I have a seemingly very difficult (for me) problem involving the small signal method using differential calculus... the question is as follows:
"Consider the following circuit containing the nonlinear element N:
The i-v relation for N is given by iA=10⋅(1−e−vA/5), where iA is in Amperes and vA is in Volts.
Solve for the voltage vA when vI=5.0V. Note that this requires that you solve the equation obtained using KVL iteratively for vA.
(Hint: Use the exponential term to solve for vA as a function of the assumed value of vA, and then iterate. Taking logs on both sides may facilitate convergence.)
The voltage vA is: ???
Find the incremental change in vA for a 2% increase in vI and use it to calculate the ratio ΔvAΔvI. ???
Find the value for the incremental resistance of the nonlinear element N by linearizing the expression for iA about the operating point when vI=5.0V. ???
Where do I start? How do I learn the mathematical machinery to understand this question?
What kind of mathematics do I need to study?
I have started watching the following video sequence by the Khan academy on YouTube http://www.youtube.com/course?list=EC19E79A0638C8D449&feature=plcp So my question is: Looking at this from a completely foreign perspective, imagine I am looking at something completely alien... that I only understand basic algebra, how do I even begin to understand what the question is asking??
"Consider the following circuit containing the nonlinear element N:
Solve for the voltage vA when vI=5.0V. Note that this requires that you solve the equation obtained using KVL iteratively for vA.
(Hint: Use the exponential term to solve for vA as a function of the assumed value of vA, and then iterate. Taking logs on both sides may facilitate convergence.)
The voltage vA is: ???
Find the incremental change in vA for a 2% increase in vI and use it to calculate the ratio ΔvAΔvI. ???
Find the value for the incremental resistance of the nonlinear element N by linearizing the expression for iA about the operating point when vI=5.0V. ???
Where do I start? How do I learn the mathematical machinery to understand this question?
What kind of mathematics do I need to study?
I have started watching the following video sequence by the Khan academy on YouTube http://www.youtube.com/course?list=EC19E79A0638C8D449&feature=plcp So my question is: Looking at this from a completely foreign perspective, imagine I am looking at something completely alien... that I only understand basic algebra, how do I even begin to understand what the question is asking??