AF ´

¶P

=

´

¶ GBW

´

¶

x

1 + sCFRF

1 + sRF (CF + CIN)

=

´

¶ GBW

´

¶

x

1 + ¨

¨

©

§ C

FRF

CFRF

2

1 + ¨

¨

©

§ R

F (CF + CIN)

CFRF

2

= 1

GBW

A =

GBW

Z

Z

=

´

¶

´

¶

p =

1

1 + sCFRF

´

¶

z =

1

1 + sRF (CF + CIN)

´

¶

F =

1 + sCFRF

1 + sRF (CF + CIN)

-

+

CF

RF

IDIODE

VOUT

LMP7717

VA

CIN

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. CD represents the photodiode capacitance which is given on its datasheet. CCM 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 CD is connected to ground.

Figure 62 shows the schematic needed to derive F, the feedback factor, for a transimpedance amplifier. In

Figure 62, CD + CCM = CIN. 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 CF 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 CF compensates the circuit.

Figure 62. Transimpedance Feedback Model

Using feedback theory, F = VA/VOUT, 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)

CF 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 CF, 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 fGBW is the gain bandwidth product of the part. For a unity gain stable part this is the frequency

where A = 1. For the LMP7717 fGBW = 88 MHz. Multiplying A and F results in the following equation:

(16)

24

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