*9.4e-20 + s0.00047 + 0.5e-7)
Plotting the impedance function in matlab (as below) or similar, we get that the minimum real part of the impedance is achieved at w=1e6 rad/sec, where |Ztotal|=0.015 Ohm. However, introducing the real model for the electrolytic reveals a nasty peak in the bodeplot at w=7e7 rad/sec. Here the impedance is |Ztotal|=1.995 MOhm.
This is revealed from the bodeplot below:
As we see, the impedance curve for the "corrected" circuit follows the ideal world for a number of frequencies, but it differs greatly, and becomes unacceptable at points.
