Lecture 26: Single stage amps, CD, BJT - University of ...ee105/sp04/handouts/lectures/...single...
Transcript of Lecture 26: Single stage amps, CD, BJT - University of ...ee105/sp04/handouts/lectures/...single...
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26
Lecture 26: Single stage amps, CD, BJT
Prof J. S. Smith
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Context
Today, we will continue to discuss biasing and small signal models for single transistor amplifiers, including the common base amplifier, and the similar bipolar transistor amplifiers, common emitter, common base, and common collector.
Next, we will be discussing the frequency response of these amplifiers
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Lecture Outline
Common Drain Amp
Bipolar:Common Emitter AmpCommon Base AmpCommon Collector Amp
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Transistor terminalsGate (Base)
– Less current than other terminals– S→D current a sensitive function of G-S voltage
(E→C) (B-E)Source (emitter)
– Relatively large amount of current– S→D current a sensitive function of G-S voltage(E→C) (B-E)
Drain (collector)– Relatively large amount of current (=Source)– S→D current not a sensitive function of voltage at this
terminal
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Source Amplifier
Isolate DC level
The input is at the gate, whichdoesn’t need any (much) current,and is a sensitive terminal (→S):large voltage and current gain
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common Gate Amplifier
DC bias:
SUP BIAS DSI I I= =
current gain=1Impedance buffer
Gain of transistortends to hold this node at ss ground:low input impedanceload for current input
Notice that IOUT must equal-Is
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CG as a Current Amplifier: Find Ai
out d ti i i= = −
1iA = −
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CG Input Resistance
At input:
Output voltage:
t outt m gs mb t
o
v vi g v g vr
⎛ ⎞−= − + + ⎜ ⎟
⎝ ⎠( || ) ( || )out d oc L t oc Lv i r R i r R= − =
gs tv v= −
( )||t oc L tt m t mb t
o
v r R ii g v g v
r⎛ ⎞−
= + + ⎜ ⎟⎝ ⎠
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Approximations…
We have this messy result
But we don’t need that much precision. Let’s start approximating:
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||1
m mbt o
oc Lin t
o
g gi r
r RR vr
+ += =
+
1m mb
o
g gr
+ >> ||oc L Lr R R≈ 0L
o
Rr
≈
1in
m mb
Rg g
=+
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CG Output Resistance
( ) 0s s tm gs mb s
S o
v v vg v g vR r
−− − − + =
1 1 ts m mb
S o o
vv g gR r r
⎛ ⎞+ + + =⎜ ⎟
⎝ ⎠
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CG Output Resistance
Substituting vs = itRS
1 1 tt S m mb
S o o
vi R g gR r r
⎛ ⎞+ + + =⎜ ⎟
⎝ ⎠
The output resistance is (vt / it)|| roc
|| 1oout oc S m o mb o
S
rR r R g r g rR
⎛ ⎞⎛ ⎞= + + +⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Approximating the CG Rout
The exact result is complicated, so let’s try tomake it simpler:
Sgm µ500≈ Sgmb µ50≈ Ω≈ kro 200
][|| SSombSomoocout RRrgRrgrrR +++=
][|| SSomoocout RRrgrrR ++≅
Assuming the source resistance is less than ro,
)]1([||][|| SmoocSomoocout RgrrRrgrrR +=+≈
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CG Two-Port Model
Function: a current buffer• Low Input Impedance• High Output Impedance
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Drain Amplifier
21 ( )2DS ox GS T
WI C V VL
µ= −
2 DSGS T
ox
IV V WCL
µ= +
Weak IDS dependence
In the common drain amp,the output is taken from aterminal of which the currentis a sensitivefunction
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CD Voltage Gain
Note vgs = vt – vout||
outm gs mb out
oc o
v g v g vr r
= −
( )||
outm t out mb out
oc o
v g v v g vr r
= − −
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CD Voltage Gain (Cont.)
KCL at source node:
Voltage gain (for vSB not zero):
( )||
outm t out mb out
oc o
v g v v g vr r
= − −
1|| mb m out m t
oc o
g g v g vr r
⎛ ⎞+ + =⎜ ⎟
⎝ ⎠
1||
out m
inmb m
oc o
v gv g g
r r
=+ +
1out m
in mb m
v gv g g
≈ ≈+
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CD Output Resistance
Sum currents at output (source) node:
|| || tout o oc
t
vR r ri
= t m t mb ti g v g v= +
1out
m mb
Rg g
≈+
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CD Output Resistance (Cont.)
ro || roc is much larger than the inverses of the transconductances ignore
1out
m mb
Rg g
≈+
Function: a voltage buffer• High Input Impedance• Low Output Impedance
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Voltage and current gain
Current tracks input
voltage tracks input
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Bipolar single stage amps.
BJT AmpsBJT BiasingCommon Emitter AmpCommon Base AmpCommon Collector Amp
– AKA Emitter Follower
β Multiplier ConceptEmitter Degeneration
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Bipolar Amplifiers
Common-emitter amplifier:
Biasing: adjustVBIAS = VBE sothat IC = ISUP.
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Small-Signal Two-Port Model
Parameters: (IC = 1 mA, β =100, VA = 3V)
oc3V|| || 3k||r 3k
1mAout o oc ocR r r r= = = ≈
25mV100 2.5k1mAin
m
R rgπβ
= = = = Ω
1mA 1 S 40mS25mV 25m mG g= = = =
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Base Amplifier
To find IBIAS, note that IBIAS = IE = - (1/αF)IC
Common-base currentgain Ai = - αF
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CB Input Resistance
Summing currents at the input node:
( ) 0t m o t ovi g v v v grπ
ππ
+ + + − =small 1
t m ti g vrπ
⎛ ⎞= +⎜ ⎟⎝ ⎠
1 11 1t m
in m mt m
v gR g gi r gπ β
− −⎛ ⎞ ⎛ ⎞= = + = + ≈⎜ ⎟ ⎜ ⎟
⎝ ⎠⎝ ⎠
25mV 251mA
= = Ω
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
CB Output Resistance
notepolarity
put roc back inafter finding vt / it
Same topology as CG amplifier, but with rπ || RS rather than RS
( )|| 1 ( ||out oc o m SR r r g r Rπ⎡ ⎤= +⎣ ⎦
( )|| 1out oc o mR r r g rπ⎡ ⎤= +⎣ ⎦SR rπ>>
( )|| 1out oc oR r r β= +
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Output Impedance Details
First draw small signal equivalent circuit with transistor and simplify as much as possibleThen (if needed) add the small signal equivalent circuitIf frequency is low, get rid of caps!
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Output Impedance Calculation
tv+
−
ti
rπ vπ
+
−
SR
mg vπ or
( )tt m
o
v vi g vr
ππ
− −= +
( || )t Sv i R rπ π= −
||( || ) t St m t S t
o o
v R ri g i R r ir r
ππ
−= − + +
||1 ( || ) S tt m S
o o
R r vi g R rr r
ππ
⎛ ⎞+ + =⎜ ⎟
⎝ ⎠
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Base Two-Port Model
Why did we consider it a current amp?
Current Amp :• Unity Current Gain (-1)• Small Input Impedance• Large (huge!) Output Impedance
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Collector Amplifier
DC Bias:output is one“VBE drop” downfrom input
“Emitter Follower”
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Collector Input Resistance
( 1) ( || || )t t t L o ocv i r i R r rπ β= + +
( 1)( || || )in L o ocR r R r rπ β= + +
( 1)in LR r Rπ β≈ + +
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Collector Output Resistance
Divider between vt and vπ :
1 1( || ) 0t m t o oci g v v r v r rπ π π− −+ + − =
tS
rv vr R
ππ
π
=+
( )1 1( || )t t m t o ocS
ri v g r v r rr R
ππ
π
− −⎛ ⎞= + +⎜ ⎟+⎝ ⎠
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Collector Output Res. (cont)
Looking into base of emitter follower: load impedance larger by factor β+1Looking into emitter of follower: “source”impedance smaller by factor β+1
( )1 1( || )t t m t o ocS
ri v g r v r rr R
ππ
π
− −⎛ ⎞= + +⎜ ⎟+⎝ ⎠
( ) 11t t mS
i v g rr Rππ
⎛ ⎞= + ⎜ ⎟+⎝ ⎠
1t S
outt
v r RRi
π
β+
= =+
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Collector Voltage Gain
KCL at the output node: note vπ = vt - vout
( ) 1 1||out oc o mv r r g v v rπ π π
− −= +
( ) ( )1 1|| ( )out oc o m t outv r r g r v vπ
− −= + −
( )( ) ( )1 1 1||out oc o m m tv r r g r g r vπ π
− − −+ + = + out tv v=
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Common-Collector Two-Port Model
typo: RL
Voltage Amp :• Unity Voltage Gain (+1)• Large Input Impedance• Small Output Impedance
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Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 26 Prof. J. S. Smith
Summary of Two-Port Parameters