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
F. Najmabadi, ECE65, Winter 2012
operation which is not covered in this course
A BJT consists of three regions
NPN transistor
Simplified physical structure
An implementation on an IC
 Device construction is NOT symmetric
 Device is constructed such that
BJT does NOT act as two
diodes back to back (when
voltages are applied to all
three terminals).
F. Najmabadi, ECE65, Winter 2012
o “Thin” base region (between E & C)
o Heavily doped emitter
o Large area collector
BJT iv characteristics includes four parameters
NPN transistor
 Six circuit variables: (3 i and 3 v)
 Two can be written in terms of the
other four:
KCL : iE = iC + iB
KVL : vBC = vBE − vCE
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
iB = f (vBE )
iC = g (iB , vCE )
F. Najmabadi, ECE65, Winter 2012
BJT operation in the “active” mode
BE junction is forward biased
(vBE = VD0)
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 e vBE / VT
 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!)
iC = I S e vBE / VT
Active mode:
iB =
iC
β
=
IS
β
iC = I S e vBE / VT
vCE ≥ VD 0
F. Najmabadi, ECE65, Winter 2012
e
v BE / VT
 In this picture, ic is independent of vBC
(and vCE ) as long as
vBC = vBE − vCE = VD 0 − vCE ≤ 0
vCE ≥ VD 0
 Base current is also proportional to
e vBE / VT and therefore, iC : iB = iC/β
BJT operation in saturation mode
BE junction is forward biased
(vBE = VD0)
Similar to the active mode, a large number of
electrons diffuse into the base.
 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.
“Deep” Saturation mode:
iB =
IS
e vBE / VT
β
iC < β iB
vCE ≈ Vsat
F. Najmabadi, ECE65, Winter 2012
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.
* 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
NPN transistor
Circuit symbol and
Convention for current directions
(Note: vCE = vC – vE)
Simplified physical structure
 BJT iv characteristics is the relationship
among (iB , iC , vBE , and vCE )
 It is typically derived as
iB = f (vBE )
iC = g (iB , vCE )
F. Najmabadi, ECE65, Winter 2012
BJT iv characteristics:
iB = f(vBE) & iC = g(iB , vCE)
Saturation:
BE is forward biased, BC is forward biased
1. Soft saturation: 0.3 ≤ vCE ≤ 0.7 V, iC ≈ β iB
2. Deep saturation: 0.1 ≤ vCE ≤ 0.3 V, iC < β iB
3. Near cut-off:
vCE ≤ 0.1 V, iC ≈ 0
iB
Cut-off :
BE is reverse biased
F. Najmabadi, ECE65, Winter 2012
iB = 0,
iC = 0
Active:
BE is forward biased
BC is reverse biased
iC = β iB
Early Effect modifies iv characteristics in
the active mode
 iC is NOT constant in the active region.
 Early Effect: Lines of iC vs vCE for
different iB (or vBE ) coincide at
vCE = − VA
 v
iC = I S e vBE / VT 1 + CE
VA

F. Najmabadi, ECE65, Winter 2012



NPN BJT iv equations
“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
iB = 0,
iB =
iC
β
=
iC = I S e
iB =
IS
β
iB = 0,
iC = 0
IS
β
v BE / VT
vBE < VD 0
e vBE / VT
 vCE
1 +
VA

e vBE / VT
vCE ≈ Vsat , iC < β iB
vBE = VD 0 , iB ≥ 0



iC = β iB , vCE ≥ VD 0
vBE = VD 0 , iB ≥ 0
vCE = Vsat , iC < β iB
For Si, VD 0 = 0.7 V, Vsat = 0.2 V
F. Najmabadi, ECE65, Winter 2012
iC = 0
PNP transistor is the analog to NPN BJT
PNP transistor
“Linear” model
Cut-off :
EB is reverse biased
Active:
EB is forward biased
CB is reverse biased
(Deep) Saturation:
Compared to a NPN:
1) Current directions are reversed
2) Voltage subscripts “switched”
F. Najmabadi, ECE65, Winter 2012
EB is forward biased
CB is reverse biased
iB = 0,
iC = 0
vEB < VD 0
vEB = VD 0 , iB ≥ 0
iC = β iB , vEC ≥ VD 0
vEB = VD 0 , iB ≥ 0
vEC = Vsat , iC < β iB
Notations
Resistors:
Use “subscript” of BJT
terminal: RC , RB , RE .
F. Najmabadi, ECE65, Winter 2012
DC voltages:
Use “Double subscript” of BJT
terminal: VCC , VBB , VEE .
Voltage sources are
identified by node
voltage!
Transistor operates like a “valve:”
iC & vCE are controlled by iB
Controlled part:
iC & vCE are set by
transistor state (&
outside circuit)
Controller part:
Circuit connected to BE sets iB
 Cut-off (iB = 0):
Valve Closed
 Active (iB > 0):
Valve partially open iC = β iB
 Saturation (iB > 0):
Valve open
F. Najmabadi, ECE65, Winter 2012
iC = 0
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.
b.
3.
BJT OFF: Set iC = 0, use CE-KVL to find vCE (Done!)
BJT ON: Compute iB
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
Example 1: Compute transistor parameters (Si BJT with β = 100).
BE - KVL : 4 = 40 × 103 iB + vBE
CE - KVL : 12 = 103 iC + vCE
Assume Cut - off : iB = 0 and vBE < VD 0 = 0.7 V
BE - KVL : 4 = 40 × 103 × 0 + vBE → vBE = 4 V
vBE = 4 V > VD 0 = 0.7 V → Assumption incorrect
BE ON : vBE = VD 0 = 0.7 V and iB ≥ 0
BE - KVL : 4 = 40 × 103 × iB + 0.7 → iB = 8.25 µ A > 0
Assume Active : iC = β iB and vCE ≥ VD 0 = 0.7 V
iC = β iB = 100 × 8.25 × 10 −6 = 8.25 mA
CE - KVL : 12 = 103 × 8.25 × 10 −3 + vCE → vCE = 3.75 V
vCE = 3.75 V > VD 0 = 0.7 V → Assumption correct
F. Najmabadi, ECE65, Winter 2012
BJT Transfer Function (1)
BE - KVL : vi = RB iB + vBE
CE - KVL : VCC = RC iC + vCE
Cut - off : iB = 0 and vBE < VD 0
BE - KVL : vi = RB × 0 + vBE → vBE = vi
iC = 0
CE - KVL : VCC = RC × 0 + vCE → vCE = VCC
For vi < VD 0 → BJT in Cutoff
iB = 0, iC = 0, vCE = VCC
BE ON : vBE = VD 0 and iB ≥ 0
BE - KVL : vi = RB × iB + VD 0 → iB =
F. Najmabadi, ECE65, Winter 2012
iB ≥ 0 → vi ≥ VD 0
vi − VD 0
RB
BJT Transfer Function (2)
BE ON : vBE = VD 0 and iB =
vi − VD 0
RB
CE - KVL : VCC = RC iC + vCE
Active :
iC = β ×
ic = β iB and vCE ≥ VD 0
vi − VD 0
RB
CE - KVL : VCC = RC iC + vCE → vCE = VCC - RC iC
vCE ≥ VD 0 → vi ≤ VD 0 +
VCC − VD 0
βRC / RB
For VD 0 ≤ vi ≤ VD 0 +
F. Najmabadi, ECE65, Winter 2012
VCC − VD 0
→ BJT in active
βRC / RB
BJT Transfer Function (3)
vi − VD 0
RB
BE ON : vBE = VD 0 and iB =
CE - KVL : VCC = RC iC + vCE
Saturaation :
vCE = Vsat and ic < β iB
CE - KVL : VCC = RC iC + Vsat → iC =
ic < β iB → vi > VIH = VD 0 +
For VD 0 +
VCC - Vsat
RC
VCC − Vsat
βRC / RB
VCC − VD 0
< vi → BJT in saturation
βRC / RB
F. Najmabadi, ECE65, Winter 2012
BJT Transfer Function (4)
vi < VD 0
VD 0 ≤ vi ≤ VD 0 +
VD 0 +
→ BJT in Cutoff
VCC − VD 0
βRC / RB
VCC − Vsat
< vi
βRC / RB
F. Najmabadi, ECE65, Winter 2012
→ BJT in active
→ BJT in deep saturation
BJT transfer function on the load line
Saturation : VIH < vi
iB increases but iC unchanged
Load Line (CE - KVL)
vCE = VCC − RC iC
Active : VD 0 ≤ vi ≤ VIH
iB & iC increase together
F. Najmabadi, ECE65, Winter 2012
Cut − off :
vi < VD 0
BJT as a switch
Load is placed in
collector circuit
 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
*Lab 4 circuit
Solved in Lecture notes (problems 12 & 13)
BJT as a Digital Gate
Resistor-Transistor logic (RTL)
RTL NOT gate (VL = Vsat , VH = VCC)
RTL NOR gate*
RTL NAND 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
*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