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ECE 342 – Jose Schutt-Aine 1
ECE 342Solid-State Devices & Circuits
16. Active Loads
Jose E. Schutt-AineElectrical & Computer Engineering
University of Illinoisjschutt@emlab.uiuc.edu
ECE 342 – Jose Schutt-Aine 2
Ideal MOS Common Source CKT
, ,i vo m ds o dsR A g r R r
m dsIntrinsic gain is g r
ECE 342 – Jose Schutt-Aine 3
PMOS Implementation of Active Load
1 1 1ds oLet r r for Q
2 2 2ds or r for Q
1 2, ||out o othen R r r
1MB m outA g R
1 11
1o ds
o
Let g gr
2 22
1o ds
o
g gr
ECE 342 – Jose Schutt-Aine 4
'1
1
42 2 200 100 0.63 /
0.4m n REF
Wg k I mA V
L
Example
Assume VDD=3 V, Vtn = |Vtp| = 0.6 V, mnCox = 200 mA/V2, mpCox=65 mA/V2, L = 0.4 mm, W = 4 mm, VAn = 20 V, |VAP| = 10 V, IREF= 100 mA. Find small-signal gain.
11
20200
0.1An
oD
V Vr k
I mA
22
10100
0.1Ap
oD
V Vr k
I mA
1 1 2|| 0.63 200 ||100 42v m o oA g r r
ECE 342 – Jose Schutt-Aine 5
IC BJT CE
, ,i vo m o out oR r A g r R r
ECE 342 – Jose Schutt-Aine 6
1 2 1 2|| ||out o o ce ceR r r r r
1 2 1 2out s sC C C C C
Cs1 & Cs2 are the collector-to-substrate capacitances of Q1 and Q2 respectively
IC BJT Common Emitter
ECE 342 – Jose Schutt-Aine 7
IC Common Emitter – High Frequency Model
• High Frequency Calculations 1. Upper corner frequencies more difficult to
evaluate than for discrete amp2. Miller effect will be larger corner
frequency lower
ECE 342 – Jose Schutt-Aine 8
1
2in highin eq
fC R
Where CM1 is the Miller capacitance associated with Cm1
IC-CE: High-Frequency Analysis
1
2out highout out
fC R
1 1in MC C C
The total input capacitance in parallel with rp1 is
The input and output corner frequencies are
ECE 342 – Jose Schutt-Aine 9
ExampleThe CE circuit (see next page) is biased so that the collector currents of Q1 and Q2 are 1.14 mA. The parameters for Q1 are: b=160, rx1= 10 W, rce1= 68 kW, Cp1 = 20 pF, and Cm1 = 2.1 pF. For device Q2, the parameters are rce2= 21 kW and Cm2 = 3.1 pF. Each device has a value of Ccs1 = Ccs2 = 2.5 pF. In this circuit, the power supply is 10 V and R1 = 10 kW. Find the midband gain and the upper corner frequency.
1 2 1 2|| || 68 || 21 16out o o ce ceR r r r r k
Evaluate rp1 and Rout
1 1
261 161 3672
1.14er r
ECE 342 – Jose Schutt-Aine 10
The midband gain is:
1 1
outMB
x
RA
r r
160 16,000695 /
10 3672MBA V V
1 1 1 1
1 1
2 2in highin eq M x
fC R C C r r
The corner frequency of the input circuit is
Example (cont’)
ECE 342 – Jose Schutt-Aine 11
Example (cont’)
The corner frequency of the output circuit is
1
2out highout out
fC R
12
1
2 2.1 3.1 2.5 2.5 10 16,000out highf
975out highf kHz
12
1 110.7
2 2 1481 10 10in highin eq
f MHzC R
For overall corner frequency, use SPICE
ECE 342 – Jose Schutt-Aine 12
Source Follower
' 1|| ||L L o
mb
R R rg
'o m gs Lv g v R
Source Follower
gs i ov v v
'
'1o m L
vi m L
v g RA
v g R
1m o
vom mb o
g rA
g g r
1
1m
vom mb
gA
g g
ECE 342 – Jose Schutt-Aine 14
Source Follower – Output Resistance
1||o o
m mb
R rg g
1/ 1o mR g
ECE 342 – Jose Schutt-Aine 15
Source Follower with Active Load
• Characteristics – Provides a buffer stage– M1 is amplifying stage– M2 is active load
ECE 342 – Jose Schutt-Aine 16
Source Follower – Incremental Model
1
1 1 1 2
mMB
m mb ds ds
gA
g g g g
ECE 342 – Jose Schutt-Aine 17
(current mirror)
Emitter Follower with Active Load
Emitter follower can be used to drive a low-impedance load
ECE 342 – Jose Schutt-Aine 18
1 1 2
1 1 1 1 2
(1 )
(1 )
m ce
MBs x m ce
g r rA
R r r g r r
Midband gain:
Emitter Follower with Active Load
ECE 342 – Jose Schutt-Aine 19
Emitter Follower with Active Load
• AC Properties1. Gain is less than 1 and near 1 for typical
element values2. Frequency response has one zero and two
poles3. Exact frequency response is difficult Use
SPICE4. Output stage of NPN current mirror serves
as high impedance load at emitter of Q1
IC - Common Gate Amplifier
Substrate is not connected to the source must account for body effect
Drain signal current becomes
D m gs mb bsi g v g v
And since gs bsv v
Body effect is fully accounted for by using m m mbg g g
ECE 342 – Jose Schutt-Aine 21
i m mb i roi g g v i
m mb ioi o i i L
ro io o L
o
1g g v
rv v v i Ri i
r r R1
r
with i sv v
IC - Common Gate Amplifier
ECE 342 – Jose Schutt-Aine 22
i o L
ini m mb o
v r RR
i 1 g g r
As o inm mb
1r , R
g g
If L iR , R
o ro i m mb o i iv i v g g r v v
vo m mb oA 1 g g r
IC - Common Gate Amplifier
ECE 342 – Jose Schutt-Aine 23
whereo L Lin o m mb o
vo m mb o
r R R1R , A g g r
A g g A
Taking ro into account adds a component (RL/Ao) to the input resistance.
vo m mb oA 1 g g r
The open-circuit voltage gain is:
The voltage gain of the loaded CG amplifier is:
Lv vo
L o vo s
RG A
R r A R
IC - Common Gate Amplifier
ECE 342 – Jose Schutt-Aine 24
x x m mb ov i g g v r v with x sv i R
orout o m mb o s out o vo sR r 1 g g r R R r A R
CG Output Resistance
o Lin
o L
e e
r RR
r R1
r 1 r
vo m oA 1 g r 'out o m o eR r 1 g r R
'e eR R || re
rr
1
CB Amplifier
ECE 342 – Jose Schutt-Aine 26
11
1o
o
Define gr
Common source amplifier, followed by common gate stage – G2 is an incremental ground
MOS Cascode Amplifier
22
1o
o
gr
LR current source impedance
1L
L
GR
ECE 342 – Jose Schutt-Aine 27
• CS cacaded with CG CascodeVery popular configurationOften considered as a single stage
amplifier• Combine high input impedance and
large transconductance in CS with current buffering and superior high frequency response of CG
• Can be used to achieve equal gain but wider bandwidth than CS
• Can be used to achieve higher gain with same GBW as CS
MOS Cascode Amplifier
ECE 342 – Jose Schutt-Aine 28
MOS Cascode Incremental Model
Lo
L
iv
G
2 2 2 2 2 2L mb s m s s o oi g v g v v v g
2 2 2 2 2 2L
L s mb m s o oL
ii v g g v g g
G
ECE 342 – Jose Schutt-Aine 29
22 2 2 21 o
L s mb m oL
gi v g g g
G
22
2 2 2
1 /L o Ls
mb m o
i g Gv
g g g
KCL at vs2
1 2 1 2 2 2 2 2 2( ) 0m gs s o m s mb s o s og v v g g v g v g v v
MOS Cascode Analysis
ECE 342 – Jose Schutt-Aine 30
1 21 1
2 2 2
1 /1 0o o L
m gs Lo m mb
g g Gg v i
g g g
1 1
1 2
2 2 2
1 /1
m gsL
o o L
o m mb
g vi
g g G
g g g
1
1 2
2 2 2
o m
in o L oL
o m mb
v g
v g G gG
g g g
Two cases
MOS Cascode Analysis
ECE 342 – Jose Schutt-Aine 31
1 2 2 2 1 2 om o m mb o o
in
vg g g g r r
v
1 2 1 2 1 2 1 2 MB m o m m m mb o oA g g g g g g r r
1 1 2 2MB m o m oA g r g r
CASE 1
The voltage gain becomes
1: 0LCase If G
MOS Cascode Analysis
ECE 342 – Jose Schutt-Aine 32
1 2
2 2 2
2 : o L oL
o m mb
g G gCase If G
g g g
1 o m
MBin L
v gA
v G
CASE 2
The voltage gain becomes
MOS Cascode Analysis
ECE 342 – Jose Schutt-Aine 33
Cascode Example
ECE 342 – Jose Schutt-Aine 34
Cascode Example
The cascode circuit has a dc drain current of 50 mA for all transistors supplied by current mirror M3. Parameters are gm1=181 mA/V, gm2=195 mA/V, gds1= 5.87 mA/V, gmb2=57.1 mA/V, gds2= 0.939 mA, gds3= 3.76 mA/V, Cdb2 = 9.8 fF, Cgd2 = 1.5 fF, Cdb3=40.9 fF, Cgd3= 4.5 fF. Find midband gain and approximate upper corner frequency
1 2
2 2 2
5.87 3.76 0.9390.109 /
0.939 195 57.1o L o
Lo m mb
g G gA V G
g g g
3 3.76 / L dsG g A V
Therefore, we use Case 2 to compute the gain
The internal conductance of the current source is:
ECE 342 – Jose Schutt-Aine 35
Cascode Example
1 1
3
18148.1 /
3.76 m m
MBL ds
g gA V V
G g
Gain can be approximated by
Upper corner frequency is approximated by
2 15 33 2
1 110.6
2 2 56.7 10 266 10ods
f MHzr C
ECE 342 – Jose Schutt-Aine 36
Common emitter amplifier, followed by common base stage – Base of Q2 is an incremental ground
BJT Cascode Amplifier
ECE 342 – Jose Schutt-Aine 37
BJT Cascode Incremental Model
2 2o m Lv g R v
2 22 2
2 2 2
1x xx
x
v r rv v v
r r r
ECE 342 – Jose Schutt-Aine 38
BJT Cascode Analysis
1 1 2 22 2
xm m
x
vg v g v
r r
Ignoring rx2
21 1 2 2
2m m
vg v g v
r
1 1 2 22
1m mg v v g
r
ECE 342 – Jose Schutt-Aine 39
BJT Cascode Analysis
11
1 1in
s x
rv v
R r r
1 12
1 12
2
1
1m in
s xm
g r vv
R r rg
r
2 1 1
1 12
2
1
1m L m in
os x
m
g R g r vv
R r rg
r
ECE 342 – Jose Schutt-Aine 40
BJT Cascode Analysis
2 2 1 1
1 1 2 21o m m L
in s x m
v g r g r R
v R r r g r
1 2
1 1 2 1o L
in s x
v R
v R r r
1 2v m LA g R
If Rs << rx1+rp1, the voltage gain can be approximated by
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