Worst-case power consumed by a circuit with MOSFETs

AI Thread Summary
The discussion focuses on analyzing the worst-case power consumption of a circuit with three MOSFETs, highlighting that the highest power occurs when all MOSFETs are activated. The relationship between the left and right sides of the circuit is established through a parallel MOSFET, which remains on regardless of the state of MOSFET C. Detailed calculations for current and voltage are provided for various combinations of the MOSFETs being on or off, leading to specific power consumption values. The ON resistance of the MOSFET is confirmed to be 1 kilo-ohm, aligning with the problem statement from MIT's OCW course. Overall, the calculations and circuit behavior are thoroughly examined to ensure accuracy in power consumption analysis.
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Homework Statement
Consider the circuit depicted below. Use the Switch-Resistor model for the MOSFETs.

Assume ##R_6=R_7=10\mathrm{k\Omega}##, the threshold voltage for the MOSFETs is ##\mathrm{2V}##, and the resistance of the MOSFET in its ON state is ##\mathrm{1k\Omega}##.

Compute the worst-case power consumed by this circuit.
Relevant Equations
##P=iV##
Here is the circuit.
1706844518821.png


Note that no current flows between the left and right sides of the circuit: their only relationship happens through the MOSFET that is parallel to B.

There are eight cases to consider: all the combinations of ON/OFF for the three MOSFETs.

Here is a summary of the eight cases according to my calculations

1706844476952.png


It seems that the highest power consumption occurs when all MOSFETs are on.

Here is more in depth explanation of how the table above was created.

It seems that whether MOSFET C is on or off, the voltage at the node right above it (beneath resistor R7) is higher than ##V_T=\mathrm{2V}##.

Thus, the MOSFET in parallel with B is always on.

Let's consider just the left side of the circuit for now.

If ##A## is off, then no current flows so ##i=0##.

Suppose A is on.

Then we have two cases:
B on, B off.

If B is on, then the left side of the circuit becomes

1706843242280.png


##i=\frac{5}{11.5\cdot 10^3}\text{A}## and ##v_{OUT}=\frac{10}{11.5}\cdot 5\text{V}##.

Power consumed by this subcircuit is ##i\cdot V_S=5\cdot\frac{5}{11.5\cdot 10^3}\mathrm{\frac{J}{S}}##.

If, on the other hand, B is off then the only difference is that the resistance that is ##1/2\mathrm{k\Omega}## above becomes ##1\mathrm{k\Omega}##.

Thus, ##i=\frac{5}{12\cdot 10^3}\mathrm{A}## and ##v_{OUT}=\frac{10}{12}\cdot 5=\frac{25}{6}\text{V}##.

Now consider the right side of the circuit.

Suppose ##C## is on. Then the current on the right side (call it ##i_2##) will be ##i_2=\frac{5\text{V}}{11\cdot 10^3}\text{A}##.

If ##C## is off, then no current flows on the right side.

Finally, to obtain power consumption I simply computed ##P=i\cdot V_S+i_2\cdot V_S## for all eight cases.

Is this the correct calculation?
 
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The ON resistance of the MOSFET is kilo-ohms??? Seems odd.
 
Here is the problem statement in full. From this problem set of MIT OCW's 6.002

1708291477245.png


The cited exercise from Agarwal's books is

1708291533867.png


and here is Figure 6.59(c)

1708291600986.png

Thus, the ON resistance is indeed 1 kilo-ohm.
 
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