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BJT Modeling (AC Analysis)

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					  Analogue Electronics I
          EAB 2014



           Jan 2009



Lecture 5 – BJT AC Analysis
 Small Signal Transistor Modeling

                                    1
  Topics To Cover
• Small-signal vs Large-signal techniques
• Reviewing the models used in small signal ac
  analysis
     re, hybrid equivalent and hybrid π model
•Refer to Chapter 5 Boylestad




                                                 2
    INTRODUCTION
• Transistor equivalent models that represents the
 operation of a transistor during ac mode.

• AC analysis techniques are determined by the
 magnitude of the input signal
      → Small Signal (low power, low I & V)
      → Large Signal (high power, high I & V)

• Small-signal transistor equivalent models:
      → re equivalent model.
      → hybrid equivalent model.
      → hybrid π model.

                                                     3
  BJT TRANSISTOR MODELING
What is a BJT modeling?

A combination of circuit elements that best
approximates the actual behavior of BJT under
specific operating conditions




                                                4
BJT TRANSISTOR MODELING
Small signal modeling steps:
• Obtain all the Q-Points through DC-Biasing (ICQ,
VCEQ, IBQ, ……etc).
• For a Common-Emitter configuration,
                             VCC


                        R1         RC
                                        C2

                   C1

         RS
                                                  VO
         VS   Vi        R2         RE        C3




                                                       5
     BJT TRANSISTOR MODELING
1. Set all DC supplies potential to zero (Ground) and assume
 all capacitors are short circuited (due to small reactance value).


                        R1        RC




           RS
                                                     VO
          VS       Vi   R2




                                                                  6
     BJT TRANSISTOR MODELING
 2. Rearrange the elements then choose the appropriate small
   signal equivalent circuit for the analysis.
                              Ii                         IO
                                   B   smallsignal   C
                                          cct.
      RS
                   R1 || R2
                                             E                RC   VO
     VS       Vi
                              Zi                         ZO



What are the important quantities to be determined?
  Input impedance, output impedance, voltage gain, current gain

                                                                        7
   TWO-PORT NETWORK REVISITED
                    Ii                                  Io

                               Two port
           Vi      Zi                                   Zo    VO
                                sy stem

Input Impedance, Zi :
•Add Rsense to determine Ii.
                                   Ii
         V − Vi                           Rsense
     Ii = s
          Rsense                                             Two port
                           Vs             Zi       Vi
                                                              sy stem
        Vi RsenseVi
    Zi = =
        I i Vs − Vi

                                                                        8
   TWO-PORT NETWORK REVISITED
   •The importance of the input impedance.
                 Ii      Rsource


            Vs           Zi        Vi
                                        Two port
                                         sy stem


                    Ω           Ω
Given: Rsource = 600Ω, Zi = 1.2kΩ, Vs = 10 mV
Using voltage divider to the input circuit,
                          Z iVs
            Vi =                    = 6.67mV
                      Z i + Rsource
              Ω
When Zi = 1.2kΩ, Vi = 6.67 mV → 66% Vs available at Vi.
When Zi = 600 Ω, Vi = 5 mV → 50% Vs available at Vi.
              Ω
When Zi = 8.2kΩ, Vi = 9.31mV → 93.2% Vs available at Vi.
→ The higher the i/p impedance, the better it is !!!

                                                           9
   TWO-PORT NETWORK REVISITED
       Output Impedance, Zo :
• The o/p impedance is determined at the o/p terminals
  looking back into the system with the applied signal set to
  zero.
• Vs is applied to the o/p terminal.
               Rso urce                      R sense    o
                                                        I

     Vs=0                   Two port    Vo         Zo       Vs
                             sy stem


       Vo RsenseVo
  Zo =    =                        Vs − Vo
       I o Vs − Vo            Io =
                                    Rsense

                                                                 10
     TWO-PORT NETWORK REVISITED
Voltage Gain (with the load connected) , Av

                               Vo
Defined by,               Av =
                               Vi


     Ii                        Io

               Two port              RL
Zi        Vi                    Vo
                system




                                              11
     TWO-PORT NETWORK REVISITED

Voltage Gain with no load , AVNL :
 Defined by,               Vo
                  AVNL   =
                           Vi   RL =∞Ω


        Rsource


Vs                       Two port
          Zi      Vi                     Vo
                          sy stem




                                              12
  TWO-PORT NETWORK REVISITED

Voltage Gain with source connected , AVS :
                              Rsource
            Z iVs
   Vi =
        Z i + Rsource   Vs                   Two port
                                Zi      Vi                       Vo
                                              sy stem
   Vi      Zi
      =
   Vs Z i + Rsource
                                            Zi         
        Vo Vi Vo                AVS =                   AVNL
  AVS =   =   ⋅                        Z i + Rsource   
        VS VS Vi


                                                                 13
    TWO-PORT NETWORK REVISITED
 Current Gain, Ai :
                    Io
Defined by,    Ai =
                    Ii
                            Ii                      Io


      Vi                              Two port
                          Zi     Vi                      RL Vo
 Ii =                                  sy stem
      Zi
        Vo
 Io = −                       Io    Vo / RL         Zi
        RL               Ai =    =−          = − AV
                              Ii    Vi / Z i        RL

                                                                 14
    Example 5.1

                               Ω
Given VS = 40mV, Rsource = 1.2kΩ, AVNL = 320, Vo = 7.68 V
Find : Vi, Ii, Zi, AVS




                                                            15
     re TRANSISTOR MODEL

• Derived directly from the operating conditions of the
 transistor.
• Can also be derived directly from the hybrid parameters.
• Employs a diode and controlled current source to describe
 the transistor behavior.
• re model for the CB, CE and CC BJT transistor will be
introduced




                                                          16
          re TRANSISTOR MODEL
          Common Base Configuration (Zi, Zo, AV, Ai)
                                                                               Ic
          IE                   IC                         Ie
      E                             C                 e                             c

                                                                           Ic = αIe

      B                             B                 b                             b



                                              Ii=Ie                 Io= − Ic
 Ii                    Io               e                                           c

Vi Z
            CB                                            re          Zo
                       Zo Vo
     i
           Amplifier                        Vi Zi                              Vo
                                                               Ic = αIe
                                        b                                           b



                                                                                        17
    re TRANSISTOR MODEL
                                 V
 Input Impedance, (Zi)       Z i = i = re  Since, Vi=Iere=Iire
                                  Ii
Output Impedance, (Zo)
•Set input source to zero (short circuit).
        Ii                           Ic         Io
                  Ie


                       re       Ic = αIe
             Vi                            Vo        Vs




          Vo                                    Since, Ii=Ie=0A
     Zo =    = ∞Ω                                          α
                                                       IC=αIE=0A
          Io
→Typically in MΩ range.
               Ω                                       Io=-IC=0A

                                                                   18
     re TRANSISTOR MODEL
                            Ii                           Ic         Io
                                      Ie

Voltage Gain, (AV)
                                           re
                            Vi   Zi                           Zo   Vo    RL
                                           Ic = αIe


      Vo
 AV =        Vo = − I o RL = −( − I C ) RL = −( −α I e ) RL = α I e RL
      Vi
             Vi = I e Z i = I e re
                  Vo β I e RL α RL RL
             AV =      =           =       ≈
                  Vi        I e re     re     re
                                 Io    I     αI
Current Gain, (Ai)        Ai =      = − c = − e = −α ≈ −1
                                 Ii    Ie     Ie

                                                                          19
    re TRANSISTOR MODEL
    Common Emitter Configuration (Zi, Zo, AV, Ai)

                      Ic                                              Ic
                           C                                               C
                                                      Ic = βIb
    Ib                                      Ib
B                                       B

                                                                 re


E                          E            E                                  E



            Ii                                        Io


           Vi                CE
                 Zi                              Zo    Vo
                           Amplif ier




                                                                               20
     re TRANSISTOR MODEL
                                                         Io=Ic
Input Impedance, (Zi)
                                      Ic = βIb
                              Ii=Ib
                                                                 Vo

                             Vi             Vbe   re




     Vi Vbe
 Zi = =            Vi = Vbe = I e re = ( β + 1) I b re
     Ii Ib

           ( β + 1) I b re
         =
       Zi =                  = ( β + 1) re ≈ β re
                 Ib

                                                                      21
         re TRANSISTOR MODEL
 Output Impedance, (Zo)
• Applied signal is set to zero, Ic=0A.
                               Io =Ic
              Ic = β Ib

     Ii =Ib
                                                            ro
                                        Vo      Vs

    Vi             V be   re


                                                        Z o = ro
•If ro is ignored, then                      Z o = ∞Ω

                                                                   22
      re TRANSISTOR MODEL
                                                              Io = Ic = β Ib
                                             Ic = β Ib
Voltage Gain, (AV)
                             Ii =Ib            Common
                                                Emitter    Zo = ∞          RL Vo

                            V i Z i = β re
                                               Amplifier
                                                 Vbe  re




      Vo
 Av =                Vo = − I o RL = − I C RL = − β I b RL
      Vi
                     Vi = I i Z i = I b β re

                          − β I b RL    RL
                     AV =            =−
                            I b β re    re
                                                                                   23
   re TRANSISTOR MODEL

                                   Io Ic β Ib
Current Gain, (Ai)            Ai =   =   =    =β
                                   Ii Ib   Ib
Finally after considering Zi, Zo, AV, and Ai,the small
signal equivalent cct. for CE can be summarized as
                Ii                          Ic      Io
                         Ib


                                 β re
                Vi                          ro     Vo
                                 Ic = βIb




                                                         24
    re TRANSISTOR MODEL
                      re equivalent circuit
                                                   Ic
                          Ie
                      e                                 c
                                re
Common Base                                     Ic = αIe

                      b                                 b


                 Ii                                     Ic    Io
                           Ib


Common Emitter                   β re
                 Vi                                     ro   Vo
                                     Ic = βIb



                                                                   25
    HYBRID TRANSISTOR MODEL
• re model fails to account for the output impedance and the
 feedback effect.
• The most popular method used.
• Normally provided at certain operating conditions such as
 at IC=1mA, VCE=10V, f=1kHZ.
• Using the same two-port system,
                   Ii                       Io
          1                                           2

              Vi                                 Vo

         1'                                        2'



                                                           26
                                                         --- (b)
    HYBRID TRANSISTOR MODEL
    Vi = h11 I i + h12Vo --- (a) I o = h21 I i + h22Vo

•The parameters relating the four variables are called
 h-parameters.
Setting Vo=0V (short circuit the o/p terminals)
solving for eqn (a).
                      Vi             ohms
                h11 =
                      Ii   V0 = 0V



h11 - short-cct. input-impedance parameter

                                                                   27
    HYBRID TRANSISTOR MODEL
Setting Ii=0A (opening the input leads)
solving for eqn (a).
                             Vi
                       h12 =                  unitless
                             Vo    Ii = 0 A


 h12 - open cct. reverse transfer voltage ratio parameter
Setting Vo=0V (short circuit the o/p terminals)
solving for eqn (b).          I
                         h21 = o         unitless
                            Ii    V0 = 0V


h21 - short-cct. Forward transfer current ratio parameter

                                                            28
    HYBRID TRANSISTOR MODEL

Setting Ii=0A (opening the input leads)
solving for eqn (b).
                      Io
              h22 =                   siemens
                      Vo   Ii = 0 A



h22 - open cct. output admittance parameter




                                                29
       HYBRID TRANSISTOR MODEL

By applying KVL and KCL to find the circuit that fits all the
equations obtained previously, we’ll get :
              h11
       Ii                                              Io




  Vi                h12Vo      h21Ii            h22          Vo




Hybrid input equiv. circuit   Hybrid output equiv. circuit

                                                              30
  HYBRID TRANSISTOR MODEL
                      hi
                Ii                                        Io




           Vi              hrVo     hf Ii        ho            Vo




h11 → hi
h12 → hr             Complete Hybrid equivalent circuit
h21 → hf
h22 → ho

                                                                31
    HYBRID TRANSISTOR MODEL
• Since hr is normally small, therefore we can assume hr = 0
 and hrVo=0 (short circuit). 1/ho=resistance is often large
enough and can be approximated by an open-circuit.

           Ii                                         Io




      Vi                hi      hfIi                       Vo




                                                                32
     HYBRID TRANSISTOR MODEL
•To distinguish parameters to be used for different configurations,
    Common Base                Common Emitter
       hi → hib                     hi → hie
       hr → hrb                     hr → hre
       hf → hfb                     hf → hfe
       ho → hob                     ho → hoe
       Vo → Vcb                     Vo → Vce

       Ii→ Ie                       Ii→ Ib


                                                             33
      HYBRID TRANSISTOR MODEL
            Common-Emitter h equivalent circuit:
                           Ic                                         Ic    Io
                                      Ii       Ib


Ie

                     Vce             Vi
                                                     hi e    hfeIb               Vo
       Vbe


               Ib

        Common-Base h equivalent circuit:
                                                                       Ic    Io
                                          Ii    Ie
 Ie                             Ic


                                      Vi
                                                      hi b    hfbIe               Vo
      Veb            Vcb

              Ib




                                                                                  34
   HYBRID TRANSISTOR MODEL
Comparison between re and h parameters:

Common-Emitter                  Common-Base

   hie = β re                       hib = re
   h fe = β ac                 h fb = −α ≅ −1



                                                35
  Example 5.2

Given IE=2.5mA, hfe=140, hoe=20us, and hob=0.5us,
determine:
a) The common-emitter hybrid equivalent circuit.
b) The common-base re model.




                                                    36
Question & Answer ?




                      37

				
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posted:4/15/2012
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Description: This article will cover how different of small-signal and large-signal techniques to Bipolar Junction Transistor (BJT). Thenm we look at hybrid equivalent and hybrid pi model.