ho6[1].l03 cs small signal
TRANSCRIPT
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Lecture 3Common Source Amplifier
Small-Signal Model
R. Dutton, B. Murmann
R. Dutton, B. Murmann 1EE114 (HO #6)
Stanford University
Let's Build Our Firs t Ampli fier
One way to amplify Convert input voltage to current using voltage controlled
current source (VCCS) Convert back to voltage using a resistor (R)
"Voltage gain" = Vout /Vin Product of the V-I and I-V conversion factors
R. Dutton, B. Murmann 2EE114 (HO #6)
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Common Source Amplifier
MOS device acts as VCCS
T
R. Dutton, B. Murmann 3EE114 (HO #6)
( )22
1
t iox D V V
L
W C I = ( ) RV V
L
W C V V
t iox DDo = 2
2
1
Biasing
Need some sort of "battery" that brings input voltage into usefuloperating region
Define V =V -V " uiescent oint ate overdrive" V OV=VGS -Vt with no input signal applied
VoVi
VO
Vo
R. Dutton, B. Murmann 4EE114 (HO #6)
"Bias"
"Signal"
VI
i
VOV
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Relationship Between Incremental Voltages
What is Vo as a function of Vi?
( ) +=+ iOV ox DDoO RV V W
C V V V 1 2
Note: V gs =Vi=(VI+Vi)
( )[ ][ ]
+=
+=
+=
OV
ii
OV
D
iiOV ox
OV iOV oxo
V V
V RV
I
V V V R LW
C
V V V R LW
C V
21
2
22
1
2
1
2
22
R. Dutton, B. Murmann 5EE114 (HO #6)
As expected, this is a nonlinear relationship
Nobody likes nonlinear equations; we need a simpler model Fortunately, a (1 st order) linear approximation to the above
expression is sufficient for 90% of all analog circuit analysis
Small Signal Approximation (1)
+=OV
ii
OV
Do V
V V R
V I
V 2
12
Assuming Vi
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Small Signal Approximation (2)
Graphical illustration:
Notation:
VO
VOV
dVo/dV i = v o/vi = Av
R. Dutton, B. Murmann 7EE114 (HO #6)
I
The slope of the above tangent is the so called "small-signalvoltage gain" of our amplifier (A v)
Notation
Total quantityQuiescentpoint value
Incrementalchange
oOo vV V +=
Total quantityQuiescentpoint value
Incrementalchange
Alternatively:(IEEE standard)
R. Dutton, B. Murmann 8EE114 (HO #6)
oOO vV v +=
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Small Signal MOS Model
Fortunately we don't have to repeat this analysis for every singlecircuit we build
Instead, we derive a linearized circuit model for the MOSrans s or an p ug n o ar rary c rcu s
R. Dutton, B. Murmann 9EE114 (HO #6)
Transconductance
The parameter that relates small signal gate voltage to draincurrent is called transconductance (g m), or y 21 in two-portnomenclature
The transconductance is found by differentiating the large signalI-V characteristic of the transistor at its operating point
( )22
1t GS ox D V V L
W C I =
( ) OV oxt GS oxGS
D
s
d m V L
W C V V
LW
C V I
vi
g ====
R. Dutton, B. Murmann 10EE114 (HO #6)
OV
Dm V
I g
2=
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Small-Signal Equivalent of CS Amplif ier
Use large signal I-V law to compute operating point (I D, VO, g m)
R. Dutton, B. Murmann 11
Make sure device operates in proper region; considerdesired signal swing
Now perform rest of calculations in small-signal land Gain, bandwidth (more later),
EE114 (HO #6)
Example (1)
Given: V I=1.5V, W=20 m, L=1 m, R=5k , VDD=5V Technology parameters: C ox = 50 A/V2, V t=0.5V a cu a e: D, O, g m, v
I +i
VO+vo
VDD
R
( ) AV .V .V A
I D =
= 50050511
2050
2
1 22
V . Ak V V O 5250055 ==
R. Dutton, B. Murmann 12EE114 (HO #6)
vi
VI
SaturationV V V V V
V .V V
t I t GS
O DS
====
1
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Example (2)
mS V .V .
AV I
gOV
Dm
15051
50022=
==
551 === k mS Rg A mv
R. Dutton, B. Murmann 13EE114 (HO #6)
Getting Started with HSpice
The above circuit was easy to analyze
In general, we want to be able to compute circuit characteristicsboth manually and by using a circuit simulator Both hand calculation and simulation is important; one does
not replace the other Double book keeping is important in design and analysis to
detect flaws in assumptions and understanding
R. Dutton, B. Murmann 14
Lets see how we can duplicate this result using HSpice
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HSpice Input File (1)
* Common sour ce ampl i f i er* B. Murmann, Fal l 2008
ev c e mo e
. model my_ nmos nmos kp=50u vt o=0. 5
*** usef ul opt i ons
. opt i on post bri ef nomod
vdd vdd 0 5
R. Dutton, B. Murmann 15
*** i nput vol t age
vi vi 0 dc 1. 5 *** val ue f or . op anal ysi s
+ ac 0. 1 *** ampl i t ude f or . ac anal ysi s+ si n 1. 5 0.1 1k *** si newave f or . t r an: V_I =1. 5V, v_i =0.1V, f =1kHz
EE114 (HO #6)
HSpice Input File (2)
*** d g s b
mn1 vo vi 0 0 my_ nmos w=20u l =1u
R vdd vo 5k
*** cal cul ate operati ng poi nt
. op
*** l arge si gnal anal ysi s ( sweep Vi )
. dc vi 0 5 0. 01
*** smal l si gnal anal ysi s ( sweep fr equency)
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. ac ec
*** t r ansi ent anal ysi s ( sweep t i me)
. t r an 1u 5m
. end
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.op Output
** ** mosf etsel ement 0: mn1
model 0: nmos114_
r e i on Satu r at i
i d 500. 0000u
vgs 1. 5000
vds 2. 5000
vbs 0.
vt h 500. 0000m
vdsat 1. 0000
vod 1. 0000
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e a . m
gam ef f 527. 6252m
gm 1. 0000m
gds 0.
EE114 (HO #6)
.dc Output
5
5.5
1.5
2
2.5
3
3.5
4
.
V o
[ V ]
R. Dutton, B. Murmann 18EE114 (HO #6)
0 1 2 3 4 50
0.51
Vi [V]
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1
[ V ]
.ac Output
102
103
0
.
f [Hz]
| v o
|
300
v o ) [ V ]
Av = v o/vi
= -0.5V/0.1V
= -5
R. Dutton, B. Murmann 19
102
103
0
100
f [Hz]
p h a s e
(
EE114 (HO #6)
.tran Output
3
3.5
1
1.5
2
2.5
[ V ]
R. Dutton, B. Murmann 20EE114 (HO #6)
0 0.5 1 1.5 2 2.5 3
x 10-3
0
0.5
t [sec]
Vi
Vo
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Another Run
Now with the following stimulus
*** i nput vol t age
vi vi 0 dc 1. 5 *** val ue f or . op anal ysi s
+ ac 1000 *** ampl i t ude f or . ac anal ysi s
+ si n 1. 5 1000 1k ** * si newave f or . t ran: V_I =1.5V, v_i =0. 1V, f =1kHz
1000V input amplitude applied to the circuit!
R. Dutton, B. Murmann 21EE114 (HO #6)
.tran Output
5
6
1
2
3
4
[ V ]
R. Dutton, B. Murmann 22EE114 (HO #6)
0 0.5 1 1.5 2 2.5 3
x 10-3
-1
0
t [sec]
Vi
Vo
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9000
10000
.ac Output
3000
4000
5000
6000
7000
8000
| v o
| [ V ]
5000V output!
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102
103
0
1000
2000
f [Hz]
EE114 (HO #6)
Important to Remember
Once a small-signal model of the circuit is constructed, all largesignal information is lost The small-signal (.ac) circuit transfer function is linear and
extends from to + Features such as finite voltage range, signal clipping, etc. are
lost and completely meaningless in a small-signal analysis (or.ac simulation)
The input amplitude in the .ac statement is irrelevant and can be
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Best to use 1V, in which case the output amplitude
corresponds to the circuit gain
EE114 (HO #6)