# two capacitors in series

Discussion in 'General Electronics Chat' started by anhnha, Jun 3, 2014.

1. ### anhnha Thread Starter Well-Known Member

Apr 19, 2012
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I simulated the circuit below including a voltage source 10V and two capacitors 1pF each in series.
I measured the voltage at the point between two capacitors and got the plot.
The voltage at that point increases linearly but at 100M seconds it is still very very small.
I guess that it takes infinite amount of time for capacitor C1 to get 5V.
Is that right?
How to explain it mathematically?

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2. ### Wendy Moderator

Mar 24, 2008
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Both caps charge at the same rate if they are the same value. Total capacitance is ½ the two caps (if they are the same value). In many ways it acts like a voltage divider, each cap will have half the total charge.

3. ### Jony130 AAC Fanatic!

Feb 17, 2009
4,173
1,188
OMG are you serious?? If you don't know how to use a simulation program don't use it. Because here you have a typical example of GIGO.
To get "proper" result you need to turn on "skip initial operating point solution".

4. ### alfacliff Well-Known Member

Dec 13, 2013
2,449
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try the formula for rc time constant with r being infinity, you might find thats what you have.

5. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
519
The diagram shows a direct supply.

I suggest you try the circuit with two capacitors and a 9V battery with real components and a real voltmeter.

You might find a suprise awaiting

6. ### anhnha Thread Starter Well-Known Member

Apr 19, 2012
783
49
I get the correct result now. How to explain it mathematically?

7. ### #12 Expert

Nov 30, 2010
17,884
9,283
If you have a resistor in there Eo = dE(e^-t/RC) where little e is a constant worth about 2.718

With no resistor, the voltage on the lower capacitor should instantly jump to 1/2 Vcc.
The formula for that is: Vcc/2 = 1/2 Vcc

If the 2 capacitors are not equal, it gets more complicated and the math works better (for me) if you think in terms of conductance.

8. ### anhnha Thread Starter Well-Known Member

Apr 19, 2012
783
49
I understand this but just don't know why LTspice requires to skip initial condition to get the correct result.
If the "Skip initial operating point solution" is unchecked then the voltage across the bottom capacitor is almost zero.

9. ### #12 Expert

Nov 30, 2010
17,884
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That's one of the reasons I don't use simulators.

10. ### studiot AAC Fanatic!

Nov 9, 2007
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519
What is the charging path for the centre connection between the capacitors?

11. ### #12 Expert

Nov 30, 2010
17,884
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I would think that the initial rise of applied voltage would be divided equally between the 2 equal capacitances, and, a simulator using an ideal voltmeter would measure half the applied voltage. So, I got (2) 1000 uf capacitors, connected them in series, hooked up my 10 meg input impedance volt meter and connected a new 9 volt alkaline battery to the most positive terminal of the capacitor string. The meter showed 4.84 volts and became lower as my meter discharged one capacitor.

That clears it up for me.

12. ### studiot AAC Fanatic!

Nov 9, 2007
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So does the simulator show the effect of the 10MΩ?

What would happen if you used an electrostatic (non contact) meter?

13. ### BobTPH Active Member

Jun 5, 2013
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I think the problem with computing initial conditions is the way this is done. Capacitors are turned into open circuits. With both capacitors open, the node between the two has no connection to anything. In real capacitors there will be a parallel resistance or leakage which overcomes this problem. Try adding a large parallel resistance (10-100M) and see what happens.

Bob

14. ### studiot AAC Fanatic!

Nov 9, 2007
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Well said Bob, you are getting there.

15. ### alfacliff Well-Known Member

Dec 13, 2013
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another possible problem with the origional circuit is that the caps are only 1pf each. making the rc time constant with non existant resistors (infinite resistance) way out of range for any simulators.

16. ### #12 Expert

Nov 30, 2010
17,884
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This seems an odd question to be posted right after I described an experiment with real parts. Were you asking me? I don't now. I don't use simulators.

17. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
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Nothing personal.

But I am achieving my objective of making people think about the circuit in both reality and the simulator.

If the centre point was perfectly isolated how could it charge to any voltage?
If the two caps were stacked up in the field of the battery you could argue that it is midway between, but if one cap was widely separated and turned at right angles to the field then...?

Equally if there is a resistance, either due to the voltmeter or capacitor imperfection then there is a charging path.
In this case you have clearly noted that the centre charges to midway then decays.
So it is a legitimate question to discuss whether the simulator reflects this real word edit : world action, and if not, how to make it so.

Last edited: Jun 5, 2014
18. ### alfacliff Well-Known Member

Dec 13, 2013
2,449
429
pc type smps use two caps in series to provide the initial supply voltge for the pwm chip. those are electrolytic and connected from the + rectifier out to ground. they supply voltage for a little while till the chip gets to running and powers off the supply. these are also the most likely to go bad from heat and age. just look for two small electrolytics near the 8 pin (usually) chip, check them and the values are usually in the pf range instead of several microfarads.

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19. ### #12 Expert

Nov 30, 2010
17,884
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I'm with you on that. For my own edification, a battery and 2 capacitors shows me the practical solution. For other people, getting a simulator to give reasonable results is an important goal. I hope you can get this worked out. It will help a lot of people.

20. ### vk6zgo Active Member

Jul 21, 2012
677
85
It makes my head hurt to think about Rhetorical questions relating to things that we know happen!

A related question is,how is it that we can charge two capacitors,put them in series & read the sum of the individual charges across the series circuit?

Why can we then discharge them?

Can LT Spice reproduce this?