I'm trying to design an inverting amplifier that has a gain of about ~30. It is required to be a two stage design with the first stage being none inverting and have an input impedance of >=500k. The input frequency would be ~160kHz to 200kHz. Below I've built a preliminary circuit that only has a gain of 20 for testing and ran into some oscillation issues. I've attached the scope capture of the oscillations and a schematic. Channel one is attached to Node1 of the attached schematic. The oscillations seem to occur with no input.
Reducing the gain of the first stage (reducing R10) or increasing R6 stops the oscillations but then I can no longer meet my specification. I'm wondering what is causing this issue. I've read this post: Why is my op-amp oscillating? and am wondering if I need to go into the math of the control system and feedback stability. Any help is greatly appreciated.
UPDATED: As suggested by Spehro Pefhany I tried grounding the input. This actually stops the oscillations. Is it possible this is due to poor layout? Layout of the circuit. Highlighted trace is the input to the none inverting in the first stage:
I've also updated the schematic to show bypass capacitors.