How To Find Pole Of Common Source Amplifier

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Post on Feb 09, 2025

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How To Find the Pole of a Common Source Amplifier

The common source amplifier is a fundamental building block in many analog circuits. Understanding its frequency response, particularly locating its dominant pole, is crucial for designing stable and high-performance circuits. This article will guide you through the process of finding the pole of a common source amplifier.

Understanding the Common Source Amplifier and its Frequency Response

A common source amplifier uses a field-effect transistor (FET), typically a MOSFET or JFET, to amplify an input signal. The gate is the input, the source is the output, and the drain is connected to a DC power supply through a load resistor. At low frequencies, the gain is relatively constant. However, at higher frequencies, parasitic capacitances within the transistor and the circuit itself significantly affect the amplifier's performance. These capacitances create poles in the amplifier's transfer function, leading to a decrease in gain and potential instability. The dominant pole is the pole that determines the low-frequency cutoff, also known as the bandwidth.

Identifying the Dominant Pole

The dominant pole in a common source amplifier is typically determined by the combination of the transistor's output capacitance (C_out) and the total resistance seen at the output node (R_out). Let's break down how to find these values:

1. Determining the Output Resistance (R_out)

R_out is the resistance seen looking into the drain terminal of the MOSFET. It's a parallel combination of several resistances:

• The load resistor (R_L): This is the resistor connected between the drain and the power supply.
• The MOSFET's output resistance (r_o): This is an intrinsic parameter of the MOSFET, representing the resistance looking into the drain with the gate shorted to the source. It's often found in the MOSFET's datasheet and is dependent on the bias point.

Therefore, R<sub>out</sub> = R<sub>L</sub> || r<sub>o</sub> where "||" denotes parallel resistance.

2. Identifying the Output Capacitance (C_out)

C_out is the total capacitance at the output node. It's often a combination of several capacitances:

• MOSFET's output capacitance (C_ds or C_db): This is the capacitance between the drain and the source (C_ds) or drain and the bulk (C_db) and is given in the MOSFET's datasheet.
• Load capacitance (C_L): This represents any external capacitance connected to the output node, including stray capacitances. This can be significant and shouldn't be neglected.
• Miller capacitance (C_Miller): This is a parasitic capacitance that is amplified by the amplifier's gain. It's formed by the gate-to-drain capacitance (C_gd) and significantly affects high-frequency performance. Calculating C_Miller requires considering the amplifier's mid-band gain (A_v): C<sub>Miller</sub> ≈ C<sub>gd</sub>(1 + |A<sub>v</sub>|). This capacitance contributes heavily to the overall C_out.

The total output capacitance is the sum of these capacitances: C<sub>out</sub> = C<sub>ds</sub> + C<sub>db</sub> + C<sub>L</sub> + C<sub>Miller</sub>

3. Calculating the Pole Frequency (f_p)

Once you have R_out and C_out, you can calculate the pole frequency (f_p) using the following formula:

f<sub>p</sub> = 1 / (2πR<sub>out</sub>C<sub>out</sub>)

This f_p represents the frequency at which the amplifier's gain drops by 3dB (approximately 70.7% of its mid-band gain). This is the dominant pole frequency.

Example

Let's say we have a common source amplifier with: R_L = 1 kΩ, r_o = 100 kΩ, C_ds = 1 pF, C_db = 0.5 pF, C_L = 2 pF, C_gd = 0.2 pF, and a mid-band gain A_v = -10.

1. R_out = 1 kΩ || 100 kΩ ≈ 990 Ω
2. C_Miller ≈ 0.2 pF (1 + 10) = 2.2 pF
3. C_out = 1 pF + 0.5 pF + 2 pF + 2.2 pF = 5.7 pF
4. f_p = 1 / (2π * 990 Ω * 5.7 pF) ≈ 28.2 MHz

Therefore, the dominant pole of this common source amplifier is approximately 28.2 MHz. Frequencies above this will experience significant gain roll-off.

Conclusion

Finding the dominant pole of a common source amplifier involves careful consideration of the output resistance and capacitance. Accurate determination of these parameters, particularly the Miller capacitance, is crucial for predicting the amplifier's high-frequency behavior and designing for stability. Remember to always consult the datasheet for the specific device being used. This detailed analysis allows for better circuit design and optimization.