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By Robert Pease

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0 GHz Frequency Figure 1-36: Frequency response results for photodiode amplifier with Cf :2, 4, 6, 8, 10 pF, with Rf ‫ ؍‬1k and Cp ‫ ؍‬60 pF. VCC IL RL Vin VL ϩ a(s) Ϫ va Vsense Rsense Figure 1-37: MOSFET current source. The voltage Vsense senses MOSFET drain current. , not oscillating). A small-signal model is shown in Figure 1-38. Following are the parameters: ␶h Time constant of op-amp high-frequency pole rout Output resistance of op-amp Cgs MOSFET gate-source capacitance Cgd MOSFET gate-drain capacitance gm MOSFET transconductance RL Load resistance The transfer function of the MOSFET source follower is estimated using the method of open-circuit time constants.

The Bode plot of the loop transmission phase and magnitude tells the story. Although the phase margin is fine, the gain margin isn’t so great, due to the underdamped pole pair. In order to help this oscillation problem, we might attempt to add a pole above crossover to damp out the underdamped pair. Let’s try adding a pole at 5 ϫ 104 radians/ second to damp the complex poles at 105 radians/sec. 77 deg. 8°. ) Figure 1-28: Step response, Attempt #1. 204 deg. 6 rad/sec) 0 Ϫ20 Ϫ40 Ϫ60 Ϫ80 Ϫ100 Ϫ100 Ϫ150 Ϫ200 Ϫ250 Ϫ300 Ϫ350 104 105 Frequency (rad/sec) Figure 1-29: Plot of the loop transmission magnitude and phase, Attempt #2, showing crossover frequency of 3993 radians/second and a phase margin of 85°.

The difference between the angle at the crossover frequency and Ϫ180° is the phase margin m. 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.

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