A variety of precision applications sense light and convert that information into a useful digital word. At the system’s front end, a preamplifier converts the photodiode’s current-output signal to a usable voltage level. Figure 1 shows the front-end circuit of this system, which comprises a photodiode, an operational amplifier, and a feedback network. The transfer function of this system is:

where A_OL(jω) is the open-loop gain of the amplifier over frequency; β is the system-feedback factor, equaling 1/(1+Z_IN/Z_F); Z_IN is the distributed input impedance, equaling R_PD||jω(C_PD+C_CM+C_DIFF); and Z_F is the distributed feedback impedance, equaling R_F||jω(C_RF+C_F).

A good tool for determining stability is a Bode plot. The appropriate Bode plot for this design includes the amplifier’s open-loop gain and the 1/β curve. System elements determining the noise-gain frequency response are the photodiode’s parasitics and the operational amplifier’s input capacitance, as well as R_F, C_RF, and C_F in the amplifier’s feedback loop.

Figure 2 shows the frequency response of the 1/β curve and the amplifier’s open-loop-gain response: f_P=1/(2π(R_PD||R_F)(C_PD+C_CM+C_DIFF+C_F+C_RF)), and f_Z+1/(2π(R_F)(C_F+C_RF)). The A_OL(jω) curve intersects the 1/β curve at an interesting point. The closure rate between the two curves suggests the system’s phase margin and, in turn, predicts the stability. For instance, the closure rate of the two curves is 20 dB/decade. Here, the amplifier contributes an approximately –90° phase shift, and the feedback factor contributes an approximately 0° phase shift. By adding the 1/β phase shift from the A_OL(jω) phase shift, the system’s phase shift is –90°, and its margin is 90°, resulting in a stable system. If the closure rate of these two curves is 40 dB/decade, indicating a phase shift of –180° and a phase margin of 0°, the circuit will oscillate or ring with a step-function input.

One way to correct circuit instability is to add a feedback capacitor, C_F, or to change the amplifier to have a different frequency response or different input capacitance. A conservative calculation that allows variation in amplifier bandwidth, input capacitance, and feedback-resistor value places the system’s pole of 1/β at half the frequency where the two curves intersect:

where f_GBW is the gain-bandwidth product of the amplifier. In this design, the system’s phase margin is 65°, and the step function’s overshoot is 5%.