APPLICATION BULLETIN ® Mailing Address: PO Box 11400 • Tucson, AZ 85734 • Street Address: 6730 S. Tucson Blvd. • Tucson, AZ 85706 Tel: (602) 746-1111 • Twx: 910-952-111 • Telex: 066-6491 • FAX (602) 889-1510 • Immediate Product Info: (800) 548-6132 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