MOS Transistor Inverter: Static Characteristics IIMOS Inverter Voltage Transfer Characteristic:The schematic figure of simple MOS transistor inverter with a resistive load is repeated in figure shown below. Since with the simple bipolar transistor inverter, the transfer characteristic can be plotted as output voltage against input voltage, Vo vs. Vin as shown in figure below.
Figure: Schematic Diagram of Simple MOS Inverter
Initially, with Vi = 0 the input voltage to transistor is beneath threshold voltage and the transistor is OFF or non-conducting and therefore the output voltage is pulled up to the supply voltage VDD. Once the input voltage is raised to be equivalent to the threshold voltage, VT, the transistor starts to conduct and therefore the output voltage drops. As VDS > VGS – VT, the transistor operates initially in saturation region. Since the input voltage is further raised, the output voltage continues to drop until ultimately VDS < VGS – VT and the transistor comes out of the saturation region to operate in non-saturation region. Ultimately the input voltage reaches an utmost of VDD and the output reaches its minimum value of VOL as formerly computed.
Figure: Voltage Transfer Characteristic of Simple MOS Transistor Inverter
Critical Logic Voltages:The similar critical input and output logic voltages can be stated as for other logic families viz.:ViLMAX = maximum voltage acceptable as the logic LO input
ViHMIN = minimum voltage acceptable as the logic HI input.
VOLMAX = maximum voltage acceptable as the logic LO output.
VOHMIN = minimum voltage acceptable as the logic HI output.a) Critical Point ViL MAX, VOH MIN:This is the point on upper left-hand portion of transfer characteristic where the slope is -1. At this point, the transistor can be taken to operate in the saturation region where, neglecting the consequences of channel length modulation for simplicity, the drain current is explained as:ID = Kn(VGS - VT)2However as VO = VDS and Vi = VGS and VO = VDD – iDRD then:Vo = VDD – KnRD (Vi - VT)2.......................... (a)On expanding it gives:Vo = VDD - KnRDVi2 + 2 KnRDViVT - KnRDVT2On differentiating:∂Vo/∂Vi = - 2 KnRDVi + 2 KnRDVTAt critical point ∂Vo/∂Vi = -1 with Vi = ViL MAX and VO = VOH MIN and hence:- 2 KnRDVi + 2 KnRDVT = - 12 KnRDViLMAX = 1 + 2 KnRDVTAnd hence,ViLMAX = VT + 1/(2 KnRD)This value is a slight higher than VT and for illustration given with VT = 1V, RD = 100kΩ and Kn = 100µAV-2, ViL MAX = 1.05V.Replacing back into equation (a) to find out the output voltage for this coordinate gives:VOHMIN = VDD – KnRD(ViL MAX - VT)2VOHMIN = VDD – KnRD[VT + (1/ KnRD) - VT]2And hence ultimately:VOHMIN = VDD – (1/4 KnRD)This value is a slight lower than VDD and for illustration given with VDD = 10V, VT = 1V, RD = 100kΩ and Kn = 100µAV-2, VOH MIN = 9.98V. The coordinate of critical point (a) is then:ViLMAX, VOHMIN = 1.05, 9.98 Vb) Critical Point ViH MIN, VOL MAXThis is the point on lower right-hand portion of the characteristic where slope is -1. At this point, the transistor can be taken to operate in non-saturation region where the drain current is explained as:ID = Kn[2(VGS - VT)VDS – V2DS]However again, as VO = VDS and Vi = VGS and VO = VDD – iDRD then:VO = VDD – 2 KnRD (Vi - VT) Vo + KnRDVo2On expanding:VO = VDD – 2 KnRDViVo + 2 KnRDVTVo + KnRDVo2On rearranging:VO [1 - KnRDVT] = VDD - 2 KnRDViVo + KnRDVo2There is a choice here to employ implicit differentiation to find ∂Vo/∂Vi or to re-arrange the expression as Vi in terms of VO and then determine ∂Vi/∂Vo. The latter is simpler as there is just one term in Vi. Then,2 KnRDViVo = VDD – [1 - 2 KnRDVT]Vo + KnRDVo2And hence,Vi = VDD/(2 KnRDVo) – [(1 - 2 KnRDVT)/ 2 KnRD) + (Vo/2)............... (b)Then,∂Vo/∂Vi = - VDD/(2 KnRDVo2) + (1/2)For ∂Vo/∂Vi = -1 we can employ ∂Vi/∂Vo= -1 and hence:- (VDD/2 KnRDVo2) + (1/2) = - 1(VDD/2 KnRDVo2) = 3/2Vo2 = VDD/3 KnRDBy taking the positive root as practical value gives:VOLMAX = √VDD/3KnRDThat for the illustration given with VDD = 10V, VT = 1V, RD = 100kΩ and Kn = 100µAV-2 , VOL MAX = 0.58V.This is significantly higher than the great value of VOL computed formerly. Then replacing this back into the expression for Vi in equation (b) above gives:
And therefore ultimately the critical input value is as shown:ViHMIN = VT + 2√VDD/3KnRD – (1/2 KnRD)That for illustration given with VDD = 10V, VT = 1V, RD = 100kΩ and Kn = 100µAV-2 provides ViH MIN = 2.1V. This gives the coordinates of critical point (b) as:ViHMIN, VOLMAX = 2.1, 0.58 VNoise Margins:Ultimately, the noise margins for simple MOS inverter can be computed approximately from the critical points evaluated from the transfer characteristic as shown:NMH = VOHMIN – ViHMIN = 9.98 – 2.1 = 7.88VNML = ViLMAX – VOLMAX = 1.05 – 0.58 = 0.47V
Latest technology based Electrical Engineering Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Electrical Engineering help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Electrical Engineering, project ideas and tutorials. We provide email based Electrical Engineering help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Electrical Engineering. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Electrical Engineering Homework help and assignment help services. They use their experience, as they have solved thousands of the Electrical Engineering assignments, which may help you to solve your complex issues of Electrical Engineering. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
Imperfection in Solids tutorial all along with the key concepts of Crystalline Defects, Point Defects, Vacancy, Self-interstitial or interstitialcy, Impurities, Schottky defect, Frenkel defect, Linear Defects, Edge dislocation, Screw dislocation, Volume (Bulk) Defects
almost all businesses that include more than a few owners and/or employees are set up as limited companies.
www.tutorsglobe.com offers thermo-chemistry homework help, thermo-chemistry assignment help, online tutoring assistance, physical chemistry solutions by online qualified tutor's help.
Reproduction in Algae-Life Cycles tutorial all along with the key concepts of Chlamydomonas, Life Cycle of Chlamydomonas, Ulothrix, Life Cycle of Ulothrix, Ulva, Laminaria, Life Cycle in Laminaria, Fucus, Life Cycle of Fucus
Resonance effect and Hyperconjugation tutorial all along with the key concepts of nonbonding electrons, Resonance effects of various groups, Hyperconjugation, Hydrogen bonding, Tautomerism
We greatly acclaimed Seedless Plant Assignment Help service, as our PhD experts are available 24/7 to fetch top grades at reasonable prices.
Nutrient Cycles tutorial all along with the key concepts of Nutrient cycling in nature, Carbon Cycle, Oxygen Cycle, Nitrogen Cycle and Water Cycle
tutorsglobe.com diabetes mellitus assignment help-homework help by online insulin tutors
Nematodes tutorial all along with the key concepts of Characteristics of Nematodes, Ascaris, Life Cycle of Nematodes and Nematode Survival Strategies
nomenclature of organic compounds tutorial all along with the key concepts of covalent bond, bond dissociation energy, structural formulas
Wondering where to get the best Optical Physics Assignment Help service to score A++ at low prices? Approach us now!
www.tutorsglobe.com offers chemical reactivity homework help, chemical reactivity assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
We promise impeccable and 100% authentic Management Information System Assignment Help service at low prices to score A++.
tutorsglobe.com virus assignment help-homework help by online microbiology tutors
tutorsglobe.com muscle pull assignment help-homework help by online muscles tutors
1932240
Questions Asked
3689
Tutors
1487892
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!