# What property determines charge current surge value in e-caps ?

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#### SYNFONIQUE

Joined Jun 5, 2021
35
Standard answer: iequalscdvdt, as the man behind the CapSite has named it. So there is the
capacitance to start with, and the ratio dv/dt to complete the product that ought to give you the
momentary charge current to the cap. But how ... ? Consulting textbooks and tutorials, you are
bound to find a phrase like: 'presents a near-short circuit', to describe the cap's behavior after
switch-on. Few if any specify the 'near'-part, however. The only thing to do then, is go look for an
R (i.e. in the cap itself, not the obvious resistances in source, wiring, etc.). A glance at one of the
many different equivalent circuit diagrams for an e-cap, reveals its series resistance ESR, which
indeed turns out to be less than one Ohm usually. And by applying this man's familiar law, we can
finally make more than an educated guess as to the value of the charge current surge. This is
because - while dv in the original formula is not easy to determine - V in Ohm's Law simply is the
full applied voltage, as there has not yet been generated a counter e.m.f. (where the 'm' stands for
'motive', not 'magnetic') directly after switch-on. So the inrush current surge equals the voltage
applied to the e-cap, divided by its ESR, or does it ? ....
I invite and await your comments and criticism as to method, reasoning and outcome of the above.
(Please try to apply as little math as possible - thank you).

#### BobTPH

Joined Jun 5, 2013
3,661
There is also the output impedance of the power source, which , in some cases will dominate.

Bob

#### mar10

Joined Mar 23, 2019
39
And how about the inductance of the supply wire. That should kill any infinite currents.

#### andrewmm

Joined Feb 25, 2011
1,757
Standard answer: iequalscdvdt, as the man behind the CapSite has named it. So there is the
capacitance to start with, and the ratio dv/dt to complete the product that ought to give you the
momentary charge current to the cap. But how ... ? Consulting textbooks and tutorials, you are
bound to find a phrase like: 'presents a near-short circuit', to describe the cap's behavior after
switch-on. Few if any specify the 'near'-part, however. The only thing to do then, is go look for an
R (i.e. in the cap itself, not the obvious resistances in source, wiring, etc.). A glance at one of the
many different equivalent circuit diagrams for an e-cap, reveals its series resistance ESR, which
indeed turns out to be less than one Ohm usually. And by applying this man's familiar law, we can
finally make more than an educated guess as to the value of the charge current surge. This is
because - while dv in the original formula is not easy to determine - V in Ohm's Law simply is the
full applied voltage, as there has not yet been generated a counter e.m.f. (where the 'm' stands for
'motive', not 'magnetic') directly after switch-on. So the inrush current surge equals the voltage
applied to the e-cap, divided by its ESR, or does it ? ....
I invite and await your comments and criticism as to method, reasoning and outcome of the above.
(Please try to apply as little math as possible - thank you).
Interesting,
you say as little maths as possible,
yet you seem quiet happy talking about dv/dt ,

which implies some good understanding of maths,

what is the end aim of this fairly open question ?

#### LowQCab

Joined Nov 6, 2012
1,096
Simply use a Current-Source / Regulator,
that keeps the Math simple, and creates
a very predictable, and Linear, Charging-Time.
.
.
.

#### SYNFONIQUE

Joined Jun 5, 2021
35
Interesting,
you say as little maths as possible,
yet you seem quiet happy talking about dv/dt ,

which implies some good understanding of maths,

what is the end aim of this fairly open question ?
My question equals the thread title. Maybe it is odd to answer it yourself next
and then ask for comments. The purpose, however, was to present a way around
the obvious formula - let us say: the way of an experienced experimenter with a
down-to-earth and hands-on approach (and for the US-members: KISS).
I mentioned the dv/dt formula only to contrast it with my 'solution'. I 'know' most of the available formulas pertaining to this issue, which doesn't mean I can work with them. So I need an
alternative (low-math) approach, which the remarkably unisono textbooks and tutorials do not
provide.
As an audio pro, my interest is in high-grade linear PSUs. So I also know, what keeps the "near-short" situation from causing equipment to fail: the overload-resilience in the rest of the circuitry, as pointed out in the other replies.
Still the expensive reservoir cap(s) suffer longevity problems in the absence of protective circuitry
(another reason to keep your set switched-on as an audiophile).
What do I aim to achieve in the end ? First of all, proposing practical low-math alternatives, directly applicable to real-world components and circuitry; and maybe establishing validity-boundaries for caps theory along the way ...

Last edited:

#### andrewmm

Joined Feb 25, 2011
1,757
My question equals the thread title. Maybe it is odd to answer it yourself next
and then ask for comments. The purpose, however, was to present a way around
the obvious formula - let us say: the way of an experienced experimenter with a
down-to-earth and hands-on approach (and for the US-members: KISS).
I mentioned the dv/dt formula only to contrast it with my 'solution'. I 'know' most of the available formulas pertaining to this issue, which doesn't mean I can work with
them. So I need an alternative (low-math) approach, which the remarkably unisono
textbooks and tutorials do not provide.
As an audio pro, my interest is in high-grade linear PSUs. So I also know, what keeps the "near-short" situation from causing equipment to fail: the overload-resilience in
the rest of the circuitry, as pointed out in the other replies.
Still the expensive reservoir cap(s) suffer longevity problems in the absence of
protective circuitry (another reason to keep your set switched-on as an audiophile).
What do I aim to achieve in the end ? First of all, proposing practical low-math alternatives, directly applicable to real-world components and circuitry; and maybe
establishing boundaries for caps theory along the way ...

So you want maths at the end, but not at the beginning,
Uhm,

To clarify

you want to know what determines the surge capacity of an electrolytic capacitor ?

Is that true ?

as such, To a first degree answer, the answer is resistance is the limiting thing.

No magic, no complicated maths,
easy to lookup and understand

Quesion over I think.

#### SYNFONIQUE

Joined Jun 5, 2021
35
So you want maths at the end, but not at the beginning,
Uhm,

To clarify

you want to know what determines the surge capacity of an electrolytic capacitor ?

Is that true ?

as such, To a first degree answer, the answer is resistance is the limiting thing.

No magic, no complicated maths,
easy to lookup and understand

Quesion over I think.
Just don't understand, how you can extract this conclusion from my post,
which I thought is detailed and straightforward enough, not to be misunderstood.
The only thing we can agree on: Answer over, I think.

#### schmitt trigger

Joined Jul 12, 2010
463
It is very common in power supplies, specially the higher power ones with large input capacitors, to employ an inrush limiter.
The simplest is a NTC thermistor. Initially it has a fairly large resistance limiting the inrush. As it heats up the resistance greatly decreases, allowing normal operations with low losses.

#### SYNFONIQUE

Joined Jun 5, 2021
35
It is very common in power supplies, specially the higher power ones with large input capacitors, to employ an inrush limiter.
The simplest is a NTC thermistor. Initially it has a fairly large resistance limiting the inrush. As it heats up the resistance greatly decreases, allowing normal operations with low losses.
Thank you for rekindling the discussion. As an "audio pro" and after many long
hours of studying the relevant literature, however I am fully aware of common ICL
technology. Unfortunately all of these solutions have their own drawbacks. Instead
of introducing ever more complexity (e.g. MOSFETs, switched capacitors, and what
have you), I believe that an improved analysis and better understanding of the
behavior in real-world e-caps could point the way to a relatively simple solution,
without switching elements, lingering heat dissipation, and the like.
In the era of ultra-low ESR, and what I call 'Farad mania', it is of vital importance to
address and tackle this problem.

#### du00000001

Joined Nov 10, 2020
78
The inrush current for a given cap is determined by:
• voltage applied
• source series resistance
• line inductance
• capacitor internal resistance and inductance

For "devices" (e.g. automotive sensors, ECUs and alike) you end up with 4+ A - - - when measuring bandwidth-limited (100 kHz limit). The peak momentary current will be the short-circuit current - mainly dominated by the series resistance.
On PCBs (with a local power source), my best guess is that the peak current will be limited by the source impendance of your power supply.

#### SYNFONIQUE

Joined Jun 5, 2021
35
The inrush current for a given cap is determined by:
• voltage applied
• source series resistance
• line inductance
• capacitor internal resistance and inductance

For "devices" (e.g. automotive sensors, ECUs and alike) you end up with 4+ A - - - when measuring bandwidth-limited (100 kHz limit). The peak momentary current will be the short-circuit current - mainly dominated by the series resistance.
On PCBs (with a local power source), my best guess is that the peak current will be limited by the source impendance of your power supply.
A voice from practice, I presume ? Refreshing as well as reassuring: (other) expert
sources estimate the 'front end's' resistance in a linear PSU to be a few Ohms (1-10).
While this may act as a kind of intrinsic brake during inrush, the real question one
has to worry about is: how does longevity of rectifier-bridge and reservoir cap(s)
suffer from frequently switching off and on of the equipment ? This is not easy to
assess - one example:
fig. 18 in https://www.vishay.com/docs/28340/056057psmsi.pdf
While it certainly gives some indication, a tendency if you like, this graph, entitled:
"Multiplier of useful life as a function of ambient temperature and ripple current
load", has a distinct flaw. The "multiplier" is in the ratio actual/rated ripple current,
as the diagram legend shows. But it is unclear if "actual" indicates the momentary
or the continuous ripple current, which is essential if the ratio >1. So I consulted:
https://www.vishay.com/docs/28356/alucapsintrobcc.pdf Definitions chapter:
"Care should be taken to ensure that the actual ripple current remains inside the
graph at any time of the entire useful life." I.m.o. this means 'continuous', which
places severe restrictions on inrush conditions. As the issue is about longevity, why
not look up 'Useful life' as well ? It is stated here in thousands of hours "or about x
years", but the addition: "(without pause and storage times)" doesn't really help the
correct interpretation. It is e.g. a well-known fact that prolonged storage leads to a
re-formation process after the e-cap becoming operational again, which not always
results in increased life time ... The audiophile chooses a no-risk policy, keeping his
precious gear always-on, but is ever more marginalized by 'green' regulations.
Let me stop here and see if anyone is still interested ...

#### crutschow

Joined Mar 14, 2008
27,734
The only currents that, I believe, significantly affect capacitor life are the continuous ripple currents from the supply operation (which are worse for high-frequency switching regulators).
It's the heat generated by these currents through the ESR of the capacitor that lowers its life.
As such, the frequency of turning the device on and off would have little effect on this heat or the capacitor life.

#### SYNFONIQUE

Joined Jun 5, 2021
35
The only currents that, I believe, significantly affect capacitor life are the continuous ripple currents from the supply operation (which are worse for high-frequency switching regulators).
It's the heat generated by these currents through the ESR of the capacitor that lowers its life.
As such, the frequency of turning the device on and off would have little effect on this heat or the capacitor life.
As far as the long term factors are concerned, you are right of course. Quoting
exemplary producer's documentation, however I've tried to demonstrate that info
therein pertinent to those factors may be clear and easily applicable to the case, the
info on transient phenomena like inrush current is not. The excess ratio relative to
the operational current is estimated to be 1:20 -30 - even for audio power amps (at
full throttle). How this translates to the actual/rated ripple current ratio, I could not
say exactly, but one should obviously take into account the risk of this ratio
exceeding the upper limit in the Vishay nomogram: >2.3 . All in all I believe that the
audiophile habit of keeping their gear 24/7 switched on, to be the better option.
Without slow start facilities, ICL, or the like, the only thing left to reliably assess the
risk of long-term damage seems to be measuring the inrush current surge. Alas,
apart from the fact that this requires sophisticated equipment, there is the random
factor of 'where on the half-sinus ripple lies t=0 this time ...".
A safer bet would be to simply calculate the division of the voltage applied to the e-
cap by its ESR from the data sheet (if available). Like I have argued before, I believe
this will give you a pretty good approximation (i.e. worst case, as internal resistance
of the 'front end' will in practice decrease the value).

#### du00000001

Joined Nov 10, 2020
78
@SYNFONIQUE
When your device is powered from the mains (more or less irrespective whether powered via a transformer or an AC/DC converter), the voltage rise on the secondary side will be slow - hampered by any capacitors to be charged. So you may basically ignore the inrush current for secondary-side capacitors. More or less the same applies for peak current in a bridge rectifier: if this is on the secondary side of a transformer, the transformer's intrinsic resistance will be the limiting factor for the inrush current.

All this said, if your capacitor is on the primary side, inrush current can be an issue. But rare events (and you can consider any switch-on event rare as compared to the permanent ripple current) do not shorten capacitor life significantly: the limiting factor (already mentioned) is the internal heating-up of the capacitor. When the device was off long enough, even a massive inrush event will do little in terms of capacitor heating compared to the ripple current once the capacitor has settled on its operating temperature.

And for rectifier diodes, the single-event current limit is 10 times (and more) higher than the nominal value. More or less based on the same considerations (heat buildup) as for the capacitors. Usually you will more often find a fuse blown than a rectifier diode damaged by inrush current.

#### SYNFONIQUE

Joined Jun 5, 2021
35
@SYNFONIQUE
When your device is powered from the mains (more or less irrespective whether powered via a transformer or an AC/DC converter), the voltage rise on the secondary side will be slow - hampered by any capacitors to be charged. So you may basically ignore the inrush current for secondary-side capacitors. More or less the same applies for peak current in a bridge rectifier: if this is on the secondary side of a transformer, the transformer's intrinsic resistance will be the limiting factor for the inrush current.

All this said, if your capacitor is on the primary side, inrush current can be an issue. But rare events (and you can consider any switch-on event rare as compared to the permanent ripple current) do not shorten capacitor life significantly: the limiting factor (already mentioned) is the internal heating-up of the capacitor. When the device was off long enough, even a massive inrush event will do little in terms of capacitor heating compared to the ripple current once the capacitor has settled on its operating temperature.

And for rectifier diodes, the single-event current limit is 10 times (and more) higher than the nominal value. More or less based on the same considerations (heat buildup) as for the capacitors. Usually you will more often find a fuse blown than a rectifier diode damaged by inrush current.
Another reassuring message - thank you, Du ! It would seem that there is not much
to worry about: the PSU will take care of itself, i.e. cap inrush current. I am not sure,
which experience your message is based upon, or how much of it is analysis. But
obviously mine are both different, tending to make me cautious. In 'my' electronics
niche, high-grade audio, there is no such thing as a transformer-less PSU, and
consequently reservoir caps are always at the secondary side. So let's start there. In
high-power amps kVA transformers are no exception, and toroids aren't well-known
for their 'braking power'. Transient current capability in rectifiers indeed is "10 times
(and more) higher than the nominal value", i.e. for plain silicon. These diodes with
multi-lane highway-broad dies can even cope with the recent trend to install banks
of reservoir caps (up to one Farad or more !) with their conveniently paralleled ESRs.
The trend - already decades long - in rectifiers, however is to SiC-technology and
Schottky gender. The sum total of these developments i.m.o. boils down to an ever
decreasing 'breaking power'in the 'front end'. In combination with the 'Farad mania'
the outcome is not to be taken lightly, I think.

#### andrewmm

Joined Feb 25, 2011
1,757
Another reassuring message - thank you, Du ! It would seem that there is not much
to worry about: the PSU will take care of itself, i.e. cap inrush current. I am not sure,
which experience your message is based upon, or how much of it is analysis. But
obviously mine are both different, tending to make me cautious. In 'my' electronics
niche, high-grade audio, there is no such thing as a transformer-less PSU, and
consequently reservoir caps are always at the secondary side. So let's start there. In
high-power amps kVA transformers are no exception, and toroids aren't well-known
for their 'braking power'. Transient current capability in rectifiers indeed is "10 times
(and more) higher than the nominal value", i.e. for plain silicon. These diodes with
multi-lane highway-broad dies can even cope with the recent trend to install banks
of reservoir caps (up to one Farad or more !) with their conveniently paralleled ESRs.
The trend - already decades long - in rectifiers, however is to SiC-technology and
Schottky gender. The sum total of these developments i.m.o. boils down to an ever
decreasing 'breaking power'in the 'front end'. In combination with the 'Farad mania'
the outcome is not to be taken lightly, I think.

in terms of our orriginal question

"What property determines charge current surge value in e-caps ?"

Where are we with this post ?

What else are you looking for ?

#### du00000001

Joined Nov 10, 2020
78
@SYNFONIQUE
My experience?
30+ years of professional work in E/E - paired with university studies.
I've even worked on the quite special topic of inrush current: automotive application, so powered from a battery with maybe 20 mOhms output impedance. Believe it or not: one of these devices has been produced in some 2-digit numbers (still in production), and I've never heard of any issue. Peak inrush current is somewhere beyond 16 Amps - through a diode rated 200 mA and into a 10µF cap. (You can be sure, these 16 A are nowhere to be found in the diode's datasheet.)

While toroids (aka "fuse killers") are infamous for their inrush current on the primary, they still obey to Ohm's law: when "overload" by some short-circuit (uncharged caps), the secondary voltage will decrease due to the secondary winding's resistance. It's just that you cannot exceed the transformer's power rating significantly.
My (inherited) rule-of-thumb for transformer-rectifier topologies is a minimum of 1000 µF per Amp output current (50 Hz grid - 60 Hz would allow for a minimum capacitance of 833 µF). (More capacitance is better but doesn't come exactly cheap).
If your secondary overall capacitance exceed this magic minimum value, the effect of the inrush current on the capacitors will decrease as the transformer is loaded beyond the value considered "reasonable". This will not damage the transformer, just reduce the effect on the capacitors.

#### SYNFONIQUE

Joined Jun 5, 2021
35
@SYNFONIQUE
My experience?
30+ years of professional work in E/E - paired with university studies.
I've even worked on the quite special topic of inrush current: automotive application, so powered from a battery with maybe 20 mOhms output impedance. Believe it or not: one of these devices has been produced in some 2-digit numbers (still in production), and I've never heard of any issue. Peak inrush current is somewhere beyond 16 Amps - through a diode rated 200 mA and into a 10µF cap. (You can be sure, these 16 A are nowhere to be found in the diode's datasheet.)

While toroids (aka "fuse killers") are infamous for their inrush current on the primary, they still obey to Ohm's law: when "overload" by some short-circuit (uncharged caps), the secondary voltage will decrease due to the secondary winding's resistance. It's just that you cannot exceed the transformer's power rating significantly.
My (inherited) rule-of-thumb for transformer-rectifier topologies is a minimum of 1000 µF per Amp output current (50 Hz grid - 60 Hz would allow for a minimum capacitance of 833 µF). (More capacitance is better but doesn't come exactly cheap).
If your secondary overall capacitance exceed this magic minimum value, the effect of the inrush current on the capacitors will decrease as the transformer is loaded beyond the value considered "reasonable". This will not damage the transformer, just reduce the effect on the capacitors.

in terms of our orriginal question

"What property determines charge current surge value in e-caps ?"

Where are we with this post ?

What else are you looking for ?
"Where are we with this post ?"
Without proof to the contrary, I now feel confident that ESR in fact is the
determining factor inside the e-cap (and that is what the question was about).
Du000001 has broadened the discussion, to include what I call the 'front end".
And rightfully so, as the resistance there is at least an order of magnitude larger.
(I'm afraid I'm beginning to sound like a moderator ...)
"What else (am I) looking for ?"
As far as e-caps are concerned: time constant - but pertaining to the charging, not
the discharging process; and establishing validity-boundaries for the theory, as
stated before. But you can rest assured: if it will ever come to working out those
issues, it will be done in a separate thread.
In the meantime you are welcome to share your views, contributing to a broader/-
better understanding of the matter.

#### andrewmm

Joined Feb 25, 2011
1,757
It seems then @SYNFONIQUE , that you have an answer,
may be you could ask for the thread to be closed as answered.

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