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Bipolar Junction Transistor (BJT) 
Lecture notes: Sec. 3 
 
Sedra & Smith (6th Ed):  Sec. 6.1-6.4* 
Sedra & Smith (5th Ed):  Sec. 5.1-5.4* 
 
* Includes details of BJT device  operation which is not covered in this course 
F. Najmabadi, ECE65, Winter 2012 
A BJT consists of three regions 
F. Najmabadi, ECE65, Winter 2012 
Simplified physical structure 
NPN transistor 
An implementation on an IC 
 Device construction is NOT symmetric 
o “Thin” base region (between E & C) 
o Heavily doped emitter 
o Large area collector 
 
 Device is constructed such that 
BJT does NOT act as two 
diodes back to back (when 
voltages are applied to all 
three terminals). 
 Six circuit variables: (3 i and 3 v) 
 Two can be written in terms of the 
other four: 
BJT iv characteristics includes four parameters 
F. Najmabadi, ECE65, Winter 2012 
NPN transistor 
CEBEBC
BCE
vvv
iii
−=
+=
   :KVL
     :KCL
Circuit symbol and 
Convention for current directions 
(Note: vCE = vC – vE) 
 BJT iv characteristics is the relationship 
among (iB  , iC , vBE , and vCE ) 
 It is typically derived as  
 
 ),( 
)( 
CEBC
BEB
vi gi
vfi
=
=
Active mode: 
 
 
 
 
0
/
/
DCE
Vv
SC
VvSC
B
Vv
eIi
eIii
TBE
TBE
≥
=
==
ββ
BJT operation in the “active” mode 
F. Najmabadi, ECE65, Winter 2012 
 If the base is “thin” these electrons get 
near the depletion region of BC junction 
and are swept into the collector if vCB ≥ 0 
(vBC ≤ 0 : BC junction is reverse biased!) 
 
 
 In this picture, ic  is independent of vBC 
(and vCE ) as long as 
 
 
 
TBE Vv
SC eIi
/=
0
0 0
DCE
CEDCEBEBC
Vv
vVvvv
≥
≤−=−=
As Emitter is heavily doped, a large number of 
electrons diffuse into the base (only a small 
fraction combine with holes) 
 
The number of these electrons scales as  TBE Vve /
BE junction is forward biased 
(vBE = VD0) 
 Base current is also proportional to 
                   and therefore, iC : iB = iC/β   
 
 
TBE Vve /
BJT operation in saturation mode 
F. Najmabadi, ECE65, Winter 2012 
 For vBC ≥ 0  BC junction is forward biased  
and a diffusion current will set up, reducing iC . 
1. Soft saturation:  vCE ≥ 0.3 V (Si)* 
vBC ≤ 0.4 V (Si), diffusion current is small and 
iC  is very close to its active-mode level. 
2. Deep saturation region:  0.1 < vCE < 0.3 V (Si)    
or vCE ≈ 0.2 V = Vsat (Si),  iC  is smaller than 
its active-mode level (iC < β iB). 
o Called saturation as iC is set by outside 
circuit & does not respond to changes in iB. 
3. Near cut-off:   vCE ≤ 0.1 V (Si) 
Both iC  & iB are close to zero. 
Similar to the active mode, a large number of 
electrons diffuse into the base. 
BE junction is forward biased 
(vBE = VD0) 
“Deep” Saturation mode: 
 
 
 
 
satCE
BC
VvS
B
Vv
ii
eIi TBE
≈
<
=
 
/
β
β
* Sedra & Smith includes this in the active region, i.e., 
BJT is in active mode as long as vCE ≥ 0.3 V. 
BJT iv characteristics includes four parameters 
F. Najmabadi, ECE65, Winter 2012 
NPN transistor 
Circuit symbol and 
Convention for current directions 
(Note: vCE = vC – vE) 
 BJT iv characteristics is the relationship 
among (iB  , iC , vBE , and vCE ) 
 It is typically derived as  
 
 ),( 
)( 
CEBC
BEB
vi gi
vfi
=
=
Simplified physical structure 
BJT iv characteristics:  
iB = f(vBE) & iC = g(iB , vCE)  
F. Najmabadi, ECE65, Winter 2012 
iB 
Cut-off : 
BE is reverse biased 
 
 
 
0     ,0 == CB ii
Active: 
BE is forward biased 
BC is reverse biased 
 
 
BC ii  β=
Saturation: 
BE is forward biased, BC is forward biased 
1. Soft saturation: 
2. Deep saturation: 
3. Near cut-off: 
 
BCCE iiv     ,V 7.03.0 β≈≤≤
BCCE iiv     ,V 3.01.0 β<≤≤
0   ,V 1.0 ≈≤ CCE iv
Early Effect modifies iv characteristics in 
the active mode  
F. Najmabadi, ECE65, Winter 2012 
 iC  is NOT constant in the active region. 
 Early Effect: Lines of iC  vs  vCE  for 
different  iB  (or vBE ) coincide at             
vCE  =  − VA  
 
 
 






+=
A
CEVv
SC V
veIi TBE 1/
NPN BJT iv equations  
F. Najmabadi, ECE65, Winter 2012 
      “Linear” model 
Cut-off : 
BE is reverse biased 
 
 
 
Active: 
BE is forward biased 
BC is reverse biased 
 
 
 
(Deep) Saturation: 
BE is forward biased 
BC is reverse biased 
 
0     ,0 == CB ii
0  
0     ,0
DBE
CB
Vv
ii
<
==






+=
==
A
CEVv
SC
VvSC
B
V
veIi
eIii
TBE
TBE
1/
/
ββ
0
0
      , 
0    ,  
DCEBC
BDBE
Vvii
iVv
≥=
≥=
β
BCsatCE
VvS
B
iiVv
eIi TBE
     ,
/
β
β
<≈
=
BCsatCE
BDBE
iiVv
iVv
     ,  
0    ,  0
β<=
≥=
V  2.0   ,V  7.0  Si,For 0 == satD VV
PNP transistor is the analog to NPN BJT 
F. Najmabadi, ECE65, Winter 2012 
PNP transistor 
Compared to a NPN: 
1) Current directions are reversed 
2) Voltage subscripts “switched” 
 
 
 
   “Linear” model 
Cut-off : 
EB is reverse biased 
 
 
Active: 
EB is forward biased 
CB is reverse biased 
 
 
 
(Deep) Saturation: 
EB is forward biased 
CB is reverse biased 
 
0  
0     ,0
DEB
CB
Vv
ii
<
==
0
0
      , 
0    ,  
DECBC
BDEB
Vvii
iVv
≥=
≥=
β
BCsatEC
BDEB
iiVv
iVv
     ,  
0    ,  0
β<=
≥=
Notations 
F. Najmabadi, ECE65, Winter 2012 
DC voltages:   
Use “Double subscript” of BJT 
terminal:   VCC , VBB , VEE .   Resistors:   
Use “subscript” of BJT 
terminal:   RC , RB , RE .   
Voltage sources are 
identified by node 
voltage! 
Transistor operates like a “valve:” 
iC & vCE are controlled by iB 
F. Najmabadi, ECE65, Winter 2012 
Controller part: 
Circuit connected to BE sets iB 
Controlled part: 
iC & vCE are set by 
transistor state (& 
outside circuit)  
 Cut-off  (iB = 0):           Valve Closed iC = 0 
 Active  (iB > 0):            Valve partially open iC = β iB 
 Saturation  (iB > 0):      Valve open iC < β iB 
iC limited by circuit connected 
to CE terminals, increasing iB 
does not increase iC 
 
Recipe for solving BJT circuits 
(State of BJT is unknown before solving the circuit) 
1. Write down BE-KVL and CE-KVL: 
2. Assume BJT is OFF, Use BE-KVL to check: 
a. BJT OFF:  Set iC = 0, use CE-KVL to find vCE  (Done!) 
b. BJT ON:  Compute iB 
3. Assume BJT in active.  Set iC = β iB . Use CE-KVL to find vCE .       
If vCE  ≥ VD0  , Assumption Correct, otherwise in saturation: 
4. BJT in Saturation. Set vCE = Vsat . Use CE-KVL to find iC . 
(Double-check iC < β iB ) 
NOTE:   
o For circuits with RE , both BE-KVL & CE-KVL have to be solved 
simultaneously.   
F. Najmabadi, ECE65, Winter 2012 
F. Najmabadi, ECE65, Winter 2012 
Example 1:  Compute transistor parameters (Si BJT with β = 100).  
CEC
BEB
vi
vi
+=
+×=
 10  12    :KVL-CE
 10 40  4    :KVL-BE
3
3
incorrect Assumption  V 7.0V 4
V 4    0 10 40  4    :KVL-BE
V 7.0  and   0   :off-Cut Assume
0
3
0
→=>=
=→+××=
=<=
DBE
BEBE
DBEB
Vv
vv
Vvi
0A   25.8    7.0 10 40  4    :KVL-BE
 0  and  V 7.0  :ON BE
3
0
>=→+××=
≥==
µBB
BDBE
ii
iVv
correct Assumption  V 7.0V 75.3
V 75.3    1025.8 10  12   :KVL-CE
mA  25.81025.8100 
V 7.0  and       :Active Assume
0
33
6
0
→=>=
=→+××=
=××==
=≥=
−
−
DCE
CECE
BC
DCEBC
Vv
vv
ii
Vvii
β
β
BJT Transfer Function (1) 
F. Najmabadi, ECE65, Winter 2012 
CECCCC
BEBBi
viRV
viRv
+=
+=
        :KVL-CE
      :KVL-BE
     0      :KVL-CE
0
     0       :KVL-BE
  and   0    :off-Cut 0
CCCECECCC
C
iBEBEBi
DBEB
VvvRV
i
vvvRv
Vvi
=→+×=
=
=→+×=
<=
   ,0   ,0
 Cutoffin  BJT    For  0
CCCECB
Di
Vvii
Vv
===
→<
      0
           :KVL-BE
 0  and    :ON BE
0
0
0
0
DiB
B
Di
BDBBi
BDBE
Vvi
R
VviViRv
iVv
≥→≥
−
=→+×=
≥=
BJT Transfer Function (2) 
F. Najmabadi, ECE65, Winter 2012 
CECCCC
B
Di
BDBE
viRV
R
VviVv
+=
−
==
        :KVL-CE
    and    :ON BE 00
BC
DCC
DiDCE
CCCCCECECCCC
B
Di
C
DCEBc
RR
VVVvVv
iR-VvviRV
R
Vvi
Vvii
/
    
             :KVL-CE
  and         :Active
0
00
0
0
β
β
β
−
+≤→≥
=→+=
−
×=
≥=
 activein  BJT    
/
For  000 →
−
+≤≤
BC
DCC
DiD RR
VVVvV
β
BJT Transfer Function (3) 
F. Najmabadi, ECE65, Winter 2012 
CECCCC
B
Di
BDBE
viRV
R
VviVv
+=
−
==
        :KVL-CE
    and    :ON BE 00
BC
satCC
DIHiBc
C
satCC
CsatCCCC
BcsatCE
RR
VVVVvii
R
V-ViViRV
iiVv
/
     
            :KVL-CE
   and        :nSaturaatio
0 β
β
β
−
+=>→<
=→+=
<=
 saturationin  BJT    
/
For  00 →<
−
+ i
BC
DCC
D vRR
VVV
β
BJT Transfer Function (4) 
F. Najmabadi, ECE65, Winter 2012 
 saturation deepin  BJT              
/
 
activein  BJT     
/
 
 Cutoffin  BJT                                  
0
0
00
0
→<
−
+
→
−
+≤≤
→<
i
BC
satCC
D
BC
DCC
DiD
Di
v
RR
VVV
RR
VVVvV
Vv
β
β
BJT transfer function on the load line 
F. Najmabadi, ECE65, Winter 2012 
CCCCCE iRVv         
)KVL-(CE Line Load
−=
 togetherincrease  & 
   :Active 0
CB
IHiD
ii
VvV ≤≤
 unchanged but  increases 
 :Saturation
CB
iIH
ii
vV <
   
:offCut
0Di Vv <
−
BJT as a switch 
 Use: Logic gate can turn loads ON (BJT in saturation) or OFF 
(BJT in cut-off) 
 ic is uniquely set by CE circuit (as vce = Vsat) 
 RB  is chosen such that BJT is in deep saturation with a wide 
margin (e.g., iB = 0.2 ic /β)  
F. Najmabadi, ECE65, Winter 2012 
Load is placed in 
collector circuit 
*Lab 4 circuit 
Solved in Lecture notes (problems 12 & 13) 
BJT as a Digital Gate 
 Other variants:  Diode-transistor logic (DTL) and transistor-transistor logic (TTL) 
 BJT logic gates are not used anymore except for high-speed emitter-coupled 
logic circuits 
o Low speed (switching to saturation is quite slow). 
o Large space and power requirements on ICs 
 F. Najmabadi, ECE65, Winter 2012 
RTL NOT gate (VL = Vsat , VH = VCC) 
Resistor-Transistor logic (RTL) 
RTL NOR gate* RTL NAND gate* 
*Solved in Lecture notes (problems 14 & 15) 
BJT β  varies substantially 
 Our BJT model includes three parameters: VD0 , Vsat and β  
o VD0 and Vsat depend on base semiconductor:  
o For Si, VD0 = 0.7 V, Vsat = 0.2 V  
 Transistor β depends on many factors: 
o Strongly depends on temperature (9% increase per oC) 
o Depends on iC (not constant as assumed in the model) 
o β  of similarly manufactured BJT can vary (manufacturer spec sheet 
typically gives a range as well as an average value for β ) 
o We will use the average β in calculations (PSpice also uses average β but 
includes temperature and iC dependence).  
o βmin is an important parameter.  For example, to ensure operation in 
deep saturation for all similar model BJTs, we need to set iC /iB < βmin 
F. Najmabadi, ECE65, Winter 2012