An ideal semiconductor diode is a nonlinear element that obeys the following I-V equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]I\,=\,I_s\,\left(\,e^{\frac{V}{V_{th}}}\,-\,1\right)[/tex]

where [itex]I_s[/itex] is a constant (saturation current) and [itex]V_{th}[/itex] is a constant (thermal voltage, [itex]V_{th}\,=\,\frac{k_B\,T}{q}[/itex]).

Assuming the applied voltage is given by

[tex]\begin{displaymath}

V\,=\,\left\{ \begin{array}{ll}

0 & for\,t\,<\,0 \\

Bt & for\,t\,\geq\,0 \\

\end{array} \right.

\end{displaymath}[/tex]

where B is a known constant.

Find an analytic expression for the charge Q(t) that has passed through the diode over the period from 0 to t. Also find the analytic expressions for the power dissipated by the diode p(t) and for the total energy dissipated by the diode w(t) over the period from 0 to t.

Now assuming [itex]I_s\,=\,1\,\times\,10^{-14},\,V_{th}\,=\,25.85\,mV[/itex] and [itex]B\,=\,90\,\frac{mV}{s}[/itex] use MATLAB to plot I(t), Q(t), p(t), and w(t). Do your plots for t = 0 to 10s.

Find the time [itex]\tau[/itex] at which a total of 1 C of charge has passed through the diode ([itex]Q(\tau)\,=\,1\,C[/itex]) and find the values of [itex]p(\tau)[/itex] and [itex]w(\tau)[/itex].

MY WORK SO FAR:

[tex]Q\,=\,\int_0^t\,i\,dt\,=\,\int_0^t\,\left(I_s\,e^{\frac{V}{V_{th}}}\,-\,I_s\right)\,dt[/tex]

[tex]Q(t)\,=\,\left[I_s\,e^{\frac{V}{V_{th}}}\,t\,-\,I_s\,t\right]_0^t\,=\,\left(I_s\,e^{\frac{V}{V_{th}}}\,-\,I_s\right)\,t[/tex]

Do I have the first part (equation for Q) of the question right?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding an expression for charge (Q) given an I-V equation

**Physics Forums | Science Articles, Homework Help, Discussion**