1. Why Op Amps Have Low Bandwidth

2. Define gain of non-inverting amplifier Let A 0 =10 5, ω 0 =10 6 Characteristic equation Open loop gain of op amp (a simplification) Closed Loop Gain Note that for this circuit β≤1. β =1 for follower. Since denominator is 1+Aβ, the condition for osicllation is Aβ=-1.

3. Gain of Op-Amp vs Frequency Phase goes to - 180 ⁰ here

4. Find closed loop gain (low freq) Closed Loop Gain For large A OL (0)=A 0 ; A 0 β>>1 (A 0 =10 5, ω 0 =10 6 ) For resistive circuits, the extreme value is β → 1 (R 2 →0, R i → ∞); a follower.

5. Find where roots are on axis Characteristic equation Find where roots are on jω axis

6. Find conditions for oscillation

7. Restrictions on closed loop gain (A 0 =10 5, ω 0 =10 6 ) For stability For oscillation or This is obviously only useful if you require large gain. It is certainly not useable for a follower. To make it useable we need to decrease the loop gain. Since we want to use a full range of β, our only choice is to decrease the open loop gain of the open loop gain.

8. Graphical explanation Phase goes to -180 ⁰ here ω = √3·ω 0 = 1.7E6 When phase is -180 ⁰, mag is 82dB. |Aβ|=1 at this frequency for stability So we need to make β=-82dB (this is only marginally stable)

9. Increasing Stability (1) To decrease the gain, redesign op amp so one of it’s open loop poles is at a much lower frequency, to decrease gain at high frequencies (where oscillations occur) Characteristic equation

10. Increasing Stability (2) Let’s find the conditions for instability Let s=jω Let’s find the value of ω d that creates marginal stability with β=1. This is quite low…

11. Graphical explanation Phase goes to -180 ⁰ here ω = ω 0 = 1E6 When phase is -180 ⁰, mag is 0 dB (i.e., 1). |Aβ|=1 at this frequency for stability So circuit is stable for β≤1 (marginally stable for β=1)