Some photodiode applications operate in dark conditions and require low-light detection. In these cases, the current output from the photodiode can be miniscule. To make the small diode current measurable, a transimpedance amplifier (TIA) with a very large gain is required. The ideal transfer function of a resistive transimpedance amplifier is given by Equation 1:

The photodiode current (I_PD) flows through the feedback resistor (R_F) and forces an output voltage (V_OUT) equal to the voltage drop across R_F. The ideal transfer function gives an intuitive understanding of TIA operation. In practice, however, nonidealities must be taken into consideration to achieve desirable performance. Figure 8-6 illustrates important nonidealities of the transimpedance amplifier circuit.

One very important consideration, is the input bias current of the op amp. The input bias current directly adds to I_PD and creates an undesired error. The input bias current typically determines the minimum measurable I_PD within a given error tolerance. For example, a 1‑pA input bias current yields a 20% error when measuring a 5‑pA photodiode current. A 1% error target requires a 50-fA input bias current maximum specification. The ultra-low input bias current of the OPA928 enables accurate, extremely low I_PD measurements. For information on how to maintain the specified input bias performance, see Section 8.4.

The input offset voltage (V_OS) of the op amp is another significant source of error. The input offset voltage forces a voltage across the effective shunt resistance of the diode (R_D) and creates an error current (I_RPD) equal to V_OS / R_PD. In many cases, V_OS can be a major source of error. For example, a V_OS of 25 μV and an R_PD of 1 GΩ creates an I_RPD of 25 fA. Take into consideration offset voltage variation with temperature and common-mode voltage.

In low-light applications, a very large R_F is needed to provide the required gain, giving rise to potential stability problems. R_F interacts with the input capacitance (C_IN) of the op amp, the photodiode capacitance (C_PD), and stray PCB capacitance to create a low-frequency zero in the noise gain transfer function (1/β). Remember that C_IN includes the differential (C_DF) and common-mode (C_CM) capacitance of the op amp. The value of C_DF and C_CM are found in the Electrical Characteristics. The zero in 1/β causes the gain to increase over frequency and is the basis for instability problems. To counteract the zero, create a pole by adding a compensation capacitor (C_F) in the feedback loop. The optimal value selection of C_F depends on several parameters and extensive literature exists on this topic. One approach is to equate two expressions of noise gain. Equation 2 makes the assumption that the noise gain only depends on the capacitance of the circuit at a high enough frequency; a reasonable approximation.

Solving Equation 2 for C_F yields a quadratic equation with one real solution. The quadratic equation is given by Equation 3:

Equation 3 yields more than 45° of phase margin and some amount of gain peaking. Increasing the value of C_F yields a higher phase margin and limits the peaking response at the expense of signal bandwidth, given by Equation 4. For a flat frequency response, use a compensation capacitor calculator. For a very large R_F, a very small capacitor (< 0.5 pA) is required to maintain stability, and stray capacitance in the feedback loop can be sufficient.

Another issue arises when using a very large R_F. All resistors are sources of thermal noise. The magnitude of noise density contribution from a resistor is directly correlated to the square root of the resistance value. In a gain configuration, the feedback resistance and input resistance contribute to the total noise of the circuit. The thermal noise resistance value in Figure 8-6 is given by the parallel combination of R_F and R_PD. Equation 5 shows the input-referred-resistor noise-density equation. The low voltage noise of the OPA928 is not a significant contributor of noise because R_F and R_PD are typically very large.

In this application, a 5-V output is required from the 500-pA current input from a Si photodiode. A 10-GΩ resistor is used to achieve the required gain of 10,000,000,000 V/A. R_PD and C_PD of the photodiode is assumed to be 5 GΩ and 35 pF, respectively. Using the specifications of the OPA928 and the aforementioned photodiode specifications, Equation 3 calculates C_F to be approximately 0.017 pF. The value obtained by calculation is impractical; therefore, the smallest standard capacitor available is used (1 pF). If settling time is a major concern, consider making the required small-value capacitor using PCB traces.