MOSFET Common-Source Amplifier

The common-source amplifier is the fundamental voltage-amplifying stage for MOSFETs, forming the backbone of analog integrated circuits and discrete designs. Its exceptionally high input impedance allows it to interface seamlessly with sensors and previous stages without loading them down, while providing substantial voltage gain. Mastering its operation, from the basic configuration to techniques for improving linearity, is essential for designing everything from audio preamps to the core gain blocks of operational amplifiers.

Basic Configuration and DC Biasing

Before a MOSFET can amplify an AC signal, it must be properly biased into its saturation region of operation. This involves establishing stable DC voltages at the gate, drain, and source terminals using a resistive network or current sources. A common method is fixed bias with a source resistor, where a voltage divider sets the gate voltage ($V_G$), and a resistor at the source ($R_S$) provides negative feedback for stable DC operating point. The key is to set the drain-source voltage ($V_{DS}$) high enough to ensure the transistor remains in saturation for the entire swing of the input signal. The DC analysis focuses on finding the quiescent point, or Q-point, defined by the drain current ($I_D$) and $V_{DS}$. Since the gate draws negligible DC current, the gate voltage is set simply by the voltage divider, making the input impedance at DC extremely high.

AC Operation and Voltage Gain

When a small-signal AC voltage ($v_{in}$) is applied to the gate, it modulates the channel conductivity, creating a corresponding AC drain current ($i_d$). This current flows through the impedance connected to the drain, producing an amplified output voltage. The core relationship is governed by the transistor's transconductance ($g_m$), which measures how much the drain current changes for a given change in gate-source voltage ($i_d=g_m\ast v_{gs}$).

The most basic common-source amplifier uses a drain resistor ($R_D$) to convert the AC drain current into an output voltage. The voltage gain ($A_v$) is the ratio of the output voltage at the drain to the input voltage at the gate. Since an increase in gate voltage causes an increase in drain current, which in turn causes a decrease in drain voltage (due to the voltage drop across $R_D$), the output is inverted. Therefore, the small-signal voltage gain is: $$A_v=-g_m{R}_D$$ The negative sign explicitly denotes this phase inversion of 180 degrees between input and output. The input impedance in the AC small-signal model is essentially infinite at low frequencies, as the gate oxide insulator prevents any AC current from flowing into the gate terminal.

The Role of Source Degeneration

Adding a resistor ($R_S$) in the source leg that is not bypassed by a large capacitor has a profound effect on the amplifier's AC performance. This technique is called source degeneration. The resistor introduces local negative feedback: if the drain current tries to increase, the voltage across $R_S$ increases, which reduces the effective gate-source voltage ($v_{gs}$), counteracting the original change.

This feedback significantly improves linearity and gain stability. Without $R_S$, the gain depends directly on $g_m$, which is a nonlinear function of the transistor's bias point. With $R_S$, the gain becomes less sensitive to variations in $g_m$ and transistor parameters, making the circuit more predictable and stable over temperature and manufacturing tolerances. However, this benefit comes at the expense of reduced voltage gain. The new gain equation with source degeneration is: $$A_v=-\frac{g_m{R}_D}{1+g_m{R}_S}$$ For large $g_m{R}_S$, the gain approximates $-R_D/R_S$, becoming entirely determined by the resistor ratio and much more linear, similar to the effect of emitter degeneration in BJT common-emitter amplifiers. This makes the degenerated common-source stage an excellent voltage-controlled current source or a highly linear amplifier when gain can be sacrificed.

Common Pitfalls

1. Incorrect DC Bias Point: The most common error is failing to properly bias the MOSFET in the saturation region for the entire AC signal swing. If the Q-point is too low, the positive output swing will push the transistor into the triode (linear) region, causing clipping and distortion. Always verify that $V_{DS}>V_{GS}-V_{th}$ (the overdrive voltage) at the Q-point and throughout the expected output voltage range.
2. Neglecting the Output Impedance: The voltage gain formula $A_v=-g_m{R}_D$ assumes the load impedance is infinite. In practice, connecting a load resistor ($R_L$) in parallel with $R_D$ reduces the effective drain resistance and thus the gain. The correct calculation for a loaded amplifier is $A_v=-g_m(R_D||R_L)$. Overlooking this leads to overestimating the actual circuit gain.
3. Misunderstanding Source Bypassing: A source resistor ($R_S$) is often used for DC stability and is then "bypassed" by a large capacitor ($C_S$) to provide an AC ground at the source terminal, restoring the full gain ($-g_m{R}_D$). Forgetting this bypass capacitor when full gain is desired, or using one that is too small (creating a high-pass filter that attenuates low-frequency signals), are frequent practical mistakes. The capacitor's impedance at the lowest frequency of interest must be much less than $R_S$.
4. Ignoring High-Frequency Limitations: While the input impedance is nearly infinite at low frequencies, the capacitance between the gate and source ($C_{gs}$) and gate and drain ($C_{gd}$) becomes significant at high frequencies. $C_{gd}$ provides a feedback path that can cause frequency roll-off and instability. Thinking of a MOSFET amplifier as having infinite input impedance at all frequencies is a critical oversight in high-speed design.

Summary

• The MOSFET common-source amplifier provides high voltage gain with a 180-degree phase inversion between input and output, and features very high input impedance because the gate draws negligible DC current.
• Its small-signal voltage gain is approximately $A_v=-g_m{R}_D$, where $g_m$ is the transistor's transconductance and $R_D$ is the drain resistance.
• Source degeneration, achieved by adding an unbypassed resistor ($R_S$) in the source leg, introduces negative feedback. This improves circuit linearity and gain stability but reduces the overall voltage gain according to the formula $A_v=-g_m{R}_D/(1+g_m{R}_S)$.
• Proper DC biasing into the saturation region is critical for undistorted amplification, and the impact of load impedance and parasitic capacitances must always be considered in practical designs.