Hi all,
Consider two capacitors, say "C1" and "C2" connected in series. And a voltage source "V" is applied. How can the charge "Q" be calculated practically?
I understand that the charge "Q" can be estimated by integrating the current "i" flowing in the circuit. In that case, how can we implement practically a Current Controlled Current Source (CCCS) that can give this current "i" elsewhere for integration and at the same time does not alter the current "i" flowing in the circuit and the node voltages?
Thanks,
Raghu
Dear Raghuram,
welcome,
Yes you can directly measure Q by integrating the the charging current of the capacitor from the starting of the charges to the end of the charge.
In order to sense this current without affecting the charging process you sense it using a Hall generator where it senses the magnetic field associated with the current flowing in the circuit and produces a voltage proportional to the sensed current. This voltage can be acquired and stored after which it can be integrated over the charging time and scaled to a charge. I this this is the most suitable measuring techniques of the charges stored on capacitors.
Best wishes
Dear Abdelhalim Zekry,
Thanks for the input. But I am looking for measuring very small current of the order of few mA or even less. Is there any circuit implementation using components / ICs for such charge measuring capability?
Thanks.
Dear Raghuram,
Welcome again,
May be one of the very interesting methods is to use current sensing resistance whose resistance is so small to have a voltage drop which is much smaller than the voltage during the charging phase. Under static conditions the voltage drop on the capacitor will be equal to the charging voltage since under this condition the charging current settles to zero.
In fact irrespective of the value of resistance used to sense the current ,the capacitor will charge ultimately to the charging source voltage. The value of the resistor will affect only the speed of the charging process. From the principle point of view you can use any suitable resistance to sense the current. Then you can acquire the voltage across the resistor using an input differential amplifier or a single ended amplifier.
However, i think the Hall generators are sensitive devices to detect small magnetic field. You may yourself investigate this point. Please see the paper in the link: https://cds.cern.ch/record/1246519/files/p233.pdf
Best wishes
Why not simply calculate the charge - Q = C.V where C = C1.C2/(C1+C2)?
Hi Cyril,
I am considering the case where the individual capacitances are unknown and non-linear too.
I would like to greet the respected colleague Cyril and welcome Raghuram.
I would like to add, the conclusion regarding our discussion till now is that one can acquire the current by sensing it using a suitable sensing resistance. The value of the series resistance will not affect the final charge on the capacitor since it is only controlled by the source voltage.
If you capacitors are nonlinear then you measure in this way the large signal capacitance C= Q/V. You can define a small signal capacitance c = dQ/dV, which can also be measured by superposing small signal voltage dV on the charging DC voltage V and measure also dQ. The incremental voltage dV can be a sinusoidal voltage with low frequency.
Best wishes
Raghuram Tattamangalam Raman
Whether your capacitors are nonlinear or not doesn't matter: with a constant voltage source, the capacitance of both capacitors is static once the charging current has dropped to.
With the conditions of unknown individual capacitances and capacitance nonlinearity, it is not possible to assess the charge on each capacitor as measuring the voltage on the node between the capacitors is no longer possible without introducing an error. Otherwise you'd better use a non-ideal voltage source (some series resistance would be welcome) and just measure the voltage on "top" of C1 as well as on the connecting node during charging. The capacitance ratio would be the inverse of the voltage ratio.
Or you might - as Abdelhalim abdelnaby Zekry already stated) start by assessing the capacitance ratio via applying an AC (non-ideal) voltage source: thus you can get the capacitance ratio (s), the integral of the current (with a DC voltage source) will give you the total charge.
The remainder is some arithmetics.
Please look at the book (Electric Circuits)
by
James Nilsson
from
Iowa state university
Raghuram Tattamangalam Raman
If you're trying to evaluate the charge Q to calculate the capacitance, you might just use a "Schering Bridge" to measure it or do you want to implement a capacitance measurement ?
Please look at the book
Fundamentals of Physics
by
David Halliday
from
University of Pittsburgh
and
Robert Resnick
Thank you Abdelhalim Zekry, Dreher and Sid Ahmed Aris for your inputs. I shall try that.
Thank you Ziad Sobih for the books suggested. I shall refer them too.
- Badges
- Science topic
- Similar topics
- Biological Science
- Bioecology
- Systems Ecology
- Landscape Ecology
- Connectivity