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By Robert Pease

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4. ) is defined as the change in open-loop gain required to make the system unstable. Systems with greater gain margins can withstand greater changes in system parameters before becoming unstable in closed loop. 5. The phase margin is defined as the negative change in open-loop phase shift required to make a closed-loop system unstable. 6. M. Ͼ 3 or so. M. ( jv) 0 Ϫ45 Ϫ90 Ϫ135 Ϫ180 Ϫ225 Ϫ270 fm log (v) vc Figure 1-10: Plot of gain margin and phase margin. Relationship Between Damping Ratio and Phase Margin The damping ratio and phase margin are directly related.

The gain of ϩ1 op-amp circuit is shown in Figure 1-17a where the op-amp has unity feedback. The block diagram of this circuit is shown in Figure 1-17b. T . 1s ϩ 1)(10Ϫ6 s ϩ 1) Vi ϩ ϩϪ a(s) [1-25] Vo Vo Ϫ 1 (a) (b) Figure 1-17: Gain of ϩ1 op-amp circuit. (a) Circuit. (b) Block diagram. which is the same as the open-loop transfer function of the op-amp a(s). Using MATLAB, the bandwidth and phase margin are calculated, as shown in Figure 1-18. The results show a phase margin of 52° and a crossover frequency of 786,150 radians/second (125 kHz).

Is defined as the change in open-loop gain required to make the system unstable. Systems with greater gain margins can withstand greater changes in system parameters before becoming unstable in closed loop. 5. The phase margin is defined as the negative change in open-loop phase shift required to make a closed-loop system unstable. 6. M. Ͼ 3 or so. M. ( jv) 0 Ϫ45 Ϫ90 Ϫ135 Ϫ180 Ϫ225 Ϫ270 fm log (v) vc Figure 1-10: Plot of gain margin and phase margin. Relationship Between Damping Ratio and Phase Margin The damping ratio and phase margin are directly related.

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