EE 435. Lecture 14. Compensation of Cascaded Amplifier Structures

Transcription

1 EE 435 Lecture 4 ompensation of ascaded Amplifier Structures

2 . Review from last lecture. Basic Two-Stae Op Amp By inspection A o m o + p o o o5 m5 + o6 o5 m5 + o6 p GB m5 L m

3 . Review from last lecture. Small Sinal Analysis of Two-Stae Miller ompensated Op Amp Differential Small Sinal Equivalent V d V d Norton Equivalent One-Port Two-Port

4 . Review from last lecture. Small Sinal Analysis of Two-Stae Op Amp Differential Small Sinal Equivalent Solvin we obtain: V OUT This simplifies to: V V OUT ( s + sl + oo) + mov sv V ( s + od ) + Vd s OUT V d OUT V s V d L + s s } ( mo s ) [ mo + ( ( oo + od ) + Lod )] + oood L + ( s ) mo s mo + oo od

5 . Review from last lecture. Small Sinal Analysis of Two-Stae Op Amp Differential Small Sinal Equivalent Summary: where ( ) A s s L + ( s ) m5 s m m5 + od o + oo o5 o4 o6 m + oo od

6 . Review from last lecture. Small Sinal Analysis of Two-Stae Miller- ompensated Op Amp ( ) A s s Note this is of the form: L + ( s ) m5 s ( ) A A s 0 m5 + s + z s s + + p p This has two neative real-axis poles and one positive real-axis zero oo od

7 How does the Gain of the Two-Stae Miller-ompensated Op Amp ompare with Internal ompensated Op Amp? ( m5-s ) A( s ) A( s) m5 s +s + s + z 0 s s + + p p ( ) A A s L m5 oo od jω L oo oo od s +s + ( ) A0 A s s s + + p p p p z Re must be developed ompensation criteria: 4β A p 0 > > β A0 p

8 Review of Basic oncepts onsider a second-order factor of a denominator polynomial, P(s), P(s)s +a s+a 0 Then P(s) can be expressed in several alternative but equivalent ways s s ω + s Q + sξ ( s p )( s p ) and if 0 + ω 0 + ω complex ( s + α + jβ)( s + α jβ) 0 0 conjuate poles, These are all -paramater characterizations of the second-order factor and it is easy to map from any one characterization to any other

9 Review of Basic oncepts ω Q 0 s + s + ω 0 θ ω o sinθ Q ω o manitude of pole Q determines the anle of the pole

10 Simple pole calculations for -stae op amp Since the poles of the -stae op amp must be widely separated, a simple calculation of the poles from the characteristic polynomial is possible. Assume p and p are the poles and p << p D(s)s +a s+a 0 but determines p D(s)(s+p )(s+p )s +s(p +p )+p p s + p s + p p thus determines p p -a and p -a 0 /a

11 an now use these results to calculate poles of Basic Two-stae Miller ompensated Op Amp From small sinal analysis: ( ) A s s p m5 L L + ( s ) m5 s m5 + oo p oo od m5 A m5 0 oo od od GB od m + m5 p m5 oo od oo od oo od m5 oo o o5 + o4 m o6

12 From Previous Inspection p A o m o + o GB + 05 o5 m5 + m o4 o6 o5 m5 + p o6 m5 L Note the simple results obtained from inspection aree with the more time consumin results obtained from a small sinal analysis

13 Feedback applications of the twostae Op Amp β How does the amplifier perform with feedback? How should the amplifier be compensated?

14 Feedback applications of the twostae Op Amp Open-loop Gain A A(s) Standard Feedback Gain + N(s) D(s) A(s) A(s)β(s) N(s) D(s) + N(s)β(s) defn FB (s) N FB (s) N(s) D FB (s) D(s) + β(s)n(s) N D FB FB (s) (s) Open-loop and closed-loop zeros identical losed-loop poles different than open-loop poles Often β(s) is not dependent upon frequency

15 Open-loop Gain A(s) N(s) D(s) Alternate Feedback Gain β(s) FB(s) + A(s) β(s) Feedback applications of the twostae Op Amp A D FB (s) D(s) + N FB (s) Standard Feedback Gain A A(s) (s) FB + A(s)β(s) + β(s) N(s) β (s) D(s) + N(s) β(s) β(s)n(s) N(s) β(s) A(s) β(s) In either case, denominators are the same and characteristic equation defined by Often β(s) and β (s) are not dependent upon frequency and in this case

16 Basic Two-Stae Op Amp with Feedback Open-loop ain ( ) -s A(s) s +s + mo c L mo oo od A FB A (s) FB where s (s) s L + s m od L o Feedback ain with constant β + s + ( mo sc ) ( mo β ) + oood + βmo ( m0 sc ) ( mo β ) + β mo 04 mo m5 + oo o5 o6

17 Basic Two-Stae Op Amp ( m0 sc ) AFB(s) s L + s( mo β ) + β mo Pole Q?

18 Basic Two-Stae Op Amp ( m0 sc ) AFB(s) s L + s( mo β ) + β mo It can be shown that Q L β mo mo β But what pole Q is desired? where + and + oo o5 m o6 Lβ Q ( β ) mo od mo o mo m5 04 Riht Half-Plane Zero Limits Performance

19 ompensation What is compensation or frequency compensation? From Wikipedia: In electrical enineerin, frequency compensation is a technique used in amplifiers, and especially in amplifiers employin neative feedback. It usually has two primary oals: To avoid the unintentional creation of positive feedback, which will cause the amplifier to oscillate, and to control overshoot and rinin in the amplifier's step response. From Martin and Johns no specific definition but makes comparisons with optimal compensation which also is not defined From Allen and Holber (p 43) The oal of compensation is to maintain stability when neative feedback is applied around the op amp.

20 ompensation From Gray and Meyer (p634) Thus if this amplifier is to be used in a feedback loop with loop ain larer than a 0 f, efforts must be made to increase the phase marin. This process is known as compensation. From Sedra and Smith (p 90) This process of modifyin the open-loop ain is termed frequency compensation, and its purpose is to ensure that op-amp circuits will be stable (as opposed to oscillatory). From Razavi (p355) Typical op amp circuit contain many poles. In a foldedcascode topoloy, for example, both the foldin node and the output node contribute poles For this reason, op amps must usually be compensated, that is, their open-loop transfer function must be modified such that the closed-loop circuit is stable and the time response is well-behaved.

21 ompensation What is compensation or frequency compensation and what is the oal of compensation? Nobody defines it or defines it correctly but everybody tries to do it!

22 ompensation ompensation (alt Frequency ompensation) is the manipulation of the poles and/or zeros of the open-loop amplifier so that the closed-loop amplifier will perform acceptably Note this definition does not mention stability, positive feedback, neative feedback, phase marin, or oscillation. Note that acceptable performance is strictly determined by the user in the context of the specific application

23 End of Lecture 4