Download MOSFET - AC Analysis (Common Source and Common Drain)

Recall Lecture 17
• MOSFET DC Analysis
1. Using GS (SG) Loop to calculate VGS
• Remember that there is NO gate current!
2. Assume in saturation
• Calculate ID using saturation equation
3. Find VDS (for NMOS) or VSD (for PMOS)
• Using DS (SD) loop
4. Calculate VDS sat or VSD sat
5. Confirm that VDS > VDS sat or VSD > VSD sat
• Confirm your assumption!
CHAPTER 7
Basic FET Amplifiers
• For linear amplifier function, FET is normally
biased in the saturation region.
AC PARAMETERS
where
The MOSFET Amplifier - COMMON
SOURCE
• The output is measured at the drain terminal
• The gain is negative value
• Three types of common source
– source grounded
– with source resistor, RS
– with bypass capacitor, CS
Common Source - Source Grounded
●
A Basic Common-Source Configuration:
Assume that the transistor is biased in the saturation region by
resistors R1 and R2, and the signal frequency is sufficiently large
for the coupling capacitor to act essentially as a short circuit.
EXAMPLE
VDD = 5V
The transistor parameters
are:
VTN = 0.8V, Kn = 0.2mA/V2
and  = 0.
520 k
Rsi
0.5 k
ID = 0.2441 mA
gm = 0.442 mA/V
320 k
RD = 10 k
Steps
1. Calculate Rout
2. Calculate vo
________________________________________________________
3. Find vgs in terms of vi
4. Calculate the voltage gain, Av
0.5 k
RTH
198.1 k
0.442 vgs
RD = 10 k
1. The output resistance, Rout = RD
2. The output voltage:
vo = - gmvgs (Rout) = - gmvgs (10) = -4.42 vgs
3. The gate-to-source voltage:
, Ri = RTH
vgs = [198.1 / (198.1 + 0.5 )] = 0.9975 vi  vi = 1.0025 vgs
4. So the small-signal voltage gain:
Av = vo / vi = - 4.42 vgs / 1.0025 vgs  - 4.41
Current Gain


Output side: iout = vo / RD = vo / 10
Input side: ii = vi / (Rsi + RTH ) = vi / (0.5 + 198.1) = vi / 198.6
Current gain
= iout / ii
= vo (198.6) = - 4.41 * 19.86 = - 87.58
vi (10)
Type 2: With Source Resistor, RS
VTN = 1V, Kn = 1.0mA / V
Perform DC analysis
Assume transistor in saturation
VG = ( 200 / 300 ) x 3 = 2 V
Hence, KVL at GS Loop:
VGS + IDRS – VTH = 0
VGS = 2 – 3ID
KVL at DS loop
VDS + 10 ID + 3ID – 3 = 0
VDS = 3 -13 ID
Assume biased in saturation mode:
Hence, ID = 1.0 (2 – 3ID - 1 )2 = 1.0 (1 – 3ID )2

9 ID2 – 7 ID + 1 = 0
VTN = 1V, Kn = 1.0 mA / V
ID = 0.589 mA
VGS = 2 – 3ID = 0.233 < VTN
MOSFET is OFF
Not OK
ID = 0.19 mA
VGS = 2 – 3ID = 1.43 V > VTN
OK
VDS = 3 -13 ID = 0.53 V
VDS sat = VGS - VTN = 1.43 – 1.0 = 0.43 V
0.53 V > 0.43 V
Transistor in saturation
Assumption is correct!
Steps
1. Calculate Rout
2. Calculate vo
________________________________________________________
3. Find v ’ in terms of vgs
4. Find v’ in terms of vi
5. Calculate the voltage gain, Av
+
V’
RTH
66.67
k
RD = 10 k
RS = 3 k
-
gm = 0.872 mA/V
1. The output resistance, Ro = RD
2. The output voltage:
vo = - gmvgsRD = - 0.872 ( vgs) (10) = - 8.72 vgs
3. Find v’
v’ = vgs + gmvgs RS  v’ = vgs(1 + 2.616) = 3.616 vgs
+
V’
RTH
66.67
k
RD = 10 k
RS = 3 k
-
4. Find v’ in terms of vi : using voltage divider
v’ = [RTH / (Rsi + RTH)] vi
But in this circuit, Rsi = 0 so, v’ = vi = 3.616 vgs
5. Calculate the voltage gain
AV= vo / vi = - 8.72 vgs / 3.616 vgs = - 2.41
Current Gain


Output side: iout = vo / RD = vo / 10
Input side: ii = vi / (Rsi + RTH ) = vi / (0 + 66.67) = vi / 66.67
Current gain
= iout / ii
= vo (66.67) = - 2.41 * 6.667 = -16.07
vi (10)
Type 3: With Source Bypass Capacitor, CS

Circuit with Source Bypass Capacitor
●
An source bypass capacitor can be used to effectively
create a short circuit path during ac analysis hence avoiding
the effect RS
●
CS becomes a short circuit path – bypass RS; hence similar to
Type 1
Steps
1. Calculate Rout
2. Calculate vo
________________________________________________________
3. Find vgs in terms of vi
4. Calculate the voltage gain, Av
IQ = 0.5 mA hence, ID = 0.5 mA
gm = 2 Kn ID = 1.414 mA/V
ro = 
RG
200 k
1.414
vgs
RD = 7 k
1. The output resistance, Rout = RD
2. The output voltage:
vo = - gmvgs (RD) = -1.414 (7) vgs = - 9.898 vgs
3. The gate-to-source voltage:
vgs = vi  in parallel ( no need voltage divider)
4. So the small-signal voltage gain:
Av = -9.898 vgs / vgs = - 9.898
Current Gain


Output side: iout = vo / RD = vo / 7
Input side: ii = vi / (Rsi + RG ) = vi / (0 + 200) = vi / 200
Current gain
= iout / ii
= vo (200) = - 9.898 * 28.57 = - 282.78
vi (7)
The MOSFET Amplifier - COMMON DRAIN
• The output is measured at the source terminal
• The gain is positive value
0.5 k
0.5 k
150
k
113.71
RTH
k
470
k
0.75
k
ID = 8 mA , Kn = 4 mA /V2
gm = 2 Kn ID = 11.3 mA/V
Steps
1. Calculate Rout
2. Calculate vo
________________________________________________________
3. Find v ’ in terms of vgs
4. Find v’ in terms of vi
5. Calculate the voltage gain, Av
gm = 2 Kn ID = 11.3 mA/V
+
v’
-
1. The output resistance: Ro = ro || Rs
2. The output voltage v = g v (r  R ) = 11.3 v (0.70755) = 8 v
o
m gs o
S
gs
gs
3. v’ in terms of vgs using supermesh:
vgs + gmvgs (ro  RS) – v’ = 0
v’ = vgs + 8 vgs = 9 vgs
4. v’ in terms of vi:
v’ = (RTH / RTH + RSi) vi = 0.9956 vi
9vgs = 0.9956 vi  vi = 9.040 vgs
5. The voltage gain A = v / v = 8 v / 9.040 v = 0.885
v
o
i
gs
gs
Current Gain


Output side: iout = vo / Rs = vo / 0.75
Input side: ii = vi / (Rsi + RTH ) = vi / (0.5 + 113.71) = vi / 114.21
Current gain
= iout / ii
= vo (114.21) = 0.885 * 11.37 = 152.28
vi (0.75)
Output Resistance for Common Drain
Ix
+
-
Vx
• ro|| Rs = 0.708 k
• vgs in terms of Vx where vgs = -Vx
• - Vx + gmvgs
+ Ix = 0
0.708
• - Vx - gmVx
0.708
+ Ix = 0
- 1.412 Vx – 11.3 Vx + Ix = 0
Ix = 12.712 Vx
0.079 k