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Lead Compensation
transfer function The equation for the inverting op amp closed-loop gain is repeated below.
–aZ F
V OUT
V IN
Z G
Z F
1 aZ G
Z G
Z F
(7–13)
G /(R G + R F ))
20 Log (KR
dB
0dB
20 Log (Aβ)
Original Transfer Function
1/τ 1 1/τ 2
1/R F C 1/R F IIR G C
Modified Transfer Function
Log(f)
Figure 7–14. Lead-Compensation Bode Plot
When a approaches infinity, Equation 7–13 reduces to Equation 7–14.
V OUT
V IN
Z F
Z IN
(7–14)
Substituting R F ||C for Z F and R G for Z G in Equation 7–14 yields Equation 7–15, which is
the ideal closed-loop gain equation for the lead compensation circuit.
V OUT
V IN
R F
R G
1
R F
Cs 1
(7–15)
The forward gain for the inverting amplifier is given by Equation 7–16. Compare Equation
7–13 with Equation 6–5 to determine A.
A
aZ F
Z G A F
aR F
R G R F
1
R F R G Cs 1
(7–16)
The op amp gain (a), the forward gain (A), and the ideal closed-loop gain are plotted in
Figure 7–15. The op amp gain is plotted for reference only. The forward gain for the inverting
op amp is not the op amp gain. Notice that the forward gain is reduced by the factor
R F /(R G +R F ), and it contains a high frequency pole. The ideal closed-loop gain follows the
ideal curve until the 1/R F C breakpoint (same location as 1/τ 2 breakpoint), and then it
7-14