# Lecture 19 OUTLINE • Common-gate stage • Source follower

```Lecture 19
OUTLINE
• Common-gate stage
• Source follower
EE105 Fall 2007
Lecture 19, Slide 1
Prof. Liu, UC Berkeley
Diode-Connected MOSFETs
Diode-connected NMOSFET
RX
Diode-connected PMOSFET
1

ro1
g m1
Small-signal analysis circuit
1
RY 
ro 2
gm2
Small-signal analysis circuit
• Note that the small-signal model of a PMOSFET is identical to
that of an NMOSFET
EE105 Fall 2007
Lecture 19, Slide 2
Prof. Liu, UC Berkeley
Common-Gate Amplifier Stage
• An increase in Vin decreases VGS and hence decreases ID.
The voltage drop across RD decreases  Vout increases
The small-signal voltage gain (Av) is positive.
Av  g m RD
EE105 Fall 2007
Lecture 19, Slide 3
Prof. Liu, UC Berkeley
Operation in Saturation Region
• For M1 to operate in saturation, Vout cannot fall below Vb-VTH.
EE105 Fall 2007
Lecture 19, Slide 4
Prof. Liu, UC Berkeley
I/O Impedances of CG Stage (l = 0)
Small-signal analysis circuit for
determining input resistance, Rin
Small-signal analysis circuit for
determining output resistance, Rout
1
Rin 
gm
EE105 Fall 2007
Rout  RD
Lecture 19, Slide 5
Prof. Liu, UC Berkeley
CG Stage with Source Resistance
Small-signal equivalent
circuit seen at input
vX 
1
gm
1
RS 
gm
vin
For l = 0:
vout vout v X
1


 g m RD 
vin
v X vin
g m RS  1
EE105 Fall 2007
Lecture 19, Slide 6
Av 
RD
1
 RS
gm
Prof. Liu, UC Berkeley
• The output impedance of a CG stage with source resistance is
identical to that of CS stage with degeneration.
Small-signal analysis circuit for
determining output resistance, Rout
Rout  rO 1  g m RS   RS  1  g m rO RS  rO
EE105 Fall 2007
Lecture 19, Slide 7
Prof. Liu, UC Berkeley
CG Stage with Biasing
• R1 and R2 establish the gate bias voltage.
• R3 provides a path for the bias current of M1 to flow.
vout
R3 || 1 / g m 

 g m RD
vin R3 || 1 / g m   RS
EE105 Fall 2007
Lecture 19, Slide 8
Prof. Liu, UC Berkeley
CG Stage with Gate Resistance
• For low signal frequencies, the gate conducts no current.
 Gate resistance does not affect the gain or I/O impedances.
EE105 Fall 2007
Lecture 19, Slide 9
Prof. Liu, UC Berkeley
CG Stage Example
Small-signal equivalent
circuit seen at input
vX 
1 1
g m1 g m 2
1 1
 RS
g m1 g m 2
vout v X
g m1 RD
Av 
 
v X vin 1  g m1  g m 2 RS
EE105 Fall 2007
vin 
Small-signal equivalent
circuit seen at output
1
vin
1  g m1  g m 2 RS

1 
Rout1  g m1rO1  RS
 rO1

gm2 



 1

Rout   g m1rO1 
|| RS   rO1  || RD
 gm2



Lecture 19, Slide 10
Prof. Liu, UC Berkeley
Source Follower Stage
vout
rO || RL
Av 

1
vin 1  r || R
O
L
gm
Small-signal analysis circuit for
determining voltage gain, Av
vin  v1  vout
EE105 Fall 2007
Equivalent circuit
vout  g m v1 ro RL 
 g m vin  vout ro RL 
Lecture 19, Slide 11
Prof. Liu, UC Berkeley
Source Follower Example
• In this example, M2 acts as a current source.
Av 
EE105 Fall 2007
Lecture 19, Slide 12
rO1 || rO 2
1
 rO1 || rO 2
g m1
Prof. Liu, UC Berkeley
Rout of Source Follower
• The output impedance of a source follower is relatively low,
whereas the input impedance is infinite (at low frequencies);
thus, it is useful as a voltage buffer.
Small-signal analysis circuit for
determining output resistance, Rout
Rout
EE105 Fall 2007
1
1

|| rO || RL 
|| RL
gm
gm
Lecture 19, Slide 13
Prof. Liu, UC Berkeley
Source Follower with Biasing
• RG sets the gate voltage to VDD; RS sets the drain current.
(Solve the quadratic equation to obtain the value of ID.)
Assuming l = 0:
1
W
2
I D   nCox VDD  I D RS  VTH 
2
L
EE105 Fall 2007
Lecture 19, Slide 14
Prof. Liu, UC Berkeley
Supply-Independent Biasing
• If Rs is replaced by a current source, the drain current ID
becomes independent of the supply voltage VDD.
EE105 Fall 2007
Lecture 19, Slide 15
Prof. Liu, UC Berkeley
```