EE539: Analog Integrated Circuit Design;
Nagendra Krishnapura (nagendra@iitm.ac.in)
10 Feb. 2006
1 SOURCE FOLLOWER
1.1
Input impedance
Equivalent circuit of the Source Follower to find input impedance is shown in the below figure.
TO FIND INPUT RESISTANCE:
it
+
+
vgs C
gs
gds
gmvgs
vt
_
vout
CL
Figure 1: Equivalent circuit of the Source Follower
From the figure ,
g m it
1
sCgs )( sCL +gds )
vt = sCitgs + vout
gm
1
1
sCL +gds + sCgs + sCgs (sCL +gds )
vout = (it +
Rin =
vt
it
=
The equivalent circuit for this input impedance is shown in the below figure,
1.2
Output impedance
The equivalent circuit for output impedance derivation is shown below
From the circuit,
1
2
sCgsgds
gm
Rin
s2CgsCL
gm
Cgs
gds
CL
Figure 2: Equivalent circuit for input impedance
Vdd
vin
Cgs
gmvgs gds
Ibias
Rout
it
vt
Figure 3: Equivalent circuit for output impedance derivation
vgs =
−vt
1+sCgs Rs
−gm vt
gm vgs = 1+sC
gs Rs
⇒
we can replace the VCCS gm vgs by equivalent admittance ygm ,
yg m =
gm
1+sCgs Rs
=
1
sC R
1
+ ggs s
gm
m
The Output admittance for the source follower is
Yout =
1
Zout
=
1
sC R
1
+ ggs s
gm
m
+ gds +
sCgs
1+sCgs Rs
The equivalent circuit for the output admittance is shown in below figure,
We can also find the output admittance by intutively from the figures shown below.
Bodeplot for this output admittance is shown below,
3
E QUIVALENT CIRCUIT FOR OUTPUT IMPEDANCE:
vt
it
Rs
gm
1+sCgsRs
Rout
gds
Cgs
Figure 4: The equivalent circuit for the output admittance
Source follower is supposed to be a good voltage source ,since it has low output impedance.But from the
Bodeplot, the output impedance increases as frequency increases (⇒ INDUCTIVE nature),So at higher
frequencies it behaves as aworst voltage source.
If we use the source follower in the following circuit configuration,at high frequencies it may tend to oscillate.
4
Vdd
Rout=gm+gmbs+gds
Vdd
Rout=gm+gmbs+gds+sCgs
Figure 5: CD amplifier
Vdd
Rout
Figure 6: CD amplifier
5
ADMITTANCE BODEPLOT:
|Y|
gm
1/Rs
gds+gmbs
1/RsCgs
log(w)
Figure 7: Bodeplot for output admittance
Vdd
Rs
+
vs −
(NEGATIVE)
Rin
Rout
(INDUCTIVE)
Figure 8: Oscillating circuit
6
2 CG amplifier
Circuit diagrams for CG amplifier with biasing is shown in below figures, DC gain for this CG amplifier
CG AMPLIFIER:
Vdd
+ vout
_
+ vin
_
RL
vout
vbias+v
Figure 9: CG AMPLIFIER
Vdd
RL
vout
vin
ibias
Figure 10: CG AMPLIFIER
configuration is
vout
vin
= gm RL
7
RL
it
vt
+
vgs
gmvgs
gds
-
Figure 11: CG amplifier equivalent circuit for output impedance calculations
2.1
OUTPUT IMPEDANCE
The output impedance of the CG amplifier is
Ro =
1
gds +GL
8
2.2
INPUT IMPEDANCE
The input impedance of the CG amplifier can be calculated from the following figure,
Rin =
1
gm ,which
is very small.
TO FIND INPUT IMEDANCE:
D
G
+
gds
vgs
gm vgs
S
it
Rin=
vt
it
vt
Figure 12: CG amplifier equivalent circuit for input imedance calculations
2.3
The small signal equivalent circuit at high frequiencies is shown in the below figure
Due to Cgs and Csb ,there is no effect on small signal gain.
vout
vin
2.4
≈
g m RL
1+sRL (Cdb +Cgd )
By considering source Resistance
The circuit diagram for the CG amplifier with source Resistance is shown in the below figure,
Equivalent circuit for this CG amplifier is shown in the below figure, For this circuit voltage gain is,
9
Vdd
RL
Cgd
vout
Cdb
Cgs
vin
Csb
Figure 13: CG amplifier small signal equivalent circuit at high frequiencies
Vdd
RL
vout
Rs
vs
Figure 14: CG amplifier with source Resistance
10
RL
G
D
+
vgs
vout
gmvgs
gds
_
S
Rs
vs
Figure 15: Equivalent circuit for this CG amplifier
11
vout
vs
1
=
Rs
+
RL
1 +g
ds
RL
gm +gds
If gm is very large compared to others(i.e.,gm gds , f rac1RL )
vout
vs
For this circuit current gain is always unity.
≈
RL
Rs