Piecewise Linear Modeling (diode)

[hogrampage]

Homework Statement

A pn junction diode is connected to a Thevenin circuit consisting of a 0-to-1V, 1kHz square wave and 1kΩ resistor. Use piecewise linear modeling to estimate the diode voltage for the low (0V), and high (1V) states of the voltage source. Assume the diode to have an approximate turn-on voltage of 0.7V for small currents.

Homework Equations

r_d = \frac{nV_{T}}{I_{D}}
i_D = \frac{V_{th}-V_{f}}{R_{th}+r_{d}}
V_D = V_f + i_Dr_d

The Attempt at a Solution

I was thinking of just picking I_D = 1mA, n = 1, and V_T = 25mV so that:

r_d = 40Ω

I don't know if I'm going about this right, or even where to go next.

 

[CWatters]

For the 1V case...

Are you familiar with the graphical method of finding the operating point? Plot a graph with two "curves" on it:

First one for the voltage source/resistor: Plot open circuit voltage, short circuit current and join with straight line.

Another for the diode, in particular the equation VD = iDrd + Vf is of the form y = mx + c ... a straight line.

Where they cross is your answer.

 

[rude man]

Homework Statement

A pn junction diode is connected to a Thevenin circuit consisting of a 0-to-1V, 1kHz square wave and 1kΩ resistor. Use piecewise linear modeling to estimate the diode voltage for the low (0V), and high (1V) states of the voltage source. Assume the diode to have an approximate turn-on voltage of 0.7V for small currents.

The Attempt at a Solution

I was thinking of just picking I_D = 1mA, n = 1, and V_T = 25mV so that:

r_d = 40Ω

I don't know if I'm going about this right, or even where to go next.

Picking i_D = 1 mA is definitely not a good idea.

You know V_D will be close to 0.7V. So what is a logical choice for i_D if the input to the 1K resistor is 1V?

 

[hogrampage]

With that info, I found i_D to be 0.3mA. Then, r_d is ~83Ω with n=1 and V_T=25mV. So, when the voltage source is 1V:

V_D=0.7+(0.0003)(83)=725mV

 

[rude man]

Assuming the piecewise-linear approximation they have in mind is a straight line along the V axis (i_D=0) up to V = 0.7V and then a straight line of slope 1/r_d up to the operating point i_D ~ 0.3 mA, then that would be correct.

 

[hogrampage]

Alright, thanks :D.