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VinnyCee
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An ideal semiconductor diode is a nonlinear element that obeys the following I-V equation:
I\,=\,I_s\,\left(\,e^{\frac{V}{V_{th}}}\,-\,1\right)
where I_s is a constant (saturation current) and V_{th} is a constant (thermal voltage, V_{th}\,=\,\frac{k_B\,T}{q}).
Assuming the applied voltage is given by
\begin{displaymath}<br /> V\,=\,\left\{ \begin{array}{ll}<br /> 0 & for\,t\,<\,0 \\<br /> Bt & for\,t\,\geq\,0 \\<br /> \end{array} \right.<br /> \end{displaymath}
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 I_s\,=\,1\,\times\,10^{-14},\,V_{th}\,=\,25.85\,mV and B\,=\,90\,\frac{mV}{s} use MATLAB to plot I(t), Q(t), p(t), and w(t). Do your plots for t = 0 to 10s.
Find the time \tau at which a total of 1 C of charge has passed through the diode (Q(\tau)\,=\,1\,C) and find the values of p(\tau) and w(\tau).
MY WORK SO FAR:
Q\,=\,\int_0^t\,i\,dt\,=\,\int_0^t\,\left(I_s\,e^{\frac{V}{V_{th}}}\,-\,I_s\right)\,dt
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
Do I have the first part (equation for Q) of the question right?
I\,=\,I_s\,\left(\,e^{\frac{V}{V_{th}}}\,-\,1\right)
where I_s is a constant (saturation current) and V_{th} is a constant (thermal voltage, V_{th}\,=\,\frac{k_B\,T}{q}).
Assuming the applied voltage is given by
\begin{displaymath}<br /> V\,=\,\left\{ \begin{array}{ll}<br /> 0 & for\,t\,<\,0 \\<br /> Bt & for\,t\,\geq\,0 \\<br /> \end{array} \right.<br /> \end{displaymath}
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 I_s\,=\,1\,\times\,10^{-14},\,V_{th}\,=\,25.85\,mV and B\,=\,90\,\frac{mV}{s} use MATLAB to plot I(t), Q(t), p(t), and w(t). Do your plots for t = 0 to 10s.
Find the time \tau at which a total of 1 C of charge has passed through the diode (Q(\tau)\,=\,1\,C) and find the values of p(\tau) and w(\tau).
MY WORK SO FAR:
Q\,=\,\int_0^t\,i\,dt\,=\,\int_0^t\,\left(I_s\,e^{\frac{V}{V_{th}}}\,-\,I_s\right)\,dt
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
Do I have the first part (equation for Q) of the question right?
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