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3 1. Photodiode amplifier circuit You are designinga CF photosensor circuit for a light detection and ranging LiDAR) system in autonomous vehicles. The circuit utilizes a transimpedance amplifier to convert low-level RF photodiode current signal to a usable voltage output. It consists of a photodiode, an amplifier, and feedback capacitor/resistor pair as shown in Figure 1. We will derive simple equations to understand the effects of parasitic elements on the stability of the detection circuit and help design a stable circuit appropriate for a real- Figure 1 Transimpedance op-amp circuit world implementation. (a) (3 pts) Is the photodiode connected in a photovoltaic mode or a photoconductive mode? (b) (4 pts) Explain why we cannot replace the photodiode with a CdS photoresistor in this circuit to achieve photodetection.2 (c) (3 pts) Which of the followings tend to impact the stability of this circuit? (One or more than one answer) (A) High-frequency signals (B) Low-frequency signals (C) Signals with rapid transitions (D) Noise (d) It is important to consider the impact of all capacitances and resistances in the circuit, including the photodiode junction characteristics and the amplifier parasitic input capacitances shown in Figure 2(a) CF CF RF Figure 2 Transimpedance amplifier circuit with a photodiode and amplifier presented in simplified models. This version accounts for the photodiode junction characteristics as well as amplifier parasitic input capacitances. The photodiode model has a photogenerated current IP, and the junction capacitance CD generated by the depletion of the pn junction. At the amplifier's non-inverting and inverting inputs there are three parasitic capacitances. CcM is the non-inverting and inverting input parasitic capacitance to AC ground. For CMOS devices, this is the gate and ESD cell to AC ground capacitance. Cpiff is the parasitic capacitance between the non-inverting and inverting input transistor's gates. All these capacitances appear in parallel, adding together to define C CD CCM CDiff, as shown in Figure 2(b). Explain why Ci includes only one CcM term in instead of two as shown in the equivalent circuit. Which of the two CcM's is not included?4 (4 pts) (e) (4 pts) Show that the feedback factor response curve B(s) is expressed by 1SREC (f) Oscillation can occur if the closed loop transimpedance amplifier circuit does not have enough phase margin for AoLB 2 1, where Ao is the open-loop gain of the op-amp. Hence, the intersection of the AoL (s) response curve with the 1/B (s) curve, i.e., AoL(s) 1/B(s) or loop gain AouB-1, denotes a critical intercept fundamental for stability analysis. Figure 3 shows the frequency responses of open loop gain AoL (s), and the reciprocal of feedback factor 1/B(s) given by 1 SRF(CiCF) β(s) 1+sRpCF Gain (dB) Ao20 dB/dec Unstable ---Stable 20 dB/dec 1/B f (log-scale) 0 dB fe Figure 3 Bode plot of three 1/B curves superimposed on an op-amp open-loop gain Aou curve. As the frequency increases well into the -20 dB/dec slope region of Aou, the dominant pole of the op- amp can add up to 90 degrees of phase shift. Similarly, the pole in β(s) can add another 90 degrees of phase shift. Addition of capacitor CF in parallel with RF introduces a zero in the feedback factor β(s), compensating the phase shift which can be seen graphically in Figure 3. A large C can decrease the phase shift more and further stabilize the circuit. However, it also reduces the usable bandwidth of the circuit. A good design requires the optimum value of CF to be calculated so that the added zero in B(s), or equivalently the pole in 1/B(s) at fi, is located at the frequency corresponding to AoLB 1. (4 pts) The zero and pole of 1/A(s) are located at the frequencies fe and f, respectively. Express f and ft i and CF in terms of RE,i, Hz. (6 2지 (g) (6 pts) Let us apply a graphic approach to determine Cp. Since both AOL and 1/β curves have a slope of 20 dB/dec, the approximate triangle formed by both curves with the horizontal axis is isosceles. Therefore, the intercept frequency fi, is the average of the other two vertices. Since the frequency is plotted in the logarithmic scale, we have log f, + log fGBwp where faswp gain-bandwidth product unity gain bandwidth of the op-amp. Use the relation and the fi and fe obtained in (f) to express C in terms of Ci, RF, and fGBwp in a form of (h) (3 pts) Continue (g), show that when Ci C, C can be reduced to (i) (4 pts) Appropriate components for this application are the Vishay Semiconductor TEFD4300 PIN photodiode and the Analog Devices ADA4666-2 amplifier. In this system, the power supply is 5 V with an output swing of the amplifier from 0.5 V to 4.5 V. To implement this output swing, VREF equals 0.5 V Know that the maximum expected output photocurrent is 10 μΑ, determine the value of feedback resistor RF to achieve a maximum output swing of 4.5 V. RF (j) (4 pts) Find CD- calculate C5 03 , CCM = | ⑩ |, and CDiff = | ⑩) | from the two datasheets and (k) (3 pts) Use the equation in (h) to calculate the Cp for this circuit. C

Answer 1

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