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!

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: Rsi RD = 10 k 0.5 k 520 k 320 k The transistor parameters are: VTN = 0.8V, Kn = 0.2mA/V2 and  = 0. ID = 0.2441 mA gm = 0.442 mA/V

Steps Calculate Rout Calculate vo ________________________________________________________ Find vgs in terms of vi Calculate the voltage gain, Av

RTH 198.1 k 0.5 k RD = 10 k 0.442 vgs The output resistance, Rout = RD The output voltage: vo = - gmvgs (Rout) = - gmvgs (10) = -4.42 vgs The gate-to-source voltage: , Ri = RTH vgs = [198.1 / (198.1 + 0.5 )] = 0.9975 vi  vi = 1.0025 vgs 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

Assume transistor in saturation 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 ID = 0.19 mA VGS = 2 – 3ID = 0.233 < VTN VGS = 2 – 3ID = 1.43 V > VTN MOSFET is OFF OK Not 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 Calculate Rout Calculate vo ________________________________________________________ Find v’ in terms of vgs Find v’ in terms of vi Calculate the voltage gain, Av

v’ = vgs + gmvgs RS  v’ = vgs(1 + 2.616) = 3.616 vgs - RTH RD = 10 k 66.67 k RS = 3 k gm = 0.872 mA/V The output resistance, Ro = RD The output voltage: Find v’ v’ = vgs + gmvgs RS  v’ = vgs(1 + 2.616) = 3.616 vgs vo = - gmvgsRD = - 0.872 ( vgs) (10) = - 8.72 vgs

RTH 66.67 k RD = 10 k RS = 3 k + V’ - 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 Calculate Rout Calculate vo ________________________________________________________ Find vgs in terms of vi Calculate the voltage gain, Av

IQ = 0.5 mA hence, ID = 0.5 mA gm = 2 Kn ID = 1.414 mA/V ro =  RG RD = 7 k 1.414 vgs

The output resistance, Rout = RD 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

ID = 8 mA , Kn = 4 mA /V2 gm = 2 Kn ID = 11.3 mA/V 0.5 k 0.5 k RTH

Steps Calculate Rout Calculate vo ________________________________________________________ Find v’ in terms of vgs Find v’ in terms of vi Calculate the voltage gain, Av

gm = 2 Kn ID = 11.3 mA/V + v’ - The output resistance: The output voltage v’ in terms of vgs using supermesh: v’ in terms of vi: The voltage gain Ro = ro || Rs vo = gmvgs (ro  RS) = 11.3 vgs (0.70755) = 8 vgs vgs + gmvgs (ro  RS) – v’ = 0 v’ = vgs + 8 vgs = 9 vgs v’ = (RTH / RTH + RSi) vi = 0.9956 vi 9vgs = 0.9956 vi  vi = 9.040 vgs Av = vo / vi = 8 vgs / 9.040 vgs = 0.885

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 + - Vx Ix ro|| Rs = 0.708 k vgs in terms of Vx where vgs = -Vx   - Vx + gmvgs + Ix = 0 0.708 - Vx - gmVx + Ix = 0 0.708 - 1.412 Vx – 11.3 Vx + Ix = 0 Ix = 12.712 Vx 0.079 k