1. If I stick a PCIe frontend/ADC card into a desktop computer, can the computer do what the FPGA does in commercial scopes?
A PC processor has the performance to implement the decimation and triggering which the FPGA handles, but many high speed PCIe and USB digitizers cannot stream continuously at high sample rates.
2. Do USB scopes have a FPGA board inside??
Yes, USB scopes have an FPGA or equivalent for handling decimation and triggering.
Don't forget the analog front-end. You'll want a 1 MOhm in parallel with 10-25 pF or so input impedance to work with standard 10x probes, and some amplification and/or attenuation to extend the range beyond the native range of the ADC. Especially since you value low noise, which presumably means you want to look at low-level signals.
You also may want some input protection so you don't blow up your expensive ADCs.
Do not underestimate the finesse that goes into a high impedance input. For high impedance attenuators, I would consider picking up a couple of the 4-pin hybrid attenuators Tektronix used in the 1970s. Add a DPDT telecom relay and you have a switchable high impedance attenuator good to 100 or maybe 200 MHz.
Input noise is dominated by the high impedance buffer, typically an FET being used as a source follower, which is the noisiest part.
Well said. In the end, low noise amounts to a well-thought front end. I don't have the faintest about how to learn concocting good front ends.
The Tektronix Circuit Concepts books "Vertical Amplifier Circuits" and "Oscilloscope Probe Circuits" available
here are a good place to start.
"Signal Conditioning in Oscilloscopes and the Spirit of Invention" by Steve Roach included in "The Art and Science of Analog Circuit Design" edited by Jim Williams discusses modern front end designs.
"Good Engineering and Fast Vertical Amplifiers" by John Addis in "Analog Circuit Design - Art, Science, Personalities" edited by Jim Williams would be useful for a discrete amplifier design.
Studying various Tektronix service manuals for their solid state oscilloscopes from the 1970s to 1980s will be helpful. They include detailed theory sections describing every circuit. The Tektronix 2230 and 2232 DSOs will be particularly helpful. The 2230 implemented a sampling rate of 20 MHz with a TTL design.
A scope without a FPGA is certainly possible, but would not have a high sampling rate. Take a look at these little scopes made with a STM32103 MCU. Just 1MSa/s, but good as a basis to learn about how a scope works.
A low sampling rate sampling oscilloscope could be made for bandwidths above 1 GHz but that entails several other design disciplines and is less generally useful.
For higher sample rates without a FPGA you would need a more powerful processor and an external ADC. Don't have examples on this.
Last year I figured there should be standard interface ADCs and processors to allow for a high sample rate design without an FPGA or custom logic, and there are, but they are incredibly expensive.