Op Amps for Everyone - The Repeater Builder's Technical ...

Bandwidth
A
aR G
R F R G
(9–2)
Equation 9–2 is rewritten below as Equations 9–3 and 9–4 for the noninverting and inverting
circuits respectively. In each case, the symbol G CLNI and G CLI represent the closed
loop gain for the noninverting and inverting circuits respectively.
A
a
R F R G
a
R G
G CLNI (9–3)
(9–4)
A
a
R F R G
a
G CLI
1
R G
In both cases the loop gain decreases as the closed loop gain increases, thus all VFA errors
increase as the closed loop gain increases. The error increase is mathematically
coupled to the closed loop gain equation, so there is no working around this fact. For the
VFA, effective bandwidth decreases as the closed loop gain increases because the loop
gain decreases as the closed loop gain increases.
A plot of the VFA loop gain, closed loop gain, and error is given in Figure 9–3. Referring
to Figure 9–3, the direct gain, A, is the op amp open loop gain, a, for a noninverting op
amp. The direct gain for an inverting op amp is (a(Z F /(Z G + Z F ))). The Miller effect causes
the direct gain to fall off at high frequencies, thus error increases as frequency increases
because the effective loop gain decreases. At a given frequency, the error also increases
when the closed loop gain is increased.
20 LOG A
Gain in dB
20 LOG (1 + Aβ)
Direct Gain
20 LOG(G CL )
CLOSED LOOP GAIN
LOG f
Figure 9–3. VFA Gain versus Frequency
9-4