How To Draw And Calculate A Mosfet Amplifier Circuit

The MOSFET amplifier circuit, a cornerstone of modern electronics, is used to amplify weak signals into stronger ones, enabling a multitude of applications from audio amplification to complex signal processing. Understanding how to draw and calculate a MOSFET amplifier circuit is fundamental for anyone involved in electronics design, offering the capability to create circuits tailored for specific performance requirements.

Understanding MOSFETs: A Brief Overview

At the heart of the MOSFET amplifier lies the Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET). This transistor, unlike its bipolar junction transistor (BJT) counterpart, is a voltage-controlled device, meaning its output current is controlled by the input voltage applied to its gate terminal.

MOSFETs come in two primary flavors:

• N-channel MOSFET (NMOS): Conducts when a positive voltage is applied to the gate.
• P-channel MOSFET (PMOS): Conducts when a negative voltage is applied to the gate.

Furthermore, they are categorized based on their mode of operation:

• Enhancement-mode MOSFET: Requires a voltage above a certain threshold to create a channel for conduction.
• Depletion-mode MOSFET: Has a channel already present and requires a voltage to deplete the channel and reduce conduction.

For amplifier design, enhancement-mode MOSFETs are more commonly used due to their simpler biasing requirements.

Common MOSFET Amplifier Configurations

Before diving into the drawing and calculation aspects, it's important to familiarize yourself with the common MOSFET amplifier configurations:

1. Common Source (CS): Offers high voltage gain and moderate input/output impedance.
2. Common Drain (CD) or Source Follower: Provides a voltage gain of less than 1, high input impedance, and low output impedance, making it suitable as a buffer.
3. Common Gate (CG): Exhibits low input impedance, high output impedance, and high voltage gain, often used in high-frequency applications.

Drawing a MOSFET Amplifier Circuit: A Step-by-Step Guide

Let's focus on the most common configuration, the Common Source (CS) amplifier, and illustrate how to draw its schematic:

Step 1: The MOSFET

Start by drawing the symbol for an N-channel enhancement-mode MOSFET. This symbol includes the source, gate, drain, and body terminals.

Step 2: DC Biasing Network

To ensure proper operation, the MOSFET needs to be biased in the saturation region. This is typically achieved using a resistor divider network connected to the gate.

• Two Resistors (R1 and R2): Connect these in series between the supply voltage (VDD) and ground. The gate is connected to the midpoint of these resistors. The values of R1 and R2 determine the gate voltage (VG).

Step 3: Drain Resistor (RD)

A drain resistor (RD) is connected between the drain terminal and VDD. This resistor develops the output voltage and sets the drain current (ID).

Step 4: Source Resistor (RS) - Optional

A source resistor (RS) connected between the source terminal and ground can provide negative feedback, improving the amplifier's stability and linearity, albeit at the cost of gain.

Step 5: Input and Output Coupling Capacitors (Cin and Cout)

These capacitors are used to block DC components from the signal source and the load, respectively, while allowing AC signals to pass through.

• Cin: Connect Cin between the input signal source and the gate.
• Cout: Connect Cout between the drain and the load resistor (RL).

Step 6: Bypass Capacitor (CS) - Optional

If a source resistor (RS) is used, a bypass capacitor (CS) is often connected in parallel with RS. This capacitor provides a low impedance path for AC signals, effectively shorting RS at the signal frequency and increasing the amplifier's gain.

Complete Schematic:

The completed schematic should show the MOSFET, biasing resistors (R1, R2), drain resistor (RD), optional source resistor (RS) with bypass capacitor (CS), input coupling capacitor (Cin), output coupling capacitor (Cout), supply voltage (VDD), and load resistor (RL).

Calculating MOSFET Amplifier Circuit Parameters

Now, let's delve into the calculations required to design a functional MOSFET amplifier circuit. These calculations involve determining the appropriate component values to achieve the desired gain, bias point, and impedance characteristics.

1. DC Biasing Analysis

The first step is to determine the DC operating point, also known as the quiescent point (Q-point), which defines the DC voltage and current levels in the circuit when no input signal is applied.

• Gate Voltage (VG): Assuming negligible gate current, VG can be calculated using the voltage divider rule:

  • VG = VDD * (R2 / (R1 + R2))

• Source Voltage (VS): VS is determined by the gate-source voltage (VGS) and the threshold voltage (Vth):

  • VS = VG - VGS

• Drain Current (ID): In the saturation region, the drain current can be approximated by the following equation:

  • ID = (1/2) * kn * (VGS - Vth)^2 * (1 + λVDS)

    Where:

    • kn = Transconductance parameter (related to the MOSFET's physical characteristics)
    • Vth = Threshold voltage
    • λ = Channel-length modulation parameter (often neglected for simplicity)
    • VDS = Drain-source voltage

  If RS is present, the equation becomes more complex:

  • ID = (VG - Vth) / (RS + (1/(2kn(VG - Vth))))

• Drain Voltage (VD): VD is calculated using Ohm's law:

  • VD = VDD - (ID * RD)

• Drain-Source Voltage (VDS): VDS is the difference between the drain and source voltages:

  • VDS = VD - VS

Ensuring Saturation:

It is crucial to ensure that the MOSFET operates in the saturation region for linear amplification. This condition is met when:

• VDS ≥ VGS - Vth

If this condition is not met, the MOSFET will operate in the triode (linear) region, resulting in non-linear amplification and distortion.

2. AC Analysis

After establishing the DC operating point, the next step is to analyze the AC performance of the amplifier. This involves determining the voltage gain, input impedance, and output impedance.

• Transconductance (gm): Transconductance is a measure of the MOSFET's ability to convert input voltage variations into output current variations. It is a crucial parameter for determining the amplifier's gain.

  • gm = ∂ID/∂VGS ≈ 2 * ID / (VGS - Vth) or gm = √(2 * kn * ID)

• Voltage Gain (Av): For a common-source amplifier without a source resistor bypass capacitor (CS), the voltage gain is:

  • Av = -gm * RD

  With a source resistor and no bypass capacitor, the gain is:

  • Av = -gm * RD / (1 + gm * RS)

  With a bypass capacitor (CS), the gain approaches the first equation.

• Input Impedance (Zin): The input impedance of a common-source amplifier is primarily determined by the biasing resistors R1 and R2:

  • Zin ≈ R1 || R2 (R1 in parallel with R2)

• Output Impedance (Zout): The output impedance of a common-source amplifier is approximately equal to the drain resistor:

  • Zout ≈ RD

3. Component Value Selection

The selection of component values depends on the desired amplifier characteristics. Here's a general approach:

• R1 and R2: Choose R1 and R2 to establish the desired gate voltage (VG). A common approach is to choose values that provide a stable VG, relatively independent of MOSFET parameter variations. Higher values for R1 and R2 will increase input impedance but also make the circuit more susceptible to noise.

• RD: Select RD to achieve the desired drain voltage (VD) and voltage gain. A larger RD will result in a higher gain but also a lower drain voltage.

• RS: If using a source resistor, choose RS to provide the desired level of negative feedback and stability. A larger RS will increase stability but reduce gain.

• Cin and Cout: Select Cin and Cout to provide a low impedance path for the signal frequency. A general rule of thumb is to choose values such that the reactance (1/(2πfC)) is much smaller than the input or output impedance at the lowest frequency of interest.

• CS: If using a bypass capacitor, choose CS to effectively short RS at the signal frequency. The reactance of CS should be much smaller than RS at the lowest frequency of interest.

Example Calculation:

Let's assume we want to design a common-source amplifier with the following specifications:

• VDD = 15V
• Desired Voltage Gain (Av) ≈ -10
• ID ≈ 1mA
• Vth = 2V
• kn = 2 mA/V^2

1. DC Biasing:

• Let's aim for VG = 4V. Choose R2 = 10kΩ. Then, using the voltage divider rule:

  • 4 = 15 * (10kΩ / (R1 + 10kΩ))
  • R1 ≈ 27.5 kΩ. We can choose a standard value of 27 kΩ.

• VGS = VG - VS. Let's initially assume VS = 0 (no RS). Then VGS = 4V.

• Check if our assumed ID matches the MOSFET equation:

  • ID = (1/2) * 2mA/V^2 * (4V - 2V)^2 = 4 mA. This is significantly different from our desired 1mA. We need to introduce RS to reduce ID.

• Let's re-introduce RS and solve for RS to get ID = 1mA:

  • 1mA = (4V - 2V) / (RS + (1/(2 * 2mA/V^2 * (4V - 2V))))
  • RS ≈ 1.5 kΩ

• Now, VS = ID * RS = 1mA * 1.5kΩ = 1.5V

• VGS = VG - VS = 4V - 1.5V = 2.5V

• Recalculate ID to verify:

  • ID = (1/2) * 2mA/V^2 * (2.5V - 2V)^2 = 0.25mA. This is still off. The initial assumption of negligible gate current is impacting the result. A more complex iterative calculation or simulation is needed for precise results. Let's proceed with the initial 1mA target and adjust later if needed.

• Let's choose RD to achieve approximately half of VDD drop across it: VD = VDD/2 = 7.5V.

  • RD = (VDD - VD) / ID = (15V - 7.5V) / 1mA = 7.5 kΩ

• VDS = VD - VS = 7.5V - 1.5V = 6V

• Check saturation: VDS (6V) > VGS - Vth (2.5V - 2V = 0.5V). Condition met.

2. AC Analysis:

• gm = 2 * ID / (VGS - Vth) = 2 * 1mA / (2.5V - 2V) = 4 mS

• Av = -gm * RD / (1 + gm * RS) = -4mS * 7.5kΩ / (1 + 4mS * 1.5kΩ) ≈ -7.5 / 7 = -4.28. The gain is less than our target of -10.

Adjustments and Iterations:

The initial calculations show that we are not meeting all of the design specifications, particularly the voltage gain. To address this, we can:

• Increase RD: Increasing RD will increase the gain, but it will also decrease VD, potentially pushing the MOSFET out of saturation.
• Decrease RS or Add CS: Decreasing RS or adding a bypass capacitor (CS) across RS will increase the gain but may also reduce stability.
• Adjust ID: Slightly adjusting the drain current by tweaking the biasing resistors (R1, R2) will affect gm and, consequently, the gain.

We can iterate through these adjustments while monitoring the DC operating point and ensuring that the MOSFET remains in saturation.

Using a Bypass Capacitor (CS):

Adding a large capacitor CS in parallel with RS effectively shorts RS for AC signals, increasing the voltage gain:

• With CS, Av ≈ -gm * RD = -4mS * 7.5kΩ = -30. This is significantly higher than our target. We would need to reduce RD or adjust the bias to reduce gm to achieve the desired gain.

Choosing Coupling Capacitors (Cin and Cout):

Let's assume the lowest frequency of interest is 100Hz. We want the reactance of the capacitors to be much smaller than the input/output impedance at this frequency.

• Let's aim for a reactance of 100 ohms at 100Hz.

• Cin: Reactance = 1 / (2 * π * f * C). Assuming Zin ≈ R1||R2 ≈ 8kΩ, a smaller reactance is desired. Let's target 100 ohms.

  • C = 1 / (2 * π * 100Hz * 100Ω) ≈ 15.9 µF. We can choose a standard value of 22 µF.

• Cout: Assuming Zout ≈ RD = 7.5kΩ. A smaller reactance is desired. Let's target 100 ohms.

  • C = 1 / (2 * π * 100Hz * 100Ω) ≈ 15.9 µF. We can choose a standard value of 22 µF.

Iterative Refinement and Simulation:

These calculations provide a starting point for the design. In practice, it is essential to use circuit simulation software (e.g., SPICE) to refine the design and verify the performance. Simulation allows you to:

• Account for MOSFET parameter variations.
• Optimize component values for the desired gain, bandwidth, and distortion.
• Analyze the circuit's stability.

Advanced Considerations

• Channel-Length Modulation: The parameter λ (channel-length modulation) was neglected for simplicity. In reality, λ affects the output impedance and gain. For more accurate results, λ should be included in the calculations, especially for short-channel MOSFETs.
• Body Effect: The body effect refers to the change in threshold voltage (Vth) due to a voltage difference between the source and the body. This effect can be significant in some applications and should be considered in the design.
• Temperature Effects: MOSFET parameters, such as Vth and kn, are temperature-dependent. The design should account for temperature variations to ensure stable performance over a range of operating temperatures.
• High-Frequency Considerations: At high frequencies, parasitic capacitances within the MOSFET become significant. These capacitances can affect the amplifier's bandwidth and stability.

Conclusion

Drawing and calculating MOSFET amplifier circuits is a crucial skill for electronics engineers and enthusiasts. By understanding the fundamentals of MOSFET operation, common amplifier configurations, and the relevant equations, you can design circuits tailored to specific applications. Remember that the design process often involves iterative refinement and simulation to achieve optimal performance. While the equations provide a strong foundation, practical considerations and real-world component variations necessitate a thorough understanding of circuit behavior and the use of simulation tools. This comprehensive guide provides the necessary knowledge to begin designing and analyzing MOSFET amplifier circuits, empowering you to create innovative electronic solutions.