Chapter 5 Bipolar Junction Transistors by dyz36301

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									         Chapter 5
Bipolar Junction Transistors
                   Chapter Goals

• Explore the physical structure of bipolar transistor
• Study terminal characteristics of BJT.
• Explore differences between npn and pnp transistors.
• Develop the Transport Model for bipolar devices.
• Define four operation regions of the BJT.
• Explore model simplifications for the forward active
  region.
• Understand the origin and modeling of the Early effect.
• Present a PSPICE model for the bipolar transistor. Discuss
  bipolar current sources and the current mirror.
Physical Structure

      • The BJT consists of 3 alternating layers
        of n- and p-type semiconductor called
        emitter (E), base (B) and collector (C).
      • The majority of current enters collector,
        crosses the base region and exits through
        the emitter. A small current also enters
        the base terminal, crosses the base-
        emitter junction and exits through the
        emitter.
      • Carrier transport in the active base
        region directly beneath the heavily
        doped (n+) emitter dominates the i-v
        characteristics of the BJT.
 Transport Model for the npn Transistor
                                       • Base-emitter voltage vBE and
                                         base-collector voltage vBC
                                         determine the currents in the
                                         transistor and are said to be
                                         positive when they forward-bias
                                         their respective pn junctions.
                                       • The terminal currents are the
• The narrow width of the base           collector current(iC ), the base
  region causes a coupling between       current (iB) and the emitter
  the two back to back pn junctions.     current (iE).
• The emitter injects electrons into   • The primary difference between
  base region; almost all of them
                                         the BJT and the FET is that iB is
  travel across narrow base and are
  removed by collector.                  significant, while iG = 0.
  npn Transistor: Forward Characteristics
                                Base current is given by
                                     i         I  v   
                                                        
                                                       
                                                    
                                i  F  S exp BE  1
                                                       
                                 B              V  
                                                       
                                     F     F        T  
                                                       
                                                        

                                20   500 is forward current gain
                                     F
                                Emitter current is given by
                                             v  I   
                                i i i  S exp BE  1
                                                    
                                 E C B        V  
                                                         

                                          F      T   
Forward transport current is
                    
                                                   
             v   
                 
                  
                               0.95              F 1.0
             
i  i  I exp BE  1
                                         F        1
 C F     S   V  
                  
              T  
                                                  F
IS is saturation current        In this forward active operation region,
1018 A  I  10 9 A                              i          i
           S                                        C        C 
                                                   i     F    i     F
VT = kT/q =0.025 V at room temperature               B          E
   npn Transistor: Reverse Characteristics
                               0    20 is reverse current gain
                                    R

                               Base currents in forward and reverse modes
                               are different due to asymmetric doping levels
                               in the emitter and collector regions.

                               Emitter current is given by
                                       I   v      
Reverse transport current is    i   S exp BC  1
                                                  
              
              v   
                  
                  
                  
                                C        V
                                            
                                                 
                                               T   
              
i  i  I exp BC  1
                 
                                      R
 R    E   S   V  
                                           
                T  
                  
                     
                                 0    R  0.95
Base current is given by             R  1
     i I     v      
                                        R
i  R  S exp BC  1
                    
 B         V  
     R  R       T   
    npn Transistor: Complete Transport
      Model Equations for Any Bias
                                  
           v       v     I      v                
  i  I exp BE   exp BC   S  exp BC             1
                            
                                                         
   C   S    V 
            
             T 
                      V
                         T   R 
                                       V              
                                   T              
                                   
            
            v        v     I      v               
  i  I exp 
            
             BE   exp BC   S  exp BE
                
                    
                               
                                                        1
                                                           
   E   S    V 
            
              T 
                       V  
                          T          V             
                     
                                 F     T              
                         
        I  v       I 
                             v                
  i  S exp BE  1  S  exp BC             1
                     
                                                
   B       V    
                
             T  
                              V              
       F               
                       R     T               


The first term in both the emitter and collector current expressions gives
the current transported completely across the base region.
Symmetry exists between base-emitter and base-collector voltages in
establishing the dominant current in the bipolar transistor.
             pnp Transistor: Operation




• The voltages vEB and vCB are positive when they forward bias
  their respective pn junctions.
• Collector current and base current exit the transistor terminals
  and emitter current enters the device.
  pnp Transistor: Forward Characteristics

                                   Base current is given by:

                                       i I     v      
                                  i  F  S exp EB  1
                                                      
                                   B         V  
                                       F  F       T   




                                   Emitter current is given by:
Forward transport current is:                   
                                                       v
                                                          
                                                            
                                                      1     
                                i  i  i  I 1
                                                     exp EB  1
                                                             
                             E C B       S  
                                                        V  
                                                             
i  i  I exp
              v  
               EB  1
                                                
                                                
                                                  F      T  
                                                          
                                                          
                                                               
                
 C F     S   V  
                 
               T  
                     
  pnp Transistor: Reverse Characteristics

                                Base current is given by:

                                    i  I     v      
                                i  F  S exp CB  1
                                                    
                                 B         V  
                                     R  R       T   




                                Emitter current is given by:
Reverse transport current is:            
                                                 v
                                                   
                                                      
                                               1     
                                i   I 1
                                         
                                               exp CB  1
                                                      
                             C     S 
                                                  V  
                                                      
             
i  i  I exp
               v  
                CB  1
                                         
                                         
                                            R     
                                                    T  
                                                       
                 
 R    E   S   V  
                  
                T  
                      
 pnp Transistor: Complete Transport
   Model Equations for Any Bias
                                 
        v        v      I      v     
        
i  I exp EB   exp CB  
        
               
                
                            S  exp CB  1
                                              
 C   S   V 
           T 
                    V
                       T   R 
                                    V  
                  
                                      T    


                                 
        v        v      I      v     
        
i  I exp EB   exp CB  
        
               
                
                            S  exp EB  1
                                              
 E   S   V 
           T 
                    V
                       T   F 
                                    V  
                  
                                      T    



                       
    I    v       I 
                           v     
i  S exp EB  1  S  exp CB  1
                   
                                   
 B       V    
            
           T  
                            V  
     F             
                     R     T    
   Circuit Representation for Transport
                 Models




In the npn transistor (expressions analogous for the pnp transistors), total
current traversing the base is modeled by a current source given by:
                            v       v   
                                         
                             
           i  i  i  I exp BE   exp BC 
                                            
            T F R       S    V 
                                      V  
                             T        T 
Diode currents correspond directly to the 2 components of base current.
                
                I   v        I     v      
          i  S exp BE  1  S exp BC  1
                                         
           B      V  
                             
                                
                                   
                                        V  
                                                

              F      T       R      T   
      Operation Regions of the Bipolar
                 Transistor
Base-emitter junction                Base-collector junction
                            Reverse Bias                 Forward Bias
    Forward Bias        Forward active region          Saturation region
                        (Normal active region)        (Not same as FET
                          (Good Amplifier)             saturation region)
                                                        (Closed switch)
     Reverse Bias           Cutoff region           Reverse-active region
                           (Open switch)            (Inverse active region)
                                                        (Poor amplifier)
    i-v Characteristics Bipolar Transistor:
   Common-Emitter Output Characteristics



For iB=0, the transistor is cutoff. If iB >0, iC
also increases.

For vCE > vBE, the npn transistor is in the
forward active region, iC = F iB is independent
of vCE..
For vCE< vBE, the transistor is in saturation.

For vCE< 0, the roles of collector and emitter
are reversed.
i-v Characteristics of Bipolar Transistor:
Common-Emitter Transfer Characteristic

                  This characteristic defines the relation
                  between collector current and base-emitter
                  voltage of the transistor.
                  It is almost identical to the transfer
                  characteristic of a pn junction diode.
                  Setting vBC =0 in the collector-current
                  expression:
                                  
                                  v   
                                         
                                      
                                      
                                  
                         i  I exp BE  1
                                     
                          C   S   V  
                                      
                                   T  
                                         
          Junction Breakdown Voltages

• If reverse voltage across either of the two pn junctions in the transistor
  is too large, the corresponding diode will break down.
• The emitter is the most heavily doped region, and the collector is the
  most lightly doped region.
• Due to these doping differences, the base-emitter diode has a relatively
  low breakdown voltage (3 to 10 V). The collector-base diode is
  typically designed to break down at much larger voltages.
• Transistors must therefore be selected in accordance with the possible
  reverse voltages in circuit.
          Simplified Forward-Active Region
                       Model
     In the forward-active region, the base-emitter junction is forward-biased
     and the base-collector junction is reverse-biased. vBE > 0, vBC < 0
     If we assume that v        4kT                    4kT
                                      0.1V v             0.1V
                            BE       q             BC          q
     then the transport model terminal current equations simplify to:
               v       I            
                                        vBE 
                                                 
      i  I exp BE  S  I exp
                  
                  
                     
                                                 
       C S      V  
                                S      V     
                   T  R
                                       T 

           I    
                vBE 
                           I      I        
                                             vBE 
                                                     
      i  S exp       
                               S  S exp           
       E        V                      V                i  i
                 T                        T 
             F                 F      F                             C    FE
          I              I     I       I                   i  i
                vBE                             vBE              FB
      i  S exp       
                               S  S  S exp                      C
       B        V                            V
                                                          
                                                                 i  (  1)i
                 T                               T          E     F    B
            F                  F     R       F
     The BJT is often considered a current-controlled current source, although
   fundamental forward active behavior suggests a voltage-controlled current
     source.
    Simplified Circuit Model for Forward-
                Active Region




• Current in the base-emitter diode is amplified by the common-emitter
  current gain F and appears at the collector
• The base and collector currents are exponentially related to the base-emitter
  voltage.
• The base-emitter diode is often replaced by a constant voltage drop model
  (VBE = 0.7 V), since it is forward-biased in the forward-active region.
       Simplified Forward-Active Region
          Model (Analysis Example)
•   Problem: Find Q-point
•   Given data: F = 50, VBC =VB - VC= -9 V
•   Assumptions: Forward-active region of operation, VBE = 0.7 V
•   Analysis:
                                          V     8200I (V      ) 0
                                            BE         E      EE
                                                  8.3V
                                          I           1.01mA
                                             E 8200
                                                I      1.02mA
                                          I  E                19.8A
                                           B  1         51
                                                F
                                          I   I  0.990mA
                                           C    F B
                                          V     (V    )V     V
                                           CE         EE     CC     R
                                          V      9 9 8.3 9.7V
                                             CE
                                          Note: V  I R here.
                                                   R E

                                   
                    Biasing for BJT

• The goal of biasing is to establish a known Q-point, which
  in turn establishes the initial operating region of transistor.
• In BJT circuits, the Q-point is represented by (VCE, IC) for
  the npn transistor or (VEC, IC) for the pnp transistor.
• In general, during circuit analysis, we use a simplified
  mathematical relationships derived for the specified
  operation region of the transistor.
• The practical biasing circuits used with BJTs are:
   – The Four-Resistor Bias network
   – The Two-Resistor Bias network
Four-Resistor Bias Network for BJT
                                 R              RR
                    V    V       1        R   1 2
                      EQ    CC R  R        EQ R  R
                                1   2           1 2
                    V    R   I V     R I      F  75
                      EQ   EQ B     BE   E E
                    4 12,000I  0.716,000( 1)I
                              B               F    B
                           4V-0.7V
                    I               2.68A        I   I 201A
                       B
                          1.2310 6            C F B
                                   I ( 1)I 204A
                                    E     F   B 
          
                              V     V     R I R I
                                 CE   CC     C C    E E
                                            
                                           R 
                                      R  E I  4.32V
               CE Loop
                              V
BE Loop
                                  CC  C   C
                                              
                                            F 

                         
                               Q-point is (4.32 V, 201 A)
    Four-Resistor Bias Network for BJT
            (Check Analysis)
• All calculated currents > 0, VBC = VBE - VCE = 0.7 - 4.32 = - 3.62 V
• Hence, the base-collector junction is reverse-biased and the assumption
  of forward-active region operation is correct.
• The load-line for the circuit is:                      
                                              R 
                                              
                                V   V    R  F I 12 38,200I
                                              
                                 CE   CC    C   C
                                              
                                               
                                                                 C
                                               F 
                                              

                                  The two points needed to plot the load
                                line are (0, 12 V) and (314 A, 0). The
                                  resulting load line is plotted on the
                                  common-emitter output characteristics
                                  for IB= 2.7 A.
                                  The intersection of the corresponding
                                  characteristic with the load line
                                  determines the Q-point.
        Four-Resistor Bias Network for BJT:
                Design Objectives
     • From the BE loop analysis, we know that
               VV         V   V
       I    EQ    BE      EQ   BE                for REQ (F 1)RE
        B R   ( 1)R     ( 1)R
           EQ    F     E     F     E
     • This will imply that IB << I2 so that I1 = I2 to good approximation in
                                                   

       the base voltage divider. Then the base current doesn’t disturb the
       voltage divider action, and the Q-point will be approximately
       independent of base voltage divider current.
     • Also, VEQ is designed to be large enough that small variations in the
       assumed value of VBE won’t have a significant effect on IB.
     • Base voltage divider current is limited by choosing I  I / 5
                                                               2 C
        This ensures that power dissipation in base bias resistors is < 17 % of
       the total quiescent power consumed by the circuit, while I2 >> IB.
    Four-Resistor Bias Network for BJT:
            Design Guidelines
•   Choose I2 = IC/5. This means that (R1+R2) = 5VCC/IC .
•   Let ICRC =IERE = (VCC - VCE)/2. Then RC = (VCC - VCE)/2IC; RE =FRC
•   If REQ<<(F+1)RE, then IERE = VEQ - VBE.
•   Then (VCC - VCE)/2 = VEQ - VBE, or VEQ = (VCC - VCE + VBE)/2.
•   Since VEQ = VCCR1/(R1 +R2) and (R1+R2) = 5VCC/IC,
                                 
              VCC VCE  2VBE  5VCC  VCC VCE  2VBE 
         R1                  
                                       5              
                   2VCC        
                                  IC         2IC       
• Then R2 = 5VCC/IC - R1.
• Check that REQ<<(F+1)RE. If not, adjust bullets 1 and 2 above.
 Note: In the LabVIEW bias circuit design VI (NPNBias.vi), bullet 1
•
   is called the “Base Margin” and bullet 2 is called the “C-E V(oltage)
   Drops”.
Problem 5.87 4-R Bias Circuit Design
    Two-Resistor Bias Network for BJT:
                 Example
• Problem: Find the Q-point for the pnp transistor in the 2-resistor bias
            circuit shown below.
• Given data: F = 50, VCC = 9 V
• Assumptions: Forward-active region operation with VEB = 0.7 V
• Analysis:
                            9 V   18,000I 1000(I  I )
                                EB         B       C B
                            9 V   18,000I 1000(51)I
                                 EB          B          B
                                 9V 0.7V
                            I           120A
                               B 69,000
                            I  50I  6.01mA
                             C     B
                             V    91000(I  I ) 2.87V
                              EC           C B

                            Q-point is : (6.01 mA, 2.87 V)
PNP Transistor Switch Circuit Design
Emitter Current for PNP Switch Design
BJT PSPICE Model
     • Besides the capacitances which are
     associated with the physical structure,
     additional model components are: diode
     current iS, capacitance CJS, related to the
     large area pn junction that isolates the
     collector from the substrate and one
     transistor from the next.
     • RB is the resistance between external
     base contact and intrinsic base region.
     • Collector current must pass through RC
     on its way to the active region of the
     collector-base junction.
     • RE models any extrinsic emitter
     resistance in the device.
BJT PSPICE Model -- Typical Values

       Saturation Current = 3 e-17 A
       Forward current gain = 100
       Reverse current gain = 0.5
       Forward Early voltage = 75 V
       Base resistance = 250 
       Collector Resistance = 50 
       Emitter Resistance = 1 
       Forward transit time = 0.15 ns
       Reverse transit time = 15 ns
         Minority Carrier Transport in Base
                      Region
• With a narrow base region, minority carrier density decreases linearly
  across the base, and the Saturation Current (NPN) is:
                             n     qADn n 2
                     I  qADn bo        i                 where
                      S      W     N   W
                               B     AB B
    NAB = the doping concentration in the base
    ni2 = the intrinsic carrier concentration (1010/cm3)
    nbo = ni2 / NAB
    Dn = the diffusivity = (kT/q)n
                                                             p     qAD p n 2
•   Saturation current for the PNP transistor is: I S  qAD p bo         i
                                                             W     N    W
                                                               B     DB B
• Due to the higher mobility () of electrons compared to holes, the npn
  transistor conducts higher current than the pnp for equivalent doping
  and applied voltages.
                 Diffusion Capacitance

• For vBE and hence iC to change, charge stored in the base region must
  also change.
• Diffusion capacitance in parallel with the forward-biased base-emitter
  diode produces a good model for the change in charge with vBE.

         dQ               1 qAnboWB    v
                                       
                                              I
                                         BE   T 
     C                            exp    
      D dv               V     2        V         F
          BE Q  point    T              T  VT

• Since transport current normally represents collector current in the
  forward-active region,
                                 I
                           C  C
                            D V F
                               T
            Early Effect and Early Voltage
• As reverse-bias across the collector-base junction increases, the width of
  the collector-base depletion layer increases and the effective width of base
  decreases. This is called “base-width modulation”.
• In a practical BJT, the output characteristics have a positive slope in the
  forward-active region, so that collector current is not independent of vCE.
• “Early” effect: When the output characteristics are extrapolated back to
  where the iC curves intersect at common point, vCE = -VA (Early voltage),
  which lies between 15 V and 150 V.
• Simplified F.A.R. equations, which include the Early effect, are:
                                                  
              v                            I   v
                                                             
                                                               
                 
                                       i   S exp BE
                                                             
        1  CE 
               
                                       B        V
                                                  
                                                              
    F   FO    V 
                                          FO
                                                  
                                                  T
                                                  
                                                  
                                                               
                                                              
                                                               
               A 
                        
                          
                             v     v
                                   
                                   
                                    
                                           
                                           
                   i  I exp
                           BE 
                                   
                                    1  CE   I
                    C S 
                           V  V  F B
                                   
                                   
                        
                           T 
                                   
                                    
                                   
                                           
                                         A 
BJT Current Mirror
      • The collector terminal of a BJT in the
        forward-active region mimics the
        behavior of a current source.
      • Output current is independent of VCC as
        long as VCC ≥ 0.8 V. This puts the BJT
        in the forward-active region, since VBC ≤
        - 0.1 V.
      • Q1 and Q2 are assumed to be a
        “matched” pair with identical IS, FO, and
        VA,.
                 V   V
         I       BB   BE  I  I  I
           REF       R       C1 B1 B2
           BJT Current Mirror (continued)
              
              V
                       V
                       
                                     
                                         I
                                               
                                                  V     
                                                           
 I      I exp BE
                      1 CE1   2 S exp BE 
   REF    S    V
              
                      
                              V    
                                             
                                                   V   
               T
              
                      
                                 A       FO     T   

                                                      V
                          
                                                   1 CE 2
                  V     V         
                                                       V
     I   I exp BE  1 CE 2   I                  A
       C2   S      V  
                                  V    
                                       
                                           REF     V         2
              
                   T          A           1 BE 
                              V                     V      
                                                      A      FO
                       1 CE2
                I              V
        MR       O             A       is the "Mirror Ratio".
             I         V
               REF 1 BE  2
                          V       
                             A      FO
 With an infinite FO and VA (ideal device), the mirror ratio is unity. Finite

 current gain and Early voltage introduce a mismatch between the output
 and reference currents of the mirror.
          BJT Current Mirror: Example
•   Problem: Find output current for given current mirror
•   Given data: FO = 75, VA = 50 V
•   Assumptions: Forward-active operation region, VBE = 0.7 V
•   Analysis:
                  V    V
          I      BB    BE  12V 0.7V  202A
           REF        R         56k
                                     1 12
          I  MR  I      (202A)      75  223A
           O         REF          1 0.7  2
                                      75 50

    
VBE =
  6.7333e-01
IC2 =
  5.3317e-04
IC21 =
  5.3317e-04
BJT Current Mirror: Altering the Mirror Ratio
            A
     I I    E          where ISO is the saturation current of a BJT
      S   SO A
                        with one unit of emitter area: AE =1(A). The
                        actual dimensions of A are technology-
                        dependent.
  The Mirror Ratio of a BJT current mirror can be changed by simply
  changing the relative sizes of the emitters in the transistors. For the
  “ideal” case, the Mirror Ratio is determined only by the ratio of the
  two emitter areas.
                       V
                    1 CE 2
                         V                          A
      I  n.I              A                     n  E2
       O      REF   V         2                     A
                  1 BE                              E1
                     V      
                       A      FO
 BJT Current Mirror: Output Resistance
• A current source using BJTs doesn’t have an output current that is
  completely independent of the terminal voltage across it, due to the
  finite value of Early voltage. The current source seems to have a
  resistive component in series with it.

                    V      v              V    v
                 1  CE2 ce2            1  CE o
                         V                    V
       i i  I            A     I             A
        O C2 REF    V         2     REF V          2
                 1 BE                1 BE 
                     V                   V      
                       A      FO            A      FO

                                  1
                                                  1
                                                      
 
                     io
                                            I       V
             Ro    
                    
                                   
                                           C2        A
                     vo
                                 
                                             
                                              V V
                                                          I
                    
                         Q pt   
                                   
                                             
                                             A CE
                                                      
                                                      
                                                             O

• Ro is defined as the “small signal” output resistance of the current
      
  mirror.


								
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