How to determine the bandwidth of an op-amp in this case?

Regarding a TIA amplifier such as below:

If IPD is a pulsed current produced by the photodiode and if the pulse width is 1 ns, what bandwidth of op-amp would be necessary?

EDIT: I also don't care about output as a pulse shape. I need the DC average at the output. What I don't know is: do I still need a large BW opamp since the current pulse is 1ns. I need DC average of the current pulse train at the output by adjusting R and C; but I want the average to be proportional to the photodiode current pulse train. So in such case, I dont need the replica of the pulse but the average. Do I still need an opamp with large BW?

• It depends on the pulse input amplitude and pulse output amplitude and shape. And Rf and Cf as they are a low pass filter anyway. Can you give any more info? Commented Jan 6 at 22:38
• GNZ - Hi, To comply with the site rule on referencing, please can you edit your question & add the document or webpage name & link of the source of that image. TY Commented Jan 6 at 22:40
• @Justme 1ns current pulse amplitude I guess less than 1A. I estimate it from diode model. Shape must be Gaussian.
– GNZ
Commented Jan 6 at 22:51
• @Justme I also dont care about output as a pulse. I need the DC average at the output. So Rf and Cf is fine. But what i dont know is: do I still need a large BW opamp since the current pulse is 1ns.
– GNZ
Commented Jan 6 at 22:53
• @GNZ I also dont care about output as a pulse. I need the DC average at the output. This critical bit of information changes the nature of your question. Please edit the question to add all the missing information, and then delete your comments that the edits have made redundant. The place for clarifying information is in the question itself, the comments are only here to request the information from you. Commented Jan 7 at 2:19

As a general rule, the minimum bandwidth required to pass a pulse of width T is 1/T. Thus for a 1 nsec pulse, you need a bandwidth of at least 1 GHz. To further narrow down the requirement, though, you need to specify the accuracy of your application. To faithfully reproduce the pulse would require at least 3 GHz.

• Isn't the bandwidth dependent on the rise and fall times of the pulse edges? It makes a difference if the 1ns pulse has 1ns or 1ps rise and fall times. Commented Jan 6 at 23:22
• For a Gaussian pulse, and assuming the duration is full width, half max then I believe the coefficient is actually 0.31 rather than 1, so the 3dB bandwidth of the pulse would be 310 MHz. If you wanted 3x higher bandwidth to avoid broadening, that would be about 930 MHz. Commented Jan 7 at 0:53
– GNZ
Commented Jan 7 at 11:19

For a 1 ns Gaussian pulse the 3dB bandwidth is 310 MHz.

For a 3 MHz repetition rate, the rate is, well, 3 MHz.

If you want to resolve each pulse you will need a bandwidth greater than 310 MHz, with higher capturing more of the tail after the 3dB point.

In this case though you want to average over one cycle rather than resolve pulses, so your bandwidth must be less than 3 MHz. Since you will probably want to reject noise and random intensity variation, you should average over many pulses. Normally I would suggest ten or twenty minimum, but since your repetition rate is pretty high and you don't need a fast update rate, 300,000 might be a good number. That would be a 10 Hz bandwidth. Of course you can pick higher bandwidth for faster updates or lower bandwidth for higher SNR.

• Thank you for the answer. To lower the opamp BW down to 10Hz should I insert a cap between the inverting input of the TIA and the ground?
– GNZ
Commented Jan 7 at 19:53
• @GNZ No, that would do bad things to the amplifier's stability. I would pick a slower, relatively low noise amplifier and then add an external low pass filter after the TIA stage to bring the bandwidth down the rest of the way. Commented Jan 7 at 19:54
• I see, do you mind if I open another question directly related to this providing a circuit and simulation? Would be glad to hear your feedback.
– GNZ
Commented Jan 7 at 19:57