Op-amp low pass on the bench

// A signal generator into an inverting op-amp low pass. Rin = 1 k into the
// summing junction, Rf = 10 k and Cf = 8 nF in parallel from that junction
// back to the output. A 10 k / 10 k divider off the 5 V rail holds the
// non-inverting input, and once feedback closes the loop, the output too, at
// half the rail: 2.5 V. This op-amp has no negative supply, so nothing here
// can swing below ground on its own, and this is the standard fix.
//
// In the pass band the gain comes from the two resistors alone:
//
//   |Av| = Rf / Rin = 10 000 / 1 000 = 10, which is 20 dB
//
// and Cf decides where that gain starts to give way:
//
//   fc = 1 / (2 pi Rf Cf) = 1 / (2 pi x 10 000 x 8e-9) = 1989 Hz
//
// Sweep it. Analysis... in the more menu, then Frequency response. Drive
// gen1, watch the output, and sweep 10 Hz to 100 kHz at 40 points a decade.
// What comes back:
//
//   pass band          flat at 20.0 dB, and 180 degrees, because an
//                       inverting stage turns the signal upside down
//   about 1.99 kHz      the marked corner: 3 dB down, 45 degrees further
//                       round than the pass band
//   a decade past it    another 20 dB down, one capacitor's worth of rolloff
//
// The corner lands at 1985 Hz, 0.2% under the formula's 1989 Hz, and closer
// than any passive filter on this bench manages. That is the op-amp doing
// its job: Rf and Cf sit inside the feedback loop, so whatever the scope's
// own 1 Mohm does to the output node, the loop corrects for it before it
// ever shows up in the reading. A passive filter has nothing watching its
// output like that; this one does.
//
// The 0.2% is the op-amp itself. Its model is rail-to-rail, the default,
// with a gain-bandwidth product of 10 MHz: at 2 kHz its open-loop gain is
// about 5000, not infinite, so the loop is a little short of perfect. Set
// the op-amp's model to 741 and sweep again. A 741's gain-bandwidth product
// is 1 MHz, a tenth of that, and the corner comes down ten times as far, to
// 1950 Hz, 2% under the formula. (A 741 on 5 V also has only 1.5 V to 3.5 V
// of swing, which this 2.5 V bias sits in the middle of.)
//
// Things to try. Make Rin 10 k instead of 1 k and the gain drops to unity,
// 0 dB, with the corner exactly where it was, because Rf and Cf are the only
// two parts that decide it. Make Cf four times smaller, 2 nF, and the corner
// moves up by four, to about 7.96 kHz: it lives alone under 1 / (2 pi Rf Cf)
// once Rf is fixed.