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Where do you see the problem? At the output of OPA277 or the input to Keysight 34461? If latter is the case, what do you use to gain up the signal by 10,000?
What you describe has the characteristics of burst noise also known as a popcorn noise caused by trapping and releasing of electrons as they cross p-n junction. This typically occurs in bipolar process where impurities are introduced during silicon wafer fabrication process. This is a known phenomenon of process defect that's very difficult to completely eliminate but for which we screen our products during final test.
