# Biasing MOSFET Amplifier

```Biasing MOSFET Amplifier
Biasing with resistors
Adjust the values of resistors and MOSFET parameters to put the
MOSFET in an operating Point such as:
Biasing with constant current source
Current source:
ID2 is constant,
Its value adjusted by the choice of R to the desired
value:
1
π
2
πΏ 1
Q1 saturation βΉ πΌπ·1 = ππ′
ππΊπ − ππ‘
2
ID1 is the current through R βΉ
πΌπ·1 = πΌππΈπΉ =
ππ·π· + πππ − ππΊπ
π
The current πΌππΈπΉ is the reference current
1
π
2
πΏ 2
If Q2 is in saturation βΉ πΌπ·2 = ππ′
Since Q2 has same VGS as Q1 then
πΌπ·2 = πΌππΈπΉ
π πΏ
π πΏ
2
1
ππΊπ − ππ‘
2
Small signal operation and models
Simple conceptual MOSFET circuit:
ο DC VGS applied on the Gate-Source for biasing
ο A small signal vgs applied: the ac signal
The DC Bias Point: Assume small signal vgs is zero
ο vGS = VGS + vgs = VGS
only DC
1
ο ππ· = πΌπ· = 2 ππ′
π
πΏ
ππΊπ − ππ‘
2
only DC
ο π£π· = ππ· = ππ·π· − ππ· πΌπ·
only DC
To ensure proper amplifier operation MOSFET must be saturated:
⇒ ππ· &gt; ππΊπ − ππ‘
ππ· has to be half way between VDD and ππΊπ − ππ‘
Signal current in the drain:
ο vGS = VGS + vgs
1
ο ππ· = 2 ππ′
ππ· =
π
πΏ
π£πΊπ − ππ‘
2
1 ′ π
π
π − ππ‘
2 π πΏ πΊπ
1
π
2
πΏ
= ππ′
2
+ ππ′
ππΊπ + π£ππ  − ππ‘
2
π
1 π 2
ππΊπ − ππ‘ π£ππ  + ππ′
π£
πΏ
2
πΏ ππ
1. First term is the DC component ID,
2. Second term has a linear dependence with the signal vgs
3. Third term has nonlinear dependence on vgs, this term is undesirable it
represent nonlinear distortion:
ο To reduce this distortion we need to keep the signal small such
1
π 2
π
that ππ′ π£ππ
βͺ ππ′
ππΊπ − ππ‘ π£ππ
2
Resulting in
πΏ
πΏ
π£ππ  βͺ 2 ππΊπ − ππ‘
or π£ππ  βͺ 2πππ
This is the small signal approximation
ππ· ≅ πΌπ· + ππ
Where
π
ππ = ππ′
ππΊπ − ππ‘ π£ππ
πΏ
the small signal component of the drain current;
it is proportional to the small signal π£ππ
Small signal parameter
The parameter that relates ππ to π£ππ  : is the MOSFET transconductance ππ
ππ =
Graphical Interpretation:
ππ =
πππ·
ππ£ππ
π£πΊπ =ππΊπ
ππ
π
π
= ππ′
ππΊπ − ππ‘ = ππ′
π
π£ππ
πΏ
πΏ ππ
iD
Slope = gm
iD Approximate
iD Exacte
id
Q
iD
t
IDQ
VGSQ
Vt
vGS
vgs
t
Voltage Gain
π£π·
π£π·
π£π·
π£π·
= ππ·π· − ππ· ππ·
= ππ·π· − ππ· (πΌπ· + ππ )
= (ππ·π· − ππ· πΌπ· ) − ππ· ππ
= ππ· + π£π
Where
π£π = −ππ ππ· = −ππ π£ππ  ππ·
π΄π£ ≡
The voltage gain is:
π£π
π£ππ
= −ππ ππ·
The minus sign indicate that π£π is 180 &ordm; out of phase with π£ππ
vgs
vd
t
Small Signal Equivalent Circuit:
ππ = ππ π£ππ
ππ΄
ππ =
πΌπ·
1 π
πΌπ· = ππ′
π − ππ‘
2
πΏ πΊπ
example
G
D
gmvgs
vgs
2
S
ro
Low frequency Equivalent circuit
At low frequency no capacitive effect.
G
D
gmvgs
vgs
At high frequency charging and discharging of
the different capacitors have to be taken into
consideration
ro
S
G
The figure shows the different capacitors in a
MOSFET and where they originate:
ο Cgs and Cgd : Oxide capacitance
ο Csb and Cdb : Junction Capacitance
S
D
Cgd
Cgs
n+
Csb
n+
p type substrate
B
Cdb
Complete high frequency small
signal Equivalent circuit:
Cgd
g mbο΅bs
g m ο΅ gs
G
ο΅ gs
ro
Cgs
Cdb
ο΅bs
S
D
Csb
B
Body and Source connected and body
effect neglected
Cgd
g m ο΅ gs
G
ο΅ gs
D
ro
Cgs
S
Cdb
Cdb can be neglected to give the simplified
high frequency small signal Equivalent
circuit
Cgd
g m ο΅ gs
G
ο΅ gs
ro
Cgs
S
D
```