Why Op Amps Have Low Bandwidth

1. Why Op Amps Have Low Bandwidth

2. Define gain of non-inverting amplifier Open loop gain of op amp (a simplification) Let A0=105, ω0=106 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. Characteristic equation

3. Gain of Op-Amp vs Frequency Phase goes to -180⁰ here

4. Find closed loop gain (low freq) Closed Loop Gain (A0=105, ω0=106) For large AOL(0)=A0; A0β>>1 For resistive circuits, the extreme value is β→1 (R2 →0, Ri→∞); 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 For oscillation This is obviously only useful if you require large gain. It is certainly not useable for a follower. (A0=105, ω0=106) 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. For stability or

8. Graphical explanation • When phase is -180⁰, mag is 82dB. • |Aβ|=1 at this frequency for stability • So we need to make β=-82dB (this is only marginally stable) Phase goes to -180⁰ here ω = √3·ω0 = 1.7E6

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 ωd that creates marginal stability with β=1. This is quite low…

11. Graphical explanation • When phase is -180⁰, 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) Phase goes to -180⁰ hereω = ω0 = 1E6