Do batteries have capacitance?

Question

I have a couple of old car battery chargers that use a center tapped transformer and two diodes as a full wave rectifier. There is no smoothing capacitor, so without a battery attached I get the expected 120Hz 0-14V (approximately) ripple. (My little oscilloscope isn't very accurate with voltage.)

When I connect the battery, the voltage smooths out way more that I would expect.

I get that the battery won't allow the circuit to fall below the battery voltage, but I would have expected a ripple between the battery voltage and the charger output peak voltage. Say for example a 120Hz ripple between 13.5V and 14.5V. But I'm seeing a very flat DC voltage instead.

Is the battery having a capacitive affect here or am I reading too much into this? Would there be a way to calculate such a capacitive equivalent?

Answer 1

The situation, particularly with lead acid batteries, is a little complicated. As the battery is charging the chemical reactions take time to penetrate through the depths of the plates.

This results in a situation where the outside of the plate is highly charged producing a higher terminal voltage. After a while (minutes-hours) this highly charged region is shared through the plate and the output voltage drops. This is known as surface charge.

It looks like and behaves like capacitance.

In your case the surface charge builds up to the peak voltage of your half wave input. If the battery is unloaded it will stay there for some time resulting in the smooth output waveform that you see.

Answer 2

Just to answer the title: You normally can't model a battery as a single capacitor but you can think of the battery as a very large capacitance (from energy storage) because the voltage across both decreases as they discharge. For an ideal battery and a capacitor you can do the math using the energy formulas.

In your case, you are combining two voltage sources, kinda "POWER OR"ing. The rectifier diodes have approx. 13V at their anodes but the battery has 14V. The rectifiers will be reverse-biased so the battery will "win", hence the pure DC you see.

Answer 3

I would have expected a ripple between the battery voltage and the charger output peak voltage. Say for example a 120Hz ripple between 13.5V and 14.5V. But I'm seeing a very flat DC voltage instead.

Once you attach the battery to the output of the charger's rectifier, current from the charger (via the rectifier) raises the battery voltage to the peak voltage in your first picture. Thereafter, once the battery has attained that peak voltage, no more charging current can flow unless the AC supply voltage rose a little bit hence, the output voltage flattens and remains at the battery charged-up level.

You don't see ripple any more because the diodes in the rectifier become reverse biased by the battery voltage (except at the very peak of the waveform in your first picture and this will result in a very small ripple voltage that you can't really see in your 2nd image).

Is the battery having a capacitive affect here or am I reading too much into this?

It does have an equivalent capacitance but, that isn't dominating what happens here. I mean, you could replace the battery with quite a small valued capacitor and still achieve a low ripple voltage but, in reality, it's the diodes getting reverse biased and auto-disconnecting themselves cyclically that is the dominant factor.

Answer 4

No, batteries do not really have capacitance, they can store and release charge with chemical reactions.

But to an outside observer, there is not much difference between a battery and a very large capacitance. Charging or discharging will not change the voltage much.

You do get ripple but since the effective resistance of the battery is very small, say in the order of 10 milliohms, even a 10A current would cause a ripple of 0.1V.

Answer 5

Even small batteries have huge capacitance. Remember that one amp-hour is 3600 amp-seconds. One coulomb is one amp-second. So very roughly for 1 volt drop 1 amp-hour is 3600F. Thus, your car battery of, say, 60 amp-hours has lots of capacitance, making ripple very low. The ESR of the car battery when in good condition is very low; it has to be milliohms to start the car. When you measure the ripple across the battery posts with a scope you might see only 30 mV peak. Those old school transformer rectifier types of chargers have a high ratio of peak to average current due to the pulses at twice the mains frequency. So you get low ripple volts and high ripple current.

Answer 6

Both batteries and large electrolytics can be modeled fairly well as network of interconnected capacitors and resistors. An under-appreciated feature of axial capacitors is that they tend to behave like a single resistor in parallel with a single capacitance, while a radial capacitor will behave as though the portions of the capacitance nearer the legs have lower series resistance than the portions further away. With batteries, the RC time constants involved will tend to be much greater than with capacitors, but in both kinds of devices can have a "surface charge" that's different from the equilbrium voltage the device would eventually reach if no more current were pushed in or pulled out.

Answer 7

Unlike the above answers, I see the battery not as a capacitor, but as a constant voltage source in series with an internal resistance. The battery voltage does not change during one cycle of AC. The rectified AC is also in series with a source resistance. Even with the battery present, there will be ripple; I urge you to go ahead and measure it. The magnitude of the ripple depends on the ratio of the two source impedances. I leave the measurement of those resistances and the calculation of the ripple as an exercise for the student. You may want to review Thevenin's theorem and its implications.