Solve Simple Diode Problem: v_d, i_D, n, Fit at 1mA

[DefaultName]

Homework Statement

Find the parameters of a piecewise linear model of a diode with the following known values:

v_d = 0.7V
i_D = 1mA
n = 2.

Make your model fit at 1mA.

Homework Equations

They are in the image below, written there.

The Attempt at a Solution

Here's my attempt. I drew out the piecewise linear equivalent, which can be seen to the right of the equal sign. The eq. that I need are on the far left top, and I start putting values in.

I also assumed the saturation current was 10^-11. That's another question I had, they never specified it, so should I assume that 10^-11 is it? It seems that the other ex. in this book uses that value, so...


http://img45.imageshack.us/img45/1165/untitledkp4.jpg

 

[antonantal]

You found the correct value for $$r_{d}$$ but then you used the value 0.921 for $$V_{d}$$ when you are told that the value of $$V_{d}$$ is 0.7. In this problem you are given the value of the forward voltage (Vd = 0.7) at a specific forward current (Id = 1mA) so you don't need to assume any value for Is, because it's value results from the equation $$I_{d} = I_{s}e^{\frac{V_{d}}{nV_{T}}}$$ where you know both $$I_{d}$$ and $$V_{d}$$.

 

[piercas]

I would first start by acknowledging the given information and clarifying any uncertainties. In this case, the given values are the voltage across the diode (v_d), the current through the diode (i_D), and the ideality factor (n). However, it is not specified what the saturation current (I_S) is, so I would clarify that with the person assigning the homework or make an educated assumption based on other examples in the book.

Next, I would use the equations given in the homework statement to solve for the unknown parameters of the piecewise linear model. Using the equation for the forward current of a diode, I_D = I_S * (e^(v_d/n*V_T)-1), I can plug in the given values and solve for I_S. Then, using the equation for the slope of the piecewise linear model, m = I_D/V_T, I can solve for V_T.

Once I have all the necessary parameters, I would then plug them into the piecewise linear model and check if it fits at 1mA. If it does not fit, I would go back and check my calculations or assumptions to see if there was an error. If it does fit, I would provide the final piecewise linear model as my solution.

In summary, as a scientist, I would approach this problem by clarifying any uncertainties, using the given equations to solve for the unknown parameters, and then checking if the resulting model fits the given data.