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Common source

The common-source amplifier is a fundamental configuration in field-effect transistor (FET) circuits, where the source terminal is grounded or serves as the common connection for both the input signal applied to the gate and the output signal taken from the drain, enabling voltage amplification of small AC signals superimposed on a DC bias while operating the FET in the saturation region.^[1]^[2] This setup inverts the phase of the output signal by 180 degrees relative to the input, providing a negative voltage gain typically greater than 1 in magnitude, such as -4.26 in example circuits.^[1]^[3] Key characteristics include a high input impedance, often in the range of several kiloohms to megohms due to the insulating gate structure of FETs, which minimizes loading on preceding stages, and a moderate output impedance determined by the drain resistor and the FET's output resistance.^[1]^[2] The small-signal voltage gain is given by A_v = -g_m (R_D \parallel r_o), where g_m is the transconductance (e.g., g_m = 2 K_n (V_{GS} - V_t) for MOSFETs), R_D is the drain load resistor, and r_o is the FET's output resistance.^[1]^[2] Biasing is achieved using a DC supply V_{DD} and gate-source voltage V_{GS} to set the quiescent point (Q-point) midway in the saturation region for linear operation, ensuring the drain current I_D remains stable against variations.^[3]^[2] This configuration offers advantages such as simplicity in design, suitability for integrated circuits due to efficient transistor usage over resistors, and effective linear amplification for applications like audio and RF signal processing.^[1]^[2] Compared to other FET amplifiers like common-drain (source follower) or common-gate, the common-source provides the highest voltage gain but with the phase inversion, making it ideal for stages requiring signal boosting without buffering.^[1] In practice, coupling capacitors are employed to isolate AC signals from DC bias, focusing operation in the mid-band frequency range for optimal performance.^[2]

Circuit Configuration

Basic Topology

The common source amplifier is a fundamental configuration of a field-effect transistor (FET) amplifier in which the source terminal serves as the common connection for both input and output signals.^[4] This topology is typically implemented using metal-oxide-semiconductor field-effect transistors (MOSFETs) or junction field-effect transistors (JFETs), providing high input impedance due to the insulated or reverse-biased gate.^[5] In the standard schematic, the input signal is applied to the gate terminal, the output is extracted from the drain terminal, and the source is grounded or connected to a common reference point. A drain resistor R_D connects the drain to the positive supply voltage V_{DD}, setting the DC load and enabling signal amplification, while a source resistor R_S (frequently bypassed by a capacitor C_S for AC coupling) may link the source to ground for stability. Gate biasing components, such as a gate resistor R_G to ground or a bias voltage source, ensure the transistor operates in its active region; input and output coupling capacitors C_{in} and C_{out} isolate DC while transmitting AC signals. The FET can be n-channel or p-channel, with connections adjusted accordingly for enhancement-mode MOSFETs or depletion-mode JFETs.^[5]^[4] The common-source configuration for FETs is analogous to the common-emitter amplifier for bipolar junction transistors. It evolved with the development of FETs, including the practical JFET demonstrated in 1953 by Dacey and Ross, and the MOSFET invented in 1959 by Atalla and Kahng.^[6]^[7] Proper biasing arrangements are crucial to establish the quiescent operating point for reliable amplification.^[5]

Biasing Arrangements

Biasing in a common source amplifier serves to establish a stable DC operating point by setting the gate-source voltage V_{GS} and drain-source voltage V_{DS} such that the MOSFET operates in the saturation (active) region, ensuring linear amplification while avoiding cutoff or triode regions.^[8] This quiescent bias point is critical for consistent performance across temperature and device variations.^[9] One common method is voltage divider bias, where two high-value resistors R_{G1} and R_{G2} form a divider from the supply V_{DD} to ground, setting a fixed gate voltage V_G = V_{DD} \cdot \frac{R_{G2}}{R_{G1} + R_{G2}}.^[10] With the source grounded, V_{GS} = V_G, and the drain current I_D follows from the MOSFET's transfer characteristic, typically I_D \approx \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{th})^2 (1 + \lambda V_{DS}).^[10] Additionally, I_D = \frac{V_{DD} - V_{DS}}{R_D}, where R_D is the drain resistor.^[9] This approach offers good thermal and supply stability due to the fixed V_G, but it requires more components and can lead to variations in V_{GS} if resistor values are not precisely matched to the device.^[8]^[10] Self-bias employs an unbypassed source resistor R_S to provide negative feedback for enhanced stability.^[9] Here, V_S = I_D R_S, so V_{GS} = V_G - V_S = V_G - I_D R_S, with V_G often zero for simplicity or set by a gate divider.^[9] The drain current is given by I_D = \frac{V_{DD} - V_{DS}}{R_D}.^[9] The R_S prevents thermal runaway by raising V_S as I_D increases with temperature, thereby reducing V_{GS} and limiting current growth.^[9] This method is simpler and uses fewer components than voltage divider bias, promoting single-supply operation, but the unbypassed R_S introduces degeneration that lowers the small-signal gain.^[9]^[10] Drain-feedback bias connects a resistor from drain to gate, establishing the bias through loop feedback.^[8] Applying Kirchhoff's voltage law yields V_{DD} = I_D R_D + V_{GS}, solving for I_D based on the device curve.^[8] This configuration achieves thermal stability via the feedback mechanism, similar to self-bias, and minimizes component count for compact designs.^[8] However, it provides less direct control over the exact V_{GS} compared to voltage divider methods, potentially complicating precise bias point selection.^[8]

Operating Principles

Small-Signal Analysis

Small-signal analysis of the common source amplifier employs a linearized model to evaluate the circuit's response to small AC perturbations around the DC bias point, assuming the transistor operates in its saturation region. This approach facilitates the prediction of amplification characteristics without considering nonlinear effects. The bias point, established through appropriate DC biasing arrangements, serves as the reference for these linear approximations.^[11] The hybrid-π model is the standard small-signal equivalent circuit for the MOSFET in this configuration. It represents the device with a voltage-controlled current source characterized by the transconductance parameter g_m = \frac{\partial I_D}{\partial V_{GS}} \big|_{Q}, where the derivative is evaluated at the quiescent bias point Q. This g_m quantifies the drain current sensitivity to gate-source voltage variations. The model also includes the output resistance r_o, which accounts for channel-length modulation and is typically large in saturation (on the order of tens to hundreds of kΩ). Additionally, the gate-source capacitance C_{gs} models the input parasitic capacitance, arising primarily from the oxide layer and given by C_{gs} = \frac{2}{3} C_{ox} W L + C_{ov}, where C_{ox} is the gate oxide capacitance per unit area, W and L are the channel width and length, and C_{ov} is the overlap capacitance; C_{gs} typically ranges from picofarads in small-signal devices. For low-frequency analysis, capacitors like the source bypass are treated as shorts, simplifying the circuit.^[12]^[13]^[11] The voltage gain A_v of the common source stage, defined as v_{out}/v_{in}, is derived by applying Kirchhoff's laws to the hybrid-π model with the source resistor R_S bypassed. The output current from the controlled source flows through the parallel combination of the drain resistor R_D and r_o, yielding

A_v = -g_m (R_D \parallel r_o),

where the negative sign indicates phase inversion. If r_o \gg R_D, this simplifies to A_v \approx -g_m R_D. For instance, in a MOSFET biased with g_m = 2 mS and R_D = 5 kΩ (assuming r_o is sufficiently large to neglect), the gain approximates A_v \approx -10. This derivation highlights the amplifier's ability to provide moderate voltage amplification with inherent phase shift.^[12]^[11] The input impedance looking into the gate is high, approaching infinity for an ideal FET due to the insulated gate structure, which draws negligible input current; in practice, it is limited by biasing resistors and C_{gs} at higher frequencies. The output impedance is approximately R_D \parallel r_o, dominated by R_D when r_o is large, making the stage suitable for driving lower-impedance loads when buffered. These impedance characteristics contribute to the common source topology's versatility in signal amplification.^[11]

Large-Signal Behavior

In large-signal operation, the common source amplifier exhibits nonlinear behavior when the input voltage amplitude exceeds the range where small-signal approximations hold, leading to distortion in the output waveform. This nonlinearity arises primarily from the quadratic relationship in the MOSFET's drain current versus gate-source voltage characteristic, which deviates from linearity at higher signal levels. As a baseline, the small-signal voltage gain provides the undistorted amplification factor, but large inputs push the transistor beyond its saturation region boundaries. Clipping occurs due to the finite output voltage swing limits imposed by the power supply rails and the MOSFET's operating regions. For a typical NMOS common source amplifier with the source grounded, drain resistor connected to V_DD, and input at the gate, a large positive input swing increases the gate-source voltage (V_GS), boosting drain current (I_D) and pulling the output voltage (V_out, at the drain) toward the lower rail; however, the transistor enters the linear (triode) region when drain-source voltage (V_DS) falls below V_DS,sat = V_GS - V_T, causing the negative output half-cycle to clip at approximately V_DS,sat. Conversely, a large negative input swing reduces V_GS below the threshold voltage (V_T), turning the MOSFET off and allowing V_out to rise to V_DD through the drain resistor, clipping the positive output half-cycle at V_DD. This results in asymmetric distortion, with the clipped waveform showing a flatter top (at V_DD) and a more rounded bottom (near V_DS,sat), limiting the maximum undistorted peak-to-peak output to roughly V_DD - V_DS,sat. Harmonic distortion in the common source amplifier stems from the nonlinear transfer characteristic of the MOSFET, particularly the square-law dependence of I_D on V_GS in saturation, which generates even-order (primarily second) and odd-order (primarily third) harmonics in the output spectrum. The second harmonic arises from the quadratic term in the device's Taylor series expansion, while the third harmonic results from the cubic term, leading to gain compression for large signals. Total harmonic distortion (THD) quantifies this as the ratio of the root-sum-square of harmonic amplitudes to the fundamental; higher overdrive voltage (larger V_DS,sat) reduces distortion for a given input swing at the cost of reduced swing headroom. Slew rate limitations in large-signal transients are imposed by the need to charge the MOSFET's gate capacitance, exacerbated by the Miller effect in the common source configuration. During rapid input voltage changes, the gate-to-drain capacitance (C_GD) experiences amplified voltage swings across the drain (output) node, effectively multiplying the capacitive load seen by the input drive circuit and slowing the rate of V_GS change; this is particularly pronounced during turn-on when the falling drain voltage feeds back to hold V_GS constant until saturation. Low-impedance drive sources are essential to supply the required charging current and mitigate this bottleneck. Power considerations in class A operation highlight the trade-off between linearity and efficiency, with the maximum output swing limited to approximately V_DD - V_DS,sat to maintain saturation. The amplifier dissipates quiescent power equal to (V_DD - V_SS) I_Q, where I_Q is the bias current, while the maximum AC output power to a load R_L is (V_out,peak²) / (2 R_L); the resulting efficiency peaks at 25% when the bias point allows V_out,peak = (V_DD - |V_SS|)/2, far below that of switching classes due to continuous conduction.

Performance Characteristics

Voltage Gain

The midband voltage gain of a common source amplifier, derived from small-signal analysis, is given by A_v = -\frac{g_m R_D}{1 + g_m R_S} for the case of an unbypassed source resistor R_S, where g_m is the transconductance, and R_D is the drain resistance.^[14] The negative sign indicates a 180° phase inversion between input and output signals.^[14] This expression assumes the output resistance r_o of the MOSFET is much larger than R_D; otherwise, the effective load becomes R_D \parallel r_o. The magnitude of the voltage gain varies with the load resistance R_L, as the effective output resistance is R_D \parallel R_L, reducing |A_v| when a finite R_L is connected.^[14] Additionally, temperature affects g_m, which typically decreases with increasing temperature due to reduced carrier mobility, thereby lowering the gain.^[15] An unbypassed R_S introduces negative feedback through source degeneration, which reduces the gain magnitude but enhances linearity by mitigating variations in g_m and improves bias stability with a stability factor S = 1 + g_m R_S.^[14]^[16] Typical midband voltage gains for common source amplifiers range from 10 to 100 at audio frequencies, depending on device parameters and biasing. For example, in a circuit with g_m = 5 mS, R_D = 5 kΩ, and R_S = 0 Ω (bypassed case for reference), the gain magnitude is |A_v| = 25; introducing R_S = 1 kΩ yields |A_v| \approx 4.2.^[14]

Bandwidth and Frequency Response

The low-frequency response of a common source amplifier is primarily shaped by the coupling and bypass capacitors, which introduce high-pass filter characteristics that attenuate signals below the midband range. These capacitors, in conjunction with the associated resistances, form time constants that determine the lower cutoff frequency f_L = \frac{1}{2\pi RC}, where RC represents the input or output coupling time constant; for instance, the input coupling capacitor interacts with the signal source resistance, while the output capacitor couples to the load resistance.^[17] At high frequencies, the amplifier's performance is limited by the FET's parasitic capacitances, with the gate-drain capacitance C_{gd} playing a dominant role due to the Miller effect, which multiplies it to an effective input capacitance C_{Miller} = C_{gd} (1 + |A_v|), where |A_v| is the magnitude of the midband voltage gain. This amplified capacitance, in parallel with the gate-source capacitance C_{gs} and combined with the drain resistance R_D, sets the upper cutoff frequency at the dominant pole f_H = \frac{1}{2\pi R_D C_{Miller}}, causing the gain to roll off and reducing the overall usable bandwidth.^[18] The gain-bandwidth product of the common source configuration, which quantifies the trade-off between amplification and frequency range, approximates \frac{g_m}{2\pi (C_{gs} + C_{gd})}, where g_m is the transconductance; for discrete FETs in older technologies, this product typically reaches around 100 MHz. In a Bode plot of the magnitude response, the gain remains flat in the midband region between f_L and f_H, with a +20 dB/decade rise at low frequencies below f_L and a -20 dB/decade roll-off at high frequencies above f_H, due to the single-pole high-pass and low-pass behaviors, respectively.^[18]

Applications and Comparisons

Practical Uses

Common source amplifiers are extensively employed in audio applications, particularly as preamplifier stages for electric guitars and microphones, where their high input impedance—often exceeding several megaohms—prevents excessive loading of weak signal sources like piezoelectric pickups or dynamic capsules. This configuration also provides inherent phase inversion, which facilitates single-ended to differential conversion or compensates for phase shifts in multi-stage designs. For instance, JFET-based common source stages are cascaded in microphone preamplifiers to deliver 20-40 dB of gain while preserving signal integrity and minimizing distortion. In guitar preamps, similar topologies enhance tonal warmth and sustain by amplifying low-level signals from magnetic or piezo transducers without introducing significant noise.^[19] In radio frequency (RF) systems, common source amplifiers function as core elements in low-noise amplifiers (LNAs) for receiver front-ends and intermediate frequency (IF) stages, leveraging tuned LC loads to provide narrowband gain peaking at specific frequencies, such as 2.4 GHz for wireless communications. Recent advancements include stacked and cascode common source topologies in mmWave power amplifiers for 5G and beyond, achieving high output power and efficiency in frequencies up to D-band (110-170 GHz).^[20] This setup achieves high linearity and low noise figures, typically below 2 dB, essential for maintaining signal-to-noise ratios in broadband receivers. Additionally, they integrate into active mixers for downconversion, where the amplifier's transconductance supports efficient frequency translation with minimal intermodulation distortion.^[21] Within integrated circuits, the common source topology is a fundamental building block in CMOS operational amplifiers, often serving as the high-gain second stage after a differential input pair to boost the overall open-loop gain to 80-100 dB while driving subsequent loads. This arrangement has been pivotal in VLSI implementations since the 1970s, enabling compact analog front-ends in mixed-signal chips for applications like data converters and sensors. For example, in a typical two-stage op-amp, the common source stage uses a current-source load to maximize output swing and efficiency in sub-micron processes.^[22]^[23] Key design trade-offs for common source amplifiers center on optimizing voltage gain, which can reach 20-40 dB, against bandwidth limitations imposed by Miller capacitance and load parasitics, often resulting in a gain-bandwidth product of several MHz in CMOS realizations. FET variants excel in low noise figures (around 1-3 dB) due to their minimal 1/f noise, making them suitable for precision audio and RF, but increasing bias current to enhance gain or speed elevates power consumption, necessitating careful sizing for battery-operated systems. In 45 nm CMOS, for instance, single-stage designs trade higher gain for reduced power (sub-1 mW) at the expense of bandwidth below 100 MHz.^[24]^[25]

Relation to Other FET Configurations

The common source (CS) amplifier configuration provides voltage gain greater than unity while exhibiting high output impedance, which can lead to significant loading effects in cascaded stages. In comparison, the common drain (CD) amplifier, or source follower, delivers approximately unity voltage gain with low output impedance, making it preferable for impedance matching and buffering applications where minimal signal distortion from loading is required.^[4]^[26]^[27] Relative to the common gate (CG) configuration, the CS offers high input impedance, rendering it well-suited for voltage-driven inputs, whereas the CG features low input impedance for current-based inputs, higher bandwidth due to reduced Miller effect, and no phase inversion. The CS introduces a 180-degree phase shift between input and output, unlike the non-inverting behavior of the CG.^[4]^[26]^[28]^[27] To mitigate limitations such as bandwidth constraints and poor isolation in the standalone CS, it is often paired with a CG stage in a cascode topology, where the CS serves as the input stage and the CG as the output stage; this arrangement yields improved high-frequency response, enhanced output resistance, and better isolation between input and output, with voltage gain approximately equal to g_{m1} R_D.^[29] The CS configuration is selected for general-purpose voltage amplification due to its balanced trade-offs in gain and impedance, a principle established in foundational texts on field-effect transistor circuits from the 1960s and 1970s.^[30]

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