"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10
"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10
"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10
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Loop Ga<strong>in</strong> Plots are <strong>the</strong> Key to Understand<strong>in</strong>g Stability<br />
5-12<br />
<strong>The</strong> amplifier ga<strong>in</strong>, A, <strong>in</strong>tercepts <strong>the</strong> amplitude axis at 20Log(A), and it breaks down at a<br />
slope of –20 dB/decade at ω = ω a. <strong>The</strong> negative slope cont<strong>in</strong>ues for all frequencies greater<br />
than <strong>the</strong> breakpo<strong>in</strong>t, ω = ω a. <strong>The</strong> closed loop circuit ga<strong>in</strong> <strong>in</strong>tercepts <strong>the</strong> amplitude axis at<br />
20Log(V OUT/V IN), and because β does not have any poles or zeros, it is constant until its<br />
projection <strong>in</strong>tersects <strong>the</strong> amplifier ga<strong>in</strong> at po<strong>in</strong>t X. After <strong>in</strong>tersection with <strong>the</strong> amplifier ga<strong>in</strong><br />
curve, <strong>the</strong> closed loop ga<strong>in</strong> follows <strong>the</strong> amplifier ga<strong>in</strong> because <strong>the</strong> amplifier is <strong>the</strong> controll<strong>in</strong>g<br />
factor.<br />
Actually, <strong>the</strong> closed loop ga<strong>in</strong> starts to roll off earlier, and it is down 3 dB at po<strong>in</strong>t X. At po<strong>in</strong>t<br />
X <strong>the</strong> difference between <strong>the</strong> closed loop ga<strong>in</strong> and <strong>the</strong> amplifier ga<strong>in</strong> is –3 dB, thus accord<strong>in</strong>g<br />
to Equation 5–12 <strong>the</strong> term –20Log(1+Aβ) = –3 dB. <strong>The</strong> magnitude of 3 dB is √2 , hence<br />
1 (A) 2 2 , and elim<strong>in</strong>ation of <strong>the</strong> radicals shows that Aβ = 1. <strong>The</strong>re is a method<br />
[4] of relat<strong>in</strong>g phase shift and stability to <strong>the</strong> slope of <strong>the</strong> closed loop ga<strong>in</strong> curves, but only<br />
<strong>the</strong> Bode method is covered here. An excellent discussion of poles, zeros, and <strong>the</strong>ir <strong>in</strong>teraction<br />
is given by M. E Van Valkenberg,[5] and he also <strong>in</strong>cludes some excellent prose to<br />
liven <strong>the</strong> discussion.<br />
5.5 Loop Ga<strong>in</strong> Plots are <strong>the</strong> Key to Understand<strong>in</strong>g Stability<br />
Stability is determ<strong>in</strong>ed by <strong>the</strong> loop ga<strong>in</strong>, and when Aβ = –1 = |1| ∠–180° <strong>in</strong>stability or oscillation<br />
occurs. If <strong>the</strong> magnitude of <strong>the</strong> ga<strong>in</strong> exceeds one, it is usually reduced to one by<br />
circuit nonl<strong>in</strong>earities, so oscillation generally results for situations where <strong>the</strong> ga<strong>in</strong> magnitude<br />
exceeds one.<br />
Consider oscillator design, which depends on nonl<strong>in</strong>earities to decrease <strong>the</strong> ga<strong>in</strong> magnitude;<br />
if <strong>the</strong> eng<strong>in</strong>eer designed for a ga<strong>in</strong> magnitude of one at nom<strong>in</strong>al circuit conditions,<br />
<strong>the</strong> ga<strong>in</strong> magnitude would fall below one under worst case circuit conditions caus<strong>in</strong>g oscillation<br />
to cease. Thus, <strong>the</strong> prudent eng<strong>in</strong>eer designs for a ga<strong>in</strong> magnitude of one under<br />
worst case conditions know<strong>in</strong>g that <strong>the</strong> ga<strong>in</strong> magnitude is much more than one under optimistic<br />
conditions. <strong>The</strong> prudent eng<strong>in</strong>eer depends on circuit nonl<strong>in</strong>earities to reduce <strong>the</strong><br />
ga<strong>in</strong> magnitude to <strong>the</strong> appropriate value, but this same eng<strong>in</strong>eer pays a price of poorer<br />
distortion performance. Sometimes a design compromise is reached by putt<strong>in</strong>g a nonl<strong>in</strong>ear<br />
component, such as a lamp, <strong>in</strong> <strong>the</strong> feedback loop to control <strong>the</strong> ga<strong>in</strong> without <strong>in</strong>troduc<strong>in</strong>g<br />
distortion.<br />
Some high ga<strong>in</strong> control systems always have a ga<strong>in</strong> magnitude greater than one, but <strong>the</strong>y<br />
avoid oscillation by manipulat<strong>in</strong>g <strong>the</strong> phase shift. <strong>The</strong> amplifier designer who pushes <strong>the</strong><br />
amplifier for superior frequency performance has to be careful not to let <strong>the</strong> loop ga<strong>in</strong><br />
phase shift accumulate to 180°. Problems with overshoot and r<strong>in</strong>g<strong>in</strong>g pop up before <strong>the</strong><br />
loop ga<strong>in</strong> reaches 180° phase shift, thus <strong>the</strong> amplifier designer must keep a close eye on<br />
loop dynamics. R<strong>in</strong>g<strong>in</strong>g and overshoot are handled <strong>in</strong> <strong>the</strong> next section, so prevent<strong>in</strong>g oscillation<br />
is emphasized <strong>in</strong> this section. Equation 5–14 has <strong>the</strong> form of many loop ga<strong>in</strong><br />
transfer functions or circuits, so it is analyzed <strong>in</strong> detail.