Programmable Gain Transimpedance Amplifiers Maximize Dynamic Range of Spectroscopy Systems (Part 2)

Select external components to ensure stability

　　Figure 4a is a good model for a photodiode amplifier. The open-loop transfer function of this system has a pole at 28 Hz due to the open-loop response of the op amp (see the data sheet), and another pole due to the feedback resistor and the parasitic resistance and capacitance of the photodiode. For the component values ​​we chose, this pole occurs at 1 kHz, as shown in Equation 1.

　　(1)

　　Note that Rsh is two orders of magnitude larger than Rf, so Equation 1 simplifies to:

　　(1a)

　　Each pole causes the open-loop transfer function to shift by 90°, for a total phase shift of 180°, well below the frequency at which the open-loop amplitude phase shift crosses 0 dB. As shown in Figure 4b, the lack of phase margin will almost certainly cause the circuit to oscillate.

　　To ensure stable operation, a capacitor can be placed in parallel with Rf to add a zero to the transfer function. This zero reduces the slope of the transfer function from 40 dB/decade to 20 dB/decade when it crosses 0 dB, resulting in a positive phase margin. The design should have at least 45° of phase margin to ensure stability. Higher phase margins result in less ringing, but the response time is increased. The zero that the capacitor adds to the open-loop response becomes a pole in the closed-loop response, so the closed-loop response of the amplifier degrades as the capacitance is increased. Equation 2 shows how to calculate the feedback capacitor to provide a 45° phase margin.

　　(2)

　　where fu is the unity gain frequency of the op amp.

　　This Cf value determines the highest practical bandwidth over which the system can operate. Although a smaller capacitor can be chosen to provide lower phase margin and higher bandwidth, the output may oscillate excessively. In addition, all components must be margined to ensure stability under worst-case conditions. In this example, Cf = 4.7 pF is chosen, which results in a closed-loop bandwidth of 34 kHz, which is typical of many spectroscopy systems.

　　Figure 5 shows the open-loop frequency response after adding the feedback capacitor. The phase response has a low point below 30°, but this is several decades away from the frequency where the gain becomes 0 dB, so the amplifier will remain stable.

　　Figure 5. Photodiode amplifier open-loop response using 1.2 pF feedback capacitor.

　　Programmable Gain TIA

　　One approach to designing a programmable-gain photodiode amplifier is to use a transimpedance amplifier with a gain that keeps the output in the linear region, even for the brightest light inputs. In this way, a programmable-gain amplifier stage can boost the output of the TIA in low-light conditions, achieving a gain close to 1 for high-intensity signals, as shown in Figure 6a. Another option is to implement the programmable gain directly in the TIA, eliminating the second stage, as shown in Figure 6b.

　　Figure 6. (a) TIA first stage followed by PGA; (b) Programmable gain TIA