Common Gate MOSFET Amplifier DC Analysis

Calculate the drain current \(I_D\) and (optionally) the drain-to-gate voltage \(V_{DG}\) for a MOSFET in saturation.

* Enter voltages with their signs as needed. If you don’t need \(V_{DG}\), set \(V_{+}=0\).

Step 1: Enter Biasing Parameters

e.g., 2 V

e.g., 0 V

Enter 0 if \(V_{DG}\) is not needed

e.g., 10000 Ω (10 kΩ)

e.g., 0.001 A/V²

Dimensionless (e.g., 10)

e.g., 1 V

MOSFET in Saturation (Common Gate): $$ I_D = \frac{1}{2}\,k’\frac{W}{L}\bigl((V_G – V_S) – V_{TH}\bigr)^2, \quad \text{for }(V_G – V_S) > V_{TH}. $$

Drain Voltage: $$ V_D = V_{+} – I_D \, R_D. $$

Drain-to-Gate Voltage: $$ V_{DG} = V_D – V_G. $$

Common Gate MOSFET Amplifier DC Analysis (In-Depth Explanation)

Common Gate MOSFET Amplifier DC Analysis (In-Depth Explanation)

In the Common Gate MOSFET Amplifier, the gate is held at a fixed DC bias, the input signal is applied at the source, and the output is taken from the drain. This configuration is particularly useful for high-frequency applications and when a low input impedance is desirable. In DC analysis, we focus on calculating the drain current and, optionally, the drain-to-gate voltage for a MOSFET operating in the saturation region.

Table of Contents

  1. Overview
  2. MOSFET Operation in Saturation
  3. Key Equations
  4. Calculation Process
  5. Practical Example
  6. Common Applications
  7. Conclusion

1. Overview

In a common gate amplifier, the MOSFET’s gate is biased with a constant DC voltage while the input signal is applied to the source. For DC analysis, we assume that the MOSFET is operating in its saturation region—a state where the drain current \(I_D\) becomes nearly independent of the drain-source voltage (\(V_{DS}\)) and is primarily controlled by the gate-source voltage \(V_{GS}\).

Additionally, one may want to calculate the drain-to-gate voltage \(V_{DG}\), which is defined as the difference between the drain voltage \(V_D\) and the gate voltage \(V_G\). This parameter can provide further insight into the biasing and operating conditions of the amplifier.

2. MOSFET Operation in Saturation

For an enhancement-mode n-channel MOSFET in saturation, the drain current is given by the well-known quadratic relationship:

\( I_D = \frac{1}{2} k’ \frac{W}{L} (V_{GS} – V_{th})^2 \)

Where:

  • \(I_D\) is the drain current.
  • \(k’ = \mu_n C_{ox}\) is the process transconductance parameter (with \(\mu_n\) being the electron mobility and \(C_{ox}\) the gate oxide capacitance per unit area).
  • \(\frac{W}{L}\) is the width-to-length ratio of the MOSFET channel.
  • \(V_{GS}\) is the gate-to-source voltage (for an n-channel device, this is typically positive when the device is on, though in a common gate amplifier, the source voltage may be negative relative to the gate bias).
  • \(V_{th}\) is the threshold voltage.

In a common gate configuration, the gate is fixed at a bias voltage \(V_G\) and the effective gate-source voltage is:

\( V_{GS} = V_G – V_S \)

Once the MOSFET is in saturation (ensured by proper biasing, such that \(V_{DS} \geq V_{GS} – V_{th}\)), the drain current can be computed using the equation above.

3. Key Equations

Drain Current: The primary equation in saturation is:

\( I_D = \frac{1}{2} k’ \frac{W}{L} (V_{GS} – V_{th})^2 \)

Optionally, if channel-length modulation is considered, the formula may include a factor \((1 + \lambda V_{DS})\), but for basic DC analysis, this factor is often omitted.

Drain-to-Gate Voltage: This parameter is calculated as:

\( V_{DG} = V_D – V_G \)

This voltage difference can be useful to verify biasing conditions and ensure that the device is operating within its intended region.

4. Calculation Process

  1. Determine Bias Conditions:
    • Set the gate bias \(V_G\) (a fixed DC voltage).
    • Measure or set the source voltage \(V_S\) so that \(V_{GS} = V_G – V_S\) is above \(V_{th}\) for saturation.
  2. Compute the Drain Current \(I_D\):
    • Calculate \(V_{GS} – V_{th}\).
    • Apply the equation \( I_D = \frac{1}{2} k’ \frac{W}{L} (V_{GS} – V_{th})^2 \) to obtain \(I_D\).
  3. Optional – Calculate \(V_{DG}\):
    • Measure the drain voltage \(V_D\) and compute \(V_{DG} = V_D – V_G\).

5. Practical Example

Example: Analyzing an n-Channel MOSFET in a Common Gate Amplifier

Given: Suppose we have the following parameters for an n-channel MOSFET:

  • \(V_G = 3.0\,V\) (Gate Bias)
  • \(V_S = 1.0\,V\) (Source Voltage)
  • \(V_{th} = 0.8\,V\) (Threshold Voltage)
  • \(k’ \frac{W}{L} = 0.5\,\text{mA/V}^2\)
  • \(V_D = 5.0\,V\) (Drain Voltage)

Step 1: Compute \(V_{GS}\)

\( V_{GS} = V_G – V_S = 3.0\,V – 1.0\,V = 2.0\,V \)

Step 2: Calculate Drain Current \(I_D\)

\( I_D = \frac{1}{2} \times 0.5\,\text{mA/V}^2 \times (2.0\,V – 0.8\,V)^2 \)

Compute the overdrive voltage:

\( V_{GS} – V_{th} = 2.0\,V – 0.8\,V = 1.2\,V \)

Now, calculate \(I_D\):

\( I_D = 0.25\,\text{mA/V}^2 \times (1.2\,V)^2 = 0.25\,\text{mA/V}^2 \times 1.44\,V^2 = 0.36\,\text{mA} \)

Step 3: (Optional) Compute Drain-to-Gate Voltage \(V_{DG}\)

\( V_{DG} = V_D – V_G = 5.0\,V – 3.0\,V = 2.0\,V \)

Results: The drain current is approximately \(0.36\,mA\) and the drain-to-gate voltage is \(2.0\,V\).

6. Common Applications

  • Amplifiers: Common gate configurations are used in high-frequency amplifiers where low input impedance is beneficial.
  • RF Circuits: Often found in radio-frequency applications for impedance matching.
  • Signal Buffering: Provides a stable DC operating point while preserving AC signal characteristics.
  • Switching Circuits: Used in digital circuits where fast switching and low capacitance are essential.

7. Conclusion

The Common Gate MOSFET Amplifier DC Analysis Calculator offers a systematic way to analyze a MOSFET operating in saturation within a common gate configuration. By calculating the drain current using the key MOSFET equation and optionally evaluating the drain-to-gate voltage, engineers can ensure proper biasing and reliable performance of the amplifier. This analysis is essential for designing robust, high-frequency circuits and optimizing signal buffering.