There are 3 commonly used methods to bias a JFET which are Gate Bias, Self Bias and Voltage Divider Bias. Here it is described how to bias a JFET using gate bias. Gate bias is also popularly known as fixed bias. The gate bias method is used usually to bias the JFET in Ohmic region. It is not used to bias JFET in its active region because of wide spread of parameters. JFET are normally ON devices because when the gate is grounded there is maximal current flow through the device. More on construction of JFET is explained in the tutorial How does JFET transistor work?. Here only gate biasing of the JFET is explained.
The gate bias circuit diagram for a JFET is shown below.
In gate bias, a negative gate voltage \(V_{GG}\)=\(V_{GS}\) is applied to the gate of the JFET to reverse bias the gate to source junction. The gate resistor RG has no effect on the operation of the bias circuit since the gate current is zero. That is since there is no gate current there is no voltage drop across the gate resistor RG. A positive drain to source voltage \(V_{DS}\) is applied between the drain and source. The negative gate to source voltage\(V_{GS}\) controls the drain current \(I_D\), that is, controls the amount of current flow from drain to source. When \(V_{GS}=0\), maximum drain current called shorted gate drain to source current, \(I_{DSS}\) flows from drain to the source. When \(V_{GS}\) is made progressively negative, then lesser and lesser drain current \(I_D\) flows from drain to source.
There are two methods to find the circuit voltages, current and resistor value.
1. Using Shockley equation for JFET
2. Using graphical method
1. Using Shockley equation for JFET
Theory:
In theory we calculate the drain current and then calculate the drain to source voltage. Here we assume we have knowledge about gate to source voltage, have knowledge of drain resistor value. This is explained now in details.
By using the Shockley equation for JFET we can find out the value of drain current \(I_D\) since we know the gate to source voltage \(V_{GS} = -V_{GG}\). The Shockley equation for JFET is below,
\(I_D = I_{DSS}(1-\frac{V_{GS}}{V_{GS(off)}})^2\) --->(1)
where \(I_{DSS}\) and \(V_{GS(off)}\) can be found in the JFET transistor datasheet.
Once we know the drain current \(I_D\) we can determine the drain to source voltage \(V_{DS}\) using the following equation.
\(V_{DD}=I_D R_D + V_{DS}\) --->(2)
In Practice:
In practice, however, we first set our requirement which means that we aim for some drain current(\(I_D\)) and some drain to source voltage(\(V_{DS}\)). Say for example we want drain current \(I_D\) of 5mA and drain to source voltage \(V_{DS}\) of 2.5V given that the power supply \(V_{DD}\) is 5V.
In this case, we calculate the gate to source voltage \(V_{GS}\) using the Shockley equation for JFET given by equation (1). Rearranging equation (1) to solve for \(V_{GS}\) gives,
\(V_{GS} = V_{GS(off)}(1 - \sqrt{\frac{I_D}{I_{DSS}}})\) --->(3)
again, \(I_{DSS}\) and \(V_{GS(off)}\) can be found in the JFET transistor datasheet.
Next we determine \(R_D\) for \(I_D=5mA\) and \(V_{DS}=2.5V\) using the equation(2).
\(R_D=\frac{V_{DD}-V_{DS}}{I_D}\) --->(4)
2. Using graphical method
We can similarly gate bias the JFET with the help of drain characteristic curve,
Shown below is the drain characteristic curve of 2N5459 JFET transistor.
We locate the drain current \(I_D\) of 5mA on the curve for which \(V_GS = -0.2V\). From the graph the value of drain to source voltage \(V_{DS}=0.529V\). Now equation (4) we can determine the drain resistor value,
\(I_D=\frac{V_{DD}-V_{DS}}{I_D} = \frac{5V-0.529}{5mA}=894\Omega\)
The following shows the gate biased 2N5459 JFET simulated result in Proteus.
The gate biased 2n5459 JFET circuit above shows the correctly calculated drain to source voltage \(V_{DS}\) and drain current \(I_{D}\).
The above calculation can also be found out using the online JFET biasing calculator.
So here it was described how to bias a JFET using gate biasing technique. A gate biased or fixed biased JFET are used in applications where voltage controlled resistor is needed.
