# ESR in Electrolytic capacitor vs Voltage rating

I would like to know why in an electrolytic capacitor the ESR decreases as voltage rating increases. And why the current rating increases as voltage rating increases. Thank you.

• Can you give a link to where you found the slide? Or to what series of capacitors are being referred to? Feb 22 '17 at 18:53
• construction variations differ depending on voltage, current ratings and l/A ratio of conductor foil thickness/ area ratio Feb 22 '17 at 18:59

Your assumption that "all" capacitors of same C and case size have lower ESR with higher V rating ( it is not universal). This depends on construction of l/A or foil length and cross-sectional area , A which for fairly high V ratings may use slightly thicker foil for longer foil wraps with a bigger gap and end up with the same ESR.
However let's assume the foil thickness or cross-sectional area is constant in small high density low voltage caps.

• ESR is commonly rated in low ESR Caps where the ESR * C = T calculation typically <=10us,
• But not general purpose caps. ESR is not given and the ESR * C = starts around 100us and increases with component size is rated instead by D.F., dissipation factor @120Hz.
• A designer should realize this component is (usually) intended for bridge rectifiers with the standard 60Hz test method rather than high frequency SMPS demanding lower ESR.
• Lower ESR High V caps may be rated by their ripple current (Arms) instead of ESR along with D.F. but some Mfr.'s may also include ESR.

# How can current ripple increase with Voltage rating?

• High V rating increases Ripple current rating due to construction of thicker foils and larger area with larger gap voltage for the same package size.
• But in the smallest case size, with low V ratings, the minimum foil thickness may already be the smallest possible, so the reverse trend does not apply and instead length of wraps is increased with dielectric gap.

# How can ESR reduce with increased Voltage rating?

An electrolytic with increased voltage rating must increase the gap, d between the conductors at the expense of the capacitance gap loss for the same size body.

This is normally done using the same foil wrapped in a cylinder with a longer length and bigger dielectric gap to achieve a higher voltage rating and the bonus is a larger conductor area, A, hence a lower conductor resistance , R.

The capacitance for parallel plates with any dielectric insulator between has the properties of the conductive foil plates and the breakdown voltage of the dielectric of any insulator medium between.

Facts: All insulators are dielectrics and they all have a fairly linear breakdown voltage in parallel plates with gap displacement. All conductors have Resistance, R, proportional to the length of the electrodes and is inversely proportional to the cross-sectional area, A for a given electrode or plate usually made of foil or metalized plastic.

$C=\frac{\epsilon A}{d} ~~~~R=\frac{l}{A}\rho ~~~~~ V_{max} = kd~ ~~$

$k =$dielectric rating [V/mm or kV/m] , l = conductor foil thickness

$C=$ Capacitance $[F] ~~~\epsilon =$ permittivity $A=area~,~ d=gap$

# Side question, How do you choose a Cap?

• Given variables for C, ESR( or D.F. or Imax), V, case size, cost , max Temp, leakage R, vendor quality (brand reputation), vendor technology (Family type) & cost
• and you may have design specs for; Cost, MTBF , C value, SMT or THT , ESR, etc
• then decide on design Rules of Thumb for voltage margin, current margin, ESR aging, C aging, Ambient Temp range, and desired MTBF
• then depending on your "bias" for above needs (cheap or reliable or best performance or just good enough) , increase your margin for Voltage, Imax, ESR and C to improve temperature rise which directly affects aging.

• Other than solder process & design defects, a capacitor is most likely to fail first in any design.

• A hot one or stressed for current and large mW dissipation in a thermal insulating package will result in poor reliability

So voltage and current margins are key to any design Rule of thumb, such as >=50% margin depending on your pressure to reduce cost and maximize MTBF.

I'm not sure about the first part of the question. I'm not even sure the premise is correct, since when I look at one series of electrolytics I don't see an obvious trend of lower ESR with higher WV. For example, in this series a 100 V 22 uF part has DF of 18, while a 400 V 22 uF part has DF of 25. DF (dissipation factor) is proportionial to C x ESR, so this indicates higher ESR for the higher voltage part.

But the second part is logical. The limitation on current rating is often due to self-heating of the capacitor. The self heating is proportional to $I^2R$, where the R is the ESR. So a lower ESR will generally give a higher allowed ripple current.

• Thank you for your answer... I've just edited with the slide I am talking about (sorry could not provide it before.. was not working from mobile)
– AM93
Feb 22 '17 at 18:16
• Also higher voltage caps are physically larger and thus able to dissipate more heat, which would increase their ripple current rating even if the ESR was the same. Feb 22 '17 at 18:26