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Unformatted text preview: ME365 Homework Set 9 Out: October 27, 2011
Due: November 10, 2011 Problem No. 1
Given:
A sensor is to be used in the laboratory. The lowpass filter has been added to avoid
aliasing. Use the following circuit diagram to answer the questions below.
Rf
Rs
Ls +
+
Vs
 Cs V1 +
Cf  Sensor Vout
 Filter Find:
(a)
(b)
(c)
(d)
(e)
(f) Find the Thevenin equivalent circuit for the sensor.
Calculate the sensor’s output impedance
Derive the sensor’s frequency response function relating Vs to V1.
Calculate the filter’s input impedance
Derive the filter’s frequency response function relating Vout to V1.
Find the total system’s frequency response function (indicate the portion of the
response that is due to loading between the sensor and filter).
(g) Show how the circuit can be changed by adding an op amp to eliminate the
loading. ME365 Homework Set 9 Out: October 27, 2011
Due: November 10, 2011 a. No voltage drop across Ls. Use voltage divi der to find Eth as voltage drop
i
across capacitor. 1 1
1 1 Zth is impedance with shorted source

1
1 1 b.
1
c. 1
1 1
1 d.
e. Lowpass filter, can derive as a voltage divi der
1 1 1 1 1
1
f.
1
1 ⋅ 1 Loading term 1 ⋅ 1
1 1
1 1 g. Add a voltage follower between the sensor and filter. 1 1 ME365 Homework Set 9 Out: October 27, 2011
Due: November 10, 2011 Problem No. 2
Given:
A mass sensor is used to detect small amounts of che micals ranging from 0 to 10 μg. The
g
sensor has a sensitivity of 100 mV/μg with an output impedance of 106 Ω. The sensor
output is then sent to a recorder through a buffer (the re is a buffer between the sensor and
the recorder). The output impedance of the buffer and the input im
mpedance of the
recorder are both 100 Ω. The output of the recorder i s in μg and it can accept voltages
over the range 0100 mV.
Find:
(a) What should be the sensitivity of the recorder so that it can display mass (in μg)?
(b) What should be the input impedance of the bu ffer so that the recorder is neither
saturated nor wasted by not using its full rang e? a. 0 to 100 mV corresponds to 0 to 10 μg.
μg
10 μg
0.1
1
100 mV
mV
b.
1 100 ⋅ 1 100 ⋅
, ,
, 10
0.25 MΩ , , ⋅1⋅ ,
, , ⋅ 0.1 100
⋅ 0.1
1 00 200
,
250 kΩ
⋅1⋅ ME365 Homework Set 9 Out: October 27, 2011
Due: November 10, 2011 Problem No. 3
Given:
It has been shown in class that an opamp circuit can be used as a summer. It is
obvious that with an inversion, a summer can also be used for subtraction. Consider
the opamp circuits below. The current through the diode is given as
1
where VD is the voltage across the diode, IS is the saturation current of the diode and
VT is the thermal voltage of the diode. IS and VT are constants, they may be assumed
to be the same for both circuits. Hint: VT is relatively small, so Vin 1 . R
Vout R
Vin Vout Find:
(a) Find the relationship between Vout and Vin for the first circuit.
(b) Find the relationship between Vout and Vin for the second circuit.
(c) Draw a circuit for multiplication and derive the relationship between input
and output.
(d) Draw a circuit for division and derive the relationship between input and
output. ME365 Homework Set 9 Out: October 27, 2011
Due: November 10, 2011 a. Inverting input is a virtual ground. Curr ent through resistor must also go
through diode (infinite input impedanc e on opamp)
0 ln
b. Similar idea as the first
0 c. ln
ln
⋅ ln ln ⋅ ⋅ ⋅ ME365 Homework Set 9 Out: October 27, 2011
Due: November 10, 2011 d. ln
ln
ln
⋅ ln ln ...
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This note was uploaded on 12/26/2011 for the course ME 365 taught by Professor Merkle during the Fall '07 term at Purdue UniversityWest Lafayette.
 Fall '07
 MERKLE

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