Question
At room temperature, what is the ac resistance of a diode conducting $0.5 \mathrm{~A}$ ?
Step 1
The key parameter we need to calculate the AC resistance (also known as dynamic or small-signal resistance) of a diode is the forward current, which is given as \( I = 0.5 \, \mathrm{A} \). Show more…
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A "good" silicon diode has a current-voltage characteristic given by $$ I=I_{0}\left(e^{e V_{b} / k T}-1\right) $$ Let $k T=0.025 \mathrm{eV}$ (room temperature) and the saturation current $I_{0}=1 \mathrm{nA.}$ ( $a$ ) Show that for small reverse-bias voltages, the resistance is $25 \mathrm{M} \Omega$. (Hint: Do a Taylor expansion of the exponential function, or use your calculator and enter small values for $V_{b} .$ ) ( $b$ ) Find the dc resistance for a reverse bias of $0.5 \mathrm{~V}$. ( $\mathrm{c}$ ) Find the dc resistance for a $0.5 \mathrm{~V}$ forward bias. What is the current in this case? $(d)$ Calculate the ac resistance $d V / d I$ for a $0.5 \mathrm{~V}$ forward bias.
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