## PHYS345 Electricity and Electronics

**Answer for P14.5**
With R_{i} = 100k, v_{i} = -15 V, and
*d*v_{o}/*d*t = 2 V/s, the feedback capacitance
should be 75 microFarad.

**Answer for P14.6**

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, X_{C} will get very large and
the parallel combination with the feedback resistor will approach R_{f} as a limit.

The breakpoint of 3 kHz is set by having 2 pi f (RC)_{f} = 1;
that is, R_{f}C_{f} = 53 microsec.
To get started, try C_{f} = 0.001 microFarad;
the specified breakpoint would then require R_{f} = 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

**Answer for P14.9**

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):

**Answer for P14.9**

Ignoring the stabilizing resistor R_{i} for the time being,
the feedback resistor R_{f} 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 R_{i} is added so that
2 pi (8 kHz) (RC)_{i} = 1;
that is, R_{i} = 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.