Introduction:The charge control equations are given for forward active mode of transistor as:iC = QF/τF – dQBC/dtiB = QF/τBF + dQF/dt + dQBC/dt + dQBE/dtiE = QF/τF + QF/τBF + dQF/dt + dQBE/dtWhere, all currents and charges are intrinsically taken as instantaneous functions of time.Delay Time, tdThe above equations do not apply to calculate the delay time, as the transistor is not in forward active mode throughout this time. The delay time is, though, very small in relation to the other switching times and is therefore ignored.Fall-Time, tf : Transistor Turn-OnThe fall-time, tf, for the output voltage is obtained by resolving the charge control equations for this condition. To resolve the above charge control equations in this concern, the currents require being associated in terms of circuit parameters. As the emitter terminal is grounded, this can’t be done for the emitter current and therefore its charge control equation is of little advantage. Throughout transistor turn-on in the forward active mode, the base of transistor can be taken as sitting at the potential of VBE ON and hence the base current can be supposed constant throughout this period as shown in figure below.Therefore, iB = (VCC - VBEON)/RBAnd, dQBE/dt = CBE (dVBE/dt) = 0
Figure: Constant Voltage on Base throughout Transistor Turn-On
In this case, the charge control equations are simplified to:iC = QF/τF - dQBC/dtiB = (QF/τBF) + (dQF/dt) + (dQBC/dt) = (VCC – VBE ON)/RBThe equation for iB is expressed in terms of circuit parameters and is therefore clearly the one to be solved. Though, since a solution for ic is needed, substitutions for QF and dQF/dt terms in terms of ic should be found. Let first consider a figure shown below:
Figure: The Effect of Collector-Base Junction Capacitance
From the circuit:dQBC/dt = CBC (dVBC/dt) = CBC d/dt[VBE ON – Vo(t)]Therefore, dQBC/dt = - CBC [dVo(t)]/dtHowever,Vo(t) = VCC - iCRCTherefore, dVo/dt = -RC (diC/dt)Hence, dQBC/dt = CBC RC (diC/dt)……………… (a)Secondly, consider:iC = QF/τF - dQBC/dt
QF = τF iC + τF (dQBC/dt)And hence,QF = τF iC + τF CBC RC (diC/dt)…………. (b) Thirdly,dQF/dt = τF (diC/dt) + τF CBC RC (d2iC/dt2)All through turn-on, the collector current starts to rise towards βF IB however is limited on reaching saturation to ICMAX << βFIB. The increase in collector current can be seen to contain an almost constant rate throughout this time as shown in figure below.Then, if (diC/dt) ≈ constant => (d2iC/dt2) → 0 and avoiding the second order derivative gives:dQF/dt ≈ τF (diC/dt)……………. (c)
Figure: Rise in Collector Current throughout Transistor Turn-On
Substituting the equations (a), (b) and (c) to replace the charge terms in the equation for base current provides:
As τF/τBF = τF/βFτF = 1/βF then, this equation can be rearranged as:(1/βF) iC + [(1/βF) CBC RC + τF + CBC RC] (diC/dt) = (VCC - VBEON)/RBOn multiplying by βF gives:iC + (CBC RC + βF τF + βF CBC RC) (diC/dt) = βF [(VCC - VBE ON)/RB]If βF >> 1 then (βF +1) CBC RC ≈ βF CBC RC and hence:iC + βF (τF + CBC RC) (diC/dt) = βF [(VCC - VBE ON)/RB]This is a first order linear differential equation in ic which can be solved by taking the Laplace Transform. Note that the Laplace Transforms of constant, K and a derivative of a function are as follows:L {K} = K/sL {dy/dt} = s L {y} – y (t = 0) = sY(s) – y (t = 0)And hence,IC(s) + βF (τF + CBC RC) [s IC (s) - iC (t = 0)] = βF [(VCC - VBE ON)/sRB]iC(t = 0) is the initial value of collector current throughout turn-on that should be taken as zero. Then,
The solution can be easily obtained by taking Inverse Laplace Transform where the Inverse Laplace transforms of the term:
This equation exhibits that in linear forward active region, throughout transistor turn-on, the collector current increases exponentially from zero towards the value of βF [(VCC - VBE ON)/RB)] Time constant of the expression can be seen to depend on transistor properties βF, τF and CBC and also the value of the external resistor RC.
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.
www.tutorsglobe.com offers Tabulation of Raw Data homework help, Tabulation of Raw Data assignment help, online tutoring assistance, geometry mathematics solutions by online qualified tutor's help.
Shares present the basic units of ownership of a business. Every companies issue ordinary shares. Preference shares assurance that if a dividend is paid, the preference shareholders will be permitted to the first part of it up to a maximum value.
tutorsglobe.com externalities-open access and public goods assignment help-homework help by online intermediate microeconomics tutors
Pesticides tutorial all along with the key concepts of Classification of Pesticides on the basis of origin and pests controlled, Production of Pesticides, Synthesizing the pesticide, Formulating the pesticide and Applying the pesticide
www.tutorsglobe.com offers Essential and Implementation Views homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
tutorsglobe.com plant physiology assignment help-homework help by online botany tutors
electronic configuration-atomic orbital model tutorial all along with the key concepts of quantum theory of atomic orbitals, shape of atomic orbitals, electronic configuration of atoms, periodic classification of elements
tutorsglobe.com energy yield from tca cycle assignment help-homework help by online tricarboxylic acid cycle tutors
tutorsglobe.com anatomical adaptations assignment help-homework help by online hydrophytes tutors
tutorsglobe.com structure and characteristics of antibodies assignment help-homework help by online immunology tutors
www.tutorsglobe.com offers tutorial and concepts in general linear programming problem glpp, standard linear programming problems and steps to change glpp to slpp, assignment help, homework help
TutorsGlobe.com Gas Law-I Assignment Help-Homework Help by Online Access Chemistry Tutors
tutorsglobe.com bacteria assignment help-homework help by online biodiversity tutors
tutorsglobe.com diabetes mellitus assignment help-homework help by online excretion tutors
Force-Centre of Gravity and Equilibrium tutorial all along with the key concepts of Concept of Force, Types of Force, Concepts of Equilibrium, Types of Equilibrium, Resultant and Equilibrium Forces, Moment of a Force, Principles of Moments, Conditions of Equilibrium and Principle of Floatation
1945615
Questions Asked
3689
Tutors
1475735
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!