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1. (20 points) You are working on a project to design a photodetector for an optical biomedical instrument that uses light interrogation to obtain information about the pulse rate. For this you look into using a photodiode (as a transducer) to convert the incident light into an output voltage. For a typical diode, the current-voltage (I-V) relation goes as I=1, (expr. ) - 1) Where Is is the diode saturation current and Vth is the thermal voltage. For a photodiode, note that the incident light falling over the diode generates the current within the diode through recombination-generation of the electron-hole pairs. The photocurrent so generated (I) is directly proportional to incident light intensity O, k is the light responsivity. Vth a. I = ko Write the photodiode output voltage V as a function of incident light intensity o (5 points) b. Write down the expression for sensitivity of this device. Find the sensitivity at very low light levels (i.e when 0 is very low). Is the sensitivity constant at different light intensity values? (5 points) c. Show that the sensitivity drops substantially at higher light levels. Write the sensitivity as a function of light intensity, and plot it on a log scale for light intensity O ranging from 0.01 Is/k to 1001s/k (5 points) d. Unfortunately for you, you need high sensitivity at high light intensity values for your device. So you look for alternate ways to overcome this limitation. For this you use a transimpedance amplifier with a tunable transresistance R. This very versatile instrument takes an input current Iin at zero input voltage, and returns an output voltage Vout that is directly proportional, Vout =R Iin. Show that the combination of the photodiode and the transimpedance amplifier yields a linear transducer with constant sensitivity that is tunable through the transresistance R. (5 points) NOTE (Taken from the wikepedia article): Re a transimpedance amplifier, (TIA) is a current to voltage converter, Current to voltage converters are used with sensors that have a current response that is more linear than the voltage response. This is the case V. out with photodiodes where it is not uncommon for the current Lin response to have better than 1% nonlinearity over a wide range of light input. The transimpedance amplifier presents a low impedance to the photodiode and isolates it from the output voltage of the operational amplifier. In its simplest form a transimpedance amplifier has just a large valued feedback resistor, R. The gain of the amplifier is set by this resistor and because the amplifier is in an inverting configuration, has a value of -Ri.