How to bias Depletion MOSFET with fixed gate biasing method

In this tutorial it is shown how to bias a depletion MOSFET with fixed gate biasing method. In fixed gate biasing method, a fixed negate gate voltage is applied to the gate. This reverse biases the gate to source junction. As the gate is made more negative, lesser drain current will flow from drain to source. A depletion MOSFET is biased in the ohmic region when fixed gate bias method is used. In ohmic region the depletion MOSFET acts a resistor. When varying negative voltage is applied to applied to the gate such that the MOSFET remains biased in the ohmic region then the device acts a voltage controlled variable resistor.

The following shows circuit diagram of fixed gate biased depletion MOSFET.

In the above circuit diagram a fixed negative gatae voltage VGG is applied to the gate of the depletion MOSFET. This reverse biases the gate to source junction and the MOSFET operates in depletion mode. As more negative gate is applied the lesser drain current will flow from drain to the source. The resistor RD is the drain resistor. The input signal is applied to the gate via the coupling capacitor CC1 and the output is coupled to the load resistor with the coupling capacitor CC2.

The steps to biasing depletion MOSFET using the fixed gate biasing technique are as follows.

Step 1: Obtain gate shorted drain current, \(I_{DSS}\), and the gate to source cutoff voltage, \(V_{GS}\), from the MOSFET datasheet.

Here we will use LDN150 N-channel depletion MOSFET and it has the following values.

\(I_{DSS}=2.34mA\) and \(V_{GS(off)}=-2.2V\)

Step 2: Choose drain current \(I_D\) which should be less than \(I_{DSS}\)

Let \(I_D=1mA\)

Step 3: Use the Shockley equation to determine the gate to source voltage, \(V_{GS}\),

\(V_{GS} = V_{GS(off)}(1 - \sqrt{\frac{I_D}{I_{DSS}}})\)  

or, \(V_{GS} = 2.2V(1 - \sqrt{\frac{1mA}{2.34mA}})=0.762V\)  

Step 4: Choose drain voltage \(V_D\)

Let's choose drain voltage, \(V_D=2.5V\)

Step 5: Calculate drain resistor, \(R_D\),

\(R_D=\frac{V_{DD}-V_{DS}}{I_D}=\frac{5V-2.5V}{1mA}=2.5k\Omega\) 

Usually, a depletion MOSFET circuit biased with fixed gate bias is used for switching application. But here we will add a coupling capacitors. Then the following steps are used to calculate the coupling capacitor values.

Step 6: Calculate input impedance

\(Z_i = R_G\)

Let \(R_G=100k\Omega\) then, \(Z_i = 100k\Omega\) 

Step 7: Calculate the input coupling capacitor value CC1,

\(CC_1 = \frac{10}{2\pi f Z_i}\)

Let the input signal frequency be 1KHz then,

\(CC_1 = \frac{10}{2\pi (1kHz)(100k\Omega)}=15.92nF\)  

Step 8: Calculate the output impedance, \(Z_o\) 

\(Z_o = R_D = 2.5k\Omega\)

Step 9: Calculate the output coupling capacitor CC2

\(CC_2 = \frac{10}{2\pi (1kHz)(2.5k\Omega)}=636.94nF\)

The above component values and the current and voltages can be directly calculated using the online Depletion MOSFET Biasing & Amplifier Design Calculator.

The following shows the circuit diagram with the calculated values.

 The following shows the measured drain current, gate voltage and the drain to source voltage.

We can see that the measured values of the current and voltage in circuit simulated agrees with the calculated values.

So here we showed how to bias a depletion MOSFET using the fixed gate biasing method. There are other methods of biasing a depletion MOSFET. See the following depletion MOSFET biasing tutorials:

- Zero Gate Biased Depletion MOSFET Amplifier Design Example