Transimpedance amplifier bandwidth limit
What limits the bandwidth you can achieve on a transimpedance
  amplifier?


I take it that this question might be related to why a feedback capacitor is placed across the transimpedance feedback resistor in many designs; particularly for photodiode amplifiers like this: -



See the 3.8 pF capacitor I refer to - it reduces the bandwidth considerably in some designs and it is there for a reason. To understand that reason you have to consider that every op-amp has a noise source inside its inputs. Data sheets refer to this as \$e_n\$ usually. So imagine a non-inverting amplifier configuration that has got \$e_n\$ at its non-inverting input to 0 volts and, on the inverting input there is the normal feedback resistor from the output plus a capacitor from the input to 0 volts.

That capacitor I refer to is the self-capacitance of the photodiode.

Next, ask yourself what the non-inverting gain equation of this circuit is when formed by a feedback resistor and a capacitor (maybe 1 pF to hundreds of pF). At high frequencies the non-inverting gain is very high. The feedback resistor might be 1 Mohm as per the diagram above and the photodiode might have 10 pF of capacitance. This means, that at a frequency of only 15.9 kHz, the gain is starting to peak.

What effect does this have?

It starts to amplify the self-generated input noise of the op-amp and this can be a problem. By 159 kHz the noise amplitude is ten times higher than at 15.9 kHz and you should be able to see that the only thing that can limit this noise-gain is the open-loop bandwidth of the op-amp.

Below is a picture of the open-loop gain of a fast op-amp. The open loop gain is in blue: -



In red is the resulting TIA gain non-inverting voltage gain; it begins at low frequencies at a value of 1 (0 dB) and at 15.9 kHz starts to rise at 20 dB/decade as the photodiode self-capacitance starts to have an effect. The green line I have shown is the effect of adding a feedback capacitor - it reduces the noise gain of the circuit.

So, if you want a reasonably clean waveform from your photodiode amplifier you have to counter the effect of what is called "noise-gain" and this means slugging the response significantly. Remember the added capacitor only attempts to clean the noise from the circuit but every pF added directly slugs the main signal from the photodiode.

It doesn't have to be a photodiode of course; any current signal to be amplified by a TIA (transimpedance amplifier) can have self-capacitance or cable capacitance in the wiring and this will bring about the same problem.