Gain margin and phase margin完整版资料

loop gain isbueniftyo(r0edb).the loop gain magnitude has dropped below 0db. Thus, an
This corresapomndps tloifaieporlehoan vthienjwgaxtihs raet se= j2oπrf1m. ore poles can become unstable.
• Thus, an amFpolifrierthhavriengethroeerormmoorerepolepsocalen bsecaomme upnlsitfaibeler., a phase shift of -180 is possible
Another measure of stability from the loop gain bode plot is the phase margin, which is determined at the frequency fpm for which the
popular method, called dominant-pole compensation, is to add
another pole at a very low frequency, such that the loop-gain drops to
unity by the time the phase reaches X (e.g. -135 degrees). In this
frequency
Af
(f
)
A(f)
1A(f )
• For a given frequency f1, if βA(f1)=-1, the close loop gain beorresponds to a pole on the jw axis at s= j2πf1. The
phase to become feedback can be used effectively.
In general, a larger gain margin results in
lveses rriyngincgloansdefastteor
de-c1a8y o0f
traantsietnht erespfroensqe.uency
• On the other hand, a large value of feedback coefficient may lead to instability in a multiple-pole amplifier.
• Thus, we must deliberately modify the pole locations (or equivalently frequency and transient response) of the amplifier before feedback can be used effectively. The is called compensation.
For three or more poles amplifier, a phase shift of -180 is possible before the loop gain magnitude has dropped below 0db.
• There are several approaches to compensate the pole location. One
way, a phase margin of X+180 (e.g. 45 degrees) could be achieved.
Before compensation
Another measure of stability from the loop gain bode plot is the phase margin, which is determined at the frequency fpm for which the
any given frequency.
For a two pole amplifier, the extreme phase is -180, which occurs until frequency approaches infinity.
For a •singleFaomrpliafier,sinisntagbilleity ias nmot pa lpirfoibelerm, ,isninscetathbe eilxittryemiesphnasoetis a-90p. roblem, since the extreme phase is -90. For a stable amplifier, the amount that the loop gain magnitude is below 0db is called the gain margin.
Pole compensation II
• Instability occurs if the magnitude of loop gain A0 is greater than 0db at the frequency for which the phase is -180.
• Each pole potentially contributes a phase shift between 0 to -90 at
loop gain is unity (0db).
This corresponds to a pole on the jw axis at s= j2πf1.
The phase difference between the actual phase and -180 degrees is the phase margin.
Gain margin and phase margin
Frequency response
For a given frequency f1, if βA(f1)=-1, the close loop gain becomes infinite.
A gain margin of zero implies that a pole lies on jw axis.
Each pole potentially contributes a phase shift between 0 to -90 at any given frequency.
replacing s=j2πf givesAthfetecrlosceodmlooppeganinsaastiaofnunction of frequency
Negative feedback is useful to reduce distortion, stabilize gain and increase bandwidth.
On For
tahe•stoatbhleeFraohmarnpdlifa,ieifr,thtthweelooaompopguaonintltemhaatgatnhmietuldopeoplisigfgiaerienram,teartgthnhiaetundueeniistxyb,tetrhleoewmam0depblifiiseprchiaslaluendsstethaeblgiesa. in
• For a stable amplifier, the amount that the loop gain magnitude is below 0db is called the gain margin. A gain margin of zero implies that a pole lies on jw axis. In general, a larger gain margin results in less ringing and faster decay of transient response.
transient response then contains a constant-amplitude sinusoid.
• In considering the stability of a feedback amplifier, we examine the bode plot for the loop gain βA(f) to find the frequency fgm for which the phase shift is -180 degrees. If the magnitude of the loop gain is less than unity at fgm, the amplifier is stable. On the other hand, if the loop gain magnitude is greater than unity, the amplifier is unstable.
-m1ar8gi0n.,
which
occurs
Thus, we muunsttdiellibferreatqelyumeondicfyytheapopleplorcoataiocnsh(oersequiinvafleinntilytyfr.equHenocywaendvtreanrs,ienitt reissponpseo)sofsthibe alemplfifoierrbetfhoree
for
which
the
Gain margilnoaondpphgasaeimnargisin 0db, resulting in very small phase margin, hence long
CFolorsaedg-ivloeontprfrgaeaqinnuesonficeaymnf1pt,lififireβirnsA(wgf1iti)hn=f-ge1e, dtahbeanccdkloisslealorogpegaifnrbeeqcoumeesnincfiyniter.esponse peaking.
On the other hand, if the loop gain magnitude is greater than unity, the amplifier is unstable.
Gain margin and phase margin
•
Closed-loop gain of amplifiers with feedback is
Af
(s)
A(s)
1A(s)
replacing s=j2πf gives the closed loop gain as a function of
• Another measure of stability from the loop gain bode plot is the phase margin, which is determined at the frequency fpm for which the loop gain is unity (0db). The phase difference between the actual phase and -180 degrees is the phase margin.
Pole compensation I
• Negative feedback is useful to reduce distortion, stabilize gain and increase bandwidth. But to achieve these benefits, the loop gain A0 must be much larger than unity.
• On one hand, we can design an amplifier with a large open-loop gain. This calls for several stages of amplification, and multi-stage amplifiers invariably introduce multiple poles.