Upload
others
View
0
Download
0
Embed Size (px)
Citation preview
1 EE 303 – Electronics I
The "Atoms" of Analog Circuit Design
C. Talarico Gonzaga University
Source: R. Dutton, B. Murmann Stanford University
2 EE 303 – Electronics I
Elementary Amplifier Configurations
CommonSource
CommonGate
CommonDrain
Transconductance Stage
Current Buffer
Voltage Buffer
One-Transistor Stages
Source: R. Dutton, B. Murmann Stanford University
3
Common Source Stage
• A common source stage is sufficient for building a simple amplifier.
• How about the other two possible single-transistor configurations?
• We'll find that common gate and common drain stages can be incorporated as valuable add-ons, for building "better" amplifiers
• Interestingly, many analog circuits can be decomposed into a combination of the above three fundamental building blocks
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
4
Widely Used Two-Transistor Stages
Cascode Stage
Current Mirror
Differential Pair
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
5
Let's Build Our First Amplifier (CS Amplifier)
• 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" = ΔVout/ΔVin – Product of the V-I and I-V conversion factors
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
6
Common Source Amplifier
• MOS device acts as VCCS
IdVi
Vo
VDD
Id =12µCox
WLVi −Vt( )2 ( ) RVV
LWCVV tioxDDo ⋅−−= 2
21µ
T
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
7
Biasing
• Need some sort of "battery" that brings input voltage into useful operating region
• Define VOV=VI-Vt, "quiescent point gate overdrive” (no input signal applied) – with no input signal applied VOV=VGS-Vt
VI
ΔVo
ΔVi
VO
VOV
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
8
Relationship Between Incremental Voltages
• What is ΔVo as a function of ΔVi?
VO +ΔVo =VDD −12µCox
WLVOV +ΔVi( )2 ⋅R
ΔVo = −12µCox
WLR ⋅ VOV +ΔVi( )2 −VOV2$%
&'
= −12µCox
WLR ⋅ 2VOVΔVi +ΔVi
2$% &'
= −2IDVOV
⋅R ⋅ ΔVi 1+ΔVi2VOV
$
%(
&
')
• As expected, this is a nonlinear relationship
• Nobody likes nonlinear equations; we need a simpler model – Fortunately, a (1st order) linear approximation to the above
expression is sufficient for 90% of all analog circuit analysis
Note: Vgs=Vi=(VI+ΔVi)
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
9
Small Signal Approximation (1)
• Assuming ΔVi << 2VOV, we have
!"
#$%
& Δ+Δ⋅⋅−=Δ
OV
ii
OV
Do V
VVRVIV
212
iOV
Do VR
VIV Δ⋅⋅−≅Δ2
• If we further pretend that the input voltage increment is infinitely small, we can find this result directly by taking the derivative of the large signal transfer function at the "operating point" VI
dVodVi Vi=VI
= −2IDVOV
⋅R = −µCoxWLVOV ⋅R = Av
small-signal voltage gain
Note: ΔVi is the max excursion of the signal Vi from VI
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
10
Small Signal Approximation (2)
• Graphical illustration:
VI
VO
VOV
dVo/dVi
• The slope of the above tangent is the so called "small-signal voltage gain" of our amplifier (Av)
= vo/vi = Av
Notation:
Vi=VI
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
11
Notation
oOo vVV +=
Total quantity Quiescent
point value Incremental
change
Total quantity Quiescent
point value Incremental
change
Alternatively: (IEEE standard)
ΔvO
ΔVo
oOO vVv +=
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
12
Small Signal MOS Model
• Fortunately we don't have to repeat this analysis for every single circuit we build
• Instead, we derive a linearized circuit model for the MOS transistor and plug it into arbitrary circuits
ID+id
+VDS+vds-+
VGS+vgs-
id
+vds-
+vgs-Conditions:
VDS>VGS-Vtvgs<<VGS-Vt
gm×vgs
Id
ID
VGS Vgs
gm
id
vgs
gm
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
13
Transconductance
• The parameter that relates small signal gate voltage to drain current is called transconductance (gm)
• The transconductance is found by differentiating the large signal I-V characteristic of the transistor at its operating point
( )221
tgsoxd VVLWCI −µ=
( ) OVoxtGSox
VVgs
d
gs
dm V
LWCVV
LWC
dVdI
vig
GSgs
µ=−µ====
OV
Dm V
Ig 2=
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
14
Small-Signal Equivalent of CS Amplifier
• Use large signal I-V law to compute operating point (ID, VO, gm) – Make sure device operates in proper region; consider
desired “signal swing”
• Now perform rest of calculations in “small-signal land” – Gain, bandwidth (more later), …
ID+DId
VO+DVo
VDD
DVi
VI
ΔVo
ΔId
ΔVi
+vo-
+vgs-
gm×vgs
R
vi
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
15
Example (1) • Given: VI=1.5V, W=20µm, L=1µm, R=5kΩ, VDD=5V • Assume the desired signal swing ΔVi at the input is small enough
for the transistor to operate in the same region at all time • Technology parameters: µCox = 50µA/V2, Vt=0.5V
• Calculate: ID, VO, gm, Av
ID+id
VO+vo
VDD
vi
VI
R( ) AV.V.
VAID µ=−⋅⋅µ
⋅= 500505112050
21 2
2
V.AkVVO 5250055 =µ⋅Ω−=
SaturationVVVVV
V.VV
tItGS
ODS ⇒⎭⎬⎫
=−=−
==
152
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
16
Example (2)
mSV.V.A
VIgOV
Dm 1
505150022
=−
µ⋅==
551 −=Ω⋅−=−= kmSRgA mv
+vo-
+vgs-
gm×vgs
R
vi
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
17
Getting Started with HSpice
• The above circuit was easy to analyze – And it is unlikely that we made a mistake
• In general, we want to be able to compute circuit characteristics both 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
• Let’s see how we can duplicate this result using HSpice…
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
18
HSpice Input File (1)
* Common source amplifier
* Filename: one.sp
* C. Talarico, Fall 2014
*** device model
.model simple_nmos nmos kp=50u vto=0.5
*** useful options
.option post brief nomod
*** Supply voltage
vdd vdd 0 5
*** input voltage
vi vi 0 dc 1.5 *** value for .op analysis
+ ac 0.1 *** amplitude for .ac analysis
+ sin 1.5 0.1 1k *** sinewave for .tran: V_I=1.5V, v_i=0.1V, f=1kHz
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
19
HSpice Input File (2) *** Circuit
*** d g s b
mn1 vo vi 0 0 simple_nmos w=20u l=1u
R1 vdd vo 5k
*** calculate operating point
.op
*** large signal analysis (sweep Vi)
.dc vi 0 5 0.01
*** small signal analysis (sweep frequency)
.ac dec 10 100 1k
*** transient analysis (sweep time)
.tran 1u 5m
.end
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
20
.op Output **** mosfets
element 0:mn1
model 0:simple_nmos
region Saturati
id 500.0000u
vgs 1.5000
vds 2.5000
vbs 0.
vth 500.0000m
vdsat 1.0000
vod 1.0000
beta 1.0000m
gam eff 527.6252m
gm 1.0000m
gds 0.
…
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
21
.dc Output
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5 V
o [V
]
Vi [V]
DC Transfer Function
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
22
.ac Output
Av = vo/vi
= -0.5V/0.1V
= -5 101 102 103 104
−0.5
0
0.5
1
1.5
|vo|
[V]
f [Hz]
Small Signal Transfer Function
101 102 103 1040
100
200
300
pha
se(v
o) [d
egre
e]
f [Hz]
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
23
.tran Output
0 0.5 1 1.5 2 2.5 3x 10−3
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
time [sec]
vol
tage
[V]
Transient Analysis (sweep time)
ViVo
NOTE: Vo is slightly above 2V and slightly below 3V. The discrepancy with hand calculation is due to the fact that the MOS behavior is not linear (the small signal model is an approximation !)
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
24
Another Run
• Now with the following stimulus
*** input voltage
vi vi 0 dc 1.5 *** value for .op analysis
+ ac 1000 *** amplitude for .ac analysis
+ sin 1.5 1000 1k *** sinewave for .tran: V_I=1.5V, v_i=1000V, f=1kHz
• 1000V input amplitude applied to the circuit!
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
25
.tran Output
0 0.5 1 1.5 2 2.5 3x 10−3
−1
0
1
2
3
4
5
6
time [sec]
vol
tage
[V]
Transient Analysis (Vi = sin 1.5 1000 1k)
ViVo
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
26
.ac Output
101 102 103 1040
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
|vo| [
V]
f [Hz]
Small Signal Transfer Function
5000V output ?!?
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
27
Important to Remember
• Once a small-signal model of the circuit is constructed, all large signal 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 set to any number (other than 0) – Best to use 1V, in which case the output amplitude
corresponds to the circuit gain
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
28
HSPICE Deck (1)
* Common source amplifier
* filename: one.sp
* C. Talarico, Fall 2014
*** device model
.model simple_nmos nmos kp=50u vto=0.5
*** useful options
.option post brief nomod
*** supply voltage
vdd vdd 0 5
*** input voltage
vi vi 0 dc 1.5 *** value for .op analysis
+ ac 0.1 *** amplitude for .ac analysis
+ sin 1.5 0.1 1k *** sinewave for .tran: V_I=1.5V, v_i=0.1V, f=1kHz
*** circuit
*** d g s b
mn1 vo vi 0 0 simple_nmos w=20u l=1u
R1 vdd vo 5k
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
29
HSPICE Deck (2)
*** calculate operating point
.op
*** large signal analysis (sweep Vi)
.dc vi 0 5 0.01
*** small signal analysis (sweep frequency)
.ac dec 10 100 1k
*** transient analysis (sweep time)
.tran 1u 5m
.alter another_run
*** input voltage
vi vi 0 dc 1.5 *** value for .op analysis
+ ac 1000 *** amplitude for .ac analysis
+ sin 1.5 1000 1k *** sinewave for .tran: V_I=1.5V, v_i=1000V, f=1kHz
.end
EE 303 – Electronics I
Source: R. Dutton, B. Murmann Stanford University
30
MATLAB script
EE 303 – Electronics I