I'm attempting to build an amplifier for a photomultiplier to measure transient pulses of light with a characteristic time constant on the order of a few microseconds and rising edge of a few nanoseconds. The anode is terminated into 50 ohms (for speed reasons), and the voltage across that resistor is amplified in three stages by three noninverting AD797s, each with a gain of 10. The configuration is the same at each stage: it's nearly the same as shown in Figure 39 of the AD797 datasheet, with R1=33.2 ohms, R2=300 ohms, Cl=5 pF. There is no resistor RL to ground, although I have a 300 ohm resistor followed by a protection diode to ground (Vbias=0.5 V) in between Vout and Vin for two successive stages. I do not have bypass capacitors, although I am using an Acopian +/-15 V linear regulated supply.
Now for the problem: Amplification after one stage works fine, with little to no distortion and a gain of 10 as expected. After two stages, however, I see a significant droop/backswing in the pulse. I've attached an Excel file with an example waveform (note, the photomultiplier produces a negative voltage across the terminating resistor, and its peak was clipped by the oscilloscope since it was off-scale). The third stage does not work at all. Even with no light input, the output at this stage oscillates between +/-2 V.
In regards to the former problem, there are two things I can think of trying: lower the gain per stage or adding a small load resistor to ground between each stage. The first is just based on intuition, but in the second case I wonder if the added resistor could serve to discharge any input capacitance present int the AD797 inputs that may be charging up during the pulse.
For the second problem, I can only guess that I would need to lay out my board better. I've attempted to keep leads as short as possible, with the largest ones being ~1 cm. Note that all elements are soldered into a breadboard.
Are these ideas worth pursuing, or would I be better off looking in another direction?