Gain Calculation of MOS Transimpedance Amplifier

The gain of a MOSFET-based transimpedance amplifier is primarily determined by the feedback resistor and the MOSFET's transconductance, expressed as V_out/I_in ≈ R_f in the ideal case.

Basic Principle

A transimpedance amplifier (TIA) converts an input current $I_{in}$ into an output voltage $V_{out}$. In a MOSFET TIA, the MOSFET acts as the active element controlling the current through the feedback network. The simplest gain expression is:

where $R_f$ is the feedback resistor between the MOSFET drain (or op-amp output) and the inverting input node. The negative sign indicates an inverting configuration, typical for TIAs .

MOSFET Contribution

For a MOSFET in the saturation region, the drain current is:

where $k$ is the MOSFET gain factor, $V_{GS}$ is the gate-source voltage, and $V_T$ is the threshold voltage . The MOSFET's transconductance $g_m$ is:

This transconductance affects the effective gain when the MOSFET is used as the active element in the TIA. The small-signal voltage gain of a common-source MOSFET stage is:

where $R_D$ is the drain resistor. In a TIA configuration, $R_D$ is replaced by the feedback resistor $R_f$, giving the transimpedance gain:

for ideal MOSFET operation with high $g_m$ and negligible channel resistance .

Practical Considerations

1. Feedback Resistor Selection: A larger $R_f$ increases gain but reduces bandwidth and increases thermal noise. The -3dB bandwidth can be estimated as:

where $C_f$ is the feedback capacitance, including parasitic capacitances . 2. MOSFET Biasing: Proper gate bias ensures the MOSFET operates in saturation for linear amplification. The Q-point must be chosen to maximize linearity and avoid clipping . 3. Noise Considerations: The total output noise includes contributions from the feedback resistor, MOSFET channel noise, and input current noise. The feedback resistor dominates at low frequencies, while shot noise from the input current source may dominate at higher frequencies . 4. Stability: Adding a small feedback capacitor $C_f$ can stabilize the TIA by compensating for input capacitance and preventing oscillations .

Summary Formula

For a MOSFET-based TIA, the approximate transimpedance gain is:

with the MOSFET's transconductance ensuring the current-to-voltage conversion remains linear. The exact gain depends on MOSFET parameters, feedback resistor, and parasitic capacitances, and should be verified with small-signal analysis or simulation .