Datasheet
AF
´
¶
P
=
´
¶
GBW
´
¶
x
1 + sC
F
R
F
1 + sR
F
(C
F
+ C
IN
)
=
´
¶
GBW
´
¶
x
¨
¨
©
§
1 +
¨
¨
©
§
C
F
R
F
C
F
R
F
2
¨
¨
©
§
1 +
¨
¨
©
§
R
F
(C
F
+ C
IN
)
C
F
R
F
2
= 1
GBW
A =
GBW
Z
Z
=
´
¶
´
¶
p
=
1
1 + sC
F
R
F
´
¶
z
=
1
1 + sR
F
(C
F
+ C
IN
)
´
¶
F =
1 + sC
F
R
F
1 + sR
F
(C
F
+ C
IN
)
-
+
C
F
R
F
I
DIODE
V
OUT
LMP7717
V
A
C
IN
LMP7717, LMP7718
SNOSAY7H –MARCH 2007–REVISED MARCH 2013
www.ti.com
Figure 61 is the complete schematic for a transimpedance amplifier. Only the supply bypass capacitors are not
shown. C
D
represents the photodiode capacitance which is given on its datasheet. C
CM
is the input common
mode capacitance of the op amp and, for the LMP7717 it is shown in the last graph of the TYPICAL
PERFORMANCE CHARACTERISTICS section of this datasheet. In Figure 61 the inverting input pin of the
LMP7717 is kept at virtual ground. Even though the diode is connected to the 2.5V line, a power supply line is
AC ground, thus C
D
is connected to ground.
Figure 62 shows the schematic needed to derive F, the feedback factor, for a transimpedance amplifier. In
Figure 62, C
D
+ C
CM
= C
IN
. Therefore it is critical that the designer knows the diode capacitance and the op amp
input capacitance. The photodiode is close to an ideal current source once its capacitance is included in the
model. What kind of circuit is this? Without C
F
there is only an input capacitor and a feedback resistor. This
circuit is a differentiator! Remember, differentiator circuits are inherently unstable and must be compensated. In
this case C
F
compensates the circuit.
Figure 62. Transimpedance Feedback Model
Using feedback theory, F = V
A
/V
OUT
, this becomes a voltage divider giving the following equation:
(12)
The noise gain is 1/F. Because this is a differentiator circuit, a zero must be inserted. The location of the zero is
given by:
(13)
C
F
has been added for stability. The addition of this part adds a pole to the circuit. The pole is located at:
(14)
To attain maximum bandwidth and still have good stability the pole is to be located on the open loop gain curve
which is A. If additional compensation is required one can always increase the value of C
F
, but this will also
reduce the bandwidth of the circuit. Therefore A = 1/F, or AF = 1. For A the equation is:
(15)
The expression f
GBW
is the gain bandwidth product of the part. For a unity gain stable part this is the frequency
where A = 1. For the LMP7717 f
GBW
= 88 MHz. Multiplying A and F results in the following equation:
(16)
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