Chapter 3
Q. 3.20
Objective: Design a JFET circuit with a voltage divider biasing circuit. Consider the circuit shown in Figure 3.61(a) with transistor parameters I_{DSS} = 12 mA, V_{P} = −3.5 V, and λ = 0. Let R_{1} + R_{2} = 100 kΩ. Design the circuit such that the dc drain current is I_{D} = 5 mA and the dc drain-to-source voltage is V_{DS} = 5 V.

Step-by-Step
Verified Solution
Assume the transistor is biased in the saturation region. The dc drain current is then given by
I_{D} = I_{DSS} \left( 1 − \frac{V_{GS}}{V_{P}} \right)^{2}
Therefore,
5 = 12 \left(1 − \frac{V_{GS}}{(−3.5)} \right)^{2}
which yields
V_{GS} = −1.24 V
From Figure 3.61(b), the voltage at the source terminal is
V_{S} = I_{D} R_{S} − 5 = (5)(0.5) − 5 = −2.5 V
which means that the gate voltage is
V_{G} = V_{GS} + V_{S} = −1.24 − 2.5 = −3.74 V
We can also write the gate voltage as
V_{G} = \left(\frac{R_{2}}{R_{1} + R_{2}} \right) (10) − 5
or
−3.74 = \frac{R_{2}}{100} (10) − 5
Therefore,
R_{2} = 12.6 k \Omega
and
R_{1} = 87.4 k\Omega
The drain-to-source voltage is
V_{DS} = 5 − I_{D} R_{D} − I_{D} R_{S} − (−5)
Therefore,
R_{D} = \frac{10 − V_{DS} − I_{D} R_{S}}{I_{D}} = \frac{10 − 5 − (5)(0.5)}{5} = 0.5 k \Omega
We also see that
V_{DS} = 5 V\gt V_{GS} − V_{P} = −1.24 − (−3.5) = 2.26 V
which shows that the JFET is indeed biased in the saturation region, as initially assumed.
Comment: The dc analysis of the JFET circuit is essentially the same as that of the MOSFET circuit, since the gate current is assumed to be zero.