Negative vs. positive feedback What is the difference? Consider what happens when there is a perturbation Positive feedback drives op amp into saturation: v OUT  ± V S

Static Analysis of Positive Feedback Circuit

Representing dynamics of op amp: time dependence Let us consider this circuit and analyze its dynamics to build insight

Time behavior of v O

Consider a Small Disturbance to v 0 (Noise) v - > v + v + > v - v + = v -

One use of instability: Build Comparator

Now, Use Positive Feedback

Without Hysteresis

Oscillator: Can Create a Clock Assume v 0 =V S at t=0, v C =0

Clock in Digital Systems We build an oscillator using an op amp Why do we use a clock in a digital system? a)1,1,0? b)When is the signal valid? Common timebase – when to “look” at a signal (e.g. whenever the clock is high) Discretization of time: one bit of information associated with an interval of time (cycle)

Physical Limitations of Op Amp Voltage limit: V S - < v out <V S +

Frequency Response Limits The product of gain and band width in any given op- amp is constant, i.e. A  = K Increasing the gain-bandwidth product by means of amplifiers in cascade. Offset voltage limit Slew rate limit