TheA hybrid-pi modelA is a popularA circuitA theoretical account used for analysing theA little signalA behaviour of bipolar junction and field effectA transistors. The theoretical account can be rather accurate for low-frequency circuits and can easy be adapted for higher frequence circuits with the add-on of appropriate inter-electrodeA capacitancesA and other parasitic elements.

## Bipolar junction ( BJT ) parametric quantities

The hybrid-pi theoretical account is a linearizedA two-port networkA estimate to the BJT utilizing the small-signal base-emitter voltageA vbeA and collector-emitter voltageA vceA as independent variables, and the small-signal base currentA ibA and aggregator currentA icA as dependent variables.

Figure 1: Simplified, low-frequency hybrid-piA BJTA theoretical account.

A basic, low-frequency hybrid-pi theoretical account for theA bipolar transistorA is shown in figure 1. The assorted parametric quantities are as follows.

A is theA transconductanceA inA mhos, evaluated in a simple manner

where:

A is theA quiescentA aggregator current ( besides called the aggregator prejudice or DC collector current )

A is theA thermic electromotive force, calculated fromA Boltzmann ‘s constantA K, theA charge of an electronA Q, and the transistor temperature inA Ks, A T. At 300 K ( about room temperature ) A VTA is about 26 millivolts ( Google reckoner ) .

A inA ohms

where:

A is the current addition at low frequences ( normally called hFE ) . HereA IBA is the Q-point base current. This is a parametric quantity particular to each transistor, and can be found on a datasheet ; A I?A is a map of the pick of aggregator current.

A is the end product opposition due to theA Early effectA ( VAA is the Early electromotive force ) .

## Related footings

The reciprocal of the end product opposition is named theA end product conductance

## .

The mutual ofA gmA is called theA intrinsic opposition

## .

MOSFET parametric quantities

Figure 2: Simplified, low-frequency hybrid-piMOSFETA theoretical account.

A basic, low-frequency hybrid-pi theoretical account for theA MOSFETA is shown in figure 2. The assorted parametric quantities are as follows.

is theA transconductanceA inA mhos, evaluated in the Shichman-Hodges theoretical account in footings of theA Q-pointA drain currentA IDA by ( see Jaeger and Blalock ) :

## ,

where:

IDA is theA quiescentA drain current ( besides called the drain prejudice or DC drain current )

VthA =A threshold voltageA andA VGSA = gate-to-source electromotive force.

The combination:

frequently is called theA overdrive electromotive force.

A is the end product opposition due toA channel length transition, calculated utilizing the Shichman-Hodges theoretical account as

## ,

utilizing the estimate for theA channel length modulationA parametric quantity I»

## .

HereA VEA is a technology-related parametric quantity ( about 4 V/I?m for theA 65 nmA engineering node ) andA LA is the length of the source-to-drain separation.

The reciprocal of the end product opposition is named theA drain conductance

## .

The COMMON-EMITTER CONFIGURATION ( CE ) is the most often used constellation in practical amplifier circuits, since it provides good electromotive force, current, and power addition. The input to the CE is applied to the base-emitter circuit and the end product is taken from the collector-emitter circuit, doing the emitter the component “ common ” to both input and end product. The CE is set apart from the other constellations, because it is the lone constellation that provides a stage reversal between input and end product signals

## High -Frequency -pi CE transistor theoretical account

## The Hybrid-Pi theoretical account is a reasonably accurate description of the BJT small-signal response up to GHz scope.

Since the common emitter circuit is considered the most of import practical constellation, we seek a CE theoretical account suitable for high frequences. Hybrid -pi or Giacoletto common emitter transistor theoretical account shown below. This circuit is rather simple and analysis of circuit utilizing this theoretical account are non hard and give consequence which are in first-class understanding with experiment at all frequences for which the transistor gives sensible elaboration. Furthermore, the resisitive constituents in this circuit may be derived from the low frequences H-parameters. All parametric quantities ( oppositions and electrical capacities ) in the theoretical account are assumed frequence invariant. Parameters may be vary with the quiescent runing point, but under given bias conditions they are moderately changeless for little signal fluctuations. For high frequence analysis the transistor is replaced this high frequence intercrossed PI-model and electromotive force addition and current addition, input electric resistances etc are determined.

## To happen current addition

Apply current splitter regulation to the end product circuit

## To happen input opposition

Using KVL to input circuit

Vs = hie ib + hre vce

Vs = ib hie + hre Illinois RL from equation ( 1 )

Vs = ib hie + hre Ai ib RL ( forty-nine =Ai ib )

Substituting in equation ( 2 )

Ri = hie + hre Ai RL

To happen electromotive force addition

Av =

since

## To happen end product opposition

Replace RL by a electromotive force beginning. Replace independent beginnings by internal

electric resistance of the beginning

Using KC L to the end product circuit.

Intelligence Community = hfe ib + i1

Intelligence Community = hfe ib + vce hoe — — – ( 4 )

Using KVL to input circuit

– ( hie ib + hre vce ) =0

replacing for ib in equation ( 4 )

replacing in equation ( 3 )

To happen end product opposition with RL

RO1 = RO||RL

Since RL is in analogue with the electromotive force beginning, entire end product opposition is the parallel combination of RL and RO

## Numeric jobs

Question A common emitter amplifier has the undermentioned h- parametric quantities. hie =1KI© , hre = 10-4, hfe =100, hoe = 12Aµmho. Find current addition, Voltage addition, Ri, Ro, power addition. Take RL = 2KI© . Besides find end product power take volt = 500 millivolt ( rms ) .

## HYBRID-p EQUIVALENT CIRCUIT

## To obtain Hybrid-p Equivalent circuit

See a PNP transistor as shown above. The emitter current IE is divided in to establish current IB and a component aIE of the aggregator current. This division of current takes topographic point in the full base bed at infinite figure of points. For mathematical convenience, it is assumed that the division of current takes topographic point at an fanciful terminus B1.

rb1e: It is the opposition of forward biased base to emitter junction and it is the opposition offered to the flow of the current IE.

rb1c: It is the opposition of contrary biased aggregator to establish junction. The flow of current in this opposition represents the rearward impregnation current Ico due to flux of minority charge bearers.

rbb1: It is the opposition of the base bed for the flow of the current IB. This is called base spreading opposition because the division of emitter current is dispersed across the full part.

aIE: This is the current in the aggregator due to transistor action. When charge bearers reach the base bed from emitter, the possible gradient at the aggregator junction will ensue in the motion of the charge bearers in to the aggregator. This forms the current. aIE depends on the emitter current IE which inturn depends upon the electromotive force across base to emitter junction.

Therefore, the electromotive force VB1E controls aIE. VB1E is the independent variable. This depends on charge bearer concentration and temperature.

cb1e and cb1c: This is the isolated electrical capacity across the two P-N junction. The reactance of the capacitance is really high at mid-frequency. Hence about, capacitances are replaced by unfastened circuit ( non considered ) . But for high frequence, the reactance becomes finite. Hence considered in the analysis.

All the above footings are called Hybrid-p parametric quantities. These parametric quantities can be represented by the undermentioned circuit and it is called Hybrid-p tantamount circuit or Giacollette tantamount circuit.

gram vb1e is the constituent of aggregator current ( aie ) expressed as a map of independent variable vb1e. gram is the Transconductance of the transistor. This represents ability of the transistor in transforming the input electromotive force vb1e in to end product current.rce: rce is the internal opposition of the current beginning.

## To happen Hybrid-p parametric quantities

## Hybrid -p equivalent circuit

Let the end product terminuss be abruptly circuited.

Sing mid- frequence, reactance of all capacitances becomes infinite. Therefore, all capacitances can be replaced by unfastened circuit.

rb1c is the opposition of contrary biased aggregator junction whose value is really high. Therefore it can be approximated to open circuit.

rce is short circuited, becomes excess. Hence can be removed

## To happen gram

where I”IC and I”VB1E are the alterations in the currents and electromotive forces around quiescent status.

We know that

IC = aIE + ICO

Since ICO is really little and a is really close to integrity,

Distinguishing with regard to VB1E

If t = 27oC

( 3 )

replacing in ( 1 )

In general

In the above equation, IC represents the District of Columbia aggregator current or quiescent current. Its value can be found diagrammatically by pulling the District of Columbia burden line, turn uping the Q point on the burden line and so mensurating IC. OR if know the biasing agreement of the transistor, so the circuit can be solved utilizing biasing technique and so IC can be calculated.

## To happen rb1e

From the two port web theory, we know that

vse = ib hie + hre vce — — – ( 4 )

Intelligence Community = ibhfe + hoe vce — — — — — – ( 5 )

OR

From equation – ( 5 )

In the intercrossed p equation circuit, VCE is already 0. Therefore obtain the ratio

From intercrossed p equation circuit and compare it to equation ( 6 ) .

Comparing to equation ( 6 ) .

hfe =gm rb1e

## To happen rbb1

From equation ( 4 )

From the hybrid-p equivalent circuit, using KVL to input circuit.

Vs = ib ( rbb1 + rb1e )

## To happen rb1c

## Rewriting the intercrossed p equivalent circuit by pretermiting all electrical capacities ( unfastened circuit )

From equation ( 4 )

Taking ib = 0 in the hybrid-p equivalent circuit, since there is no electromotive force bead across rbb1, vs = vb1e.

Substituting in equation ( 8 ) .

From the intercrossed -p tantamount circuit. Applying electromotive force splitter regulation to circuit ( 2 ) .

rb1e is the opposition of the forward biased junction and rb1c is the opposition of the contrary biased junction.

Therefore rb1e can be neglected in the denominator.

## To happen rce

From equation- ( 5 )

Using KCL at the end product terminus

Intelligence Community = i1 + gram vb1e + i2

replacing in the above equation

Since rb1e & lt ; & lt ; rb1c, rb1e + rb1crb1c

## To happen Cb1C

Cb1C is the junction electrical capacity of contrary biased aggregator to establish junction. When a PN junction is rearward biased, the breadth of the depletion bed additions and electrical capacity lessenings. Therefore Cb1C is really low of the order of few pico Fs.

To happen Cb1e

This is the electrical capacity of forward biased PN junction. When a PN junction is frontward biased, breadth of the depletion bed lessenings and electrical capacity additions.

Cb1e + Cb1C =

Where foot is called the passage frequence.

foot = hfe fb

fb is called upper cutoff frequence.

fb =

## Numrical Problem:

A transistor amplifier is runing with a dc status 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 parametric quantities given that CC=3PF. Take fT=1MHz.

## Solution

## Mentions and notes

^A R.C. Jaeger and T.N. Blalock ( 2004 ) .A Microelectronic Circuit DesignA ( Second Edition ed. ) . New York: McGraw-Hill. pp.A Section 13.5, clairvoyance. Eqs. 13.19.A ISBNA 0-07-232099-0.

^A R.C. Jaeger and T.N. Blalock.A Eq. 5.45 pp. 242 and Eq. 13.25 p. 682.A ISBNA 0-07-232099-0.

^A R.C. Jaeger and T.N. Blalock.A Eq. 4.20 pp. 155 and Eq. 13.74 p. 702.A ISBNA 0-07-232099-0.

^A aA bA W. M. C. Sansen ( 2006 ) .A Analog Design Essentials. DordrechtI? : Springer. p.A A§0124, p. 13.A ISBNA 0-387-25746-2.

G.B GUPTA

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