# Bulk capacitor hold up time calculation

#### Bjtpower_magic

##### Junior Member level 3
Hi Team,

I have requirement for power supply output
1. Output ripple 100mV
2. Hold up time>1 Seconds.

I have switching frequency of 40KHZ-100KHZ
How to calculate capacitor value

Regards,
Marx

#### zenerbjt

##### Full Member level 2
Hold up time is by dt = C.dv/i

For ripple, you need to tell us the topology and inductor values, or transformer inductances etc etc.

#### wwfeldman

>1 second is a long hold up time - please check

hold up time is determined by how much voltage drop one can tolerate
(which is not the same as the allowed ripple) and by the current draw.

apply zenerbjt's equation to your situation
dt is the hold up time
C is the desired capacitance
dv is the acceptable voltage drop
i is the current draw

#### zenerbjt

##### Full Member level 2
Ripple voltage on output capacitor of SMPS.

The ripple voltage is the sum of the squares of the two constituent parts.
One part is from the actual peak current magnitude which goes into the capacitor and its product with the ESR of the capacitor.

V1 = I(PK) * ESR
………………………………………………………………
Other part is the actual charge that goes into the capacitor each switching cycle (this obviously equals the charge that goes out of the capacitor each switching cycle).

The voltage increase from this constituent is V2 = dQ/C
……………………………………………………………………..

And the overall ripple voltage is….

SQRT (V1^2 + V^2)
--- Updated ---

As an example......the calculation given works for the following attached boost converter...which is in LTspice simulation here.

Of course, you can just cheat and measure it on the LTspice sim
--- Updated ---

And id say youd want to do the calc at your lowest switching frequency, and the maximum power.

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#### dick_freebird

To me "hold up time" is about when the converter drops
out altogether. Not ripple attenuation.

The hold up time would be something like
have to say where you start, where you want to call it
done, and how hard you're trying to sag it.

#### Bjtpower_magic

##### Junior Member level 3
The voltage increase from this constituent is V2 = dQ/C
……………………………………………………………………..
How to calculate dQ?

#### wwfeldman

dQ is i dt
you want dV, etc, as has been stated in previous posts

dQ is hard to measure
V, dV, I, t are easy to measure and easy to use

#### Akanimo

Hi Team,

I have requirement for power supply output
1. Output ripple 100mV
2. Hold up time>1 Seconds.

I have switching frequency of 40KHZ-100KHZ
How to calculate capacitor value

Regards,
Marx
Is it an offline or DC-DC Power supply?
--- Updated ---

Oh! You meant for the output? What topology is it and why output and not input?

#### Bjtpower_magic

##### Junior Member level 3
dQ is i dt
what is I?
is it Load current? ripple current?
--- Updated ---

Is it an offline or DC-DC Power supply?
--- Updated ---

Oh! You meant for the output? What topology is it and why output and not input?
it is flyback topology.
Hold up time requirement is applicable for output, so we want to have Hold up time for output only.

#### Easy peasy

the calc is easy, say you have 12V out, and you can have the volts fall to 11V min, and the holdup time is 0.5 seconds, and the load is 200mA average

dv/dt = i/c, So C = i * dt/dv = 0.2A * 0.5sec / 1Vc = 0.1 Farads, or 100 000 uF, 16V.

This is why supercaps are used at lower voltages
--- Updated ---

if you have a high voltage electro on the rectified mains side - the calc is the same

e.g. you can have the volts drop from 300V to 250V, the load is 50W, so the I = 181mA ( ave ) and the holdup time is 0.5 seconds

now the HV Cap = 0.181 * 0.5 / 50 = 1818 uF 400VDC

and now you can have just the output cap needed to filter the ripple current and provide the required Vripple at switching freq ...

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#### Akanimo

it is flyback topology.
Hold up time requirement is applicable for output, so we want to have Hold up time for output only.
Sure, holdup time requirement is for output holdup. Depending on topology and on configuration (i.e. whether step up or step down), it can be implemented either with the output capacitor or the bulk capacitor.
If the flyback converter is Stepdown, then implementation with bulk capacitor is fine. The calculation is a long one and to explain it here will take a lot of typing so I will refer you to Chapter 5 of the textbook Switching Power Supply Design and Optimization (2nd Edition) by Sanjaya Maniktala

Additional point: also consider that sufficient duty cycle is also a factor. If the duty cycle is limited too early, then no amount of capacitance by the bulk capacitor will help.
--- Updated ---

1 sec is a really long time I must say. I am actually wondering why 1 sec. Even 50 ms is a long time. A lot can be achieved with hold up time significantly shorter than 1 sec.

Can you say why 1 sec is required?

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#### wwfeldman

what is I?
is it Load current? ripple current?
--- Updated ---

@Easy peasy
you estimated a hold up capacitor on the input side
did you include the power to operate the converter, or just the load power?
considering you calculated a 2000 uF capacitor, its easy to use a bigger
cap to incorporate the efficiency

@Bjtpower
ensure margin for temperature variations, aging, and component variations

#### KlausST

##### Super Moderator
Staff member
Hi,

" I is the load current "
are you sure?
I´d say I is the capacitor current (in it´s legs)

Usually a bulk capacitor is connectoed to a node where source current (SMPS, battery, rectifier..) meets a load current.

Klaus

#### zenerbjt

##### Full Member level 2
I am just wondering if you should put a secondary circuit in there..involving a big capacitor being charged up to 60V say, and then a buck on the output of it which switches in and suplies the output when it drops out....i mean this stops your vout drooping too much.

#### KlausST

##### Super Moderator
Staff member
Hi,

Let´s assume the output capacitor is allowed to drop from 12V to 11V.
since W = 0.5 * C * U^2 you just can harvest (12^2 - 11^2) / 12^2 = (144 -121) / 144 = 23/144 = 16% of the stred energy.

If you do the same with an input capacitor of a flyback SMPS, then the nominal voltage at (230V RMS) is about 320V.
But the flyback may work down to 50V (depends on flyback IC).
Thus you can use (320^2 -50^2)/320^2 = (102400 - 2500) / 102400 = 99900/102400 = 97% of the stored energy before the 12V will start to drop.

This results in a 6 times smaller and cheaper capacitor. (mathematically, ignoring efficiency and other influences)

Thus - for me - the better solution is to use the input capacitor as energy storage.

Klaus

#### wwfeldman

@KLAUS

" " I is the load current "
are you sure?
I´d say I is the capacitor current (in it´s legs) "

no argument
if the source is gone, then the load current and the capacitor current are the same

@zenerbjt
60V cap with a buck converter on output can work
but it adds a level of circuit, components and complexity instead of something
(relatively) easily done with a properly chosen and placed capacitor

#### KlausST

##### Super Moderator
Staff member
Hi,

if the source is gone, then the load current and the capacitor current are the same
For sure you are right. I forgot about loss of source. Sorry.

Klaus

#### Easy peasy

I am just wondering if you should put a secondary circuit in there..involving a big capacitor being charged up to 60V say, and then a buck on the output of it which switches in and supplies the output when it drops out....I mean this stops your Vout drooping too much.
This is often done - all the way up to 400V on a 450V electro ( the higher volt electro stores more energy in a smaller volume )

#### Bjtpower_magic

##### Junior Member level 3
Ripple voltage on output capacitor of SMPS.

The ripple voltage is the sum of the squares of the two constituent parts.
One part is from the actual peak current magnitude which goes into the capacitor and its product with the ESR of the capacitor.

V1 = I(PK) * ESR
………………………………………………………………
Other part is the actual charge that goes into the capacitor each switching cycle (this obviously equals the charge that goes out of the capacitor each switching cycle).

The voltage increase from this constituent is V2 = dQ/C
……………………………………………………………………..

And the overall ripple voltage is….

SQRT (V1^2 + V^2)
--- Updated ---

As an example......the calculation given works for the following attached boost converter...which is in LTspice simulation here.

Of course, you can just cheat and measure it on the LTspice sim
--- Updated ---

And id say youd want to do the calc at your lowest switching frequency, and the maximum power.
Hi ZenerBJT,
Multiple query here,
V2=dQ/C=I.dT/C
Where I is load current and dt=1/F, C=Capacitor used value like 1800uF?

#### Akanimo

When you apply AC voltage through a bridge rectifier to the bulk capacitor, you get a waveform across the capacitor. In normal operation, the waveform rises to the peak of the applied sinusoidal voltage as the cap charges and then sags to a level and gets charged again. This happens at a frequency that is twice the line frequency. The idea is that you have to determine that voltage level that it sags to and use that as your initial voltage. You will need another voltage (the level that this initial voltage will not have to decay to within the hold up time), and that will be your final voltage. You will need resistance value for your calculation. This resistance is Vinitial*Vinitial/Pin or Vinitial/Iin_ave. Of course you already have the hold up time.

Your expression will now be Vfinal = Vinitial*e^(-t/tau).

Now,
Time constant, Tau = R*C and t = holdup time = 1 sec.

You now have Vfinal/Vinitial = e^(-t/(R*C)) and you solve for C.

Now, the question is how to find Vinitial. This is why I referred you to the textbook in Post #11.
--- Updated ---

This voltage is determined at worst case. For flyback, this is at low line and maximum load. Note that that valley voltage, Vinitial, is not the peak voltage mains voltage at low line (i.e. Vinitial is not equal to Vac*SQRT(2)).

Determining that valley voltage is not trivial because the mains voltage is sinusoidal.
--- Updated ---

For reliability:
Note that C is the capacitance of the bulk capacitor at the End-of-Life (EOL) of your converter.

At the EOL of your your capacitance will have dropped from its Beginning-of-Life (BOL) value by 20%. So to select the bulk capacitor, we will have to compensate for this. For instance, an EOL value for a capacitor with (C = 1uF) means it has degraded by 20% in capacitance already, such that this capacitance C is 80% or 0.8 (i.e. 100% - 20% or 1-0.2) of the BOL value. So to obtain the BOL value, we have [1uF*1/(1-0.2) = 1.25*1uF]. So generally, this means 1.25*C.

We now consider capacitor tolerances. Capacitors have tolerances: 20%, 10%, 5%...and so on. At worst case, a 1uF cap with 20% tolerance will have capacitance of (100%-20%)*1uF = (1-0.2)*1uF = 0.8*1uF. So to be sure we get a 1uF capacitor we have to select a 1uF*1/(1-0.2) = 1.25*1uF. So, generally, we compensate for this with the formula C*[1/(1-tolerance)].

We then combine the two results for capacitor lifespan degradation and tolerance to select the capacitance of the bulk capacitor at BOL. Thus, C_bulk = C*1.25*[1/(1-tolerance)].

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