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Chapter 8: Problem 7

Determine the value of \(g_{m}\) for a JFET \(\left(I_{D S S}=8 \mathrm{~mA}, V_{P}=-5 \mathrm{~V}\right)\) when biased at \(V_{G S_{Q}}=V_{P} / 4\).

Short Answer

Expert verified
The value of the transconductance \(g_{m}\) for the given JFET operating parameters is 0.012 S.

Step by step solution

01

Identify Given Values

From the problem, we know that \(I_{D S S}\) is 8 mA, \(V_{P}\) is -5 V and \(V_{G S_{Q}}\) is \(V_{P} / 4\).
02

Determine Value of \(V_{G S_{Q}}\)

We calculate the value of \(V_{G S_{Q}}\) by dividing \(V_{P}\) by 4. Solving for \(V_{G S_{Q}}\), we get \(V_{G S_{Q}} = \frac{V_{P}}{4} = \frac{-5~V}{4} = -1.25~V\).
03

Calculate Transconductance

We substitute the given values into the formula for transconductance. Following the formula: \(g_{m}=2 I_{D S S}\left(1-\frac{V_{G S}}{V_{P}}\right) / |V_{P}|\), we substitute and get \(g_{m}=2*8*10^{-3}\left(1-\frac{-1.25}{-5}\right) / |-5|=0.016 \left(1-0.25\right) / 5=0.012~S\).

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Most popular questions from this chapter

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

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?

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).

Calculate the value of \(g_{m}\) for a JFET \(\left(I_{D S S}=12 \mathrm{~mA}, V_{P}=-3 \mathrm{~V}\right)\) at a bias point of \(V_{G S}=\) \(-0.5 \mathrm{~V}\)

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