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12008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Early Effect & BJT Biasing
Early Effect
DC BJT Behavior DC Biasing the BJT
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22008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Early Effect
Collector voltage has some effect on collector current itincreases slightly with increases in voltage. This phenomenon
is called the Early Effect and is modeled as a linear increase
in total current with increases in vCE:
iC=I
Se
vBE
VT 1vCEVA
VA
is called the Early voltage and ranges from about 50 V.
to 100 V.
NMOS transistorn=
1
VA
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32008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Early Effect - ContinuediC=I
Se
vBE
VT 1 vCEV
ATotal (bias+signal) quantities:
iC=I
CvBE=V
BE vCE=VCE
iC=IC=ISe
VBE
VT
1
VCE
VA
=IC
'
1
VCE
VA
Consider dc (bias) condition (signal = 0):
Call the idealized collector bias current I'C:
IC
'=I
Se
VBE
VT
iC=ICic vBE=VBEvbe vCE=VCEvce
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42008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
We shall define: ro=
VA
IC
'
IC=I
C
'V
CE
ro
IC=I
C
' 1VCEVA
=IC' VCEVA
IC'
Rearranging slightly:
Early Effect - Continued
The dc current due to both emitter and collector voltages is:
MOS transistor
ro=VA
IDIC
'=ISe
VBE
VT
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52008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Although the bias current including the Early effect is bettermodeled as:
IC=I
C
'V
CE
ro
We almost always will ignore the second term above anduse our usual expression for the bias current:
ICI
C
'=I
Se
VBE
VT
Early Effect - Continued
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62008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
The Early term adds ro
to the large signal model:
Early Effect - Continued
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72008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
For typical operating conditions:
VA50100V.
IC1mA.
ro=
VA
IC
100
103=100k
We usually can ignore ro
since, in practice, ro
is in parallel
with other resistors, which are much smaller than .For the time being, you will be told if you must include r
oin
your pencil-and-paper circuit designs.
Early Effect - Continued
100 k
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82008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Early Effect Scilab Simulation
VsubA=100;vCE=0.01:0.01:12; //array 0.01 to 12 in .01 V. stepsfor ICprime = 2:2:10 //mA.ICp = ICprime*sign(vCE); //ICp value for each vCE oneplot(vCE,ICp); //Current in mA.
ro=VsubA/ICprime;//Add bias Early effectIC=ICp+vCE/ro;plot(vCE,IC)
end//Plot load line for 1 KOhm Rc - 12V VccRc=1;
Gc=1/Rc;Vcc=12;vCLL = 0:0.01:12;ILoLin=Gc*Vcc-Gc*vCLL;plot(vCLL,ILoLin)
ILoLin
VCLL
ILoLin=
1
RC
VCCV
CLL
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92008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Simulation Results
ILoLin=1
RC
VCCVCLL
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102008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Active Mode Conditions
Base-emitter diode forward biased:
Base-collector diode back biased:
vBE0.7V
vBC=v
BEv
CE0.5V
vCE
0.5vBE
vCE
0.2V
vCE0.2V
Forward-Active(ideal cond.)
VBE > 0V
BC< 0
iE
= iC
+ iB
vCE
= vCB
+ vBE
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112008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Amplifier Biasing GoalsWe wish to set a stable value ofI
Cso that we can apply a
signal voltage or current signal to the emitter-base circuit andobtain an amplified (undistorted) version of the signal between
the collector and ground.
The transistor cannot saturate during operation, i.e.
vCE0.2V.
And it cannot cut offduring operation, i.e.iC0mA.
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122008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Amplifier DC Bias Problem
iC=I
Ci
c
vBE=V
BEv
be
vCE=V
CEv
ce
TimevI
= vBE
vO
= vCE
RC
VCC
iC
vO
VCE
VCC
0
Time
vi= v
be
VBE
Time
vo
= vce
VCEsat
= 0.2 V
vI
0.5 1.51.0
Q
cutoff saturation
fwdactive
slope = Av
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132008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Amplifier Action Base current source: A small change in base current
results in a large collector current( ).
This yields a large change in col-
lector voltage.Base voltage source:
A small change in base voltageresults in a large change in collec-tor current (i
C= I
Sexp(v
BE/V
T)).
This yields a large change in col-lector voltage.
ib
vCE
iC
iB
Source vBE
VCC
RC
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142008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Voltage Source Input With Collector Load
Solution of the simultaneousequations exists where the twocurves: the exponential (i
C
,vBE
) and
the straight line (iC,v
CE) intersect:
iC=
ISe
vBE
VT
iC=
VCCv
CE
RC
VCCv
CE
RC
=ISe
vBE
VT
Load Line
BJT
Circuit
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152008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Scilab Plot of NPN Characteristic//Calculate and plot npn BJT collector//characteristic using active mode modelVsubT=0.025;VTinv=1/VsubT;IsubS=1E-14;
vCE=0:0.01:10;for vBE=0.58:0.01:0.63iC=IsubS*exp(VTinv*vBE);plot(vCE,1000*iC); //Current in mA.
endVcc=10;
Rc=10000;vLoad=0:0.01:10;iLoad=(Vcc-vLoad)/Rc;plot(vLoad,1000*iLoad);
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162008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
NPN Transistor Load Line
Vce (V.)
Ic (mA.)
0 1 2 3 4 5 6 7 8 9 10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0Plot OutputvBE=0.63V.
vBE=0.62V.
vBE=0.60V.
Load Line
iC=
VCCv
CE
RC
VCC=10V
RC=10k
vBE=0.04V
vCE7V
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172008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Amplifier ActionNote that as v
BEvaries from about 0.59 V to O.63 V, v
CE
varies from about 8 V to 1V!A 0.04 V peak-to-peak swing ofv
BEresults in an 7 V peak-
to-peak swing in vCE - A ratio of 7/0.04, or about 175.The output magnitude is about 175 times the input magni-tude, for a gain of 175.
The input signal has two components: a DC one called thebias voltage, and an AC one called the (small) signal volt-
age. For proper operation, let:
VBIAS
=VBEMAXVBEMIN/2=0.61V
vSIGNAL
=VBEMAXVBEMIN/2=0.02V
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182008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Candidate Bias Configurations
Base voltagesource
Base currentsource
Emitter currentsource
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192008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Drive Base With a Current Source
Assume: =100
IC=IB=1005106
IC=0.5mA.
For this collector current:
VCE=V
CCR
CIC
VCE=1010
40.510
3=5V
The transistor is almost right in thecenter of the desired operatingregion!
VCE
IC
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202008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Current Bias Beta DependenceUnfortunately, beta is very poorly controlled and may easilyvary from 50 to 200. And beta is also temperature dependent!
IC=505106=0.25mA.
For beta of 50:
The device with a VCE
= 7.5 V
is close to theIC
cutoff point.
For beta of 200:
IC=2001056=1.0mA.
The device is saturated, VCE
tries to be 0 V!
There are huge problems associated with trying to drive aBJT with a base current source! BIAS POINT IS UNSTABLE.
VCE=101040.25103=7.5V VCE=1010
4
1103=0V
VCE=V
CCR
CIC
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212008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Drive base with a voltage source
For anIC
of 0.5 mA:
VBE=V
Tln
IC
IS
Given: IS=1014
A
IC=0.510
3Aand:
VBE
=0.025ln
0.5
10
11
VBE=0.02524.635=0.6159V
OK. Apply 0.6159 volts to thebase and we have the desiredcollector current!
Again, the transistor is nearly atthe center of the desired operating
region!
IC=ISe
VBE
VT
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222008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Voltage Bias ISand VCEDependenceUnfortunately,I
Sis highly temperature-dependent, doubling
for a 5 degree C increase in temperature. If the base-emittervoltage is chosen to give 0.5 mA collector current at 20 degreesC (68 F), it will double at 25 C and halve at 15 C.
IC
is also highly sensitive to VBE
. Consider two values of
collector current,IC
and 10IC:
10IC
IC
=
ISe
VBE10
VT
ISe
VBE1
VT
VBE10
VVE1=V
Tln 10
VBE10VBE1=0.0252.3025=0.0576V.
Less than a 60 mV change in VBE voltage increases IC by anorder of magnitude (10X). BIAS POINT IS UNSTABLE.
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232008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Emitter Current SourceThis holds collector current close to its desired value since:
IC= I
E
Changes in IC
for in the range determined by the
extremes ofare negligible
5020050
51
200
201
There is considerable variation in base current, however, but
this is usually of no consequence.
IB=
IE
1I
E
51I
B
IE
201
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242008 Kenneth R. Laker (based on P. V. Lopresti 2006) update 11Sep08 KRL
Conclusion
Biasing a BJT poses large stability problems, sinceits characteristics are highly sensitive to temperature
and since its electrical properties (principally beta)vary widely from one device to another!
The next lecture will cover some techniques for
stabilizing BJT operation.
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