DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139
TRANSISTOR BIAS STABILTY AS A FUNCTION OF βF VARIATIONS
by Ron Roscoe
+15V
IC = 4 mA
RB
2N3904
IB
RE = 2200 Ω
IE = 4 mA
Figure 1: Single resistor transistor biasing circuit.
β F = 100;
Ron Roscoe
I E = ( β F + 1) I B ;
IC = β F I B ;
1
I E ≈ IC
09/16/96
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month
YYYY].
I B RB + 0.7V + IC RE = VCC
I B RB + 0.7V + β F I B RE = VCC
I B ( RB + β F RE ) = VCC − 0.7V
IB =
IC =
(VCC − 0.7V )
(1)
RB + β F RE
β F (VCC − 0.7V )
RB + β F RE
RB + β F RE =
(2)
β F (VCC − 0.7V )
IC
RB + 100 × 2200Ω =
100(15V − 0.7V )
4mA
1430
× 103 Ω
4
RB + 220 kΩ = 358 kΩ
RB = 138kΩ
RB + 220kΩ =
Variation of Collector Current with Beta
IC
βF
2.9 mA
50
4.0 mA
100
5.0 mA
200
5.4 mA
300
ΔIC=2.5 mA
Ron Roscoe
2
09/16/96
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month
YYYY].
+15V
+15V
IC = 4 mA
IC = 4 mA
R2
IB
2N3904
2N3904
RTH= RB
RB
RE =
2200Ω
R1
VTH= VB
IC = 4 mA
RE = 2200Ω
VB
[b]
[a]
[c]
Figure 2: Two-resistor biasing circuit and Thevenin Equivalent for analysis.
VB =
R1
× Vcc
R1 + R2
(3)
RB =
R1 R2
R1 + R2
(4)
VB − I B RB − 0.7V − IC RE = 0
VB = I B RB + 0.7V + β F I B RE
VB − 0.7V = I B RB + β F I B RE = I B ( RB + β F RE )
IB =
IC =
(VB − 0.7V )
(5)
RB + β F RE
β F (VB − 0.7V )
RB + β F RE
(6)
Equation (6) is an equation with two unknowns: VB and RB. Analyzing the
denominator of equation (6) we note that if RB is kept small compared to the
product βFRE then the βF’s in the numerator and denominator will cancel if we can
B
B
B
Ron Roscoe
3
09/16/96
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month
YYYY].
ignore RB. As a general rule of thumb, keeping RB no greater than ten times RE
will give good bias stability over a wide range of βF values. RB cannot be lowered
to zero since the internal impedance of the battery is zero, and thus any AC
source that is capacitor-coupled into the transistor stage will be shorted out. We
will continue the example using RB = 22kΩ. Now we can solve eqn. (6) for VB.
B
B
B
B
B
4mA × (22kΩ + 220kΩ) = 100(VB − 0.7V )
4mA × 242kΩ = 100VB − 70
968 + 70 = 100VB
VB = 10.4V
Given VB= 10.4 V and RB= 22kΩ, we can now solve equations (3) and (4) for R1
B
B
VB =
R1
× VCC
R1 + R2
⎛V ⎞
⎛ 15V ⎞
. R1
and R2. R1 + R2 = R1⎜ CC ⎟ = R1⎜
⎟ = 145
⎝ 10.4V ⎠
⎝ VB ⎠
. R1
R1 + R2 = 145
0.45 R1 = R2
R1 R2
= RB = 22kΩ
R1 + R2
R1 × 0.45 R1
= 22kΩ
R1 + 0.45 R1
0.45 R12
= 22kΩ
145
. R1
0.310 R1 = 22kΩ
R1 = 70.9kΩ
use 68kΩ
. kΩ use 33kΩ
R2 = 0.45 R1 = 0.45 × 70.9kΩ = 319
Check IC variation with change in βF using equation (6):
Ron Roscoe
4
09/16/96
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month
YYYY].
IC =
β F (VB − 0.7V )
RB + β F RE
IC =
(6)
β F (10.4 − 0.7V )
22kΩ + β F 2200Ω
βF
50
100
200
300
IC
3.7 mA
4.0 mA
4.2 mA
4.3 mA
ΔIC=0.6 mA
Looking at the partial circuit shown in Figure 2c; we can see that our goal is to
keep the product of the collector (emitter) current and the emitter resistor
constant. This voltage is 8.8 volts for IC = 4 mA. Note that the 0.7V base-emitter
voltage is essentially constant. If we can keep the voltage drop due to IB RB as
small as possible by keeping RB small (since we have no control over IB); then it
becomes obvious that the emitter resistor voltage drop is essentially set by the VB
battery voltage minus the base-emitter voltage.
B
B
B
B
B
Ron Roscoe
5
09/16/96
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month
YYYY].