Transcript EECS 215: Introduction to Circuits

Piezoresistive sensor
2. RESISTIVE CIRCUITS
CIRCUITS by Ulaby & Maharbiz
Overview
Ohm’s Law
Voltage across resistor is proportional to current
  iR

R
i
Resistance: ability to resist flow of electric current
r  resistivity
Conductivity
Example 2-1: dc Motor
What fraction of power supplied by the
battery is dissipated in the motor?
Solution:
= 98% of P
Tech Brief 3: Superconductivity

Critical temperature TC is the
temperature at which a material
becomes superconducting (zero
resistance & no power dissipation)
Circuit Topology
Branch: single element, such as a resistor or source
Node: connection point between two or more branches
Extraordinary Node: connection point between at least 3 branches
Loop: closed path in a circuit
node
branch
loop
Planar Circuits
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Planar circuits: can be drawn in 2-D without
branches crossing each other
Whenever possible, re-draw circuit to simplify!
Kirchhoff’s Current Law
Sum of currents entering a node is zero
Also holds for closed boundary
Kirchhoff’s Voltage Law (KVL)
Sum of voltages around a closed path is zero
Sum of voltage drops = sum of voltage rises
Example 2-4: KCL/KVL
Solution:
Loop 1
Loop 2
Three equations w/three unknowns:
Determine all currents & voltages
Equivalent Circuits
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If the current and voltage characteristics at nodes are
identical, the circuits are considered “equivalent”
Identifying equivalent circuits simplifies analysis
Resistors in Series
Equivalent resistance (series) is sum of resistances
Voltage divided over resistors (voltage divider)
Adding Sources In Series
Combining voltage sources
Unrealizable Circuit
Resistors in Parallel
Source Transformation
Hence,
For the two circuits to be equivalent :
Example 2-8: Source Transformation
R1,R2,R3=Delta
R3,R4,R5=Delta
R1,R3,R4=Y
R2,R3,R5=Y
Circuit with no two resistors sharing the same current or same voltage
Hence,
( Assuming no connection at node 3)
Simultaneous solution leads to:
Example 2-9: Y-Δ Circuit
Wheatstone Bridge
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Measurement instrument
based on differential
measurement
Balanced Condition:
Determine unknown
resistance based on
“balanced” condition
For balanced condition
Example 2-10: Wheatstone Sensor
Determine Vout
Tech Brief 4: Resistors As Sensors

Piezoresistive Sensors
Tech Brief 4: Resistors As Sensors

Thermistor Sensors
Example 2-12: Piezoresistor Cantilever
(400 times greater than w/o cantilever)
Linear i-v relationships
The Diode
Current can flow only from + to – through a diode.
Multisim
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SPICE simulator software
Powerful tool for analyzing circuits
See tutorial and examples on CD that accompanies
the text
Multisim: Creating a Circuit
Multisim: DC Operating Point Solution
Summary