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81
6.7 The Common-Gate and Common-base Amplifiers with active Loads
6.7.2 The Common-Base Amplifier
(a) Active-loaded common-base amplifier.
82
- Analysis with RL Input Resistance R in :
i
i in
i
v
R =
(b) Small-signal analysis
performed directly on the
circuit diagram with the BJT T
model used implicitly.
ii = vi/ re+i ro =vi / re+(vi−vo)/ro
=vi / re+(vi−ioRL)/r o
=vi /re+[vi−(ii−vi/r π)RL]/r o
i o
L
o
Li
o
i
e
i v rr
R
r
Ri
r
v
r
v
π
i o
L
e o
i o
L v rr
R
r r
i r
R
π
r π
R
r
r
r R
L
e
o
o L
e
L
e
o
o L
r
R
r
r
r R
out x x 83 R =v /i
Output Resistance Rout:
i x = v
Rr
R r
r
v
R
v
e
e
e
π
π
π
R e′ =Re||r π
i x Re′= v
ix R′e =
mo
x xo
g r
v ir
v (^) x −v=(i (^) x+gmv)r o
m o
x xo
g r
v ir
v
= ro +( 1 +gmro)R e′ o vo e
=r +A R′
- Take RL out; 2. Take voltage source out; 3. add vx
84
(c) Small-signal analysis with the
output open-circuited.
Input Resistance (open circuit) Ri:
i
i i
i
v
R π
π
r
v r
v
i
i
Ro =r o
Open Circuit Voltage Gain Avo:
i
o vo v
v A = (^) mo i
m io i g r v
g vr v = +
= 1
Output Resistance (open circuit) Ro:
87
Summary
Common-Gate, Common-Base
Common-Source, Common-Emitter
Open Circuit
Voltage Gain Avo
≅
Input Resistance <<
Output Resistance (^) >>
High-frequency
response
Better (no Miller effect)
Avo = 1 +gmro Avo =−gmR L′
e
L e
o
o L in
r
R r
r
r R R
( 1 )
1
= Rin=∞
Rout = ro+AvoR e′ out o
R =r
88
6.8 The Cascode Amplifier
6.8.1 The MOS Cascode
Cascode configuration: by placing a common-gate (common-base) amplifier stage in cascade with a common-source (common-emitter) amplifier stage.
Common-source
Common-gate
89
Small Signal Analysis:
Q 1 : Avo 1 =−gm 1 ro 1
Rin = ∞( ii = 0 )
Rout 1 =ro 1
Q 2 :
2 2 2
2
vo
L
m mb
in A
R
g g
R +
Avo 2 = 1 +(gm 2 +gmb 2 )ro 2
Rout =ro 2 +Avo 2 ro 1
≅( gm 2 ro 2 )ro 1
Rd 1 =Rout 1 || Rin 2
90
vo 1 =−gm 1 ro 1 v i
The cascode with the output open-circuited (or RL→∞).
=−A 01 v i
vo=
vo 01 vo 2
A =−A A
Avo 2 vo 1 =Avo 2 ( −Avo 1 vi)
01 02
≅−A A
For the usual case of equal intrinsic gains,
2 2 Avo =−A 0 =−( gmro)
93
( for CS, on Slide 55.)
Rgs 1 = R sig
Rgd 1 =( 1 +gm 1 Rd 1 )Rsig +Rd 1
Rgd Rsig gmRL R L
Cgs 1 sees
Cgd 1 sees
( C (^) db 1 +Cgs 2 ) sees
( C (^) L +Cgd 2 ) sees
Rd 1
RL ||R out
94
[( 1 ) ]
1 2 1 2
1 1 1 1 1
db gs d L gd L out
H gs sig gd m d sig d
C C R C C R R
C R C g R R R
H
fH
In the case when Rsig is very small,
τH ≅( C L+Cgd 2 )(RL||Rout )
L gd 2 L out
H C C R R
f
95
A 0 times larger
A 0 times smaller
96
Example 6.
This example illustrates the advantages of cascoding
by comparing the performance of a cascode
amplifier with that of a common-source amplifier in
two cases:
(a) The resistance of the signal source is significant, Rsig = 10kΩ
(b) Rsig is negligibly small.
Assume all MOSFETs have W/L of 7.2μm/0.36μm and are operating at ID = 100μA, gm = 1.25mA/V, =0.2, ro = 20kΩ, Cgs = 20fF, Cgd = 5fF, Cdb = 5fF, and CL=5fF. For case (a), let RL = ro = 20kΩ for the CS amplifier and RL =
Rout for the cascode amplifier. For all cases, determine Av, fH, and ft.
99
[( 1 ) ]
1 2 1 2 2
1 1 1 1 1
db gs d L db gd L out
H gs sig gd m d sig d
C C R C C C R R
C R C g R R R
( 5 5 5 ) ( 20 || 640 ) 653 ps
20 10 5 [( 1 1. 5 ) 1. 22 ] ( 5 20 ) 1. 22
+ + + × =
= × + + + + + ×
244 MHz
× ×
fH
f t =| Av| f H = 23. 5 × 244 = 5. 73 GHz
