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Chapter 8: Problem 6

A JFET \(\left(I_{D S S}=10 \mathrm{~mA}, V_{P}=-5 \mathrm{~V}\right)\) is biased at \(I_{D}=I_{D S S} / 4\). What is the value of \(g_{m}\) at that bias point?

Short Answer

Expert verified
The transconductance \(g_m\) at the bias point is 1.5mS.

Step by step solution

01

Understanding the Given Values

First, we note the given values, which are \[I_{D S S}=10 \mathrm{~mA}\], \[V_{P}=-5 \mathrm{~V}\] and \[I_{D}=I_{D S S} / 4\].
02

Calculating Bias Current

At the bias point, the drain current \(I_{D}\) is set to be a quarter of the saturation current \(I_{D S S}\). So we calculate \(I_{D}\) by dividing \(I_{D S S}\) by 4. Thus \[I_{D} = I_{D S S} / 4 = 10mA / 4 = 2.5mA\].
03

Calculating Transconductance

Now we calculate the transconductance \(g_m\), which measures the ratio of the variation in the output current to the small variation in the input voltage. The equation for \(g_m\) for a JFET is: \[g_m = I_{DSS} / |V_P| * (1 - (I_D/I_{DSS}) )\]. Substitute the values into the equation to get: \[g_m = 10mA / |-5V| * (1 - (2.5mA/10mA) )\]. Calculate the result to get the value for \(g_m\).

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Most popular questions from this chapter

Determine the pinch-off voltage of a JFET with \(g_{m 0}=10 \mathrm{mS}\) and \(I_{D S S}=12 \mathrm{~mA}\).

If a JFET having a specified value of \(r_{d}=100 \mathrm{k} \Omega\) has an ideal voltage gain of \(A_{v}(\mathrm{FET})=-200\), what is the value of \(g_{m}\) ?

Sketch the ac equivalent model for a JFET if \(g_{f s}=5.6 \mathrm{mS}\) and \(g_{a s}=15 \mu \mathrm{S}\).

Calculate \(g_{m 0}\) for a JFET having device parameters \(I_{D S S}=12 \mathrm{~mA}\) and \(V_{P}=-4 \mathrm{~V}\).

a. Plot \(g_{m}\) versus \(V_{G S}\) for an \(n\) -channel JFET with \(I_{D S S}=12 \mathrm{~mA}\) and \(V_{P}=-6 \mathrm{~V}\). b. Plot \(g_{m}\) versus \(I_{D}\) for the same \(n\) -channel JFET as part (a).
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