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"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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Voltage-Feedback <strong>Op</strong> Amp Compensation<br />

Lead Compensation<br />

slopes down at –20 dB/decade. Lead compensation sacrifices <strong>the</strong> bandwidth between <strong>the</strong><br />

1/R FC breakpo<strong>in</strong>t and <strong>the</strong> forward ga<strong>in</strong> curve. <strong>The</strong> location of <strong>the</strong> 1/R FC pole determ<strong>in</strong>es<br />

<strong>the</strong> bandwidth sacrifice, and it can be much greater than shown here. <strong>The</strong> pole caused<br />

by R F, R G, and C does not appear until <strong>the</strong> op amp’s ga<strong>in</strong> has crossed <strong>the</strong> 0-dB axis, thus<br />

it does not affect <strong>the</strong> ideal closed-loop transfer function.<br />

20 Log a<br />

aZF<br />

20 Log<br />

ZG + ZF<br />

ZF<br />

20 Log<br />

ZG<br />

0dB<br />

<strong>Op</strong> Amp Ga<strong>in</strong><br />

Ideal Closed-Loop Ga<strong>in</strong><br />

Figure 7–15. Invert<strong>in</strong>g <strong>Op</strong> Amp With Lead Compensation<br />

1<br />

τ1<br />

A<br />

1 1<br />

and<br />

τ2 RFC<br />

1<br />

(RC || RG)C<br />

<strong>The</strong> forward ga<strong>in</strong> for <strong>the</strong> non<strong>in</strong>vert<strong>in</strong>g op amp is a; compare Equation 6–11 to Equation<br />

6–5. <strong>The</strong> ideal closed-loop ga<strong>in</strong> is given by Equation 7–17.<br />

VOUT VIN Z F Z G<br />

Z G<br />

R F R G<br />

R G<br />

RF RGCs 1<br />

RFCs 1<br />

(7–17)<br />

<strong>The</strong> plot of <strong>the</strong> non<strong>in</strong>vert<strong>in</strong>g op amp with lead compensation is shown <strong>in</strong> Figure 7–16.<br />

<strong>The</strong>re is only one plot for both <strong>the</strong> op amp ga<strong>in</strong> (a) and <strong>the</strong> forward ga<strong>in</strong> (A), because <strong>the</strong>y<br />

are identical <strong>in</strong> <strong>the</strong> non<strong>in</strong>vert<strong>in</strong>g circuit configuration. <strong>The</strong> ideal starts out as a flat l<strong>in</strong>e, but<br />

it slopes down because its closed-loop ga<strong>in</strong> conta<strong>in</strong>s a pole and a zero. <strong>The</strong> pole always<br />

occurs closer to <strong>the</strong> low frequency axis because R F > R F||R G. <strong>The</strong> zero flattens <strong>the</strong> ideal<br />

closed-loop ga<strong>in</strong> curve, but it never does any good because it cannot fall on <strong>the</strong> pole. <strong>The</strong><br />

pole causes a loss <strong>in</strong> <strong>the</strong> closed-loop bandwidth by <strong>the</strong> amount separat<strong>in</strong>g <strong>the</strong> closed-loop<br />

and forward ga<strong>in</strong> curves.<br />

7-15

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