Question

Op-Amp Circuit Stability Although op-amps behave as single-pole amplifiers which are "unconditionally stable," it's still possible to make unstable amplifiers if you don't know what you're doing. The most famous example of this is the voltage differentiator 1. Consider the following circuit: a. Find the expression for this amplifier's ideal gain Aco (s), assuming the op-amp is ideal (a(s) - o. Hint: It's just an inverting amplifier with z and z2 R (5pts) b. Suppose the gain-setting components have values R-100kΩ and C-15.9 15nF Draw a Bode plot of Aco (jf) (again, assuming the op-amp is ideal). At what frequency f is lAo = 17(round to the nearest Hz) (10pts) From vo back to the op-amp's inverting input vm, the RC network forms a voltage divider. What expression describes the voltage transfer function of this divider, Um (s) vo(s) of this transfer function? (1opts) c. Draw a Bode plot of this transfer function mUf) What is the pole frequency voir) d. To make the math easy, we will assume the op-amp's DC gain is a,-1000V/mV, and it has a single pole at fo = 1 Hz. In other words, the op-amp's gain can be expressed as ao1000V/mV a(jf) = Draw a Bode plot of aGf). What is the op-amp's unity-gain frequency, fy? (1opts) e. Now that you know both the amplifier's gain a(if) and the RC network's voltage transfer function, draw a Bode plot of the amplifier's loop gain T(Gf), annotating the DC magnitude, pole frequencies, and crossover frequency fe. What is the crossover frequency f? What is the phase margin P. M.? (1opts) f. From the asymptotic gain model, we know that AGf) -Ao (Tl1) (neglecting feedforward effects) Draw a Bode plo of A) (opts)

Answer 1

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