I recently bought this ($45!) oscilloscope: http://www.gabotronics.com/development-boards/xmega-xprotolab.htm. Looking at its schematic, I see the circuitry for one of the two analog input channels:
The website says that the scope can handle -15 to +20V per analog channel. The oscilloscope is based on the ATxmega32A4U microcontroller. According to the website, each input pin can handle 1.6 to 3.6V.
It looks like the scope's circuit uses a voltage divider and then an op-amp. My question is this: How are circuits like these generally designed? For example, how are the parameters for the voltage divider and the op-amp's feedback resistor calculated?