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It is required to use a $\textsf{JFET}$ of figure as linear resistor. The parameters of the $\textsf{JFET}$ are as follows: $$ \mathrm{W}=100 \mu \mathrm{m}, \mathrm{L}=\mu \mathrm{m}, \mathrm{a}=2.5 \mu \mathrm{m} \text {. } $$

The doping in the n-layer is $N_0=10^{16} / \mathrm{cm}^3$ and the electron mobility is $1500 \mathrm{~cm}^2 / \mathrm{V}$-sec. The depletion layer width of each junction due to the built in potential is $0.25 \mu \mathrm{m}$. The two $p^{+}$-gate regions are connected together externally. The resistances of the regions outside the gate are negligible. Determine the minimum value of the linear resistor which can be realized using this $\textsf{JFET}$ without forward biasing the gate junctions.