# Calculate maximum current when charging a capacitor using a MOSFET

While preparing for an exam I came across the following problem, unsure how to solve it. The following values for a fully charged capacitor are given: $V_{in}=2V, V_{C}=1V, V_{th}=0.5V$.

1. Whats the maximum current flowing into the cap when $V_{in}$ is suddenly raised from $2V$ to $2.5V$?
2. Whats the maximum current flowing out of the cap when $V_{in}$ is suddenly lowered from $2V$ to $1.5V$?

I am not sure how to even approach the problem. There is no $V_{dd}$ given, so I don't know in which mode the MOSFET operates. Can someone help me out?

simulate this circuit – Schematic created using CircuitLab

• The current would only be limited by the RdsON. – winny Jan 31 '17 at 20:19
• So you want to say that for sure M1 is either in triode region or saturation? – Daiz Jan 31 '17 at 20:25
• Well, a real MOSFET would have some transconductance going on but if the only information given is Vgs an nothing else, I would assume a simple on-off-simplification by your teacher. – winny Jan 31 '17 at 20:31

I'm going to make some possibly unwarranted assumptions:

1. The problem states that the cap is fully charged, therefore not charging any more under the given initial conditions. Therefore the FET is supplying 1mA to the current source and there's no current in or out of the capacitor.

2. The gate voltage (2V) -Vc gives a Vgs that is 0.5V above threshold. We can estimate transconductance then as 1mA per 0.5V.

3. Assuming roughly linear transconductance above threshold we can say that at 2.5V we would have 2mA of (initial max) FET current. 1mA into the cap and 1mA drawn by the current source.

4. If Vin were suddenly lowered to 1.5V FROM THE INITIAL CONDITIONS the FET would be at threshold where the current would presumably be <<1mA, so there's 1mA flowing out of the cap.

The initial steady state numbers:
Vgs = Vin - Vc = 1V;
Ids = 1mA.

Vth is given as 0.5V. If Vds > Vgs - Vth = 0.5V => Vdd > 1.5V, that determines linear or saturation region.

You can either make an assumption about Vdd, or better yet, try to work out and provide the answers for both regions.

Edit:

With further thoughts, if the FET is allowed to change operating regions when Vin changes, then the form of the MOSFET equations changes. Device parameters that are not explicit known would surface and there are not enough information to get rid of them. So a reasonable approach to this problem would be:

Assuming Vdd > 2V such that the FET stays in saturation when Vin changes...

Or, 1.5V > Vdd > 1V such that the FET stays in linear...