Chapter 8: Problem 4

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 \(V_{G S}=\) \(-0.5 \mathrm{~V}\)

Short Answer

Expert verified

After performing the calculations, the transconductance \(g_{m}\) for this JFET will be given as the result obtained from the equation in Step 4. Note: The final result can vary a bit depending on the values of constants used and how the calculations are performed.

Step by step solution

Understand the relationship

The relationship between \(g_{m}\), \(I_{D S S}\), \(V_{P}\), and \(V_{G S}\) for a JFET can be expressed by the equation: \(g_{m} = -2 * \sqrt{|I_{D S S}| * (1 - (V_{GS}/V_P))} / |V_{P}|.\) This equation is derived based on the physical properties of JFETs body diodes. The minus sign in the equation shows that the gate voltage \(V_{G S}\) value is inverted with a negative sign.\(I_{D S S}\) is the maximum drain current, \(V_{P}\) is the pinch-off voltage, and \(V_{GS}\) is the gate-source voltage.

Substitute the given values

Now we can substitute the given values: \(I_{D S S} = 12\) mA, \(V_{P} = -3\) V, and \(V_{G S} = -0.5\) V into the equation. So, \(g_{m} = -2 * \sqrt{|12 * 10^-3| * (1 - ((-0.5)/(-3)))} / |-3|\)

Simplify the equation

Simplify the equation: \(g_{m} = -2 * \sqrt{0.012 * (1 - (0.5/3))} / 3\)