OPA4872 Datasheet, PDF (14/27 Pages) Texas Instruments – 4:1 High-Speed Multiplexer

OPA4872
SBOS346C – JUNE 2007 – REVISED MARCH 2011
R_I, the buffer output impedance, is a critical portion of
the bandwidth control equation. R_I for the OPA4872 is
typically about 30Ω. A current-feedback op amp
senses an error current in the inverting node (as
opposed to a differential input error voltage for a
voltage-feedback op amp) and passes this on to the
output through an internal frequency dependent
transimpedance gain. The Typical Characteristics
show this open-loop transimpedance response. This
open-loop response is analogous to the open-loop
voltage gain curve for a voltage-feedback op amp.
Developing the transfer function for the circuit of
Figure 32 gives Equation 4:
V_{O =}
a
1+
R_F
R_G
V_I
R_F +
1+
R_I 1+
Z_(S)
R_F
R_G
= ^aNG
1+ ^{RF + RI NG}
Z_(S)
where:
NG ⁼
1+
R_F
R_G
(4)
This formula is written in a loop-gain analysis format,
where the errors arising from a noninfinite open-loop
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
Equation 4 determines the frequency response.
Equation 5 shows this as the loop-gain equation:
Z_{(S) = Loop Gain}
R_F + R_I NG
(5)
If 20 × log(R_F + NG × R_I) 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
the denominator of Equation 5, at which point the
loop gain reduces to 1 (and the curves intersect).
This point of equality is where the amplifier
closed-loop frequency response given by Equation 4
starts to roll off, and is exactly analogous to the
frequency at which the noise gain equals the
open-loop voltage gain for a voltage-feedback op
amp. The difference here is that the total impedance
in the denominator of Equation 5 may be controlled
somewhat separately from the desired signal gain (or
NG).
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The OPA4872 is internally compensated to give a
maximally flat frequency response for R_F = 523Ω at
NG = 2 on ±5V supplies. Evaluating the denominator
of Equation 5 (which is the feedback transimpedance)
gives an optimal target of 663Ω. As the signal gain
changes,
the
contribution
of
the
NG × R_I term in the feedback transimpedance will
change, but the total can be held constant by
adjusting R_F. Equation 6 gives an approximate
equation for optimum R_F over signal gain:
R_F = 663W - NG x R_I
(6)
As the desired signal gain increases, this equation
will eventually predict a negative R_F. A somewhat
subjective limit to this adjustment can also be set by
holding R_G to a minimum value of 20Ω. Lower values
load both the buffer stage at the input and the output
stage, if R_F gets too low, actually decreasing the
bandwidth. Figure 33 shows the recommended R_F
versus NG for ±5V operation. The values for R_F
versus gain shown here are approximately equal to
the values used to generate the Typical
Characteristics. They differ in that the optimized
values used in the Typical Characteristics are also
correcting for board parasitics not considered in the
simplified analysis leading to Equation 5. The values
shown in Figure 33 give a good starting point for
design where bandwidth optimization is desired.
600
550
500
450
400
350
300
250
200
150
100
0
5
10
15
20
Noise Gain
Figure 33. Feedback Resistor vs Noise Gain
The total impedance going into the inverting input
may be used to adjust the closed-loop signal
bandwidth. Inserting a series resistor between the
inverting input and the summing junction increases
the feedback impedance (denominator of Equation 4),
decreasing the bandwidth.
14
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