Hello.
I have managed to wire up a 2 stage opamp using an LM324. I have used the schematic from this datasheet and fed the output on one opamp quarter (I think thats how youd describe it?) in to the + of another.
http://www.ti.com/lit/ds/symlink/lm124-n.pdf (page 11).
Its taking a very low (around 10mV) 1ms pulse in to the first opamp quarter to boost it to around 200mV which is then fed in to the second opamp to boost it from 200mV to near 3300mv (3.3V).
Here is the three stages in a video...https://www.youtube.com/watch?v=vIFJ8izFI4c&list=UUoDIROjGP1j2mfgvbXX1OkA
Seeming as it can work, I would like to replace the arduino nano with a 40Mhz transducer in order to amplify the transducer signal to near 3-5V. The transducer gives off more than a few mV so I hope that it can be used with the LM324. Here is a video of the transducer:
https://www.youtube.com/watch?v=3iStBMkUlw4&feature=youtu.be
Where I am a bit stuck:
a) The opamp claims 1Mhz bandwidth...when I set the input signal from the nano at 24us period (aprox 40KHz), the output from the first op-amp is distorted ("sharks fin") and there is not an output on the second final boosting opamp...
What is going on? Even when I bump up the initial voltage, there is still a sharksfin style wave on the first output and then still no second output... (acutally....when I set the oscilooscope to 20mV I can see the sharksfin type wave...but really noisy).

b) The wiring I am unsure about. I do not know if GND needs to be tied from the opamp supply and the transducer?
c) Can I happily use say a 2n2222a transistor to boost the signal to 5v because of the voltage loss in the opamp.