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zenterix
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TL;DR Summary: I took a few hours to come up with the solution below. The problem isn't the math or anything, but rather the concepts involved. We are asked to find the relationship between two voltages in a MOSFET operating under different conditions.
The MOSFET in the circuit below is characterized by the equation in its saturation region according to the SCS model. The MOSFET operates in the saturation region for and . Suppose the MOSFET is characterized by the SR model in its triode region. In other words, in the triode region.
Assume that is constant with respect to and , but its value is some function of . Further suppose that when .
a) For , what value of makes the MOSFET versus characteristic continuous between its triode and saturation regions of operation?
b) Plot versus for the circuit shown below. This circuit is useful in plotting the MOSFET characteristics. Assume that and . Use the value of calculated in (a). Use a volt scale for and a millivolt scale for .
Consider the following circuit
If and then the MOSFET is in an ON state (ie, closed state) and is operating in the triode region of its i-v plot. That is, it behaves as a linear resistor with resistance .
If, on the other hand, then the MOSFET operates in the saturation region and the current though it is fixed given .
For part a) of this problem, all we have to do is make sure that the end of the triode region (where ), represented by , equals the beginning of the saturation region, represented by .
Solving for we obtain .
My questions are about part b).
Using the result of part a), we can compute .
Given , the MOSFET is in an ON state, and it seems that oscillates in some interval within the range and (because ).
When we are in the saturation region then we have which we can equate to and so .
Suppose we call the sinusoidal voltage on the right . Let's consider first only positive values for this voltage.
Using KVL we have
which is true as long as we are in saturation, ie ie and .
So it seems that as long as we are in saturation region, is fixed and changes in time and is between and .
Considering only positive , when the condition is not met we are in the triode region, in which the MOSFET behaves like a linear resistor.:
We know what is by using the expression from part a): .
We can now determine the current and the voltages across each resistor.
The relationship of with is then given by where both variables are in volts, and if we measure in then we have , which we plot as
Is this analysis correct and would the analysis when be similar?
If we plot the relationship for all positive values of then it seems that we get
The MOSFET in the circuit below is characterized by the equation
Assume that
a) For
b) Plot
Consider the following circuit
If
If, on the other hand,
For part a) of this problem, all we have to do is make sure that the end of the triode region (where
Solving for
My questions are about part b).
Using the result of part a), we can compute
Given
When we are in the saturation region then we have
Suppose we call the sinusoidal voltage on the right
Using KVL we have
which is true as long as we are in saturation, ie
So it seems that as long as we are in saturation region,
Considering only positive
We know what
We can now determine the current
The relationship of
Is this analysis correct and would the analysis when
If we plot the relationship for all positive values of
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