How much noise is too much noise in a photodiode-preamplifier circuit? You can derive the noise performance of a transimpedance amplifier (Figure 1a) with calculations or by using a Spice simulation (Reference 1). When calculating the noise performance of the circuit, consider six regions in the frequency spectrum (Figure 1b) and add each region with a root-sum-square equation or the following equation (Reference 2):

The first five regions are equal to the multiple of the areas under the closed-loop-gain and amplifier-noise-density curves. The area under the noise-density curve in the e₁, flicker-noise (1/f), region is V_1/f:fB–fA=A_N, where A_N is the amplifier’s input-noise-density at 1 Hz and f_B is the corner frequency where the flicker noise tapers off. For many CMOS or FET amplifiers, the flicker-noise region usually ranges from dc to 100 or 1000 Hz. A calculation proves that the contribution to noise in this low-frequency region is relatively low:

where R_F is the feedback resistor and R_PD is the device’s parallel resistance.

In the e₂ region, multiply the broadband noise of the amplifier, the closed-loop dc-noise gain (1+R_F/R_PD), and the square root of the region’s bandwidth. Again, the contributed noise in this region is usually relatively low because of its location in the lower frequency range.

Calculate the noise contribution and the e₃ region in the same manner with f_P=1/[2π(R_PD||R_F) (C_PD+C_CM+C_DIFF+C_F+C_RF)] and f_Z=1/[2π(R_F) (C_F+C_RF)].

where C_PD is the device’s capacitance and C_DIFF is the differential amplifier’s capacitance.

The noise in regions e₄ and e₅ uses the higher-frequency gain of the closed-loop-gain curve with the value of C₁ being the parallel combination of the input capacitors, or [C_P–R1||2C_CM||C_DIFF], and C₂ is the parallel combination of C_F and C_RF.

The sixth part of the noise equation, e₆, represents the noise contribution of the feedback resistor. The amplifier does not gain the contribution of noise from the feedback resistor:

where K is Boltzmann’s constant, which is 1.38×10^–23; T is temperature in Kelvin; R_F is the feedback resistor in ohms; and BW is the bandwidth of interest.

When asking how much noise is too much noise in this photodiode-preamp circuit, consider that a 12-bit system operating with a 5V input range has an LSB of 1.22 mV. The LSB for a 16-bit system with the same input-voltage range is 76.29 µV. Both LSBs are peak-to-peak numbers, and the values in this column are root-mean-square values (Reference 3).