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AnalogElectronics_Lecture4_PartB_low
and high frequency model of CE
BJT.*
Bijay_Kumar Sharma
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0�
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 -0500�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
Figure 11b. The reoriented T Model to represent CE BJT.
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It should be noticed that in T-Model under normal orientation has controlled current(αfie) coming outof 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
.
Figure 9
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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
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.COMPARISON BETWEEN HYBRID-pi MODEL OF CE BJT AND T MODEL OF CB BJT
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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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