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bai tap Sensor

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ME220 Introduction to Sensors Homework #3, due 5:00 pm, Wednesday 5/7/08
1. Force Sensor + Circuit Calculations
A resistive contact force sensor has a response given by:
 F
R = R0 1 + 
 β
where R0 = 1000 Ω, β = 200N, F is the applied force (in Newtons), and R is the resistance of the
sensor.
This sensor is to be used for measuring forces ranging from 0 to 50N.
Please design a measuring circuit that will produce an output voltage that ranges from 0V to 4V
as the applied force ranges from 0 to 50N. Please design this circuit so that the nonlinearity in
the relationship between force and voltage is less than 1% of the full scale output.
You are allowed to use operational amplifiers, resistors, and circuit examples from the lectures,
handouts, and reading from the book.
2. Smart Home Thermostat
Heating and cooling of a building can be one of the largest sources of energy consumption in a
residence (just look at the power meter the next time your A/C comes on). In an effort to save
energy, a “smart home” heating and air conditioning thermostat allows for the variation of the
room temperature based on a variety of factors such as time of day, season, and heating load (i.e.,
orientation of the room with respect to the sun).
You are trying to design a retrofit system to a classic bimetallic unit and need to pick the
temperature sensor (don’t worry about the “smarts” - that is for another day).
A. Amount of Expansion and Hysteresis
The classic mechanical thermostat (shown in figure 1) uses a bimetallic strip.
Calculate difference in the lengths of the materials for a 1 meter long strip of copper
and iron for a temperature change of 5°C (thermal expansion coefficients can be
found in the textbook or elsewhere)?

1

Figure 1. Picture of mechanical thermostat (source: )
Assume that the copper and iron were bonded together to form a cantilever beam that
was 1 meter long, and flat at room temperature, and the copper and iron layers were
each 1 mm thick. When the temperature changes by 10°C, how much does the end of
the cantilever deflect? Again, the textbook may be some help here.
B. RTD
It is possible to replace this with a Resistance Temperature Detector (RTD).
Calculate and plot as a function of temperature the resistance for room temperatures
from 15°C to 30°C for Copper, Nickel, and Platinum. See course website or
 for specs. Assume
International Electrotechnical Commiss...
1
ME220 Introduction to Sensors Homework #3, due 5:00 pm, Wednesday 5/7/08
1. Force Sensor + Circuit Calculations
A resistive contact force sensor has a response given by:
+=
β
F
RR 1
0
where R
0
= 1000 , β = 200N, F is the applied force (in Newtons), and R is the resistance of the
sensor.
This sensor is to be used for measuring forces ranging from 0 to 50N.
Please design a measuring circuit that will produce an output voltage that ranges from 0V to 4V
as the applied force ranges from 0 to 50N. Please design this circuit so that the nonlinearity in
the relationship between force and voltage is less than 1% of the full scale output.
You are allowed to use operational amplifiers, resistors, and circuit examples from the lectures,
handouts, and reading from the book.
2. Smart Home Thermostat
Heating and cooling of a building can be one of the largest sources of energy consumption in a
residence (just look at the power meter the next time your A/C comes on). In an effort to save
energy, a “smart home” heating and air conditioning thermostat allows for the variation of the
room temperature based on a variety of factors such as time of day, season, and heating load (i.e.,
orientation of the room with respect to the sun).
You are trying to design a retrofit system to a classic bimetallic unit and need to pick the
temperature sensor (don’t worry about the “smarts” - that is for another day).
A. Amount of Expansion and Hysteresis
The classic mechanical thermostat (shown in figure 1) uses a bimetallic strip.
Calculate difference in the lengths of the materials for a 1 meter long strip of copper
and iron for a temperature change of 5°C (thermal expansion coefficients can be
found in the textbook or elsewhere)?
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