# Zero Gate Bias of Depletion MOSFET

In zero gate biasing method the gate of the depletion MOSFET is grounded. This type of biasing is usually used when we want to bias the transistor in the ohmic region. FET transistors are usually biased in ohmic region when they are employed in circuit as switching device or when they are used as a voltage controlled resistor. But in case of depletion mode MOSFET, when biased in ohmic region the D-MOSFET can be used also as an amplifier because the D-MOSFET can be operated with both positive and negative gate to source voltage.

Here a depletion type MOSFET is biased with zero gate biasing method. The depletion mode MOSFET used is LND150. Example calculation worked out is provided where we show how to get Q-point or operating point in the ohmic region through biasing. Finally it is shown how a depletion mosfet can be used as voltage controlled resistor and amplifier with animation and video.

### Circuit Diagram of Zero Gate Bias of Depletion MOSFET

The following shows circuit diagram of depletion MOSFET LND150 with gate shorted and supply voltage of 5V.

In the above circuit, the gate is just shorted to ground via the 10MOhm resistor RG. This resistor is actually not required in case of switching application where dc voltage input is used to control the resistance of the MOSFET. The RG resistor is used in application where there is ac signal input and the MOSFET is used as an amplifier. The gate current is zero for FET transistors because of the inherent high impedance between the gate and the source. This means that the gate to source voltage $$V_{GS}$$ of FET is also zero. In the above circuit the input voltage signal is applied at the gate and output is taken from the drain or the source.

For the circuit above, the drain current $$I_D$$ is the drain current at shorted gate(also called Saturated Drain-to-Source Current)pecified in datasheet as $$I_{DSS}$$. Unlike JFET this is not the maximum drain current because the depletion MOSFET also accepts positive gate to source voltage $$V_{GS}$$. From the datasheet of LND150 the value of Saturated Drain-to-Source Current $$I_{DSS}$$ varies between 1mA and 3mA. The gate to source off $$V_{GS(off)}$$ varies from -1V to -3V. We may take the average value of $$I_{DSS}$$ and $$V_{GS(off)}$$ from the datasheet and approximate the drain to source resistance $$R_{DS}$$ as follows,

$$R_{DS} \simeq \frac{V_{P}}{I_{DSS}}$$

But, pinch off voltage is equal to gate to source voltage, $$V_{P}=V_{GS(off)}$$

so, $$R_{DS} \simeq \frac{V_{GS(off)}}{I_{DSS}}$$

or, $$R_{DS}\simeq \frac{2V}{2mA}$$

that is, $$R_{DS}\simeq 1k\Omega$$

We will use simulation model of LND150 and draw the drain graph in Proteus software. The drain graph of LND150 transistor is shown below.

From the graph when $$V_{GS}$$ = 0V, $$I_D=I_{DSS}=2.33mA$$. So from the graph the drain to source resistance is,

$$R_{DS}\simeq \frac{2V}{2.33mA}$$

that is, $$R_{DS}\simeq 850\Omega$$

### Operating Point(Q-point) in Ohmic Region

To bias the depletion MOSFET in the ohmic region the operating point must lie in the ohmic region and for the transistor LND150 this is indicated in the graph below.

So to bias the transistor in the ohmic region we have to select the operating point inside the ohmic region. To do this we choose drain current $$I_D$$ at the operating point lesser than $$I_{DSS}=2.33mA$$. That is,

$$I_D < I_{DSS} \;or\; I_D < 2.33mA$$ for ohmic region biasing point

Let the drain current at the operating point(Q-point) be 1.25mA, that is, $$I_{DQ}=1.69mA$$.

### Calculating Drain Resistor($$R_D$$)

We use a resistor called drain resistor $$R_D$$ to set the desired drain current $$I_{DQ}=1.69mA$$. The following circuit drawing shows the drain resistor included in the zero gate bias circuit.

### Plotting Q-point

To determine the drain resistor $$R_D$$, however first we have to draw a load line through the Q-point and find out where the load line will interest the drain current axis . Let $$I_{(DL}$$ denote intersection of the load line with the drain current axis line. This is as shown below.

From the graph we can determine that $$I_{(DL}=2.3mA$$. From the KVL in the output loop, we have,

$$V_{DD}=I_{(DL} R_D+V_D$$

and since $$V_D=V_{DS}=0$$ for getting $$I_{(DL}$$ on the graph we have,

$$R_D=\frac{V_{DD}}{I_{(DL}}$$

or, $$R_D=\frac{5V}{2.3mA}$$

that is, $$R_D=2.17k\Omega$$

The following shows the electrical circuit with calculated drain resistor $$R_D=2.17k\Omega$$ and the measured voltages and current.

### Depletion MOSFET as Voltage Controlled Resistor

Using the zero gate biased depletion MOSFET biased in the ohmic region can be used as a voltage controlled resistor. When variable DC voltage is applied to the gate we the resistance of the depletion mode MOSFET changes. This is illustrated in the following animation where variable power supply is applied to the gate.

As can be seen from the circuit animation in case of depletion MOSFET, when the gate to source voltage is reduced to negative voltage from 0V, that is the gate is reversed biased then the resistance of the depletion MOSFET increases. If the gate to source voltage is increased to positive voltage than the resistance of the MOSFET decreases.

### Depletion MOSFET as Amplifier

Unlike JFET amplifier which are biased in the saturation region for amplifier design purpose, the depletion MOSFET can work as an amplifier even in the ohmic region. This is because unlike JFET works only when gate is reversed biased with respect to the source. The depletion MOSFET however can operate with both positive and negative gate to source voltage. Hence even if the gate is at ground, the output drain current can swing positively and negatively. There depletion MOSFET can work as an amplifier. The following shows circuit diagram of depletion type MOSFET amplifier working in both the depletion mode and enhancement mode.

In the above circuit schematic, C1 and C2 are coupling capacitors. How to determine their values are explained in the tutorial How to bias a BJT using voltage divider biasing and also in  How to design Common Gate JFET Amplifier.

The following animation shows how a depletion type MOSFET with zero gate bias works as an amplifier.

### Video Demonstration

The following shows video of how depletion MOSFET works as a voltage controlled resistor and can also work as an amplifier with high input impedance.