Download ECE137A Notes Set 1: Bipolar Transistors Characteristics

ECE137A Notes Set 1:
Bipolar Transistors Characteristics
Mark Rodwell
University of California, Santa Barbara
[email protected]
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 1
Why study bipolar transistors ?
MOSFETs are now much more common, being 99.999% dominant in digital
ICs, and probably 95% of analog ICs. Bipolar transistors are however still
used in faster high resolution analog - digital converters, and used widely in radio
frequency and optical communications ICs.
Quality mosfets are also very difficult to obtain in the discrete form needed for the
lab projects. Insofar as they are available, the data sheets give very limited design
information. It is therefore very difficult to design satisfactory lab projects using
MOSFETs. Quality discrete bjts are widely available, and their characters itics
are such that only limited information is needed for data sheets.
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 2
Terminal Characteristics: NPN bipolar transistor
for Vcb > 0
(collector base junction reverse biased)
I E = I es (eV
Ic
be
/ VT
− 1)
Ib = I E / β
Vcb
where
Ib
Vbe
Ie
VT = kT / q = 25.8 mV at 300 Kelvin (room temperature)
VT is called the " thermal voltage"
k = Boltzmann' s constant = 1.38(10 − 23 ) Joule/Kelvin
T = absolute temperature
q = electron charge = 1.6022(10 −19 ) Coulomb
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 3
Terminal Characteristics: PNP bipolar transistor
For the PNP bipolar transistor , current directions and
Ie
voltage polarities are simply reversed.
Veb
Ib
Vbc
Ic
Again, if the collector base junction is reverse biased
(Vbc > 0), then
I E = I es (eV
eb
/ VT
− 1)
Ib = I E / β
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 4
Voltage Polarities and Notation
You may have been taught the notation to the
right, where Vbe = Vb − Ve and Veb = Ve − Vb
This leads to Vbe = −Veb .
Vcb
Vbe
Vbc
Vbe
Although this is the standard textbook notation, it is often difficult to
keep polarities correct. Instead, I recommend defining the polarity of
voltages by drawing + and - signs on the circuit diagram associated
with any variable defining a voltage. Further, whenever possible,
DC voltage and current variables are defined so their values are
POSITIVE when the transistor is operated normally.
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 5
Polarities of voltages: NPN and PNP
A diode is forward biased if
Idiode
N
the P - side is more positive
than the N - side.
P
Vdiode
Ic
Vcb
A forward - baised diode
Ie
Ib
Ic
N
Vbe
conducts significantly.
P
N
Ie
Vcb
Vbe
Ib
Conventional (Ben Franklin)
Ie
Ie
Veb
current flows from P to N in
a forward - biased diode.
Ic
P
Ib
Vbc
N
P
Ic
Vbc
Veb
Ib
Electrons, being negative,
move from N to P
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 6
Polarities of voltages: NPN and PNP
Idiode
N
In a normally - operating BJT
the base - emitter junction
is forward - biased,
P
Vdiode
Ic
Vcb
Ie
Ib
Ic
N
and the base - collector junction
Vbe
P
N
Ie
is reverse - biased.
Vcb
Vbe
Ib
Ie
By this rule, we can determine
the correct voltage polarities
and current directions.
Ie
Veb
Ic
P
Ib
Vbc
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
N
P
Ic
Vbc
Veb
Ib
page 7
Common-emitter current gain β or HFE
The collector voltage VC is made sufficiently positive,
forcing Vcb > 0 (reverse - biased collector - base junction).
+Vc
Ib
Vcb
Ic
Common - emitter current gain
IC
= β = H FE
IB
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 8
Common-base current gain α
The collector voltage VC is made positive,
forcing Vcb > 0 (reverse - biased collector - base junction).
+Vc
Ic
Vcb
Common - base current gain
I
IC
IC / I B
=
α≡ C =
I E IC + I B (IC / I B ) + 1
⇒α =
β
β +1
or β =
Ib
IE
α
1−α
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 9
Typical values of DC current gain
This can vary tremendously.
General - purpose BJTs used in Analog - digital converters
and similar circuits : β ≅ 300 − 500 → α ≅ 0.997 - 0.998
Jellybean 2N3904 - 2N3906 BJTs used in lab projects :
β ≅ 50 − 300 → α ≅ 0.95 − 0.997
Specialized (power, microwave, ...) transistors
β ≅ 20 − 200 → α ≅ 0.95 − 0.998
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 10
Common-base DC characteristics
+Vcb
A fixed value of emitter current I E is applied, and VCB
is varied. The collector current I C and the base - emitter
A
Ic
voltage VBE are measured.
Vbe
The emitter current is then changed to a new value,
VCB again varied and I C and VBE again measured
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
IE
page 11
Common-base DC characteristics
base-collector
breakdown voltage
Vbr,cbo
Ic
+Vcb
Ic=10 mA
A
Ie=10 mA
Ic
Ic=5 mA
Ie=5 mA
Vbe
Vcb
IE
~0.5 Volts
Ic
very slight
variation of Vbe
with Vcb
exponential
I-V curve
Vbe
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 12
Base-emitter voltage
I 

I
Vbe = VT ln E + 1 ≅ VT ln E  ⇐ actual relationship
 I ES 

 I ES
Vbe = Vbe ,on ⇐ rough approximation
+Vcb
A
Ic
Vbe ,on is typically in the range of 0.6 - 0.7 volts
Vbe
for 60' s - vintage BJTs used in the lab,
0.8 - 0.9 volts for 2000 - vintage devices.
IE
0.02
10
-4
10
-6
10
-8
10
-10
10
-12
emitter current, amps
current, amps
0.01
0.015
0.01
0.005
0
0
0.1
0.2
0.3
0.4
0.5
Vbe, volts
0.6
0.7
0.8
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
-0.005
-0.2
0
0.2
0.4
Vbe, volts
0.6
0.8
page 13
Common-base curves measured on a microwave BJT
breakdown
+Vcb
60
A
Ic, mA
Ie= 55 mA
Ie= 45 mA
40
Ic
Ie= 35 mA
20
Vbe
0
IE
-20
-1
0
1
2
3
4
V , Volts
cb
20
Ic, mA
15
10
5
0
-5
0
0.2
0.4
0.6
Vbe, Volts
0.8
1
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 14
PNP Transistor: common-base DC characteristics
Ic
~0.5 Volts
Ic
Vcb
Veb
Ic=10 mA
Ie=10 mA
Ic=5 mA
Ie=5 mA
IE
A
Vbc
base-collector
breakdown voltage
Vbr,cbo
Plots of PNP characteri stics are standard in texts.
In practice, we use them infrequently.
The most important point is to remember the correct
polarities of voltages and the correct directions of currents.
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 15
Common-Emitter DC characteristics
In the linear region, I c ≅ β ⋅ I b
+Vce
There is also some variation of I c with collector voltage.
Ic
This is called the Early effect.
The slope of the curve dI C / dVCE ~
IC
VCE + V A
Ib
V A , the Early voltage, is typically 50 - 100 V
Ic
saturation region
Vcb<0
increasing
Ib
-Va
Vce,sat
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
linear region
Vcb>0
Vce
page 16
Common-emitter curves measured on a microwave BJT
20
0.7
0.6
0.5
Ic, mA
Ic, mA
15
10
0.4
0.3
0.2
0.1
5
0
-0.1
0
0
0
0.5
1
1.5
2
2.5
VCE, V
1
2
3
4
5
VCE, V
6
7
8
Above curves are for 150,300,450,600,750 uA base current
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 17
Modes of operation: Linear Active
The BJT has 2 PN junctions. Each can be forward or
reverse - biased. The 4 combinations give us 4 modes of
Ic
operation
N
Vcb
Linear Active Mode :
Normal mode of operation for linear amplification
BE junction forward biased
Ib
P
Vbe
N
BC junction reverse biased
Ie
Ic
Ic
saturation region
Vcb<0
Vcb
increasing
Ib
Ib
Vbe
-Va
Vce,sat
linear region
Vcb>0
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
Ie
Vce
page 18
Modes of operation: Saturation
Saturated
BE junction forward biased
BC junction forward biased
Sometimes used deliberate ly when we want
a low - voltage switch.
Saturation is one limit on the maximum voltage
swing of the transistor used as an amplifier
Ic
Vcb
saturation region
Vcb<0
increasing
Ib
Vbe
-Va
Vce,sat
linear region
Vcb>0
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
Vce
page 19
Modes of operation: Cutoff
Cut off
BE junction reverse biased, or not sufficiently
forward biased to turn junction on.
BC junction reverse biased
If the base - emitter voltage is too small (barely forward
biased) then the emitter current will be near zero.
The transistor is off.
Cutoff is a second limit on the maximum voltage
swing of the transistor used as an amplifier.
There is also a reverse active mode, in which the BE
junction is reverse biased and the BC junction is forward
biased. The transistor then operates similarly to the forward
active mode, but with very low current gain.
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 20
DC model for bias analysis
Use either
Vbe = Vbe ( on ) (quick)
Vbe = VT ln( I E / I ES ) (more accurate)
Ib
B
C
β(Ib)
the 2nd relationship is necessary for
current mirrors and for bias currents
in push - pull and similar stages.
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
E
page 21
AC small-signal model
gmVbe
Ib
First find g m :
g m vbe = βI b
B
∂I
gm ≡ c
∂Vbe
Rbe
or β(Ib)
C
Rce
Vbe
or Rπ
or R0
Vce constant
but I c = αI ES ( eV
be
/ VT
− 1) ≅ αI ES eV
be
/ VT
E
hence
∂I c
∂Vbe
Vce constant
IC
=
VT
g m = I C / VT = α / re ≅ 1 / re
Note we have defined re the " small signal emitter resistance "
re = VT / I E = 26mV / I E at room temperature.
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 22
AC small-signal model
Now find Rπ or Rbe :
∂I
( Rbe ) −1 ≡ b
∂Vbe
gmVbe
Ib
or β(Ib)
B
Vce constant
But I b = I C /β and I c = g mVbe so I b = g mVbe / β
Rbe
C
Rce
Vbe
or Rπ
or R0
E
Now find R0 or Rce :
( Rce ) −1 ≡
∂I c
∂Vce
Vbe constant
Best to find from a curve - tracer or from a data sheet
Estimate from :
∂I c
∂Vce
Vbe constant
→ Rce =
I c ,bias
=
VCE ,bias + V A
VCE ,bias + V A
I c ,bias
class notes, ECE137A, rodwell, University of California, Santa Barbara, copyrighted
page 23