[Moved]: RC settling and the miller effect

[diarmuid]

Here is a question which has been bothering me about caps:

1.) Charge stored on a cap is given by Q = C. V. Therefore if I double the voltage across a cap, I double
the amount of charge it can store hence doubling its effective capacitance. This is the idea behind the
Miller effect.

2.) The charging up of a series RC circuit is given by vo(t) = vi(t).[1-e^(-t/RC)] and from this we say
that the rise time of such a circuit is completely determined by its RC time constant.

My question then is:

If I am charging up a series RC circuit where C is connected between vout and ground, circuit charges in a certain time.
Say now C is connected between vout and a voltage > ground. By virtue of 1 above, would this not make C appear
smaller and hence reduce the rise time over the first case?

Likewise, if I connect C between vout and a voltage < grount. By virtue of 1 above, would this not make C appear
larger and hence increase the rise time over the first case?

In simulations I see identical rise times so I am missing something very basic here. Any ideas?

Thanks,

Diarmuid

 

[FvM]

Re: RC settling and the miller effect

"voltage < or > ground" can be a DC offset which doesn't change the "effective" capacitance. Or a variable voltage depending on the capacitor voltage (generally a*Vcap). Miller and similar effects are observed only in the second case.

 

[CataM]

Re: RC settling and the miller effect

Say now C is connected between vout and a voltage > ground. By virtue of 1 above, would this not make C appear
smaller and hence reduce the rise time over the first case?

Of course not, your capacitor will charge to a lower voltage than the one when is connected directly to ground, time is not influenced.

Likewise, if I connect C between vout and a voltage < grount. By virtue of 1 above, would this not make C appear
larger and hence increase the rise time over the first case?

Of course not, capacitor will charge to a higher voltage than the one when is connected directly to ground, time is not influenced.

So.. charge time of a capacitor is only dependent on R and C (C by it's physical construction) and the settling time is 3 times the time constant.

 

[shanmei]

Re: RC settling and the miller effect

Miller effect works when both the ends of cap are connected to ac.

 

[diarmuid]

Re: RC settling and the miller effect

Thanks guys. I see things clearer now. With the settling case I am looking at a DC offset as the voltage on one side of the cap is clamped to a reference value
where as for the miller effect the voltages on both sides are varying giving rise to a varying effective capacitance. Cheers.