Find V-I characteristic for this circuit with ideal diode

  • #1
zenterix
689
83
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.
1724220751480.png

This circuit has an ideal diode, which is modeled as

1724220787195.png


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

1724220909572.png


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

1724220948089.png


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,

1724221104587.png


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

1724221134504.png


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,

1724221296723.png


I am not sure if I solved this problem correctly and there is no solution available in the book I am reading.
 
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  • #2
The problem asks for THE input characteristic and THE transfer characteristic. In the analysis in the OP, there are two cases and thus a pair of each of these characteristics. Is this correct?

I'd like to add just a few more details of my calculations.

Consider the first case, in which ##v>e_2##.

1724221854568.png


I've added the currents ##i_4## and ##i_5##.

First of all, note what ##i_3## is graphically

1724221902055.png


It is just ##i_2## shifted down by ##I##.

To compute ##i_4## and ##i_5## we apply KCL again to the bottom node.

$$i_1+i_5=i_4$$

$$i_2+i_4=I$$

$$\implies i_5=I-i_1-i_2=-i\ \ \ \text{and}\ \ \ i_4=I-i_2=-i_3$$

Graphically, putting all the currents together we have

1724222140135.png
 
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