Op amp

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Great for amplifying weak signals from sensors to a more useful level. Also used in filters, integrators, etc.

quick summary

Many sensors need an amplifier to "buffer" their output signal. Often a single op amp is adequate. For very weak signals, you may want a "difference amplifier" or "instrumentation amplifier".
All ADCs need an anti-aliasing filter on their input. Often a single op amp, 2 caps and 4 resistors is adequate.
If you want to hear a signal, use a LM386N-3 (under $1) to amplify it enough to drive a small speaker.
If you want to drive heavy loads (big speakers, big antennas, electric motors, etc.), too heavy for typical op amps to drive, use op amps to amplify the signal to the desired voltage, followed by power transistors to drive the load [Veselinovic].

details

Suppliers such as Jameco, Digikey, and Newark each have pages and pages of fine print listing hundreds of op-amps, from "low-cost" quad op amps for under $0.40 each to "hi speed precision" op amps for well over $10 each. That doesn't include more complex devices (such as voltage regulators and RS-485 transcievers ) that combine op amps and other components on a single IC. Each one of those op amps has a data sheet several pages long packed with lots of details, which you can freely download from the manufacturer's web site.

"But in reality, there are only two important specifications that you should initially consider when selecting an op amp for your active, low-pass filter. ... Gain Bandwidth Product and Slew Rate." [Baker 2003]