1. Using Kirchoffs Current and Voltage laws (KCL and KVL), find and ? for the top circuit and 0 for the bottom circuit.
2.Consider the two-port voltage-in, voltage-out instrument on the left.
a. Find the input impedance () as seen at the input terminal.
b. Find the output impedance () as seen at the output terminal.
c. Find the transfer function ()().
Consider the two-port current-in, current-out instrument on the left.
d. Find the input impedance () as seen at the input terminal.
e. Find the output impedance () as seen at the output terminal.
f. Find the transfer function ()().
3. A photodetector converts photonic energy represented as light intensity, [2] into electrical energy represented as electrical current, [] through the following relationship:
=+2++,
where =109 [], =0.2 [2/], =2109 [42], =10109 [2], =0.5109 []
a. Find an expression for the sensitivity of the photodetector.
b. Calculate the output current range of the photodetector, if it measures indoor lighting between 1 and 10 /2.
The photodetector output is amplified by an amplifier with a linear input-output relationship given by ,=,107 [/]. The amplifier output, ,, is then fed into an 8-bit analog-to-digital converter (ADC) which linearly converts the , into digital outputs. The input range of the ADC corresponds to , for indoor lighting ranging from 1 to 10 /2. Thus, the ADCs reference voltage is: =(,|=102,|=12)
c. Find the resolution of the ADC.
d. Determine the indoor light intensity at which the system has the worst accuracy, and calculate the accuracy at that light intensity. Use the percentage accuracy expression:
= ? ? ?100
(Hint: The true value is ,, which has a nonlinear dependence on . However, the ADC converts , linearly into digital outputs and thus creating an error. By converting the ADC output, which ranges from 0 to 256, into the corresponding value using the linear relationship, you can determine the measured value of the system. Identify the light intensity where the error is maximum. If solving analytically is not feasible, solve numerically using MATLAB.)
4. You create an instrument that transforms stress () applied to a flexible diaphragm into voltage output (). Stress () generates strain () in the diaphragm using the equation =, where represents Youngs Modulus. You attach two strain gauges, 1 and 2, to the diaphragms surfaces as shown below.
The strain gauges possess the same nominal resistance (0) and gauge factor (). Strain () differentially changes the resistances of RG1 and RG2 as follows:
1= 00
2= 0+0
Then you build a Wheatstone Bridge using 1, 2, and two constant resistors , as shown below.
a) Find the output voltage, , as a function of and .
b) Youngs modulus of the diaphragm is given as =3 x 109 with the units of Pascal. =100. Find the sensitivity of the instrument. (Hint: Input of the instrument is stress, and the output of the instrument is .)
