Lecture 12-1
BJT Circuit Analysis
• Assuming that the transistor is in the active region, solve for the voltages and currents --- why this assumption?
• In general, the problem requires solution of a set of nonlinear equations:
Q1
RB100E3Ω
+2VVIN
RC1E3Ω
+ 5VVCC
IS=1e-16β 100=
Lecture 12-2
BJT Circuit Analysis
• SPICE solves the system of nonlinear equations to obtain the voltages and currents
• Is this circuit in the active region?
Q1Default
RB100E3Ω
+ 2VVIN
RC1E3Ω
+ 5VVCC
IB
12.206 µA +
-
VOUT
3.779 V+
-
VBE
779.365 mV
IC
1.221 mA
Lecture 12-3
BE Diode Characteristic
• We can effectively use a simplified model for the diode if we know the approximate operating range of the BE diode characteristic
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
1
2
3
mA
IE
Q1Default
+ 0VVBE
0.000 pA
Lecture 12-4
BE Diode Characteristic
• Note that “VON” changes if we’re analyzing an order of magnitude less current
• So how do we know what the real “VON” is?
Q1Default
+ 0VVBE
0.000 pA
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.1
0.2
0.3
mA
IE
Lecture 12-5
Simplified BJT Circuit Analysis
• Assuming VBE is 0.78 volts, we can approximate this circuit solution by hand analysis
Q1
RB100E3Ω
+2VVIN
RC1E3Ω
+ 5VVCC
IS=1e-16β 100=
Lecture 12-6
Simplified BJT Circuit Analysis
• What happens as RC is decreased?
• Will it remain in the active region?
Q1
RB100E3Ω
+2VVIN
RC500Ω
+ 5VVCC
IS=1e-16β 100=
Lecture 12-7
Simplified BJT Circuit Analysis
• What happens as RC is increased?
• Will it remain in the active region?
Q1
RB100E3Ω
+2VVIN
RC5000Ω
+ 5VVCC
IS=1e-16β 100=
Lecture 12-8
Saturation
• When both the EBJ and CBJ are forward biased, the transistor is no longer in the active region, but it is in the saturation region of operation
• We can easily solve for the maximum iC that we can have before we reach saturation for this circuit
Q1RB
+VIN
RC
+ 5VVCC
Lecture 12-9
Saturation
• With both diodes forward biased, the collector-to-emitter voltage, vCE, saturates toward a constant value
_
VBC
+
_VBE
+
~0.4 volts
~0.7-0.9 volts
VBC
VBE
_
+
_
+ _
+
vCEsat 0.3volts≅
0 1 2 3 4 5
-1
0
1
2
mA
IC
VCE
Lecture 12-
Saturation
• In saturation, increasing iC shows little increase in iB. Why?
0.0 0.2 0.4 0.6 0.8 1.0
-1
0
1
2
mA
IC
VCE
Lecture 12-
Regions of Operation
• The complete i-v characteristic is:
0 1 2 3 4 5
-1
1
3
mA
VCE
IB=1µAIB=5µA
IB=10µA
IB=15µA
IB=20µA
IC
Lecture 12-
Regions of Operation
VCE
IB=1µAIB=5µA
IB=10µA
IB=15µA
IB=20µA
0.0 0.2 0.4 0.6 0.8 1.0
1
3
mA saturation active
cut-off
IC
Lecture 12-
Temperature Variations
• The collector current vs. the base-emitter voltage follows a diode characteristic, which like a diode, is temperature dependent
0.6 0.7 0.8
0
2
4
mA
VBE
T=32ºCT=27ºC
T=22ºC
Q1Default
+ 0VVBE
R41E3Ω
+ 15VVCC
• Does this value of RC significantly impact the values for iC in this example?
IC
Lecture 12-
Temperature Variations
• In saturation, the collector current no longer increases with increasing VBE. Why not?
VBE
T=32ºCT=27ºC
T=22ºC
Q1Default
+ 0VVBE
R4100E3Ω
+ 15VVCC
0.6 0.7 0.8
0.0
0.1
0.2
mA
IC
Lecture 12-
Base Width Variation
n-typep-typen-typeCE
BVBE VCB
x
• In the active region, iC does vary somewhat with VCB (hence RC in our previous examples) due to the variation it causes in the base width.
• Effective base width, W*, decreases with increasing VCB
• What do you expect would happen to iC as W* decreases?
W*
Lecture 12-
Early Voltage
• The IC vs. VCE curves in the active region have a finite slope to them due to this iC dependence on VCB
• Early showed that these slopes all converge to one negative voltage point
VCE
IB=1µA
IB=5µA
IB=10µA
IB=15µA
IB=20µA-20 -10 0 10
-1
1
3
mA VAF=20 in SPICE(VA in the book)
-VA
IC
Lecture 12-
Early Voltage
• The finite slope in the active region due to decreasing base width can be approximated by
ic Isevbe VT⁄
1vceVA-------+
=
• This means that the output resistance between the collector and emitter is not infinite --- very important for analog design
vce∂∂iC go 0≠=
0 1 2 3 4 5 6
-1
1
3
iC (mA)
at some fixed ib point
vce
Lecture 12-
Early Voltage
• The output conductance, or resistance, at a fixed ib point represents the slope of the line tangent to that point on the curve:
ic Isevbe VT⁄
1vceVA-------+
=
• Generally not considered for dc bias point calculations, but ro can have a significant impact on a transistor amplifier gain
Lecture 12-
Early Voltage
αie
ieIsα----e
vbe VT⁄=
E
B
C
ib
• The equivalent circuit models can be modified accordingly:
ro
VAiC-------=
βib
E
B
C
ibIsβ----e
vbe VT⁄=
ro
VAiC-------=
or
Lecture 12-
dc Bias Point Calculations
• ro is generally not considered for hand calculations of dc bias point -- why?
• For hand calculations: use VBE=0.7 and assume that the transistor is in the active region; Later verify that your assumptions were correct.
4V
10V
3.3kΩ
RC
What’s the maximum value that RC can be without reaching saturation? Assume β =100.
Lecture 12-
dc Bias Point Calculationsdc Bias Point Calculations
4V
10V
3.3kΩ
RC
Lecture 12-
• What value of RC saturates the transistor?
10V
2kΩ
RC
β 100=
-10V
Lecture 12-
dc Bias Point Calculations
• What value of VCC saturates the transistor for this same circuit?
10V
2kΩ
1kΩ
β 100=
VCC