Hybrid Pi Ce Transistor Model

Hybrid Pi Ce Transistor ModelThe hybrid-pi homunculus is a popular traffic circle model used for analyzing the small(a) signal behavior of bipolar joint and field order transistors. The model rout out be quite faultless for low- relative frequency roofys and can easily be adapted for higher frequency roundabouts with the humanitarian of appropriate inter-electrode capacitances and other parasitic elements.Bipolar coincidence (BJT) statementsThe hybrid-pi model is a linearized two-port engagement approximation to the BJT using the small-signal base-emitter electric potential vbe and storage battery-emitter voltage vce as main(a) variables, and the small-signal base actual ib and collector topical ic as reliant 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 ar as follows. is the transconductance in siemens, evaluated in a simple modewhere is the quiescent collector current (also called the collector influence or DC collector current) is the thermal voltage, calculated from Boltzmanns constant k, the fear of an electron q, and the transistor temperature in kelvins, T. At 300 K (approximately path temperature) VT is about 26 mV (Google calculator). in ohmswhere is the current fall upon at low frequencies (commonly called hFE). Here IB is the Q-point base current. This is a parameter specific to individually transistor, and can be found on a datasheet is a manoeuvre of the choice of collector current. is the create safeguard due to the Early effect (VA is the Early voltage).Related termsThe reciprocal of the produce resistance is named the output conductance.The reciprocal of gm is called the intrinsic resistance.MOSFET parametersFigure 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 atomic number 18 as foll ows.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),whereID is the quiescent drain current (also called the drain crook or DC drain current)Vth = threshold voltage and VGS = gate-to-source voltage.The combinationoften 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 .Here VE is a technology-related parameter (about 4 V/m for the 65 nm technology node) and L is the length of the source-to-drain sepa ration.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 government agency crystalize. The infix to the CE is applied to the base-emitter circuit and the outpu t is taken from the collector-emitter circuit, making the emitter the element common to both excitant 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 signalsHigh -Frequency -pi CE transistor modelThe Hybrid-Pi model is a fairly accurate commentary of the BJT small-signal response up to GHz range.Since the common emitter circuit is considered the most essential practical configuration , we seek a CE model commensurate 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 argon not difficult and give result which are in refined agreement with experiment at all frequencies for which the transistor gives reasonable amplification. moreover , the resisitive components in this circuit may be derived from the low frequencies H-parameters. All parameters (resistances and cap acitances) in the model are assumed frequency invariant. Parameters may be modify 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 dumbfound current gainApply current divider rule to the output circuitTo unwrap input resistanceApplying KVL to input circuitVs = move ib + hre vceVs = ib hie + hre iL RL from par (1)Vs = ib hie + hre Ai ib RL ( iL =Ai ib )Substituting in equation (2)Ri = hie + hre Ai RLTo assure voltage gainAv =sinceTo pay back output resistanceReplace RL by a voltage source. Replace separate sources by internalimpedance of the sourceApplying KC L to the output circuit.iC = hfe ib + i1iC = hfe ib + vce hoe(4)Applying KVL to input circuit ( hie ib + hre vce) =0substituting for ib in equation (4)substituting in equation (3) To find output resistance with RLRO1 = RORLSince RL is in parallel with the voltage source, come up output resistance is the parallel combination of RL and RONumerical problemsQuestion A common emitter amplifier has the following h- parameters. hie =1K, hre = 10-4, hfe =100, hoe = 12mho. Find current gain, Voltage gain, Ri, Ro, power gain. Take RL = 2K. Also find output power take vS = 500 mV ( rms).HYBRID-p EQUIVALENT CIRCUITTo obtain Hybrid-p identical circuitConsider 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 wide base seam at infinite number of points. For mathematical convenience, it is assumed that the division of current takes place at an imaginary end B1.rb1e It is the resistance of former unilateral base to emitter junction and it is the resistance offered to the flow of the current IE.rb1c It is the resistance of upset biased colle ctor to base junction. The flow of current in this resistance represents the reverse saturation current Ico due to flow of minority caution 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 crossways the entire region.aIE This is the current in the collector due to transistor action. When charge carriers consecrate 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.thusly, 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 in truth high at mid-frequen cy. 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 stand for by the following circuit and it is called Hybrid-p akin circuit or Giacollette equivalent circuit.gm vb1e is the component of collector current(aie) expressed as a business office 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 parametersHybrid -p equivalent circuitLet the output terminals be oblivious 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 real high. Therefore it can be approximated to open circuit.rce is short circuited, becomes redundant. Hence can be removedTo find gmwhere IC and VB1E are the changes in the currents and voltages somewhat quiescent condition.We know thatIC = aIE + ICOSince ICO is very small and a is very close to unity,Differentiating with respect to VB1EIf t = 27oC(3)substituting in (1)In widely distributedIn the above equation, IC represents the dc collector current or quiescent current. Its value can be found graphically by drawing the dc incubus line, locating the Q point on the load line and consequently 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 rb1eFrom the two port network theory, we know thatvse = ib hie + hre vce (4)ic = ibhfe + hoe vce (5)ORFrom equation -(5)In the hybrid p equation circuit, VCE is already 0. Therefore obtain the ratioFrom hybrid p equation circuit and equate i t to equation (6). study to equation (6).hfe =gm rb1eTo find rbb1From equation (4)From the hybrid-p equivalent circuit, applying KVL to input circuit.Vs = ib(rbb1 + rb1e)To find rb1cRewriting the hybrid p equivalent circuit by neglecting all capacitances( open circuit)From equation (4)Taking ib = 0 in the hybrid-p equivalent circuit, since on that point 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 rceFrom equation-(5)Applying KCL at the output terminalic = i1 + gm vb1e + i2substituting in the above equationSince rb1e To find Cb1CCb1C 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 decre ases. Therefore Cb1C is very low of the order of few pico farads.To find Cb1eThis 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 fbfb is called upper cutoff frequency.fb =Numrical ProblemA 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.SolutionReferences and notes R.C. Jaeger and T.N. Blalock (2004). Microelectronic Circuit Design (Second Edition ed.). New York McGraw-Hill. pp. scratch 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. Dordrecht Springer. p. 0124, p. 13. ISBN 0-387-25746-2.G.B GUPTAMillman halkias