2. resistive circuits circuits by ulaby & maharbiz piezoresistive sensor all rights reserved. do...
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2. RESISTIVE CIRCUITS
CIRCUITS by Ulaby & Maharbiz
Piezoresistive sensor
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Ohm’s Law
Voltage across resistor is proportional to current
iR
Resistance: ability to resist flow of electric current
iR
r = resistivity
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ConductivityAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
Resistor Codes
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Example 2-1: dc Motor
= 98% of P
What fraction of power supplied by the battery is dissipated in the motor?
Solution:
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Tech Brief 2: Superconductivity
Critical temperature TC is the temperature at which a material becomes superconducting (zero resistance & no power dissipation)
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Kirchhoff’s Current Law
Sum of currents entering a node is zeroAlso holds for closed boundary
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Example
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Kirchhoff’s Voltage Law (KVL)
Sum of voltages around a closed path is zero
Sum of voltage drops = sum of voltage rises
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Example : KCL/KVL
Determine all currents & voltages
Solution:
Three equations w/three unknowns:
Loop 1
Loop 2
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Equivalent Circuits
If the current and voltage characteristics at nodes are identical, the circuits are considered “equivalent”
Identifying equivalent circuits simplifies analysis
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Resistors in Series
Equivalent resistance (series) is sum of resistances
Voltage divided over resistors (voltage divider)
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Adding Sources In Series
Unrealizable Circuit
Combining voltage sources
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Resistors in ParallelAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
Source Transformation
Hence,
For the two circuits to be equivalent :
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Example 2-10: Source Transformation
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Circuit with no two resistors sharing the same current or same voltage
R1,R2,R3=Delta
R3,R4,R5=Delta
R2,R3,R5=Y
R1,R3,R4=Y
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Between nodes 1 and 2:
( Assuming no connection at node 3)
Hence,
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Simultaneous solution leads to:
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Example 2-12: Y-Δ CircuitAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
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Wheatstone Bridge
Measurement instrument based on differential measurement
Balanced Condition:
Determine unknown resistance based on “balanced” condition
For balanced condition
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Wheatstone Sensor
Determine Vout
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Tech Brief 3: Resistors As Sensors Piezoresistive Sensors
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Tech Brief 3: Resistors As Sensors
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Tech Brief 3: Resistors As Sensors
Thermistor Sensors
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Example 2-16: Piezoresistor Cantilever
(400 times greater than w/o cantilever)
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Linear i-v relationships
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The Diode
Current can flow only from + to – through a diode.
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Multisim
SPICE simulator software Powerful tool for analyzing circuits See tutorial and examples on CD that
accompanies the text
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Multisim: Creating a CircuitAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
Multisim: DC Operating Point Solution
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Multisim Solution WindowAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press
SummaryAll rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press