# Field Effect Transistor

### Contents

**Recall Field Effect Transistor**1**Recall the advantages of Field Effect Transistor over Bipolar Junction Transistor**1**Classify Field Effect Transistor**2**Describe the construction of N-Channel Junction Field Effect Transistor**2**Describe the construction of P-Channel Junction Field Effect Transistor**3**Describe the working of N-Channel/P-Channel JFET when i. V**4_{GS}= 0 V ii. V_{GS}is negative**Describe the Characteristics of N-Channel/P-Channel JFET: i. Drain Characteristics ii. Transfer Characteristics**5**Recall the following parameters of JFET: i. Static & Dynamic Drain Resistance ii. Input Resistance iii. Transconductance g iv. Amplification Factor (μ)**7**Analyse the Fixed-Bias Configuration of JFET: i. Mathematical Analysis ii. Graphical Analysis**8**Analyse the Self-Bias Configuration of JFET**10**Analyse the Voltage-Divider Bias Configuration of JFET**11**Determine Operation Point in the Voltage-Divider Bias Configuration of JFET**12**Analyse graphically the Common-Source JFET Amplifier**14**Describe the Low-Frequency Small Signal Model of JFET**15**Analyse the following Amplifiers and find out the Input Impedance, Output Impedance and Voltage Gain: i. Common Source ii. Common Drain iii. Common Gate Amplifier**16

Recall Field Effect Transistor

A field-effect transistor (FET) is a type of electronic device that is used as a voltage-controlled switch or amplifier. FETs are three-terminal devices, consisting of a source, a drain, and a gate. The gate terminal is used to control the flow of current between the source and drain terminals.

FETs are classified into two main types: junction FETs (JFETs) and metal-oxide-semiconductor FETs (MOSFETs). JFETs are the simplest type of FET and are used primarily as voltage-controlled resistors. MOSFETs, on the other hand, are widely used in digital and analog circuits, and are capable of high-frequency operation and high input impedance.

FETs have a number of advantages over bipolar junction transistors (BJTs), including low input bias current, high input impedance, low noise, and ease of integration. They are widely used in a variety of applications, including power electronics, digital circuits, analog circuits, and radio-frequency (R_{F}) circuits.

Recall the advantages of Field Effect Transistor over Bipolar Junction Transistor

The advantages of Field Effect Transistor (FET) over Bipolar Junction Transistor (BJT) are:

- High Input Impedance: FETs have high input impedance, which means they do not draw much current from the input signal source.
- Low Noise: FETs are less prone to generating noise, making them a good choice for low-noise applications.
- Improved Linearity: FETs can provide improved linearity compared to BJTs, making them suitable for use in analog circuits where linearity is important.
- Simplified Biassing: FETs typically require simpler biassing circuits compared to BJTs, making them easier to use in some applications.
- Easy to Fabricate: FETs are easier to fabricate on a large scale, which makes them a more cost-effective solution in some applications.
- Higher Input Voltage Range: FETs can handle higher input voltage ranges compared to BJTs, making them suitable for use in high-voltage applications.

Classify Field Effect Transistor

Field Effect Transistors (FETs) can be classified into two main types:

- Junction Field Effect Transistor (JFET): JFETs are the simplest type of FETs and are commonly used in analog circuits. They consist of three regions: source, gate, and drain, and the current flow between source and drain is controlled by the voltage applied to the gate.
- Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET): MOSFETs are the most widely used type of FETs and are commonly used in digital circuits. They consist of four regions: source, drain, gate, and the insulating layer (oxide) between the gate and channel. The current flow between source and drain is controlled by the voltage applied to the gate.

Additionally, MOSFETs can be further classified into two types:

a) N-Channel MOSFET: In an N-Channel MOSFET, the current flows from source to drain through a channel that is doped with n-type material.

b) P-Channel MOSFET: In a P-Channel MOSFET, the current flows from source to drain through a channel that is doped with p-type material.

Describe the construction of N-Channel Junction Field Effect Transistor

The N-Channel Junction Field Effect Transistor (JFET) is a three-terminal device consisting of a n-type semiconductor material that forms the channel between the source and drain regions. The channel is sandwiched between two p-type regions, which serve as the gate electrodes.

The source and drain regions are heavily doped to provide a low resistance path for the flow of current between them. The gate region is reverse-biassed with respect to the channel, which creates a depletion region in the channel. This depletion region acts as a resistance to the flow of current between the source and drain.

By controlling the voltage applied to the gate, the size of the depletion region can be adjusted, thereby controlling the resistance to the flow of current between the source and drain. When a negative voltage is applied to the gate, the depletion region grows, which reduces the cross-sectional area of the channel and increases its resistance. Conversely, when a positive voltage is applied to the gate, the depletion region decreases in size, which increases the cross-sectional area of the channel and reduces its resistance.

The JFET operates in the depletion mode, meaning that the channel is always partially depleted of charge carriers and a voltage applied to the gate is used to control the size of the depletion region and the resistance of the channel.

Describe the construction of P-Channel Junction Field Effect Transistor

A P-channel junction field effect transistor (JFET) is a three-layer, semiconductor device consisting of a p-type semiconductor channel with two n-type regions, also known as source and drain, diffused into the p-type material. The source and drain form the input and output terminals, respectively, of the JFET, while the channel acts as a variable resistance controlled by the voltage applied to a third terminal called the gate.

The construction of a P-channel JFET is similar to that of an N-channel JFET. The main difference lies in the type of semiconductor material used to create the channel and the polarity of the voltage applied to the gate terminal. In a P-channel JFET, the channel is formed by a p-type semiconductor material, and a positive voltage applied to the gate terminal will reduce the channel resistance between the source and drain terminals, allowing more current to flow.

To construct a P-channel JFET, a piece of p-type semiconductor material is first prepared. Then, two n-type impurities are diffused into the material at opposite ends to form the source and drain regions. The gate terminal is formed by depositing a metal layer on top of the channel in a manner that does not contact the source or drain regions. The source, drain, and gate terminals are connected to the external circuit through metal contacts.

In summary, a P-channel JFET is constructed by diffusing n-type impurities into a p-type semiconductor channel to form the source and drain regions, and depositing a metal layer on top of the channel to form the gate terminal.

Describe the working of N-Channel/P-Channel JFET when i. V_{GS}= 0 V ii. V_{GS}is negative

The working of an N-channel junction field effect transistor (JFET) and a P-channel JFET depends on the voltage applied to their gate-source terminal (V_{GS}). The operation of the two devices can be explained as follows:

- N-Channel JFET:

i. V_{GS} = 0 V: When the voltage applied to the gate-source terminal (V_{GS}) of an N-channel JFET is 0 V, the pn-junction between the gate and channel is reverse-biassed. This results in the channel resistance remaining at its maximum value, and only a very small leakage current flows through the gate. In this state, the drain current (I_{D}) is controlled by the source-drain voltage (V_{DS}) and the channel resistance between the source and drain regions.

ii. V_{GS} is negative: When the voltage applied to the gate-source terminal is negative, the pn-junction between the gate and channel is forward-biassed, which reduces the channel resistance and increases the drain current. The drain current is inversely proportional to the magnitude of V_{GS}. The more negative the voltage applied to the gate, the lower the channel resistance, and the higher the drain current.

- P-Channel JFET:

i. V_{GS} = 0 V: When the voltage applied to the gate-source terminal (V_{GS}) of a P-channel JFET is 0 V, the pn-junction between the gate and channel is reverse-biassed, resulting in the channel resistance remaining at its maximum value, and only a very small leakage current flows through the gate. In this state, the drain current (I_{D}) is controlled by the source-drain voltage (V_{DS}) and the channel resistance between the source and drain regions.

ii. V_{GS} is negative: When the voltage applied to the gate-source terminal is negative, the pn-junction between the gate and channel is reverse-biassed, which increases the channel resistance and decreases the drain current. The drain current is directly proportional to the magnitude of V_{GS}. The more negative the voltage applied to the gate, the higher the channel resistance, and the lower the drain current.

Describe the Characteristics of N-Channel/P-Channel JFET: i. Drain Characteristics ii. Transfer Characteristics

The characteristics of an N-channel junction field effect transistor (JFET) and a P-channel JFET can be classified into two types: drain characteristics and transfer characteristics.

1. Drain Characteristics:

Drain characteristics refer to the relationship between the drain current (I_{D}) and the drain-source voltage (V_{DS}) for a fixed gate-source voltage (V_{GS}). Drain characteristics are usually plotted on a graph with the drain current as the y-axis and the drain-source voltage as the x-axis. The drain characteristics of an N-channel JFET and a P-channel JFET are shown below:

i. N-Channel JFET: In an N-channel JFET, the drain current is proportional to the drain-source voltage for a fixed gate-source voltage. This results in a straight line characteristic on the drain current vs. drain-source voltage graph. The slope of the line is determined by the transconductance (g_{m}) of the JFET.

ii. P-Channel JFET: In a P-channel JFET, the drain current is proportional to the drain-source voltage for a fixed gate-source voltage. This results in a straight line characteristic on the drain current vs. drain-source voltage graph. The slope of the line is determined by the transconductance (g_{m}) of the JFET.

2. Transfer Characteristics:

Transfer characteristics refer to the relationship between the drain current (I_{D}) and the gate-source voltage (V_{GS}) for a fixed drain-source voltage (V_{DS}). Transfer characteristics are usually plotted on a graph with the drain current as the y-axis and the gate-source voltage as the x-axis. The transfer characteristics of an N-channel JFET and a P-channel JFET are shown below:

The transfer characteristics of an N-channel JFET (Junction Field-Effect Transistor) and a P-channel JFET describe the relationship between the input voltage (gate-to-source voltage, VGS) and the output current (drain current, ID). Here’s a comparison of the transfer characteristics for both types of JFETs:

N-Channel JFET Transfer Characteristics:

- When VGS = 0 (no voltage applied between the gate and the source), the JFET is in the cutoff region, and the drain current ID is almost zero.
- As VGS becomes more negative (below zero), the JFET starts to conduct, and the drain current ID increases.
- The relationship between VGS and ID is typically linear within a certain range, known as the ohmic region or the triode region.
- When VGS is sufficiently negative, the JFET reaches saturation, and the drain current ID remains constant, reaching a maximum value known as IDSS (the drain current with VGS = 0).
- In saturation, the JFET acts as a current-controlled current source, maintaining a relatively constant drain current regardless of changes in VGS.

P-Channel JFET Transfer Characteristics:

- When VGS = 0, the JFET is in the cutoff region, and the drain current ID is almost zero.
- As VGS becomes more positive (above zero), the JFET starts to conduct, and the drain current ID increases.
- Similar to the N-channel JFET, the relationship between VGS and ID is typically linear within the ohmic or triode region.
- As VGS becomes more positive, the JFET eventually reaches saturation, and the drain current ID remains constant, reaching a maximum value (-IDSS) with VGS = 0.
- In saturation, the P-channel JFET also acts as a current-controlled current source, maintaining a relatively constant drain current despite variations in VGS.

Overall, the transfer characteristics of both N-channel and P-channel JFETs exhibit similar behavior, with the primary difference being the polarity of the applied gate-to-source voltage that determines the direction of the current flow. N-channel JFETs require negative VGS to enhance the channel conductivity, while P-channel JFETs require positive VGS.

It’s worth noting that the specific transfer characteristics can vary slightly between different JFET models, and external biasing and circuit configurations can also affect the overall behavior.

Recall the following parameters of JFET: i. Static & Dynamic Drain Resistance ii. Input Resistance iii. Transconductance g iv. Amplification Factor (μ)

JFET parameters are properties of the device that describe its electrical behaviour and performance in a circuit. The following are some important parameters of a junction field effect transistor (JFET):

- Static Drain Resistance (R
_{DS}):

Static drain resistance, also known as drain resistance, is the resistance between the drain and source terminals of a JFET when the drain current (I_{D}) is constant. It is represented as R_{DS} and is an important parameter for determining the power dissipation and maximum safe operating temperature of a JFET.

- Dynamic Drain Resistance (r
_{d}):

Dynamic drain resistance, also known as small-signal drain resistance, is the resistance between the drain and source terminals of a JFET when the drain current (I_{D}) is not constant. It is represented as r_{d} and is an important parameter for determining the gain and stability of a JFET in an amplifier circuit.

- Input Resistance (R
_{in}):

Input resistance, also known as gate resistance, is the resistance between the gate and source terminals of a JFET when the drain current (I_{D}) is constant. It is represented as R_{in} and is an important parameter for determining the input impedance and loading effect of a JFET in a circuit.

Analyse the Fixed-Bias Configuration of JFET: i. Mathematical Analysis ii. Graphical Analysis

The fixed-bias configuration of a JFET (junction field-effect transistor) is a common circuit configuration used for amplification purposes. In this configuration, the gate terminal of the JFET is connected to a fixed voltage source, while the drain and source terminals are connected to a load resistor and a voltage supply.

**i. Mathematical Analysis:**

To analyze the fixed-bias configuration of a JFET mathematically, we can use the following steps:

- Draw the circuit diagram and label the components and nodes.
- Apply Kirchhoff’s voltage law (KVL) to the drain-source loop to obtain an expression for the drain current Id in terms of the drain-source voltage V
_{ds}and the load resistor R_{L}. - Apply the current-voltage relationship of the JFET to express the drain current I
_{d}in terms of the gate-source voltage V_{gs}and the drain-source voltage V_{ds}. - Equate the two expressions for I
_{d}and solve for V_{gs}in terms of V_{ds}and R_{L}.

The resulting expression for V_{gs} is given by:

V_{gs} = -sqrt(2I_{d}*R_{L}) – V_{ds}

where I_{d} is the drain current, R_{L} is the load resistor, and V_{ds} is the drain-source voltage.

**ii. Graphical Analysis:**

To analyze the fixed-bias configuration of a JFET graphically, we can use the load line method. The load line represents the combination of the JFET’s current-voltage characteristic and the load resistor’s voltage-current characteristic.

To draw the load line, we can plot the load resistor’s characteristic curve on the same graph as the JFET’s characteristic curve. The intersection point of the two curves represents the operating point of the circuit.

The JFET’s characteristic curve is a plot of the drain current Id versus the drain-source voltage V_{ds}, with the gate-source voltage V_{gs} held constant. The load resistor’s characteristic curve is a plot of the voltage V_{ds} across the load resistor versus the current I_{L} through the load resistor.

The load line is a straight line connecting the points (0, V_{supply}) and (V_{supply}/R_{L}, 0), where V_{supply} is the voltage supply. The intersection point of the load line and the characteristic curves represents the operating point of the circuit.

In summary, the fixed-bias configuration of a JFET can be analyzed mathematically using Kirchhoff’s laws and the JFET’s current-voltage relationship, or graphically using the load line method. Both methods provide useful insights into the behavior of the JFET in this configuration and can be used to design and optimize JFET-based circuits.

Analyse the Self-Bias Configuration of JFET

The self-bias configuration is a biassing method used to establish a stable operating point for a junction field-effect transistor (JFET). The self-bias configuration uses the drain-source voltage (V_{DS}) to establish the gate-source voltage (V_{GS}), eliminating the need for an external voltage source to bias the gate. The following is an analysis of the self-bias configuration of a JFET:

- Circuit Configuration:

In a self-bias configuration, the drain terminal of the JFET is connected to a load resistor (R_{L}), and the source terminal is connected to ground. A feedback resistor (R_{F}) is connected between the gate and the drain, and the gate-source junction is reverse-biassed by the drain-source voltage (V_{DS}).

- Operating Point:

The operating point of the JFET in the self-bias configuration is established by the interdependence of the drain current (I_{D}) and the drain-source voltage (V_{DS}). The drain current (I_{D}) sets the drain-source voltage (V_{DS}) and the drain-source voltage (V_{DS}) sets the gate-source voltage (V_{GS}). The operating point is the steady-state operating conditions of the JFET and determines the drain current (I_{D}) and drain-source voltage (V_{DS}) for a given gate-source voltage (V_{GS}).

Analyse the Voltage-Divider Bias Configuration of JFET

The voltage-divider bias configuration is a commonly used bias arrangement for JFETs, where the gate-source voltage (V_{GS}) is established through the use of two resistors, R_{1} and R_{2}, connected in a voltage divider configuration.

- Mathematical Analysis:

The gate-source voltage (V_{GS}) can be calculated using the following equation:

V_{GS} = V_{DD} (R_{2} / (R_{1} + R_{2}))

where V_{DD} is the supply voltage and R_{1} and R_{2} are the values of the resistors. The drain current (I_{D}) can be calculated using the transfer characteristic curve of the JFET, which represents the relationship between the drain current (I_{D}) and the drain-source voltage (V_{DS}) for different gate-source voltages (V_{GS}).

- Graphical Analysis:

The voltage-divider bias configuration can be analysed graphically by drawing the load line and the transfer characteristic curve on the same graph. The operating point is the intersection of the load line and the transfer characteristic curve and represents the steady-state operating conditions of the JFET. The drain current (I_{D}) and drain-source voltage (V_{DS}) can be calculated from the operating point using Ohm’s law and Kirchhoff’s laws.

- Stability:

The stability of the operating point in the voltage-divider bias configuration can be improved by choosing the values of the resistors R_{1} and R_{2} carefully. A properly chosen value of R_{1} and R_{2} ensures that the operating point remains stable and does not oscillate. The stability of the operating point can be further improved by increasing the value of R_{1} or by decreasing the value of R_{2}.

Determine Operation Point in the Voltage-Divider Bias Configuration of JFET

To determine the operating point in the voltage-divider bias configuration of a JFET, we need to calculate the DC biasing conditions that establish the desired drain current (ID) and drain-source voltage (VDS). Here are the steps to determine the operating point:

- Identify the JFET Parameters:
- Obtain the necessary parameters for the specific JFET being used, including the pinch-off voltage (VP) and the maximum drain current (IDSS).

- Determine the Desired Operating Point:
- Decide on the desired drain current (ID) and the drain-source voltage (VDS) for the JFET.
- The drain current should be within the specified range of the JFET’s IDSS, and the drain-source voltage should be within a safe operating range.

- Calculate the Drain Resistor (RD):
- Choose an appropriate value for the drain resistor (RD) to establish the desired drain current.
- RD can be calculated using Ohm’s law: RD = VDS / ID, where VDS is the desired drain-source voltage and ID is the desired drain current.

- Determine the Gate Resistor (RG):
- Select a suitable value for the gate resistor (RG) to limit the gate current and ensure stability.
- A common practice is to set RG to a high value, typically in the range of 100kΩ to 1MΩ.

- Calculate the Voltage Divider Resistors (R1 and R2):
- Determine the values of the voltage divider resistors (R1 and R2) based on the desired gate-source voltage (VGS).
- VGS should be selected to ensure that the JFET operates within the desired region (typically in the ohmic region for linear applications).
- The voltage divider ratio can be calculated using the equation: VGS = Vin * (R2 / (R1 + R2)), where Vin is the input voltage.

- Verify the Operating Point:
- Once the values of RD, RG, R1, and R2 are determined, calculate the actual drain current (ID) and gate-source voltage (VGS) using the appropriate equations and the measured or specified component values.
- Verify that the calculated values of ID and VGS match the desired operating point.
- Adjust the component values if necessary to achieve the desired operating point.

By following these steps and calculating the appropriate resistor values, you can determine the operating point in the voltage-divider bias configuration of a JFET amplifier. It’s crucial to consider the JFET’s datasheet specifications and ensure that the operating conditions are within safe and reliable limits.

Analyse graphically the Common-Source JFET Amplifier

To analyze the Common-Source JFET Amplifier graphically, we can plot the input-output characteristics, voltage gain, and frequency response of the amplifier. Let’s break down the analysis step by step:

- Input-Output Characteristics:
- Plot the input-output characteristics of the Common-Source JFET Amplifier by varying the input voltage (Vin) and measuring the corresponding output voltage (Vout).
- The input voltage Vin is typically applied between the gate and source terminals, while the output voltage Vout is measured across the drain resistor.
- As Vin varies, observe the corresponding changes in Vout. The plot will show how the amplifier responds to different input levels.

- Voltage Gain:
- Determine the voltage gain (Av) of the Common-Source JFET Amplifier by calculating the ratio of the change in output voltage (ΔVout) to the change in input voltage (ΔVin) for a small-signal input.
- Measure the output voltage with respect to a small change in input voltage while keeping the input signal frequency low (within the small-signal range).
- The voltage gain can be calculated as Av = ΔVout / ΔVin.
- Plot the voltage gain as a function of frequency to observe the frequency response characteristics of the amplifier.

- Frequency Response:
- Analyze the frequency response of the Common-Source JFET Amplifier by plotting the gain versus frequency.
- Apply a sinusoidal input signal with varying frequencies to the amplifier and measure the corresponding output voltage.
- Calculate the gain (Av) at each frequency by dividing the output voltage amplitude by the input voltage amplitude.
- Plot the gain as a function of frequency to observe how the amplifier amplifies different frequency components of the input signal.
- Take note of the cutoff frequencies, bandwidth, and any frequency-dependent changes in gain.

By analyzing the Common-Source JFET Amplifier graphically, we can understand its behavior, gain characteristics, and frequency response. These graphical representations help in designing and optimizing the amplifier circuit for specific applications. It’s important to consider the biasing conditions, load impedance, and JFET parameters while interpreting the graphs.

Describe the Low-Frequency Small Signal Model of JFET

The low-frequency small signal model of a Junction Field-Effect Transistor (JFET) is a simplified representation used for analyzing the small-signal behavior of the JFET at low frequencies. It allows us to study the JFET’s response to small AC signals superimposed on the DC bias conditions. The small signal model consists of several components, including resistances and capacitances. Here’s a breakdown of the components in the low-frequency small signal model of a JFET:

- Input Resistance (Rin):
- Represents the resistance between the gate and the source terminals of the JFET.
- It is typically high, as the gate-source junction of a JFET is reverse-biased.

- Output Resistance (Rout):
- Represents the resistance between the drain and the source terminals of the JFET.
- It is typically high, as the drain-source junction of a JFET is reverse-biased.

- Transconductance (gm):
- Represents the small-signal conductance between the drain and the source terminals of the JFET.
- It determines the JFET’s ability to amplify small AC signals.
- The value of gm is related to the DC drain current (ID) and the JFET’s transconductance parameter (gm = √(2ID/gm)).

- Capacitances:
- Junction Capacitances:
- Gate-Source Capacitance (Cgs): Represents the capacitance between the gate and the source terminals.
- Gate-Drain Capacitance (Cgd): Represents the capacitance between the gate and the drain terminals.

- These capacitances are typically small and have minimal impact at low frequencies but become more significant at higher frequencies.

- Junction Capacitances:

The low-frequency small signal model of a JFET is often represented using a circuit diagram that includes these components connected in a specific configuration. This model allows engineers to analyze and design JFET amplifier circuits, determine gain and frequency response, and study the impact of biasing and load conditions on the JFET’s small-signal performance.

It’s important to note that the specific values of these components may vary depending on the JFET model and its operating conditions. Hence, the low-frequency small signal model provides a simplified representation that captures the essential characteristics for analysis at low frequencies.

Analyse the following Amplifiers and find out the Input Impedance, Output Impedance and Voltage Gain: i. Common Source ii. Common Drain iii. Common Gate Amplifier

The input impedance, output impedance, and voltage gain of the following three types of amplifiers can be described as follows:

- Common Source Amplifier:

- Input Impedance: High (Typically greater than 1 megaohm)
- Output Impedance: Low (Typically less than 100 ohms)
- Voltage Gain: Medium to High (Typically between 10 and 100)

- Common Drain Amplifier (AKA Source Follower):

- Input Impedance: Low (Typically less than 100 ohms)
- Output Impedance: High (Typically greater than 1 megaohm)
- Voltage Gain: Nearly unity (Typically less than 1.5)

- Common Gate Amplifier:

- Input Impedance: High (Typically greater than 1 megaohm)
- Output Impedance: High (Typically greater than 1 megaohm)
- Voltage Gain: Low (Typically less than 10)

It’s important to note that the actual values of input impedance, output impedance, and voltage gain can vary greatly depending on the specific implementation and design of the amplifier circuit. These values should be considered rough approximations.