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.
tutorsglobe.com organ of corti assignment help-homework help by online ear tutors
Operators tutorial all along with the key concepts of Linear Operators, Eigen-values of a Linear Operator, Expectation value, Commutators and simultaneous Eigen-states and Matrix Elements of a Linear Operator
tutorsglobe.com water transport assignment help-homework help by online plant physiology tutors
Principles of independent assortment tutorial all along with the key concepts of Mendel's Second Law of Inheritance, Genotypes and Mendel's first law
Paramecium tutorial all along with the key concepts of Physical Appearance of paramecium, paramecium Feeding, Respiration process in Paramecium, Movement in Paramecium, Reproduction and Importance of paramecium
tutorsglobe.com herpes viruses assignment help-homework help by online medical parasitology tutors
avail impeccable general microbiology assignment help service with 24/7 support of phd experts at feasible prices to score high grades.
if the items on the statement of financial position are listed randomly along with assets at the top of the statement and equity and liabilities beneath, it can be confusing, although it may consist of all of the information and be mathematically accurate.
www.tutorsglobe.com offers synthetic preparation homework help, synthetic preparation assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
www.tutorsglobe.com offers answering questions to comparison of national income over time, assignment help - homework help in economics subject.
tutorsglobe.com positive or normative economics assignment help-homework help by online nature and scope of economics tutors
Algae tutorial all along with the key concepts of General features of Algae, Forms of algae, Reproduction in Algae and Importance of Algae
tutorsglobe.com amoebiasis assignment help-homework help by online protozoan microbiology tutors
tutorsglobe.com protein metabolism assignment help-homework help by online biochemistry tutors
tutorsglobe.com nephron assignment help-homework help by online excretion tutors
1952507
Questions Asked
3689
Tutors
1472267
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!