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AnalogElectronics_Lecture4_PartB_low

and high frequency model of CE

BJT.∗

Bijay_Kumar Sharma

This work is produced by The Connexions Project and licensed under the

Creative Commons Attribution License †

Abstract

Part B of Lecture 4 derives the Hybrid-pi model of CE BJT from T-model of CB BJT at low and

high frequencies.

AnalogElectronics_Lecture4_PartB_low and high frequency model of CE BJT.INCREMENTAL MODEL OF CE BJT FROM T MODEL OF CB BJT

∗Version 1.1: Aug 4, 2009 12:34 pm GMT-5†http://creativecommons.org/licenses/by/3.0/

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Figure 1

Figure 11a. Low Frequency Incremental T Model of CB BJT.Let us re-orient this as CE con�guration.

Figure 2

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Figure 11b. The reoriented T Model to represent CE BJT.It should be noticed that in T-Model under normal orientation has controlled current(αfie) coming out

of collector node since base current is coming out of base node. But in reoriented T Model controlledcurrent(αfie) coming into collector node since base current is coming into base node.

Input Mesh Equation:

Figure 3

Figure 4

Figure 5

Where gm = trans conductance = IC/VT whereas re = VT/ IE and IC= αFIE

Figure 6

The output current is =

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Figure 7

Here

Figure 8

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Figure 9

Figure 12. Bode Plot of beta and alpha and location of ωβ and ωα.Beta cuto� frequency = ωβ and alpha cuto� frequency = ωα .Cut-o� frequency = -3dB frequency= this is the frequency where parameter falls to 0.707 of its �at band value or midband value= corner frequency= half power frequency

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Figure 10

Figure 13. Low Frequency Hybrid-π Model of CE BJT.

Figure 11

This is due to EARLY EFFECT or due to Base Width Modulation. A parameter Early Voltage VA isused for determining the output impedance of the hybrid �π Model. This output impedance is 1/hoe . Thede�nition of Early Voltage VA is given in Figure 14.

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Figure 12

Figure 13

Figure 14. The de�nition of Early Voltage for a CE BJT.

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COMPARISON BETWEEN HYBRID-pi MODEL OF CE BJT AND T MODEL OF CB BJT

Figure 14

Figure 15

T-model of CB BJT Hybrid-pi Model of CE BJT

Unilateral model Non Unilateral model

hrb=

Table 1

In CB BJT,if we consider base spreading resistance to be zero then

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Figure 16

Figure 17

For CE BJT if we consider rµ to be in�nity then:

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Figure 18

Figure 19

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Figure 20

Incremental model at high frequency

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Figure 21

Figure 16. High frequency T-Model of CB BJT.

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Figure 22

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Figure 23

Figure 24

Here τ t is the transit time taken by the minority carriers to cross the base width. The mechanism of

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transit is both di�usion and drift.Now let us consider CE BJT at high frequency:Here βf (short circuit current gain in CE BJT) is arrived at in exactly the same manner as αf was arrived

at in CB BJT.

Figure 25

Figure 17. High Frequency Hybrid-π Model of CE BJT.

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Figure 26

Figure 27

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