Recall Last Lecture The MOSFET has only one current, ID Operation of MOSFET NMOS and PMOS For NMOS, VGS > VTN VDS sat = VGS – VTN For PMOS VSG > |VTP| VSD sat = VSG + VTP

ID versus VDS (NMOS) or ID versus VSD (PMOS)

PMOS NMOS VTP is NEGATIVE VTN is POSITIVE VSG > |VTP| to turn on Triode/non-saturation region Saturation region VSDsat = VSG + VTP NMOS VTN is POSITIVE VGS > VTN to turn on Triode/non-saturation region Saturation region VDSsat = VGS - VTN

DC analysis of FET

MOSFET DC Circuit Analysis - NMOS The source terminal is at ground and common to both input and output portions of the circuit. The CC acts as an open circuit to dc but it allows the signal voltage to the gate of the MOSFET. In the DC equivalent circuit, the gate current into the transistor is zero, the voltage at the gate is given by a voltage divider principle: VG = VTH = R2 VDD R1 + R2 Use KVL at GS loop: VGS –VTH + 0 = 0 VGS = VTH

MOSFET DC Circuit Analysis - NMOS Assume the transistor is biased in the saturation region, the drain current: Use KVL at DS loop IDRD + VDS – VDD = 0 If VDS > VDS(sat) = VGS – VTN, then the transistor is biased in the saturation region. If VDS < VDS(sat), then the transistor is biased in the nonsaturation region.

EXAMPLE: Calculate the drain current and drain to source voltage of a common source circuit with an n-channel enhancement mode MOSFET. Assume that R1 = 30 k, R2 = 20 k, RD = 20 k, VDD = 5V, VTN = 1V and Kn = 0.1 mA/V2 VTH = 20 5 = 2V hence VGS = VTH = 2V 30 + 20 VDSsat = VGS – VTN = 2 – 1 = 1V, so, VDS > VDSsat, our assumption that the transistor is in saturation region is correct

EXAMPLE The transistor has parameters VTN = 2V and Kn = 0.25mA/V2. VDD = 10V The transistor has parameters VTN = 2V and Kn = 0.25mA/V2. Find ID and VDS RD = 10k R1 = 280k R2 = 160k

Solution 1. VTH = 160 10 = 3.636 V 160 + 280 KVL at GS loop: VGS – VTH + 0 = 0  VGS = VTH 2. Assume in saturation mode: ID = Kn(VGS - VTN)2 So, ID = 0.669 mA 3. KVL at DS loop: VDS = VDD – IDRD = 10 – 0.669 (10) = 3.31 V 4. VDS sat = VGS – VTN = 3.636 – 2 = 1.636 V So, VDS > VDSsat , therefore, assumption is correct! Answer: ID = 0.669 mA and VDS = 3.31 V

MOSFET DC Circuit Analysis - PMOS Different notation: VSG and VSD Threshold Voltage = VTP VG = VTH = R2 VDD R1 + R2 Use KVL at GS loop: VSG + 0 + VTH – VDD = 0 VSG = VDD - VTH

MOSFET DC Circuit Analysis - PMOS Assume the transistor is biased in the saturation region, the drain current: Calculate VSD: Use KVL at DS loop: VSD + IDRD - VDD = 0 ID = Kp (VSG + VTP)2 VSD = VDD - IDRD If VSD > VSD(sat) = VSG + VTP, then the transistor is biased in the saturation region. If VSD < VSD(sat), then the transistor is biased in the non-saturation region.

Calculate the drain current and source to drain voltage of a common source circuit with an p-channel enhancement mode MOSFET. Also find the power dissipation. Assume that, VTP = -1.1V and Kp = 0.3 mA/V2 5V Use KVL at SG loop: VSG + 0 +2.5 – 5 = 0 VSG = 5 – 2.5 = 2.5 V Assume biased in saturation mode: Hence, ID = 0.3 ( 2.5 – 1.1)2 = 0.5888mA Calculate VSD Use KVL at SD loop: VSD + IDRD – 5 = 0 VSD = 5 - IDRD VSD = 5 – 0.5888 ( 7.5) = 0.584 V 50 k VSG > |VTP | 50 k 7.5 k

VSD sat = VSG + VTP = 2.5 – 1.1 = 1.4V Hence, VSD < VSD sat. Therefore assumption is incorrect. The transistor is in non-saturation mode! ID = 0.3 2 ( 2.5 – 1.1) (5 – IDRD) – (5 – IDRD)2 ID = 0.3 2.8 (5 – 7.5ID) – (5-7.5ID)2 ID = 0.3 14 – 21ID – (25 – 75ID + 56.25ID2) ID = 0.3 14 – 21ID -25 +75ID – 56.25ID2 56.25 ID2 – 50.67 ID + 11 = 0 ID = 0.536 mA ID = 0.365 mA

ID = 0.536 mA ID = 0.365 mA VSD = 5 – IDRD = 0.98 V VSD = 5 – IDRD = 2.26 V VSD sat = VSG + VTP = 2.5 – 1.1 = 1.4V 0.98V < 1.4V Smaller than VSD sat : OK! 2.26V > 1.4V Bigger than VSD sat : not OK Answer: ID = 0.536 mA and VSD = 0.98V Power dissipation = ID x VSD = 0.525 mW

LOAD LINE Common source configuration i.e source is grounded. It is the linear equation of ID versus VDS Use KVL VDS = VDD – IDRD ID = -VDS + VDD RD RD

ID (mA) VDS (V) VGS VDS ID Q-POINTS y-intercept x-intercept

DC Analysis where source is NOT GROUNDED For the NMOS transistor in the circuit below, the parameters are VTN = 1V and Kn = 0.5 mA/V2.  

b) Write down the branch current equation for the source terminal. What is the value of VG ? b) Write down the branch current equation for the source terminal. c) Get an expression for VGS in terms of ID VG = -1V ID VS – (-5) = ID 1 VS + 5 = ID use KVL: 0 + VGS+ 1(ID) -5 +1 = 0 VGS = 4 - ID Or use node voltages: VGS = VG - VS VGS = -1 – ( ID – 5) VGS = 4 - ID

d) The transistor is biased in saturation mode, calculate ID d) The transistor is biased in saturation mode, calculate ID. You will know which value of ID that you need to choose by calculating VGS. Justify your answer. ID

ID e) Write down the branch current equation for the drain terminal f) Calculate VDS and confirm that the transistor is biased in saturation mode. 5 - VD = ID 2 VD = 5 - 2ID Use KVL: IDRD + VDS + IDRS – 5 – 5 = 0 1.354 (2) + VDS + 1.354 – 10 = 0 VDS = 10 – 1.354 – 2.708 = 5.938 V Or use node voltages: VDS = VD - VS where VD = 5 - 2( 1.354) = 2.292 V And VS = ID - 5 = - 3. 646 V So, VDS = 2.292 – (-3.646) = 5.938 V VDS sat = VGS – VTN = 2.646 – 1 = 1.646 V VDS > VDS sat  CONFIRMED