1. Recall Lecture 17 MOSFET DC Analysis
Using GS (SG) loop to calculate VGS
Remember that there is NO gate current!
Assume in saturation
Calculate ID using saturation equation
Find VDS (for NMOS) or VSD (for PMOS)
Using DS (SD) loop
Calculate VDS sat or VSD sat
Confirm that VDS > VDS sat or VSD > VSD sat
Confirm your assumption!

2. CHAPTER 7
Basic FET Amplifiers

3. For linear amplifier function, FET is normally biased in the saturation region.

4. Need to do DC Analysis first to find ID
AC PARAMETERS
where
Need to do DC Analysis first to find ID
vgs
gmvgs

5. 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

6. 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. +
vgs -
gmvgs

7. EXAMPLE The transistor parameters are:
VDD = 5V
RD = 10 k
520 k
320 k
0.5 k
The transistor parameters are:
VTN = 0.8V, Kn = 0.2mA/V2 and  = 0.
Voltage Divider biasing:
Change to Thevenin Equivalent
RTH = 198 k
VTH = V

8. gm = 0.442 mA/V DC ANALYSIS Calculate the value of VGS VGS – VTH = 0
Confirm your assumption: VDS > VDSsat, our assumption that the transistor is in saturation region is correct
Assume the transistor is biased in the saturation region, the drain current:
Use KVL at DS loop
IDRD + VDS – VDD = 0
VDS = VDD – IDRD = 2.56 V
Calculate the value of VGS
VGS – VTH = 0
VGS = V
Calculate VDSsat = VGS – VTN = – 0.8 = V
gm = mA/V

9. Equivalent resistance at the output side, ROUT
COMMON EMITTER GROUNDED
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vbeROUT
INPUT SIDE
Calculate Ri
Get vbe in terms of vs – eg: using voltage divider.
Go back to vo equation and calculate the voltage gain
COMMON SOURCE GROUNDED
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vgs ROUT
____________________________________________
INPUT SIDE
Get vgs in terms of vi eg: using voltage divider.
Go back to vo equation and calculate the voltage gain

10. The output resistance, Rout = RD The output voltage:
RTH
198.1 k
0.5 k
RD = 10 k
0.442 vgs +
vgs -
The output resistance, Rout = RD
The output voltage:
vo = - gmvgs (Rout) = - gmvgs (10) = vgs
Get vgs in terms of vi - voltage divider
vgs = [198.1 / ( )] = vi  vi = vgs
Go back to vo equation and calculate the voltage gain
Av = vo / vi = vgs / vgs 

11. Current Gain Output side: io = vo / RD = vo / 10
RSi vi RD
RTH
Output side: io = vo / RD = vo / 10
Input side: ii = vi / (Rsi + RTH ) = vi / ( ) = vi / 198.6
Current gain
= io / ii
= vo (198.6) = * =
vi (10)

12. Type 2: With Source Resistor, RS
VTN = 1V, Kn = 1.0 mA /V2
RTH = k
VTH = ( 200 / 300 ) x 3 = 2 V

13. Calculate the value of VGS KVL at GS loop:
DC ANALYSIS
Assume the transistor is biased in the saturation region, the drain current:
Calculate the value of VGS
KVL at GS loop:
0 + VGS+ 3(ID) - 2 = 0
VGS = 2 - 3ID
VTN = 1V, Kn = 1.0 mA / V
ID = mA
Replace in VGS equation in step 1
VGS = 2 - 3ID
VGS= V
ID = mA
VGS = 1.43 V
Why choose VGS = 1.43 V ?
Because it is bigger than VTN

14. gm = 0.872 mA/V Use KVL at DS loop IDRD + VDS + IDRS – 3 = 0
Calculate VDSsat = VGS – VTN = 1.43 – 1 = 0.43V
Confirm your assumption: VDS > VDS sat , our assumption is correct
IDRD + VDS + IDRS – 3 = 0
VDS = V
gm = mA/V
 = 0
ro = 
VA = 

15. Equivalent resistance at the output side, ROUT
COMMON EMITTER with RE
OUTPUT SIDE
Get the equivalent resistance at the output side, ROUT
Get the vo equation where vo = -  ib ROUT
INPUT SIDE
Calculate Rib = vb / ib : KVL at loop (extra step)
Calculate Ri
Get vb in terms of vs – eg: using voltage divider.
Go back to vo equation and calculate the voltage gain
COMMON SOURCE with RS
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vgs ROUT
________________________________________________________
INPUT SIDE
Get v’ in terms of vgs : KVL
Get v’ in terms of vi – eg: using voltage divider
Go back to vo equation and calculate the voltage gain

16. v’ = vgs + gmvgs RS  v’ = vgs(1 + 2.616) = 3.616 vgs
RTH
66.67 k
RD = 10 k
RS = 3 k + v’ -
The output resistance, Rout = RD
The output voltage:
Find v’
v’ = vgs + gmvgs RS  v’ = vgs( ) = vgs
vo = - gmvgsRD = ( vgs) (10) = vgs

17. 5. Calculate the voltage gain
RTH
66.67 k
RD = 10 k
RS = 3 k + v’ -
4. Find v’ in terms of vi
v’ = vi  in parallel
vi = vgs
5. Calculate the voltage gain
AV= vo / vi = vgs / vgs =

18. Current Gain Output side: io = vo / RD = vo / 10vi RD
RTH
Output side: io = vo / RD = vo / 10
Input side: ii = vi / (RTH ) = vi / ( ) = vi / 66.67
Current gain
= io / ii
= vo (66.67) = * =
vi (10)

19. 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

20. Equivalent resistance at the output side, ROUT
COMMON EMITTER with CE
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vbeROUT
INPUT SIDE
Calculate Ri
Get vbe in terms of vs – eg: using voltage divider.
Go back to vo equation and calculate the voltage gain
COMMON SOURCE with CS
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vgs ROUT
____________________________________________
INPUT SIDE
Get vgs in terms of vi eg: using voltage divider.
Go back to vo equation and calculate the voltage gain

21. IQ = 0.5 mA hence, ID = 0.5 mA ro =  gm = 1.414 mA/V + vgs -RG
200 k
RD = 7 k
1.414 vgs +
vgs -

22. The output resistance, Rout = RD The output voltage: RG
200 k
RD = 7 k
1.414 vgs +
vgs -
The output resistance, Rout = RD
The output voltage:
vo = - gmvgs (RD) = (7) vgs = vgs
3. The gate-to-source voltage:
vgs = vi  in parallel ( no need voltage divider)
4. So the small-signal voltage gain:
Av = vgs / vgs =

23. Current Gain Output side: io = vo / RD = vo / 7vi RD RG
Output side: io = vo / RD = vo / 7
Input side: ii = vi / (RG ) = vi / ( ) = vi / 200
Current gain
= io / ii
= vo (200) = * =
vi (7)

24. The MOSFET Amplifier - COMMON DRAIN
The output is measured at the source terminal
The gain is positive value

25. VTN = 0.92 V, Kn = 4 mA /V2 ,  = 0.01 V-1 VDD = 11 V 0.5 k
RS = 0.75 k
0.5 k
VDD = 11 V
VTN = 0.92 V, Kn = 4 mA /V2 ,  = 0.01 V-1
RTH = k
VTH = ( 470 / 620 ) x 11 = 8.34 V

26. Calculate the value of VGS KVL at GS loop:
DC ANALYSIS
Assume the transistor is biased in the saturation region, the drain current:
Calculate the value of VGS
KVL at GS loop:
0 + VGS (ID) – 8.34= 0
VGS = 8.34 – 0.75ID
ID = mA
Replace in VGS equation in step 1
VGS = 2 - 3ID
VGS= V
ID = 8 mA
VGS = 2.34 V
Why choose VGS = 2.34 V ?
Because it is bigger than VTN

27. gm = 11.3 mA/V Use KVL at DS loop VDS + IDRS – 11 = 0 VDS = 5 V
Calculate VDSsat = VGS – VTN = 2.34 – 0.92 = 1.42 V
Confirm your assumption: VDS > VDS sat , our assumption is correct
VDS + IDRS – 11 = 0
VDS = 5 V
gm = 11.3 mA/V
ro = 12.5 k
VA = 100 V
 = 0.01 V-1

28. RTH k
0.5 k
vgs
gmvgs

29. COMMON COLLECTOR COMMON DRAIN OUTPUT SIDE
Get the equivalent resistance at the output side, ROUT
At node x, use KCL and get io in terms of ib where io = ib +  ib
Get the vo equation where vo = io ROUT
INPUT SIDE
Find vb in terms of ib using supermesh
Calculate Rib – input resistance seen from base: Rib = vb / ib
Calculate Ri
Get vb in terms of vs.
Go back to vo equation and get the voltage gain
COMMON DRAIN
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Calculate vo = gmvgsRout
________________________________________________________
INPUT SIDE
Find v’ in terms of vgs : supermesh
Find v’ in terms of vi
Go back to vo equation and get the voltage gain

30. vo = gmvgs (ro  RS) = 11.3 vgs (0.70755) = 8 vgs+ v’ - k
RS = 0.75 k
12.5 k
The output resistance:
The output voltage
v’ in terms of vgs using supermesh:
v’ in terms of vi:
The voltage gain
Ro = ro || Rs = k
vo = gmvgs (ro  RS) = 11.3 vgs ( ) = 8 vgs
vgs + vo– v’ = 0
v’ = vgs + 8 vgs = 9 vgs
v’ = (RTH / RTH + RSi) vi = vi
9vgs = vi  vi = vgs
Av = vo / vi = 8 vgs / vgs = 0.885

31. Current Gain Output side: io = vo / Rs = vo / 0.75
RSi vi
Rs = 0.75 k
RTH
RTH k
Output side: io = vo / Rs = vo / 0.75
Input side: ii = vi / (Rsi + RTH ) = vi / ( ) = vi /
Current gain
= i / ii
= vo (114.21) = * =
vi (0.75)

32. Output Resistance for Common Drain
vgs + - Vx Ix
RSi
Independent voltage source turned off
12.5 k RS
0.75 k
RTH
11.3 vgs ro
In parallel
ro|| Rs = k
vgs in terms of Vx where vgs = - Vx
0.708 k
11.3 vgs
vgs + - Vx Ix

33. - 1.412 Vx – 11.3 Vx + Ix = 0 Ix = 12.712 Vx 0.079 k vgs + - Vx Ix
Use nodal analysis
- Vx gmvgs Ix = 0
0.708
vgs = - Vx and gm = 11.3 mA/V
- Vx gmVx Ix = 0
0.708
Vx – 11.3 Vx + Ix = 0
Ix = Vx
0.079 k

34. SUMMARY

35. COMMON EMITTER GROUNDED
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vbeROUT
INPUT SIDE
Calculate Ri
Get vbe in terms of vs – eg: using voltage divider.
Go back to vo equation and calculate the voltage gain
COMMON SOURCE GROUNDED
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vgs ROUT
____________________________________________
INPUT SIDE
Get vgs in terms of vi eg: using voltage divider.
Go back to vo equation and calculate the voltage gain

36. Equivalent resistance at the output side, ROUT
COMMON EMITTER with RE
OUTPUT SIDE
Get the equivalent resistance at the output side, ROUT
Get the vo equation where vo = -  ib ROUT
INPUT SIDE
Calculate Rib = vb / ib : KVL at loop (extra step)
Calculate Ri
Get vb in terms of vs – eg: using voltage divider.
Go back to vo equation and calculate the voltage gain
COMMON SOURCE with RS
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vgs ROUT
________________________________________________________
INPUT SIDE
Get v’ in terms of vgs : KVL
Get v’ in terms of vi – eg: using voltage divider
Go back to vo equation and calculate the voltage gain

37. COMMON EMITTER with CE
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vbeROUT
INPUT SIDE
Calculate Ri
Get vbe in terms of vs – eg: using voltage divider.
Go back to vo equation and calculate the voltage gain
COMMON SOURCE with CS
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Get the vo equation where vo = - gm vgs ROUT
____________________________________________
INPUT SIDE
Get vgs in terms of vi eg: using voltage divider.
Go back to vo equation and calculate the voltage gain

38. COMMON COLLECTOR COMMON DRAIN OUTPUT SIDE
Get the equivalent resistance at the output side, ROUT
At node x, use KCL and get io in terms of ib where io = ib +  ib
Get the vo equation where vo = io ROUT
INPUT SIDE
Find vb in terms of ib using supermesh
Calculate Rib – input resistance seen from base: Rib = vb / ib
Calculate Ri
Get vb in terms of vs.
Go back to vo equation and get the voltage gain
COMMON DRAIN
OUTPUT SIDE
Equivalent resistance at the output side, ROUT
Calculate vo = gmvgsRout
________________________________________________________
INPUT SIDE
Find v’ in terms of vgs : supermesh
Find v’ in terms of vi
Go back to vo equation and get the voltage gain