bruce mayer, pe registered electrical & mechanical engineer bmayer@chabotcollege
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BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt1
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
Bruce Mayer, PERegistered Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering 43
Chp 2.8Chp 2.8DependentDependent
SourcesSources
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt2
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
Ckts With Dependent SourcesCkts With Dependent Sources A Convention About Dependent Sources
• Unless Otherwise Specified The Current And Voltage Variables Are Assumed In SI Units Of Amps And Volts
XDIV
CONTROLLINGVARIABLE
DEPENDENTVARIABLE
• For This Example The Multiplier, , Must Have Units Of V/A or Ω
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt3
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
Other Dependent SourcesOther Dependent Sources
Three More Types of Dependent Sources• VD = VX ( a Unitless Scalar)
• ID = VX ( in Units of A/V, or Siemens)
• ID = IX ( a Unitless Scalar)
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt4
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
Analysis StrategyAnalysis Strategy General Strategy
• Treat Dependent Sources As Regular Sources And Add One More Equation For The Controlling Variable
Plan for Ckt at Rt• Single Loop Circuit
• Use KVL To Determine Current– KVL:
AV
KVL
05312 11 IkVIkV A
• 1-Equation, TWO-Unknowns: I1 and VA
– Controlling Variable Provides the Extra Equation
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt5
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
Analysis Example cont.Analysis Example cont. The Dependent Source
Control Equation
11 k22000 IIVA
mAk
VIVIk
IkIkIkV
26
12126
052312
11
111
VmAkIkVO 10255 1
Substitute VA Relation Into KVL
Use Ohm’s Law to Find VO
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt6
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
ExampleExample Find VO a
Strategy• If VS Is Known, Then VO Can Be Determined
Using Voltage Divider
• To Find VS We Note That We Have A Single Node-Pair– Mark Node-A
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt7
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
Example cont.1Example cont.1 Apply KCL (out POS) & Ohm at Node-A
kVI SO 3
This Single Eqn Contains TWO Unknowns• Use The Equation For The Dependent Source
Controlling Variable To Eliminate IO In Favor Of VS
• Sub For IO (Be Sure Maintain Consistent Units)
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt8
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
Example cont.2Example cont.2• Solving for VS (mult. Both sides by LCD of 6 kΩ)
VVVVk
V
k
V
k
V
kk SS
SSS 1256003
4
361
106
VVkk
kVV SO 8
3
212
42
4
• Now Apply The Voltage Divider Equation to Find VO
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt9
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
ExampleExample Find VO
The Plan• A One Loop Problem
• Find The Current
• Then Use Ohm’s Law
The Dependent Source Is Just One More Voltage Source• Apply KVL
KVL TOTHIS LOOP
012312 IkVIkV O
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt10
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
Example cont.Example cont. Use the Dependent Source Control Equation
to Eliminate VO
Solving for the Current, I
Finally, Solve for VO Using Ohm’s Law
mA2
121123
I
VIkIkIk
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt11
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
FET Amp ExampleFET Amp Example Find Voltage Gain or Amplification
tvtv
Ai
ov
KVL
KCL
The Plan• One Loop On The Left → KVL
• One Node-pair On Right → KCL
KVL
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt12
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
FET Amp Example cont.1FET Amp Example cont.1 Ohm’s Law
0)(
)( L
Ogm R
tvtvg
LoL Rtvti
Determined by a Voltage Divider
Load Resistor & vo
Apply KCL At Large Node
Then vo
Li
And from Above have vg as a function of vi
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt13
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
FET Amp Example cont.2FET Amp Example cont.2 Finally the Gain
Note That the Common-Source FET is an INVERTING Amplifier
BMayer@ChabotCollege.edu • ENGR-44_Lec-02-8_Dep-Sources.ppt14
Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis
WhiteBoard WorkWhiteBoard Work
Let’s Work Problem This Problem
8
4
4 3 I S
I o
6 V
If the OutPut Current Io is 2A
Then Find the Supply Current IS
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