Upload
magdalene-knight
View
219
Download
2
Tags:
Embed Size (px)
Citation preview
A. Rivetti – INFN Sezione di Torino
Lecture II
Lecture II:
• Linear circuit theory review• Amplifier basics• MOS small signal model
A. Rivetti – INFN Sezione di Torino
Nodal analysis
Is VsR1
R2
R3
R4
Nodal analysis provides a systematic and reliable method to calculateall voltages and currents in a linear circuit
Nodal analysis
A. Rivetti – INFN Sezione di Torino
Writing nodal equations
R2 R4
Is VsR1 R3
v1 v2
0
0
4
2
3
2
2
12
2
21
1
1
RVv
Rv
Rvv
Rvv
RvI
s
s
Nodal analysis
A. Rivetti – INFN Sezione di Torino
Writing the circuit matrix
Is VsR1
R2
R3
R4v1 v2
RV
I
v
v
RRRR
RRRs
s
42
1
4322
221
1111
111
Nodal analysis
A. Rivetti – INFN Sezione di Torino
Solving the circuit matrix
RRRR
RRR
4322
221
1111
111
RRRRV
RI
s
s
4324
2
1 111
1
RV
R
IRRs
s
42
21
2 1
11
1
1v 2
2v
Nodal analysis
A. Rivetti – INFN Sezione di Torino
Lecture II
Lecture II:
• Linear circuit theory review• Amplifier basics• MOS small signal model
A. Rivetti – INFN Sezione di Torino
Amplifier characteristic
)()()()( ...2
210 txatxatxaaty n
n
The input-output characteristic of an amplifier is usually a non-linearfunction Over some interval of the input signal, this function can be approximated by a polynomial:
For narrow range of the input signal, we may write:
)()(10
txaaty
The above expression does not obey the superposition principle
Amplifier basics
A. Rivetti – INFN Sezione di Torino
Small signal model
If a0 does not depend on the signal, we can write:
)()(1
txaty
This is an expression that obeys the superposition principle
The small signal model takes into account only variations of signalswithin a circuit The small signal equivalent circuit can be studied with the methodsof linear circuit analysis
Amplifier basics
A. Rivetti – INFN Sezione di Torino
Voltage amplifier
Vs(t) Ri
Rs
VoutVi(t)
AV = Vout/Vi Input impedance high (ideally infinite) Output impedance small (ideally zero)
Amplifier basics
A. Rivetti – INFN Sezione di Torino
VA small signal model
AVViVoutVs(t) RI
RS
Vi(t)
RO
RL
Note: impedances may also be complex
Amplifier basics
A. Rivetti – INFN Sezione di Torino
Current amplifier
AV = Iout/Ii Input impedance small (ideally zero) Output impedance high (ideally infinite)
RiRs IoutIi(t)Is(t)
Amplifier basics
A. Rivetti – INFN Sezione di Torino
CA small signal model
Note: impedances may also be complex
Amplifier basics
RiRs Ii(t)Is(t) RLIout(t)RoIs(t)
A. Rivetti – INFN Sezione di Torino
Transconductance amplifier
Vs(t) Ri
Rs
IoutVi(t)
AV = Iout/Vi Input impedance high (ideally infinite) Output impedance high (ideally infinite) Important: the gain is not a number
Amplifier basics
A. Rivetti – INFN Sezione di Torino
TCA small signal model
Note: impedances may also be complex
Amplifier basics
Vs(t) RI
RS
Vi(t) RLIout(t)RoIs(t)
A. Rivetti – INFN Sezione di Torino
Transimpedance amplifier
AV = Vout/Ii Input impedance small (ideally zero) Output impedance small (ideally zero) Note: Gain is not a number
Amplifier basics
RiRs VoutIi(t)Is(t)
A. Rivetti – INFN Sezione di Torino
TA small signal model
Note: impedances may also be complex
RiRs Ii(t)Is(t) AVViVout
RO
RL
Amplifier basics
A. Rivetti – INFN Sezione di Torino
Lecture II
Lecture II:
• Linear circuit theory review• Amplifier basics• MOS small signal model
A. Rivetti – INFN Sezione di Torino
Simplified small signal DC model
RS
gm VGS
IDS= = n COX
W
L(VGS – VTH) 2 n COX
WL
IDS=
The MOS transistor in saturation can be seen as a voltage controlledcurrent source
Vs(t) Vs(t) gmVs
MOS small signal DC model
A. Rivetti – INFN Sezione di Torino
Practical example
What is the equivalent small signal model of this?
W=100 mL=10 mnCOX=190 A/V2
VTH=0.6 VVdrain=2.5 VVgate=1.25 V
MOS small signal DC model
Vgate
Vdrain
Vs
A. Rivetti – INFN Sezione di Torino
Gm simulation(1)
MOS small signal DC model
Vs=1mV pk-pk
355.7
356.7
0 1 2time (S)
curr
ent (
A)
A. Rivetti – INFN Sezione di Torino
Gm simulation (2)
MOS small signal DC model
Vs=250mV pk-pk
355
660
curr
ent (
A)
0 1 2time (S)
A. Rivetti – INFN Sezione di Torino
Including the output impedance
RS
gm VGS
IDS= = n COX
W
L(VGS – VTH) 2 n COX
WL
IDS=
ro1
IDS
=
The MOS transistor in saturation can be seen as a voltage controlledcurrent source with finite output impedance
Vs(t) Vs(t) rogmVs
MOS small signal DC model
A. Rivetti – INFN Sezione di Torino
Bulk transconductance
gmb VBS
IDS= = n COX
W
L(VGS – VTH)
VSB
VTH
=gm
2F + VSB
MOS small signal DC model
RS
Vs(t) Vs(t) rogmVs gmbvbs
For a more accurate model, the bulk effect must also be taken into account
A. Rivetti – INFN Sezione di Torino
Small signal DC model
The saturated MOS transistor is a voltage controlled current source with finite output impedance
RS
Vs(t) Vs(t) rogmVs gmbvbs
gm models the gate transconductancegmb models the bulk transconductance (the bulk effect)
MOS small signal DC model