lecture 03 two port networks
DESCRIPTION
Two Port NetworksTRANSCRIPT
EEE 51: Second Semester 2014 -‐ 2015 Lecture 3
Two-‐Port Networks Single-‐Stage Amplifiers
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Today
• Two-‐Port Networks • Single-‐Stage Amplifiers
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Two-‐Port Network ReducEon
• Can reduce any linear circuit into 4 parameters
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Linear à R, L, C, dependent sources
V1+−
+−V2
I1 I2
V1+−
I1
+−V2
I2
2-‐Port Network
Given 2 terminal parameters (V or I), we can get the other 2 (V or I)
I1I2
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y11 y12y21 y22
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V1V2
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V1V2
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z11 z12z21 z22
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I1I2
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V1I1
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%&&= A B
C D
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V2−I2
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V1I2
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h11 h12h21 h22
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I1V2
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these representaEons for EEE 51?
The Bilateral Hybrid-‐π Two-‐Port Network
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Thevenin equivalent:
Norton equivalent:
Unilateral equivalents?
The Unilateral Hybrid-‐π Two-‐Port Network
• Requires only 3 parameters
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The Thevenin Equivalent (Ri, Av, Ro)
The Norton Equivalent (Ri, Gm, Ro)
Looks very familiar…
OperaEng CondiEons (1)
• No-‐Load à No power draw at the output
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Open circuit
Short circuit vo = 0
io = 0
OperaEng CondiEons (2)
• Zero-‐Input à No excitaEon at the input
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vin+−
iin
vin = 0+−
iin
vin+−
iin = 0
vin+−
iin
Solving for the Hybrid-‐π Parameters (1)
• Circuit Transconductance
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Solving for Gm: vin
+−
+−vout
iin iout
No-‐load vout = 0
Gm =ioutvin no-load
Solving for the Hybrid-‐π Parameters (2)
• Circuit Voltage Gain
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Solving for Av: vin
+−
+−vout
iin iout
No-‐load iout = 0
Av =voutvin no-load
Solving for the Hybrid-‐π Parameters (3)
• Circuit Output Resistance
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Solving for Ro: vin
+−
+−vout
iin ioutZero-‐input iin = 0vin = 0
Ro =voutiout zero-input
or
Solving for the Hybrid-‐π Parameters (4)
• Circuit Input Resistance
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Solving for Ri: vin
+−
+−vout
iin iout
No-‐load iout = 0
Ri =viniin no-load
Cascading Two-‐Port Networks
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Circuit A Circuit B
Equivalent 2-‐Port Circuit taking into account loading effects
Av,eq = Av,A ⋅Ri,B
Ri,B + Ro,A⋅Av,B
Ri,eq = Ri,ARo,eq = Ro,B
So Far… • We can analyze small signals
separately from large signals
• We can use 2-‐port networks to reduce/combine small signal circuits
• Let’s look at the small signal behavior of our basic electronic circuit building blocks: – Single-‐stage amplifiers
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C
E
B D
S
G
Where do we put in the input?
Where do we get the output?
Choices:
Where do we start?
Transistor Amplifier Analysis
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DC Analysis
Transistor Circuit
Small Signal Analysis
Transistor DC currents
Large signal models
2-‐Port Parameters
IC = IS eVBEVT −1( ) 1+VCEVA
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IC,Q,VCE,Q
gm, ro, rπ
Av,Gm,Ro,Ri
The Basic Common-‐Emi`er (CE) Amplifier
• Full vs. simplified schemaEcs
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Common-‐Emi`er DC Analysis
• ObjecEve: Determine IC,Q
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VCC − IC,QRL −VCE,Q = 0
IC,Q = IS eVINVT −1( ) 1+VCE,QVA
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KVL equaEons à 2 equaEons, 2 unknowns (assumpEons?)
In most cases, we will deal with: VOUT =VCE,Q <<VA
IC,Q = IS eVINVT −1( )
Thus,
VOUT =VCC − IC,QRL
=VCC − RLIS eVINVT −1( )
Common-‐Emi`er Amplifier Small Signal Analysis
• Given IC,Q:
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ro =VAIC,Q
gm =IC,QVT
rπ =β ⋅VTIC,Q
What about the other circuit elements? • Resistors • Independent voltage/current sources
Linear Two-‐Terminal Devices
• Small signal conductance / resistance:
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R VDC IDC
Rsmall signal =∂V∂I
V
I
IDC
V VDC
V
I I
Slope=1/R
Rsmall signal = R Rsmall signal = 0 Rsmall signal →∞
CE Amplifier Small Signal Equivalent Circuit
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Gm = gmRi = rπRo = ro || RLAv = −GmRo= −gm ro || RL( )
“inverEng amplifier”
Define: Intrinsic Transistor Gain (ao)
• Ideal bias circuit:
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Gm = gmRi = rπRo = roAv = −GmRo = −gmro = ao
ao à largest voltage gain out of a single transistor
RL →∞Why?
ao = −gmro = −IC,QVT
⋅VAIC,Q
= −VAVT
= −q ⋅VAkT
How do we interpret voltage gain?
• Large signal transfer characterisEc:
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VOUT =VCC − RL ⋅ IS ⋅eVINVT
VCE,satNote:
IC,max =VCC −VCE,sat
RL
Regions of operaEon?
vin
vout
Small Signal Voltage Gain
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Av =∂VOUT∂VIN
VOUT =VCC − RL ⋅ IS ⋅eVINVT Av =
∂VOUT∂VIN
= −RLIS ⋅e
VINVT
VT= −RL
IC,QVT
AssumpEons? • VA à ∞
Compare to Av = −gm ro || RL( )
Choosing the Bias Point?
• Largest gain? à Point C
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VCC = 5VRL = 500Ω
Transient Response at Point C: Output Swing
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VCC = 5VRL = 500Ω
VCE,sat
Transient Response at Point A: Output Swing
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VCC = 5VRL = 500Ω
Transient Response at Point B: Output Swing
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VCC = 5VRL = 500Ω
Choosing the Bias Point à Swing vs. DistorEon
• Depends on what you need
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VCC = 5VRL = 500Ω
Quiescent DC Power
• AmplificaEon requires power input
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PDC =VCCIC,Q +VIN IB,Q
=VCCIC,Q +VINIC,Qβ
= IC,Q VCC +VINβ
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In general: • Higher gain à larger IC,Q à higher DC power consumpEon
Next MeeEng
• Single-‐Stage Amplifiers – Common-‐Emi`er Biasing – Common-‐Source Amplifier
– Common-‐Base / Common-‐Gate Amplifier
– Common-‐Collector / Common-‐Drain Amplifier
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