Recall Lecture 18 Introduction to FET Amplifier AC

Recall Lecture 18 • Introduction to FET Amplifier • AC parameters, gm and ro

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

COMMON COLLECTOR COMMON DRAIN OUTPUT SIDE 1. Equivalent resistance at the output side, Req 2. Calculate vo = gmvgs Req ____________________________ INPUT SIDE 3. Find vi in terms of vgs using supermesh vi = vgs+ vo

OUTPUT SIDE 1. Equivalent resistance at the output side, Req = ro||RS 2. Calculate vo = gmvgs Req = gmvgs (ro||RS ) ____________________________ INPUT SIDE 3. Find vi in terms of vgs using supermesh vi = vgs+ vo = vgs+ gmvgs (ro||RS ) = vgs(1+ gm(ro||RS ) )

VDD = 11 V 150 k 0. 5 k v. S 470 k RS = 0. 75 k VTN = 0. 92 V, Kn = 4 m. A /V 2 , = 0. 01 V-1 RTH = 113. 7 k VTH = ( 470 / 620 ) x 11 = 8. 34 V

DC ANALYSIS 1. Calculate the value of VGS KVL at GS loop: 0 + VGS + 0. 75(ID) – 8. 34= 0 VGS = 8. 34 – 0. 75 ID 2. Assume the transistor is biased in the saturation region, the drain current: ID = 12. 22 m. A ID = 8 m. A Replace in VGS equation in step 1 VGS = 2 - 3 ID Why choose VGS = 2. 34 V ? Because it is bigger than VTN VGS= - 0. 825 V VGS = 2. 34 V

3. Use KVL at DS loop VDS + IDRS – 11 = 0 VDS = 5 V 4. 5. Calculate VDSsat = VGS – VTN = 2. 34 – 0. 92 = 1. 42 V Confirm your assumption: VDS > VDS sat , our assumption is correct gm = 11. 3 m. A/V = 0. 01 V-1 VA = 100 V ro = 12. 5 k

+ v. S vi RTH 113. 7 1 k - vgs + v. S vi - RTH gmvgs

+ vi vgs 113. 71 k RS = 0. 75 k 11. 3 vgs - 12. 5 k 1. The output resistance: Req = ro || Rs = 0. 70755 k 2. The output voltage v = g v (R ) = 11. 3 v (0. 70755) = 8 v o m gs eq gs gs 3. Find vi in terms of vgs using supermesh vi = vgs+ vo vi = vgs+ 8 vgs = 9 vgs

Equation of vo : vo = gmvgs (Req) = 11. 3 vgs (0. 70755) = 8 vgs vi = 9 vgs Av vi = vo open circuit voltage Avvi = 8 vgs = 8 vi 9 Av = 0. 889 open circuit voltage gain

RSi = 0. 5 kΩ v. S Ri = RTH = 113. 71 kΩ vo To find new voltage gain, vo/vs with input signal voltage source, vs vi in terms of vs use voltage divider: vi = [ Ri / ( Ri + Rs )] * vs = 0. 9956 vs vo = Avvi because there is no load resistor vo = 0. 889 (0. 9956 vs) vo/vs = 0. 885

Output Resistance for Common Drain Ix vgs RTH gm vgs ro RS Vx + - Vx Ix vgs gm vgs + - ro RS

vgs in terms of Vx where vgs = - Vx Ix vgs ro gm vgs Use nodal analysis Vx + Vx = gmvgs + Ix ro Rs Vx + Vx = - gm. Vx + Ix ro Rs Vx + gm. Vx = Ix ro Rs RS + - Vx

v. S

vgs + vi 100 k - 2 vgs 125 k 1. The output resistance: Req = ro = 125 k 2. The output voltage v = g v (R ) = 2 v (125) = 250 v o m gs eq gs gs 3. Find vi in terms of vgs using supermesh vi = vgs+ vo vi = vgs+ 250 vgs = 251 vgs

Equation of vo : vo = gmvgs (Req) = 250 vgs vi = 251 vgs Av vi = vo open circuit voltage Avvi = 250 vgs = 250 vi 251 Av = 0. 996 open circuit voltage gain

Ro v. S Ri = 100 kΩ RL = 4 k Since we have RL we have to calculate Ro ro = 125 k , gm = 2 m. A/V and there is no RS So, Ro = 0. 498 k vi in terms of v. S vi = vs in parallel vo = [ RL / ( RL + Ro )] * Avvi this is because we have load resistor RL vo = [ 4 / ( 4. 498)] (0. 996 vs) vo / vs = 0. 886

CURRENT GAIN ii v. S l l Ri = 100 k Output side: io = vo / 4 Input side: ii = vs / Ri = v. S / 100 Current gain = io / ii = vo (100) = 0. 886 * 25 vs (4) = 22. 15 Ro = 0. 498 k io RL = 4 k

TYPE OF BJT AMPLIFIER COMMON SOURCE WITH SOURCE GROUNDED COMMON SOURCE WITH RS (assume ro = ) COMMON SOURCE WITH BYPASS CAPACITOR, CS OPEN CIRCUIT VOLTAGE GAIN INPUT RESISTANCE, Ri OUTPUT RESISTANCE, RO RTH or RG ro||RD RTH or RG COMMON DRAIN RTH or RG RD ro||RD

SUMMARY

COMMON EMITTER GROUNDED OUTPUT SIDE 1. Get the equivalent resistance at the output side, RO 2. Get the vo equation where vo = - gm vbe. RO INPUT SIDE 3. Calculate Ri 4. Get vbe in terms of vi COMMON SOURCE GROUNDED OUTPUT SIDE 1. Equivalent resistance at the output side, RO 2. Get the vo equation where vo = - gm vgs RO ______________________ INPUT SIDE 3. Get vgs in terms of vi vs

COMMON EMITTER with RE OUTPUT SIDE 1. Get the equivalent resistance at the output side, Ro 2. Get the vo equation where vo = - gmvbe. Ro INPUT SIDE 3. Calculate Rib = r + (1+ ) RE 4. Calculate Ri = Rib // RTH 5. vbe in terms of vi COMMON SOURCE with RS OUTPUT SIDE 1. Equivalent resistance at the output side, RO 2. Get the vo equation where vo = - gm vgs RO ____________________________ INPUT SIDE 3. Get vi in terms of vgs : KVL

COMMON EMITTER with CE OUTPUT SIDE 1. Get the equivalent resistance at the output side, RO 2. Get the vo equation where vo = - gm vbe. RO INPUT SIDE 3. Calculate Ri 4. Get vbe in terms of vi COMMON SOURCE with CS OUTPUT SIDE 1. Equivalent resistance at the output side, RO 2. Get the vo equation where vo = - gm vgs RO ______________________ INPUT SIDE 3. Get vgs in terms of vi

COMMON COLLECTOR COMMON DRAIN OUTPUT SIDE 1. Equivalent resistance at the output side, Req 2. Calculate vo = gmvgs. Req ____________________________ INPUT SIDE 3. Find vi in terms of vgs using supermesh vi = vgs+ vo