Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

Shown in fig 1270 are three cases illustrating this

Info icon This preview shows pages 686–689. Sign up to view the full content.

View Full Document Right Arrow Icon
Shown in Fig. 12.70 are three cases illustrating this point. In Fig. 12.70(a), Barkhausen’s criteria ω 0 ω 0 180 20log ω ω 0 ω 0 180 (a) (b) KH 20log KH KH KH PX ω GX ω 0 ω 0 180 20log KH KH ω GX ω PX ω GX ω PX (c) K ( ) H s K ( ) H s K ( ) H s Figure 12.70 Systems with (a) coincident gain and phase crossovers, (b) gain crossover slightly below phase crossover, (c) gain crossover well below phase crossover. are met and the system produces oscillation in response to an input step. In Fig. 12.70(b),
Image of page 686

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 662 (1) 662 Chap. 12 Feedback , but the step response “rings” for a long time because the system is “marginally” stable and behaves “badly.” We therefore postulate that a well-behaved system is obtained only if a sufficient “margin” is allowed between and [Fig. 12.70(c)]. Note that in this case, at remains quite more positive than . A measure commonly used to quantify the stability of feedback systems is the “phase margin” (PM). As exemplified by the cases in Fig. 12.70, the more stable a system is, the greater is the difference between and . Indeed, this difference is called the phase margin: (12.191) Example 12.41 Figure 12.71 plots the frequency response of a multipole amplifier. The magnitude drops to 0 0 ω p1 ω p2 135 ω ω (log scale) (log scale) H H 20log Figure 12.71 unity at the second pole frequency. Determine the phase margin of a feedback system employing this amplifier with . Solution The plot suggests that the phase reaches at the second pole frequency (i.e., the poles are far apart). Thus, the phase margin is equal to . Exercise Is the phase margin greater or less than if ? How much phase margin is necessary? For a well-behaved response, we typically require a phase margin of . Thus, the above example is not considered an acceptable design. In other words, the gain crossover must fall below the second pole. 12.8.5 Frequency Compensation It is possible that after the design of an amplifier is completed, the phase margin proves inad- equate. How is the circuit modified to improve the stability? Called “frequency compensation,” this task can be accomplished by shifting toward the origin (without changing ). In other words, if is forced to drop to unity at a lower frequency, then the phase margin increases [Fig. 12.72(a)].
Image of page 687
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 663 (1) Sec. 12.8 Stability in Feedback Systems 663 ω 0 ω 0 180 20log KH KH ω p1 ω p1 ω 0 ω 0 180 20log ω KH KH PX ω GX ω GX Original Design Design Compensated (log scale) (log scale) Original Design Design Compensated PX ω (a) (b) Figure 12.72 (a) Concept of frequency compensation, (b) effect on phase profile. How can be shifted toward the origin? We recognize that if the dominant pole is trans- lated to lower frequencies, so is . Figure 12.72(b) illustrates an example where the first pole is shifted from to , but other poles are constant. As a result, decreases in magnitude.
Image of page 688

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 689
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern