## PHYS345 Electricity and Electronics

Answer for P14.5

With Ri = 100k, vi = -15 V, and dvo/dt = 2 V/s, the feedback capacitance should be 75 microFarad.

To get the low-pass response, an integrator response is needed, thus a feedback capacitor and an input resistor. To get a low-frequency gain of thirty, add a feedback resistor in parallel with the capacitor; at low frequencies, XC will get very large and the parallel combination with the feedback resistor will approach Rf as a limit.

The breakpoint of 3 kHz is set by having 2 pi f (RC)f = 1; that is, RfCf = 53 microsec. To get started, try Cf = 0.001 microFarad; the specified breakpoint would then require Rf = 53k. 51k is a standard 5% value, 53.6k is available in 1% tolerance.

Using a 1% 53.6k feedback resistor should have a 1.79k input resistor for a gain of 30. The standard 1% value of 1.78k is a good choice from the table of standard resistor values

The magenta line is the Bode plot that you should have constructed from the circuit parameters shown in the problem statement. The black line shows the roll-off of open loop gain typical for op amps. The red line shows the exact form of the frequency dependence of the bass-boost circuit, with breakpoints at 44 Hz and 400 Hz.

From a MathCAD document (with edited graph):

Ignoring the stabilizing resistor Ri for the time being, the feedback resistor Rf should be selected to be 25k to get the desired outcome with a 0.1 microFarad input capacitor.

From a MathCAD document (with edited graph):

To set a breakpoint at the intersection of the unstabilized differentiator gain and the op amp roll-off, an input resistor Ri is added so that 2 pi (8 kHz) (RC)i = 1; that is, Ri = 200 ohm.

"http://www.physics.udel.edu/~watson/phys345/protected/exercises/answers/1119.html"
Last updated Dec. 7, 1998.
Copyright George Watson, Univ. of Delaware, 1998.