Capacitor Current

[Edward Cit]

Hello Everyone,

My knowledge of electronics is a quite limited so the following question may
not make any sense.

If I fully charge a capacitor is it possible to calculate how much current I
can get out of it? For example, lets say I fully charge a 1000uF 400V
capacitor and then discharge the capacitor into a coil, how much current
will flow through the coil?

Does this make any sense? Does it have a simple answer?

Thanks in advance

 

[default]

On Sat, 16 Aug 2003 18:25:20 -0700, "Edward Cit"
<ed@stevens8436.fslife.co.uk> wrote:

Hello Everyone,

My knowledge of electronics is a quite limited so the following question may
not make any sense.

If I fully charge a capacitor is it possible to calculate how much current I
can get out of it? For example, lets say I fully charge a 1000uF 400V
capacitor and then discharge the capacitor into a coil, how much current
will flow through the coil?

Does this make any sense? Does it have a simple answer?

Thanks in advance

The question does make sense, it lacks a simple answer.

The current will peak at some value depending on the capacitor's
"External Series Resistance" and then decay exponentially. The higher
the ESR the slower the discharge and lower the peak current. The
higher the inductance of the coil the slower/lower discharge also.

ESR is a function of capacitor construction and leads and connections
to the foil. A 1,000 ufd / 400V is a candidate for high ESR unless
specially constructed (for say photo flash or heavy ripple current
applications)

If you have a low ESR cap and few turns in the coil, of heavy wire,
the peak current can be very high. In the case of very high voltage
and low ESR and inductance (like used for Tesla coils, Marx
generators, some lasers and such) it takes some pretty rugged caps to
suffer that abuse for long.


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[default]

On Sun, 17 Aug 2003 17:10:10 -0700, "Terry Given"
<the_domes@xtra.co.nz> wrote:

Hello Everyone,

My knowledge of electronics is a quite limited so the following question
may
not make any sense.

If I fully charge a capacitor is it possible to calculate how much
current I
can get out of it? For example, lets say I fully charge a 1000uF 400V
capacitor and then discharge the capacitor into a coil, how much current
will flow through the coil?

Does this make any sense? Does it have a simple answer?

Thanks in advance

The question does make sense, it lacks a simple answer.

The current will peak at some value depending on the capacitor's
"External Series Resistance" and then decay exponentially. The higher
the ESR the slower the discharge and lower the peak current. The
higher the inductance of the coil the slower/lower discharge also.

a pretty good answer, but it gets better:


ESR is a function of capacitor construction and leads and connections
to the foil. A 1,000 ufd / 400V is a candidate for high ESR unless
specially constructed (for say photo flash or heavy ripple current
applications)


oh yes. the ESR may range from 20mOhm (0.02 Ohms) to 2 Ohms.
So the ESR would limit the current to anywhere from 200A (2R esr) to 20,000A
(0R02 esr)


If you have a low ESR cap and few turns in the coil, of heavy wire,
the peak current can be very high. In the case of very high voltage
and low ESR and inductance (like used for Tesla coils, Marx
generators, some lasers and such) it takes some pretty rugged caps to
suffer that abuse for long.


yep. If you loook up Nichicon, or united-chemicon caps on the internet, you
can download the databooks that tell you how to figure out cap life, which
depends entirely on ambient temperature and "ripple" current. It gets
moderately tricky, but its all there. Only really relevant when designing
equipment for sale.


What ends up governing the cap current is usually the CHARACTERISTIC
IMPEDANCE of the overall circuit, Z = sqrt(L/C) where L is the total
inductance, INCLUDING the cap's internal stray inductance (often called
ESL). for most electrolytic caps its about 30nH = 0.03uH, and is almost
never specified in datasheets. Unless the external inductance is tiny, you
can usually ignore this term....

Say you are discharging your 1000uF 0R02 30nH cap into a coil, whose
inductance is 250uH. Z=sqrt((250uH+30nH)/1000uF) = 0R5 - this is much higher
than the ESR, so the current would therefore be sinusoidal, peak value
400V/0.5Ohm = 800A. The period would be 2*pi*sqrt(250uH*1000uF) = 3.14ms. If
there was a diode in the circuit, you would therefore get a half-sinewave of
current, peak 800A, duration 1.57ms

BUT say the inductance was more like 1uH. Z = sqrt((1uH+30nH)/1000uF) =
32.1mOhm. This is about the same size as the ESR, so the current WONT look
very sinusoidal, and the peak will be more like 400V/50mOhm = 8000A. To
analyse it properly, look at it as a 2nd order RLC circuit, and figure out
the damping factor, which will be pretty close to 0.7.

Where you need to be careful is in adding up all the series R's (copper is
not a room temperature superconductor, and if the frequency content of the
current pulse is high, skin effect may make the actual resistance quite a
bit higher than the dc value) and all of the L's - if you are not using an
air-cored coil, it will saturate, causing the inductance to drop, perhaps
dramatically. Saturate a ferrite core coil (one with no air gap) and the
inductance will drop by a factor of around 5,000 - basically by the relative
permeability of the core material.
Roger that. I was trying to keep it simple.

I've been building my own hifi equipment and more than a few Tesla
coils in the past, good caps, and wire/cable do make a difference . .

Build for a bandwidth over 5 MHZ and hi-fi sounds much better. For TC
the bandwidth to build for is 30 MHZ even if the coil runs at 100 KHZ.

In both high frequency applications I found construction to be more
important than dielectric losses, where I "rolled my own" (well the
stacked foil, edge connected caps work better so I didn't roll many)



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[Terry Given]

Hello Everyone,

My knowledge of electronics is a quite limited so the following question
may
not make any sense.

If I fully charge a capacitor is it possible to calculate how much
current I
can get out of it? For example, lets say I fully charge a 1000uF 400V
capacitor and then discharge the capacitor into a coil, how much current
will flow through the coil?

Does this make any sense? Does it have a simple answer?

Thanks in advance

The question does make sense, it lacks a simple answer.

The current will peak at some value depending on the capacitor's
"External Series Resistance" and then decay exponentially. The higher
the ESR the slower the discharge and lower the peak current. The
higher the inductance of the coil the slower/lower discharge also.

a pretty good answer, but it gets better:

ESR is a function of capacitor construction and leads and connections
to the foil. A 1,000 ufd / 400V is a candidate for high ESR unless
specially constructed (for say photo flash or heavy ripple current
applications)

oh yes. the ESR may range from 20mOhm (0.02 Ohms) to 2 Ohms.
So the ESR would limit the current to anywhere from 200A (2R esr) to 20,000A
(0R02 esr)

If you have a low ESR cap and few turns in the coil, of heavy wire,
the peak current can be very high. In the case of very high voltage
and low ESR and inductance (like used for Tesla coils, Marx
generators, some lasers and such) it takes some pretty rugged caps to
suffer that abuse for long.

yep. If you loook up Nichicon, or united-chemicon caps on the internet, you
can download the databooks that tell you how to figure out cap life, which
depends entirely on ambient temperature and "ripple" current. It gets
moderately tricky, but its all there. Only really relevant when designing
equipment for sale.


What ends up governing the cap current is usually the CHARACTERISTIC
IMPEDANCE of the overall circuit, Z = sqrt(L/C) where L is the total
inductance, INCLUDING the cap's internal stray inductance (often called
ESL). for most electrolytic caps its about 30nH = 0.03uH, and is almost
never specified in datasheets. Unless the external inductance is tiny, you
can usually ignore this term....

Say you are discharging your 1000uF 0R02 30nH cap into a coil, whose
inductance is 250uH. Z=sqrt((250uH+30nH)/1000uF) = 0R5 - this is much higher
than the ESR, so the current would therefore be sinusoidal, peak value
400V/0.5Ohm = 800A. The period would be 2*pi*sqrt(250uH*1000uF) = 3.14ms. If
there was a diode in the circuit, you would therefore get a half-sinewave of
current, peak 800A, duration 1.57ms

BUT say the inductance was more like 1uH. Z = sqrt((1uH+30nH)/1000uF) =
32.1mOhm. This is about the same size as the ESR, so the current WONT look
very sinusoidal, and the peak will be more like 400V/50mOhm = 8000A. To
analyse it properly, look at it as a 2nd order RLC circuit, and figure out
the damping factor, which will be pretty close to 0.7.

Where you need to be careful is in adding up all the series R's (copper is
not a room temperature superconductor, and if the frequency content of the
current pulse is high, skin effect may make the actual resistance quite a
bit higher than the dc value) and all of the L's - if you are not using an
air-cored coil, it will saturate, causing the inductance to drop, perhaps
dramatically. Saturate a ferrite core coil (one with no air gap) and the
inductance will drop by a factor of around 5,000 - basically by the relative
permeability of the core material.

 

[Dan Barlow]

default wrote:

I've been building my own hifi equipment and more than a few Tesla
coils in the past, good caps, and wire/cable do make a difference . .

Build for a bandwidth over 5 MHZ and hi-fi sounds much better. For TC
the bandwidth to build for is 30 MHZ even if the coil runs at 100 KHZ.

I was looking for high bandwidth op-amps and found you needed at least
10 MHz Gain-Bandwidth Product to actually have good audio response up
to 30KHz. Video needs on the order of 150 MHz. Something about
the phase information needing more bandwidth than the theoretical "pure
sinewave" 2*f. Since they're so cheap I'm going to just standardize
on high GBW op-amps and make sure I RF bypass them so they don't
oscillate. I understand good RF filtering is important in any audio
amp anyway.

In both high frequency applications I found construction to be more
important than dielectric losses, where I "rolled my own" (well the
stacked foil, edge connected caps work better so I didn't roll many)

What dielectric did you end up using? Mylar rolls from old overhead
projectors had pretty good DC voltage range, but were horrible at high
frequency.
-Dan Barlow

 

[default]

On Mon, 18 Aug 2003 15:38:45 -0400, Dan Barlow <danbarlow@radix.net>
wrote:

default wrote:

I've been building my own hifi equipment and more than a few Tesla
coils in the past, good caps, and wire/cable do make a difference . .

Build for a bandwidth over 5 MHZ and hi-fi sounds much better. For TC
the bandwidth to build for is 30 MHZ even if the coil runs at 100 KHZ.

I was looking for high bandwidth op-amps and found you needed at least
10 MHz Gain-Bandwidth Product to actually have good audio response up
to 30KHz. Video needs on the order of 150 MHz. Something about
the phase information needing more bandwidth than the theoretical "pure
sinewave" 2*f. Since they're so cheap I'm going to just standardize
on high GBW op-amps and make sure I RF bypass them so they don't
oscillate. I understand good RF filtering is important in any audio
amp anyway.
I think the idea is to eliminate the phase shift in audio amps,

perhaps because the phase angle (shift) is different for different
frequencies.

Then the transient response is important in music. You may never hear
over 20KHZ, but you can definitely tell good bandwidth when it comes
to things like cymbal crashes, bells, wood block, rim shots, and other
high rise time signals. Not many musical instruments put out sine
waves.

In both high frequency applications I found construction to be more
important than dielectric losses, where I "rolled my own" (well the
stacked foil, edge connected caps work better so I didn't roll many)

What dielectric did you end up using? Mylar rolls from old overhead
projectors had pretty good DC voltage range, but were horrible at high
frequency.
-Dan Barlow
Tesla coil use is probably the hardest, most demanding application

that a cap has to handle. The dielectric strength has to be high, the
dielectric constant should be high, The dielectric loss must be very
low, and the high frequency response has to be very high.

The best caps I made were made with polystyrene sheet (sold as a
window glazing plastic), low density, heavy polyethylene sheet, and
polypropylene sheeting. And - even though the specs say it shouldn't
be a great dielectric material - glass plate works very well (but
maybe it was more due to the conductive plates than the glass
dielectric).

With glass plates, the dielectric is physically strong and can
withstand a lot of compression (less air space and ozone developing
between the electrode and dielectric). With glass it is easy to use
flashing aluminum as the plate material (thick and a better conductor
than aluminum foil - flashing would punch holes through a soft plastic
like polyethylene)

Dielectric loss varies with frequency it may be high at lower
frequencies and improve with higher ones (backwards to what one would
expect), and it isn't a linear thing. Temperature also affects, loss
and constant.

With all caps I terminated them on the edges with a folded strip of
flashing bolted to the electrode layers and brought out of the
container as a wide strip of metal. Bind the works together and with
glass I heated the plates and container overnight and back filled it
with molten paraffin wax. Other caps were dry and not back filled
(high losses at the edges of the electrodes - corona), or immersed in
pure mineral oil.

AIN plastics in Mount Vernon, NY stocks most of the sheet plastic.

Mylar is not the best material to use for caps. The dielectric loss
is relatively high. The physical properties are good - resists
tearing and cold-flowing, good dielectric strength and high constant.
Just too lossy to make a great cap.

Silver mica works well for small caps in audio applications and
polystyrene for larger capacity ones. Photoflash, and switching
supply electrolytics, properly bypassed with high frequency small caps
works well for very large caps.


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[Roy]

Wow you do pose complicated questions! nevertheless I will try to answer. Your
coil will have a resistance due to the copper wire. Let us assume it is eight
ohms, the initial current will be 400V/8ohms = 50Amp. Now the capacitor will
discharge rather rapidly, at first let us ignore the inductance of the coil.
The current will discharge according to the equation: i = Io e^-t/RC = 50 e ^ -t
/8*0.001 = 50 e^-t/.008 . this means that after .008 seconds the i = 50*0.367
and after two periods i.e. 0.016 seconds the i = 50*0.135 .
This will result in a decaying current which is fast initially but much slower
as time moves on:
c | x
u | x
r | x
r | x
e | x
n | x
t | x
________________________________________
time -->
The inductance will cause oscillations superimposed on this curve but it is
too difficult to draw it in ASCI mode.
Hope this beginning of an explanation will help you, cheers from Roy.


"Edward Cit" <ed@stevens8436.fslife.co.uk> wrote in message
news:bhlpei$kij$1@news6.svr.pol.co.uk...

Hello Everyone,

My knowledge of electronics is a quite limited so the following question may
not make any sense.

If I fully charge a capacitor is it possible to calculate how much current I
can get out of it? For example, lets say I fully charge a 1000uF 400V
capacitor and then discharge the capacitor into a coil, how much current
will flow through the coil?

Does this make any sense? Does it have a simple answer?

Thanks in advance

 

[Terry Given]

"Edward Cit" <ed@stevens8436.fslife.co.uk> wrote in message
news:bhlpei$kij$1@news6.svr.pol.co.uk...
Hello Everyone,

My knowledge of electronics is a quite limited so the following question
may
not make any sense.

If I fully charge a capacitor is it possible to calculate how much
current I
can get out of it? For example, lets say I fully charge a 1000uF 400V
capacitor and then discharge the capacitor into a coil, how much current
will flow through the coil?

Does this make any sense? Does it have a simple answer?

Thanks in advance

One of 3 things will happen:
a) current will be limited by series resistance of circuit - ESR of cap + R
of coil. As outlined before, Imax = V/(R+ESR) with exponential decay
envelope, time constant C*(R+ESR). You cant always ignore ESR - I had a
problem once with a 10uF cap across a TL431 used as a voltage reference -
the TL431 oscillated. why? the cap had 27 Ohms ESR at room temperature. Yep,
27 ohms. I changed it for a better cap.....

b) current will be limited by characteristic impedance of L-C circuit,
Z=sqrt(L/C). Get sinusoidal current, peak amplitude V/Z, period
2*pi*sqrt(LC), slowly decaying away. In this case R + ESR is small compared
to Z.

c) R+ESR is comparable to Z0 - the sinusoidal current will be fairly heavily
damped, and the peak current will be less than either a) or b) gives.

in practice, coils are designed to be not-too-lossy, so usually case (b)
dominates.

I recommend finding a textbook (maths, EE, control systems) and learning the
2nd order RLC circuit - most problems can be solved with that circuit. learn
how to calculate damping factor (or Q if your a radio nut, there is a
reciprocal relationship). If damping is low (< 0.3), use V/Z (ie case b). if
damping is high (>2) use V/R (ie case a). If damping is between the two (ie
case c) use V/R and multiply by the peak overshoot you read from a graph
(lazy approach). Once you master the RLC circuit its actually pretty
straightforward to calculate the exact values; really lazy people just draw
a spice circuit with the right values of R,L,C and press the go button.

a word of warning: especially when using multilayer coils, use the AC
resistance - go look up skin effect. basically as frequency increases,
resistance of wire increases (proportional to sqrt(f)). So once you know
period (and hence f) have a look and see how this affects the coil
resistance. with a multilayer coil, the resistance at say 100kHz can be 10x
or 100x the dc value - clearly this will have a huge impact on the values
you calculate. Remember, circuits always obey the laws of physics - if you
dont see what you expect, something is going on.....as bob pease would say,
go measure the amount of funny.

when in doubt - measure a real thing. spice is happy to spit out crap - a
spice voltage source can supply 10,000,000,000A as easily as 10mA. And its
real easy to screw up a calculation.