Noise considerations
First of all, BIG THANKS to Jarek Rutkowski for doing the math - I've just repeated it for the photodiode we have in the current FSI FMC design:
The total voltage noise density of the OPA857 can be calculated from the following formula:
e_opa = Gt * sqrt(in_opa^2 + (NEP * R)^2) [1]
Where:
Gt =
transimpedance gain
in_opa =
input referred current noise density of the TIA
NEP =
noise equivalent power of the photodiode
R =
responsivity of the photodiode [A/W]
For the photodiode used in the design (FCI-InGaAs-120):
NEP = 4.50E-15
R[typ] = 0.9
For the low gain setting of the OPA857:
Gt = 5 kOhm
in_opa = 2.5 pA/sqrt(Hz)
Putting the above data in [1]:
e_opa = 12.5 nV/sqrt(Hz)
In case of the high gain regime, the corresponding e_opa
is around 30 nV/sqrt(Hz)
The rms noise power over a bandwidth is an integral of the noise power density over the bandwidth. Let's for the sake of simplicity assume the distribution is flat, this simplifies then to:
v_noise_rms = sqrt( e_opa^2 * BW ) [2]
For the design BW = 100 MHz, the result of [2] is
v_noise_rms = 125 uV
(for the low-gain setting)
and
v_noise_rms = 300 uV
(for the high-gain setting)
Note that the above calculations are for ideal case and only consider the noise of the TIA and photodiode (no PSRR effects/ADC noise/driver noise taken into account), so they can be assumed the best we can (theoretically) get.
The ADC full scale is 2V peak-peak, so assuming the ADC is ideal, one LSB scales to:
Vlsb = 345 uV rms.
Given that the actual ENOB
is 11.4, we can add a fraction of a decibel to get the actual ADC noise level:
Vlsb(enob) ~~ 500 uV rms
The above value is comparable with the rms noise of the TIA alone.
The circuit submitted for a review includes a 20dB amplification stage post-TIA followed by an even larger gain attainable by the subsequent DVGA.
So in the least noisy case, the ADC (with the THS4541 alone) will see:
v_noise_rms = 1.25 mV
. This corresponds to two bits of ADC resolution which are "consumed" by noise.
The optimal THS4541 gain noise-wise would be therefore around 6 dB (2x) instead of 20 dB (10x) (just as the TI's application diagram in the OPA857 datasheet says...)
Furthermore, the DVGA following the THS4541 has no beneficial effects on the system's sensitivity/dynamic range, as it is defined by the choice of the photodiode and the TIA. All subsequent elements of the amplification chain just amplify the TIA+PD's noise and reduce the dynamic range of the acquisition chain instead of improving it.