I have a question because I'm learning in my own time about oscilloscopes. I set the trigger mode to automatic instead of normal which would capture a steady signal such as this.
When the trigger mode is at automatic. **`
Why does the signal on the oscilloscope become less stable when I reduce the voltage from the function generator
At 1 volt I get:
At .7 volts I get
Disclosure: I'm observing an op-amp powered by 15 volts + -.... 2000 and 39000 Ohm resistor in series in an non-inverted op-amp
Automatic triggering is probably not what you think it means; in many oscilloscopes "auto" mode means that after a pre-defined timeout period if no actual trigger point was reached, the oscilloscope will begin capturing data anyways. There's no reason the frequency this happens has to be aligned at all with the signal you're actually trying to capture, so it shouldn't be a surprise if you get phase error in the resulting super-imposed image (which is why it looks "unstable").
In the first image, the trigger is being properly found so it will correctly periodically trigger and the oscilloscope will tell you it's actually triggering rather than hitting this timeout forced data capture.
In the second image, the triggering circuit never fires (either the trigger level is never met, or if some internal filtering/heuristics is preventing such a small deviation from actually triggering). Instead, you're hitting the auto trigger timeout. There should be a corresponding hint on the display that the trigger has never actually been reached, and instead the auto trigger timeout period has passed.
More information on auto triggering: link
Why does the signal on the oscilloscope become less stable when I reduce the voltage from the function generator
The oscilloscope does not automatically scale the input. The main problem is that you don't have a high enough signal to noise ratio on Channel 1 for reliable triggering. It's not necessarily noise inherent to your system, just the limits of the oscilloscope settings.
Try this: set your trigger mode to Normal and capture a single sequence until you get a trigger that "looks" wrong - meaning it triggered in the wrong place. This usually happens on the opposite edge, where a bit of noise hits right at the trigger voltage.
As st2000 points out, this isn't an artifact of the "Auto" trigger mode as the oscilloscope believes it's triggering properly. You would see the same thing even if you had the scope set to "Normal". You can see for yourself the difference in trigger modes by setting the trigger voltage to something way out of the range of the input signal, such as +5V. After it doesn't trigger for a while, it will start showing signals, but they will appear to move incoherently (because the trigger isn't synchronizing the waveforms to the same point of the curve).
In general, the best volts/division setting for each channel is the lowest volts/division possible without clipping the signal. This really helps digital oscilloscopes provide the best accuracy in measurements even if it doesn't "look" as good.
Possible fixes:
Channel 1 to something much lower, such as 500 mV/division.I read the manual for the Agilent 54622A. It has 3 trigger modes: Normal, Auto & (maybe) Auto Level (54620-series only). I clearly see the menu set for Auto in your pictures. As has been pointed out, Auto self triggers the scope if no trigger is seen over some given amount of time. Guessing, the scope continued to trigger on channel 1 until you attenuated channel 1's signal below the trigger threshold. At which point, Auto kicked in and forced a trigger albeit not synchronized with your attenuated signal.
