Hybrid Pi Ce Transistor Model

Hybrid Pi Ce Transistor Model The hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate inter-electrode capacitances and other parasitic elements. Bipolar junction (BJT) parameters The hybrid-pi model is a linearized two-port network approximation to the BJT using the small-signal base-emitter voltage vbe and collector-emitter voltage vce as independent variables, and the small-signal base current ib and collector current ic as dependent variables. Figure 1: Simplified, low-frequency hybrid-pi BJT model. A basic, low-frequency hybrid-pi model for the bipolar transistor is shown in figure 1. The various parameters are as follows. is the transconductance in siemens, evaluated in a simple mode where: is the quiescent collector current (also called the collector bias or DC collector current) is the thermal voltage, calculated from Boltzmanns constant k, the charge of an electron q, and the transistor temperature in kelvins, T. At 300 K (approximately room temperature) VT is about 26 mV (Google calculator). in ohms where: is the current gain at low frequencies (commonly called hFE). Here IB is the Q-point base current. This is a parameter specific to each transistor, and can be found on a datasheet; ÃŽÂ ² is a function of the choice of collector current. is the output resistance due to the Early effect (VA is the Early voltage). Related terms The reciprocal of the output resistance is named the output conductance . The reciprocal of gm is called the intrinsic resistance . MOSFET parameters Figure 2: Simplified, low-frequency hybrid-piMOSFET model. A basic, low-frequency hybrid-pi model for the MOSFET is shown in figure 2. The various parameters are as follows. is the transconductance in siemens, evaluated in the Shichman-Hodges model in terms of the Q-point drain current ID by (see Jaeger and Blalock): , where: ID is the quiescent drain current (also called the drain bias or DC drain current) Vth = threshold voltage and VGS = gate-to-source voltage. The combination: often is called the overdrive voltage. is the output resistance due to channel length modulation, calculated using the Shichman-Hodges model as , using the approximation for the channel length modulation parameter ÃŽÂ » . Here VE is a technology-related parameter (about 4 V/ÃŽÂ ¼m for the 65 nm technology node) and L is the length of the source-to-drain separation. The reciprocal of the output resistance is named the drain conductance . The COMMON-EMITTER CONFIGURATION (CE) is the most frequently used configuration in practical amplifier circuits, since it provides good voltage, current, and power gain. The input to the CE is applied to the base-emitter circuit and the output is taken from the collector-emitter circuit, making the emitter the element common to both input and output. The CE is set apart from the other configurations, because it is the only configuration that provides a phase reversal between input and output signals High -Frequency -pi CE transistor model The Hybrid-Pi model is a fairly accurate description of the BJT small-signal response up to GHz range. Since the common emitter circuit is considered the most important practical configuration , we seek a CE model suitable for high frequencies. Hybrid -pi or Giacoletto common emitter transistor model shown below. This circuit is quite simple and analysis of circuit using this model are not difficult and give result which are in excellent agreement with experiment at all frequencies for which the transistor gives reasonable amplification. Furthermore , the resisitive components in this circuit may be derived from the low frequencies H-parameters. All parameters (resistances and capacitances) in the model are assumed frequency invariant. Parameters may be vary with the quiescent operating point , but under given bias conditions they are reasonably constant for small signal variations. For high frequency analysis the transistor is replaced this high frequency hybrid PI-model and voltage gain and current gain , input impedances etc are determined. To find current gain Apply current divider rule to the output circuit To find input resistance Applying KVL to input circuit Vs = hie ib + hre vce Vs = ib hie + hre iL RL from equation (1) Vs = ib hie + hre Ai ib RL ( iL =Ai ib ) Substituting in equation (2) Ri = hie + hre Ai RL To find voltage gain Av = since To find output resistance Replace RL by a voltage source. Replace independent sources by internal impedance of the source Applying KC L to the output circuit. iC = hfe ib + i1 iC = hfe ib + vce hoe(4) Applying KVL to input circuit ( hie ib + hre vce) =0 substituting for ib in equation (4) substituting in equation (3) To find output resistance with RL RO1 = RO||RL Since RL is in parallel with the voltage source, total output resistance is the parallel combination of RL and RO Numerical problems Question A common emitter amplifier has the following h- parameters. hie =1KÃŽÂ ©, hre = 10-4, hfe =100, hoe = 12 µmho. Find current gain, Voltage gain, Ri, Ro, power gain. Take RL = 2KÃŽÂ ©. Also find output power take vS = 500 mV ( rms). HYBRID-p EQUIVALENT CIRCUIT To obtain Hybrid-p Equivalent circuit Consider a PNP transistor as shown above. The emitter current IE is divided in to base current IB and a component aIE of the collector current. This division of current takes place in the entire base layer at infinite number of points. For mathematical convenience, it is assumed that the division of current takes place at an imaginary terminal B1. rb1e: It is the resistance of forward biased base to emitter junction and it is the resistance offered to the flow of the current IE. rb1c: It is the resistance of reverse biased collector to base junction. The flow of current in this resistance represents the reverse saturation current Ico due to flow of minority charge carriers. rbb1: It is the resistance of the base layer for the flow of the current IB. This is called base spreading resistance because the division of emitter current is spread across the entire region. aIE: This is the current in the collector due to transistor action. When charge carriers reach the base layer from emitter, the potential gradient at the collector junction will result in the movement of the charge carriers in to the collector. This forms the current. aIE depends on the emitter current IE which inturn depends upon the voltage across base to emitter junction. Therefore, the voltage VB1E controls aIE. VB1E is the independent variable. This depends on charge carrier concentration and temperature. cb1e and cb1c: This is the stray capacitance across the two P-N junction. The reactance of the capacitor is very high at mid-frequency. Hence approximately, capacitors are replaced by open circuit (not considered). But for high frequency, the reactance becomes finite. Hence considered in the analysis. All the above terms are called Hybrid-p parameters. These parameters can be represented by the following circuit and it is called Hybrid-p equivalent circuit or Giacollette equivalent circuit. gm vb1e is the component of collector current(aie) expressed as a function of independent variable vb1e. gm is the Transconductance of the transistor. This represents ability of the transistor in transforming the input voltage vb1e in to output current.rce: rce is the internal resistance of the current source. To find Hybrid-p parameters Hybrid -p equivalent circuit Let the output terminals be short circuited . Considering mid- frequency, reactance of all capacitors becomes infinite. Therefore, all capacitors can be replaced by open circuit. rb1c is the resistance of reverse biased collector junction whose value is very high. Therefore it can be approximated to open circuit. rce is short circuited, becomes redundant. Hence can be removed To find gm where ΆIC and ΆVB1E are the changes in the currents and voltages around quiescent condition. We know that IC = aIE + ICO Since ICO is very small and a is very close to unity, Differentiating with respect to VB1E If t = 27oC (3) substituting in (1) In general In the above equation, IC represents the dc collector current or quiescent current. Its value can be found graphically by drawing the dc load line, locating the Q point on the load line and then measuring IC. OR if know the biasing arrangement of the transistor, then the circuit can be solved using biasing technique and then IC can be calculated. To find rb1e From the two port network theory, we know that vse = ib hie + hre vce (4) ic = ibhfe + hoe vce (5) OR From equation -(5) In the hybrid p equation circuit, VCE is already 0. Therefore obtain the ratio From hybrid p equation circuit and equate it to equation (6). Equating to equation (6). hfe =gm rb1e To find rbb1 From equation (4) From the hybrid-p equivalent circuit, applying KVL to input circuit. Vs = ib(rbb1 + rb1e) To find rb1c Rewriting the hybrid p equivalent circuit by neglecting all capacitances( open circuit) From equation (4) Taking ib = 0 in the hybrid-p equivalent circuit, since there is no voltage drop across rbb1, vs = vb1e. Substituting in equation (8). From the hybrid -p equivalent circuit. Applying voltage divider rule to circuit(2). rb1e is the resistance of the forward biased junction and rb1c is the resistance of the reverse biased junction. Therefore rb1e can be neglected in the denominator. To find rce From equation-(5) Applying KCL at the output terminal ic = i1 + gm vb1e + i2 substituting in the above equation Since rb1e To find Cb1C Cb1C is the junction capacitance of reverse biased collector to base junction. When a PN junction is reverse biased, the width of the depletion layer increases and capacitance decreases. Therefore Cb1C is very low of the order of few pico farads. To find Cb1e This is the capacitance of forward biased PN junction. When a PN junction is forward biased, width of the depletion layer decreases and capacitance increases. Cb1e + Cb1C = Where fT is called the transition frequency. fT = hfe fb fb is called upper cutoff frequency. fb = Numrical Problem: A transistor amplifier is operating with a dc condition of (10V,10mA). The operating temperature is 300C. The H-parameters of the transistor are hie =1Ko, hre =2.5X10-4, hfe=100, hoe=25X10-5mho. Calculate hybrid-p parameters given that CC=3PF. Take fT=1MHz. Solution References and notes ^ R.C. Jaeger and T.N. Blalock (2004). Microelectronic Circuit Design (Second Edition ed.). New York: McGraw-Hill. pp. Section 13.5, esp. Eqs. 13.19. ISBN 0-07-232099-0. ^ R.C. Jaeger and T.N. Blalock. Eq. 5.45 pp. 242 and Eq. 13.25 p. 682. ISBN 0-07-232099-0. ^ R.C. Jaeger and T.N. Blalock. Eq. 4.20 pp. 155 and Eq. 13.74 p. 702. ISBN 0-07-232099-0. ^ a b W. M. C. Sansen (2006). Analog Design Essentials. DordrechtÃŽÂ ¼: Springer. p. 0124, p. 13. ISBN 0-387-25746-2. G.B GUPTA Millman halkias

The Box Tree Case

Strike always results to the loss of trust between the employer and striking workers. In the case of the Box Tree Restaurant, the workers went on strike after losing their trust on their former employer, Augustin Paege, who denied them of their commissions because he wanted to reduce his payroll expenses by $100,000. After the strike, these workers could be expected to hold back as far as trusting their employer is concerned. On the other hand, after what Baruch and her replacement employees went through at the hands of the striking workers, they are not expected either to easily trust the returning workers.The most critical job for Gila Baruch, therefore, if she wants to â€Å"restore the once sterling reputation† of Box Tree, is to rebuild trust among all parties concerned. (Corsun, Young, & Shinnar, n. d. ) The situation, however, is not hopeless. Rebuilding trust is still possible. But they should do several things urgently. First, everybody should resort to â€Å"self-ac ceptance. † This means that they should learn to accept who they are and be secured in their identity so that they could develop trust in others. (Messina, n. d.) For instance, Baruch should accept the fact that if not for the strike she would not end up owning a promising business. The replacement workers are on the same boat as Baruch. They have the strikers to thank for their jobs. If not for the strike, there would not have been any vacancy in the restaurant for them to fill. In addition, they should not forget that they, too, are workingmen like the strikers and as such, want to be fairly compensated for their time and effort – exactly what the strikers wanted in the first place.Finally, the returning strikers should be aware that they are also indebted to Baruch and the replacement workers who made it possible for the Box Tree to stay in operation in spite of the work stoppage that they tried to instigate. Without them, the restaurant would have collapsed, they wo uld have completely lost their jobs, and then their strike would have been an exercise in futility. Once they accept who they are and what the strike has done for their benefits, they should be able to trust each other because their livelihood, in fact, clearly depends on one another.Another way by which trust could be rebuilt is for everybody to work hard for the establishment of â€Å"a healing environment. † This means that Baruch, the replacement workers, and the returning strikers should adopt a â€Å"healing mode† which will enable everybody to employ â€Å"forgiveness, understanding, and healthy communication to resolve problems and issues. † Once they are in this mode, they would be able to forget the insults and the animosities during the strike and heal the wounds they created, thereby allowing for an atmosphere conducive for the rebuilding of trust.(Messina, n. d. ) They, particularly the replacement workers and the returning strikers, should also str ive for a â€Å"reduction of a sense of competition. † In other words, they should do away with their jealousies and stop being defensive with one another. Instead, everybody should start cooperating for the common good. (Messina, n. d. ) The replacement workers, specifically, should not make a big thing out of the seniority status afforded the returning strikers and instead accept the fact that they joined the company at a much later time.The affected parties should likewise â€Å"let go of their fear. † Fear is such a restricting feeling which impedes people from behaving normally and objectively towards one another. A person who fears another for any reason could never trust that person. (Messina, n. d. ) The replacement workers, for instance, should not feel threatened by the return of the strikers. They should find security in Baruch’s desire â€Å"to reward [their] hard work and loyalty† during the strike. (Corsun, Young, & Shinnar, n. d.) The retur ning workers, on the other hand, should not be afraid that Baruch will be treating them with suspicion because of what they did. They should instead show Baruch that they mean no harm for her and the restaurant and that their only reason for returning to their jobs was to resume working and continue earning for their families. Reference Corsun, D. L. , Young, C. A. & Shinnar, R. S. (n. d. ). The Box Tree. Order #32096240 attachment. Messina, J. J. (n. d. ). Building Trust. Retrieved October 10, 2007 from http://www. coping. org/growth/trust. htm

Importance Of Purpose Audience Tone And Content In Academic Writing and two methods of weight lose Essay

?Importance Of Purpose Audience Tone And Content In Academic Writing Purpose audience tone and content all of these are part of writing process and are extremely important for a good piece of academic writing. Paragraph divide ideas into logical and manageable parts. Purpose, tone and audience these three elements shape the content of each paragraph. Purpose: The reason why the writer is writing the paragraph and what is his hope to achieve with the paper. Without a sturdy purpose the paper is worthless. Tone: The thoughts the writer conveys about the paragraph’s subject. If the tone is not appropriately chosen and used all through the paper then it can seem cluttered and possibly even incoherent. Audience: It’s extremely significant and this is the individual or group whom the writer intends to reach or address. It may be a specific group, teacher, student or general group. Fig: Purpose, Audience, Tone, and Content Triangle (source: https://new. edu/resources/purpose-audience-tone-and-content) From the figure we can see that purpose , audience and tone all are focuses to content. Introduction: Weight loss, in the context of medicine, health, or physical fitness, is a reduction of the total body mass, due to a mean loss of fluid, body fat oradipose tissue and/or lean mass, namely bone mineral deposits, muscle, tendon, and other connective tissue. Weight loss is one of today’s most trendy obsessions among individuals. Weight loss can have positive and negative consequence on an individual. It can occur unintentionally due to an underlying disease or can arise from a conscious effort to improve an actual or perceived overweight or obese state. Weight loss in the context of medicine , health or fitness , is a reduction in body mass of an individual, because of an average loss of liquid , fat or tissue such as muscle , tendon or tissue conjunctive . One of today’s most popular obsessions among individuals is weight loss. Weight loss can have positive and negative implication on an individual. A large of number of people now day checks out new ways to lose weight to fit modern way of life. A few people favor to use artificial techniques similar to consuming pills and equipment claiming to provide weight loss, at the same time others try natural procedures such as modifying diet, lifestyle, and cardio-training and the techniques for burning fat.

Principles of Banking and Finance - 1898 Words

What does Sub-Prime Crisis means? Sub Prime lending which is also known as near-prime, non-prime and second chance lending, means lending to people who might have trouble repaying the loan due to income ability or credit ratings which previously would not have been available to them. Credit ratings that might be not favorable to them with the standards set up initially by Financial Institutions slowly dwindle to less strict under-writing of loans. which could also due to an influx of foreign capital making lending easier to these group of people, the investment banks that sold the repackage mortgages to the consumers which is one of the way to fund for capital, and the Housing Urban Development of America policy to ensure that its†¦show more content†¦If there are not to give favorable ratings to these products they risk the underwriter of these securities to another rating agency. It would be hard to sell these products if they are not being given a rating to begin with. O nce they are sold the banks have in a way diverted part of the risk to the consumers. Investors should not rely too heavily on these ratings agencies opinions but instead carry out their own homework in the safeness of debt level as well as others related securities. Probably the opinions of the agencies enable them to get a conclusion, however based on past decade of event, it can only be consider as off base when it comes to the risk of credit event. Investors should try to put themselves in the shoes of the product pushers, asking themselves very important points like, why do you need to sell these products? Do you own any of these products yourself? If it is as good as you mention have the private investors bought and participated a substantial amount of their savings in it? Perhaps there need to be some form of intermediaries whereby no conflict of interest will affect their opinion and report of these products. 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