- #1

zenterix

- 689

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- Homework Statement
- For the circuit below, find the input characteristic, ##i## versus ##v##, and the transfer characteristic ##i_2## versus ##v##. ##I## is fixed and positive.

- Relevant Equations
- Express your results in graphs, labeling all slopes, intercepts, and coordinates of any break points.

This circuit has an ideal diode, which is modeled as

That is, when the potential difference across the diode is ##\leq 0## then we replace the diode with an open circuit and no current flows through it; when the potential difference is ##\geq 0## we replace the diode with a short circuit.

Initially, I drew the following picture

Suppose ##v>e_2##. Then we have

KCL on the two top nodes gives us the equations

$$i=i_1+i_3=\frac{v}{R_1}+i_3$$

$$i_3+I=i_2=\frac{v}{R_2}$$

and putting them together we get

$$i=\frac{v}{R_1}+\frac{v}{R_2}-I=v\cdot R_1 || R_2-I$$

In addition,

$$i_2=\frac{v}{R_2}$$

Graphically,

Next consider the case in which ##v<e_2##. We have

and so

$$i = i_1=\frac{v}{R_1}$$

$$i_2=I=\frac{e_2}{R_2}$$

$$i_2+i_3=I\implies i_3=0$$

Graphically,

I am not sure if I solved this problem correctly and there is no solution available in the book I am reading.