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R = 663
NGxR
W -
F
I
(6)
V
O
V
I
=
R
+
F
I
1+
Z
(S)
1+
R
F
R
G
a
R
R NG
+
F
I
Z
(S)
1+
a
NG
1+
R
F
R
G
NG = 1+
R
F
R
G
(4)
=
LoopGain
Z
(S)
R +R
F
I NG
(5)
600
550
500
450
400
350
300
250
200
150
100
NoiseGain
0
20
10
15
5
F
eedbackResistor(
)
W
www.ti.com........................................................................................................................................................................................... SBOS444 – DECEMBER 2008
RI, the buffer output impedance, is a critical portion of
The OPA4872 is internally compensated to give a
the bandwidth control equation. RI for the OPA4872 is
maximally flat frequency response for RF = 523 at
typically about 30
. A current-feedback op amp
NG = 2 on ±5-V supplies. Evaluating the denominator
senses an error current in the inverting node (as
of
Equation 5 (which is the feedback transimpedance)
opposed to a differential input error voltage for a
gives an optimal target of 663
. As the signal gain
voltage-feedback op amp) and passes this on to the
changes, the contribution of the NG × RI term in the
output through an internal frequency dependent
feedback transimpedance will change, but the total
show this open-loop transimpedance response. This
gives an approximate equation for optimum RF over
open-loop response is analogous to the open-loop
signal gain:
voltage gain curve for a voltage-feedback op amp.
Developing the transfer function for the circuit of
As the desired signal gain increases, this equation
will eventually predict a negative RF. A somewhat
subjective limit to this adjustment also can be set by
holding RG to a minimum value of 20 . Lower values
load both the buffer stage at the input and the output
stage, if RF gets too low, actually decreasing the
bandwidth. Figure 33 shows the recommended RF versus NG for ±5-V operation. The values for RF
versus gain shown here are approximately equal to
where:
the
values
used
to
generate
the
Typical
Characteristics. They differ in that the optimized
correcting for board parasitics not considered in the
This formula is written in a loop-gain analysis format,
shown in
Figure 33 give a good starting point for
where the errors arising from a noninfinite open-loop
design where bandwidth optimization is desired.
gain are shown in the denominator. If Z(S) were
infinite over all frequencies, the denominator of
Equation 4 would reduce to 1 and the ideal desired
signal gain shown in the numerator would be
achieved.
The
fraction
in
the
denominator
of
If 20 × log(RF + NG × RI) were drawn on top of the
open-loop
transimpedance
plot,
the
difference
between the two calculations would be the loop gain
at a given frequency. Eventually, Z(S) rolls off to equal
loop gain reduces to 1 (and the curves intersect).
This
point
of
equality
is
where
the
amplifier
Figure 33. Feedback Resistor vs Noise Gain
closed-loop frequency response given by
Equation 4starts to roll off, and is exactly analogous to the
frequency at which the noise gain equals the
The total impedance going into the inverting input
open-loop voltage gain for a voltage-feedback op
may be used to adjust the closed-loop signal
amp. The difference here is that the total impedance
bandwidth. Inserting a series resistor between the
in the denominator of
Equation 5 may be controlled
inverting input and the summing junction increases
somewhat separately from the desired signal gain (or
NG).
decreasing the bandwidth.
Copyright 2008, Texas Instruments Incorporated
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