Lecture 2: Circuit Elements & Schematics Nilsson 2.1-2.5
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Transcript of Lecture 2: Circuit Elements & Schematics Nilsson 2.1-2.5
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Lecture 2:Circuit Elements & SchematicsNilsson 2.1-2.5
ENG17 (Sec. 2): Circuits I
Spring 2014
April 3, 2014
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Overview
• Voltage & Current Sources
• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources
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5 Ideal Basic Circuit Elements
• Voltage Sources• Current Sources• Resistors• Inductors• Capacitors
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Ideal SourcesVoltage Source(const. voltage)
Current Source(const. current)
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Dependent Sources
Voltage Sources Current Sources
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Schematics
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Schematics (w/dependents)
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Schematics - GND
• Ground (GND) is a common connection• Typically connect to Earth GND• Always a zero [V] reference potential
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Overview
• Voltage & Current Sources
• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources
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Ohm’s Law
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Conductance
• Conductance, G– Units: siemens [S]
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Power & Ohm’s Law
𝑉=𝐼𝑅
𝑃= 𝐼𝑉
Therefore…
Ohm’s Law
Power Relationship
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Examples
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Overview
• Voltage & Current Sources
• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources
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Designing a Circuit Model
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Additional Elements
Short Circuit
Open Circuit
Switch
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Schematic
1.5V 9V
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Overview
• Voltage & Current Sources
• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources
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The Setup
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Kirchhoff’s Current Law (KCL)
The algebraic sum of all the currents at any node in a circuit equals zero.
Therefore:• Assign signs to currents at each node• Positive (+) for current leaving a node• Negative (-) for current entering a node• Or vice versa
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Kirchhoff’s Voltage Law (KVL)
The algebraic sum of all the voltages around any closed path in a circuit equals zero.
Therefore:• Assign signs to voltages in a loop• Positive (+) for voltage rise• Negative (-) for voltage drop• Or vice versa
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Observations
• 7 equations 4 equations– Because I and V are related
through R, we only need one
• With only 2 branches at a node (in series), we only need to know 1 current
𝑣1=𝑖1𝑅1
𝑣𝑐=𝑖𝑐𝑅𝑐
𝑣 𝑙=𝑖𝑙𝑅 𝑙
𝑖𝑠− 𝑖1=0𝑖1+𝑖𝑐=0−𝑖𝑐−𝑖𝑙=0𝑖𝑙−𝑖𝑠=0
𝑣 𝑙−𝑣𝑐+𝑣1−𝑣𝑠=0
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KCL Example
𝑁𝑜𝑑𝑒𝑎 : 𝑖1+𝑖4−𝑖2−𝑖5=0
𝑁𝑜𝑑𝑒𝑏 : 𝑖2+𝑖3− 𝑖1− 𝑖𝑏− 𝑖𝑎=0
𝑁𝑜𝑑𝑒𝑐 : 𝑖𝑏−𝑖3−𝑖4− 𝑖𝑐=0
𝑁𝑜𝑑𝑒𝑑 : 𝑖5+𝑖𝑎+ 𝑖𝑐=0
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KVL Example
𝐿𝑜𝑜𝑝𝑎 :−𝑣1+𝑣2+𝑣4−𝑣𝑏−𝑣3=0
𝐿𝑜𝑜𝑝𝑏 :−𝑣𝑎+𝑣3+𝑣5=0
𝐿𝑜𝑜𝑝𝑐 :𝑣𝑏−𝑣4−𝑣𝑐−𝑣6−𝑣5=0
𝐿𝑜𝑜𝑝𝑑 :−𝑣𝑎−𝑣1+𝑣2−𝑣𝑐+𝑣7−𝑣𝑑=0
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Overview
• Voltage & Current Sources
• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources
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Finding vo
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Finding vo
KVL:
KCL:
Ohm’s Law:
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Recap
• Voltage & Current Sources
• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources