ETC AB-050

```APPLICATION BULLETIN
®
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COMPENSATE TRANSIMPEDANCE AMPLIFIERS INTUITIVELY
By Tony Wang and Barry Ehrman
Transimpedance amplifiers are used to convert low-level
photodiode currents to usable voltage signals. All too often the
amplifiers have to be empirically compensated to operate
properly. The problem can be easily understood if one looks
at all the elements involved. Figure 1 shows the typical
photodiode application.
ACL(f) =
The ideal transimpedance transfer function is, by inspection:
RF
VOUT = –IS • ZF = –IS • 1 + j 2 π f R C
F F
=
This equation suggests that the frequency response is strictly
due to the feedback network. This does not explain why
transimpedance amplifiers are prone to oscillate. Figure 2
provides more insight into the stability problem. The photodiode is replaced with an ideal current source in parallel with
its equivalent resistance, RD, and capacitance, CD. The op amp
input capacitance cannot be considered insignificant and
should be included as part of CD.
RF + R D
RD
RF + R D
RD
RFRD
1+j2πf
•
RF + RD
(CF + CD)
1 + j 2 π f RFCF
1+j
f
fZ
1+j
f
fp
•
The dc gain is set solely by the resistors. The pole frequency,
fP, is set by the feedback network, just as in the transimpedance
function. The zero frequency, fZ, is determined by (a) the sum
of the feedback and the diode capacitances and (b) the parallel
combination of the feedback and the diode resistances.
Typically, the feedback resistor is much smaller than the
photodiode’s equivalent resistance. This makes the dc resistive gain unity. The value of the parallel combination is
essentially equal to the feedback resistor alone. Therefor, fZ
will always be lower than fP, as shown in Figure 3.
The noise gain (i.e., the noninverting closed-loop gain) of this
configuration determines the stability of the circuit. The
reason for this is that any noise signal, no matter how small,
can trigger an unstable circuit into oscillation. From inspection, the transfer function can be determined to be:
Log Av
CF
RF
1
VOUT
fP
fZ
Log f
FIGURE 3. Bode Plot of Noise Gain.
FIGURE 1. Typical Photodiode Transimpedance Amplifier.
Log Av
AOL
CF
RF
CD
RD
VOUT
1
fZ
FIGURE 2. Photodiode Modelled with Ideal Elements.
1993 Burr-Brown Corporation
fP2 fP3 fP1
fGBW
Log f
FIGURE 4. Various Feedback Responses Intersecting Op Amp
Open-loop Gain.
AB-050
Printed in U.S.A. March, 1993
Simple substitution yields a quadratic equation whose only
real, positive solution is:
1
CF =
(1 + 1 + 8π RFCDGBW)
4π RFGBW
Figure 4 depicts three different scenarios for the intersection
of the closed-loop response curve with the open-loop gain
curve. Stability degradation will occur when fP falls outside
the open-loop gain curve. For fP1 the circuit will oscillate. If fP
lies inside the open-loop gain curve, the transimpedance
circuit will be unconditionally stable. This is the case for fP2
but stability is traded off for transimpedance bandwidth. The
optimum solution paces fP on the open-loop gain curve as
shown for fP3.
This simple equation selects the appropriate feedback capacitor for guaranteed stability once the op amp’s minimum gainbandwidth and the photodiode’s maximum capacitance are
determined.
Since fP is determined by the feedback network, judicious
selection of CF is all that is necessary. This process can be
greatly simplified by noting that the high frequency asymptote
for the noise gain is determined by capacitance values alone:
CF + C D
ACL(f > > fP) =
CF
Further insight can be gained with some simplifying assumptions and a little algebra:
fP ≈
fP
=
2π RFCD
This result indicates that, for a given op amp and photodiode,
transimpedance bandwidth is inversely related to the square
root of the feedback resistor. Thus, if bandwidth is a critical
requirement, the best approach may be to opt for a moderate
transimpedance gain stage followed by a broadband voltage
gain stage.
This value should be equal to the op amp’s open-loop gain at
fP. The open-loop gain is found by dividing the op amp’s gainbandwidth product (GBW) by fP. Setting these two expressions equal yields:
GBW
GBW
CF + C D
CF
2
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