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.
tutorsglobe.com leaf assignment help-homework help by online root-stem and leaf tutors
Get the un-matched Electromagnetism Physics Assignment Help service from PhD experts that you need today for top grades.
tutorsglobe.com noise pollution assignment help-homework help by online ear tutors
Homing and Navigation tutorial all along with the key concepts of Initiation of navigation/migration, Orientation and navigation, Tools form studying migration and Navigation process in animals
Chemotherapy of Specific Diseases tutorial all along with the key concepts of Chemotherapy of Hodgkin's disease, Pharmaco-dynamics and pharmco-kinetics, Pharmacodynamics, Pharmacokinetics, Absorption, Metabolism and Excretion
Cement and binding minerals tutorial all along with the key concepts of Mineral composition of Cement, Classes of Cements, Natural Cements, Aluminous Cement and Portland cement
Polymer Degradation tutorial all along with the key concepts of Hydrolytic Degradation, Oxidative Degradation, Ionizing-Radiation Degradation, Galvanic action
Avail excellent Mealy & Moore Machines Assignment Help service and get rid of all writing problems with PhD experts at feasible prices and score A++
www.tutorsglobe.com offers Administration Overheads homework help, assignment help, case study, writing homework help, online tutoring assistance by accounting tutors.
Theory of Sampling tutorial all along with the key concepts of Fundamental principles of sampling, Sampling techniques, Types of Samples, Gross and Laboratory size Samples, Chain of custody procedure, Treatment or Preparation of Sample, Statistics of Sampling, Sample Decomposition
Theory and lecture notes of Bertrand’s Paradox all along with the key concepts of bertrand’s paradox, bertrand’s paradox assumptions, bertrand’s paradox models. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Bertrand’s Paradox.
Theory and lecture notes of Industrial Revolution all along with the key concepts of American Long Run Growth, Productivity Growth Slowdown, Productivity Slowdown in the G-7 Economies, End of the Productivity Slowdown. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Industrial Revolution.
Counters tutorial all along with the key concepts of Asynchronous (Ripple) Counter, Operation of ripple counter, Mod of Counter, Frequency Division, Synchronous Counter, Controlled Synchronous Counter, Ring Counter, Mod 10 (Decade) Counter
tutorsglobe.com importance of working capital assignment help-homework help by online working capital management tutors
tutorsglobe.com function of finance department assignment help-homework help by online financial management tutors
1965064
Questions Asked
3689
Tutors
1475595
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!