ee101: bjt circuits (part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · ee101: bjt circuits...
TRANSCRIPT
![Page 1: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/1.jpg)
EE101: BJT circuits (Part 1)
M. B. [email protected]
www.ee.iitb.ac.in/~sequel
Department of Electrical EngineeringIndian Institute of Technology Bombay
M. B. Patil, IIT Bombay
![Page 2: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/2.jpg)
BJT amplifier: basic operation
E
C
0.2 0.4 0.6 0.8 0
IC
α IE
IE
IB
RC
VCC
VB
Vo
RC
VCC
VB
t
t
VBE
IC
* In the active mode, IC changes exponentially with VBE .
* Vo = VCC − IC RC ⇒ the amplitude of Vo is simply IC RC which can be mademuch larger than the input voltage amplitude.
* Note that both the input (VBE ) and output (Vo) voltages have DC (“bias”)components.
M. B. Patil, IIT Bombay
![Page 3: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/3.jpg)
BJT amplifier: basic operation
E
C
0.2 0.4 0.6 0.8 0
IC
α IE
IE
IB
RC
VCC
VB
Vo
RC
VCC
VB
t
t
VBE
IC
* In the active mode, IC changes exponentially with VBE .
* Vo = VCC − IC RC ⇒ the amplitude of Vo is simply IC RC which can be mademuch larger than the input voltage amplitude.
* Note that both the input (VBE ) and output (Vo) voltages have DC (“bias”)components.
M. B. Patil, IIT Bombay
![Page 4: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/4.jpg)
BJT amplifier: basic operation
E
C
0.2 0.4 0.6 0.8 0
IC
α IE
IE
IB
RC
VCC
VB
Vo
RC
VCC
VB
t
t
VBE
IC
* In the active mode, IC changes exponentially with VBE .
* Vo = VCC − IC RC ⇒ the amplitude of Vo is simply IC RC which can be mademuch larger than the input voltage amplitude.
* Note that both the input (VBE ) and output (Vo) voltages have DC (“bias”)components.
M. B. Patil, IIT Bombay
![Page 5: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/5.jpg)
BJT amplifier: basic operation
E
C
0.2 0.4 0.6 0.8 0
IC
α IE
IE
IB
RC
VCC
VB
Vo
RC
VCC
VB
t
t
VBE
IC
* In the active mode, IC changes exponentially with VBE .
* Vo = VCC − IC RC ⇒ the amplitude of Vo is simply IC RC which can be mademuch larger than the input voltage amplitude.
* Note that both the input (VBE ) and output (Vo) voltages have DC (“bias”)components.
M. B. Patil, IIT Bombay
![Page 6: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/6.jpg)
BJT amplifier biasing: why?
E
B
C
0 1 2 3 4 5
1
2
3
4
5
0
Vi
RC
VCC
Vo
RB Vo(Volts)
Vi (Volts)
Consider a more realistic BJT amplifier circuit, with RB added to limit the basecurrent (and thus protect the transistor).
* The gain of the amplifier is given bydVo
dVi.
* Since Vo is nearly constant for Vi < 0.7 V (due to cut-off) and Vi > 1.3 V (dueto saturation), the circuit will not work an an amplifier in this range.
* Further, to get a large swing in Vo without distortion, the DC bias of Vi shouldbe at the centre of the amplifying region, i.e., Vi ≈ 1 V .
M. B. Patil, IIT Bombay
![Page 7: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/7.jpg)
BJT amplifier biasing: why?
E
B
C
0 1 2 3 4 5
1
2
3
4
5
0
Vi
RC
VCC
Vo
RB Vo(Volts)
Vi (Volts)
Consider a more realistic BJT amplifier circuit, with RB added to limit the basecurrent (and thus protect the transistor).
* The gain of the amplifier is given bydVo
dVi.
* Since Vo is nearly constant for Vi < 0.7 V (due to cut-off) and Vi > 1.3 V (dueto saturation), the circuit will not work an an amplifier in this range.
* Further, to get a large swing in Vo without distortion, the DC bias of Vi shouldbe at the centre of the amplifying region, i.e., Vi ≈ 1 V .
M. B. Patil, IIT Bombay
![Page 8: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/8.jpg)
BJT amplifier biasing: why?
E
B
C
0 1 2 3 4 5
1
2
3
4
5
0
Vi
RC
VCC
Vo
RB Vo(Volts)
Vi (Volts)
Consider a more realistic BJT amplifier circuit, with RB added to limit the basecurrent (and thus protect the transistor).
* The gain of the amplifier is given bydVo
dVi.
* Since Vo is nearly constant for Vi < 0.7 V (due to cut-off) and Vi > 1.3 V (dueto saturation), the circuit will not work an an amplifier in this range.
* Further, to get a large swing in Vo without distortion, the DC bias of Vi shouldbe at the centre of the amplifying region, i.e., Vi ≈ 1 V .
M. B. Patil, IIT Bombay
![Page 9: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/9.jpg)
BJT amplifier biasing: why?
E
B
C
0 1 2 3 4 5
1
2
3
4
5
0
Vi
RC
VCC
Vo
RB Vo(Volts)
Vi (Volts)
Consider a more realistic BJT amplifier circuit, with RB added to limit the basecurrent (and thus protect the transistor).
* The gain of the amplifier is given bydVo
dVi.
* Since Vo is nearly constant for Vi < 0.7 V (due to cut-off) and Vi > 1.3 V (dueto saturation), the circuit will not work an an amplifier in this range.
* Further, to get a large swing in Vo without distortion, the DC bias of Vi shouldbe at the centre of the amplifying region, i.e., Vi ≈ 1 V .
M. B. Patil, IIT Bombay
![Page 10: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/10.jpg)
BJT amplifier biasing: why?
t (msec) t (msec) t (msec)
E
B
C
A B C
A B C
4.50
4.60
4.70
4.80
4.90
5.00
0 0.2 0.4 0.6 0.8 1
0.70
0.72
0.74
0.76
0.78
0.80
0.95
0.97
0.99
1.01
1.03
1.05
1.25
1.27
1.29
1.31
1.33
1.35
0.15
0.25
0.35
0.45
0.55
0.65
0 0.2 0.4 0.6 0.8 12.40
2.60
2.80
3.00
3.20
3.40
0 0.2 0.4 0.6 0.8 1
0 1 2 3 4 5
1
2
3
4
5
0
Vi
Vo
Vi
RB
RC
VCC
Vo Vo
Vi
(SEQUEL file: ee101 bjt amp1.sqproj)M. B. Patil, IIT Bombay
![Page 11: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/11.jpg)
BJT amplifier
E
B
C
0 1 2 3 4 5
1
2
3
4
5
0
Vi
RC
VCC
Vo
RB Vo(Volts)
Vi (Volts)
* The key challenges in realizing this amplifier in practice are
- adjusting the input DC bias to ensure that the BJT remains in the linear(active) region with a certain bias value of IC .
- mixing the input DC bias with the signal voltage.
* The first issue is addressed by using a suitable biasing scheme, and the secondby using “coupling” capacitors.
M. B. Patil, IIT Bombay
![Page 12: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/12.jpg)
BJT amplifier
E
B
C
0 1 2 3 4 5
1
2
3
4
5
0
Vi
RC
VCC
Vo
RB Vo(Volts)
Vi (Volts)
* The key challenges in realizing this amplifier in practice are
- adjusting the input DC bias to ensure that the BJT remains in the linear(active) region with a certain bias value of IC .
- mixing the input DC bias with the signal voltage.
* The first issue is addressed by using a suitable biasing scheme, and the secondby using “coupling” capacitors.
M. B. Patil, IIT Bombay
![Page 13: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/13.jpg)
BJT amplifier
E
B
C
0 1 2 3 4 5
1
2
3
4
5
0
Vi
RC
VCC
Vo
RB Vo(Volts)
Vi (Volts)
* The key challenges in realizing this amplifier in practice are
- adjusting the input DC bias to ensure that the BJT remains in the linear(active) region with a certain bias value of IC .
- mixing the input DC bias with the signal voltage.
* The first issue is addressed by using a suitable biasing scheme, and the secondby using “coupling” capacitors.
M. B. Patil, IIT Bombay
![Page 14: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/14.jpg)
BJT amplifier
E
B
C
0 1 2 3 4 5
1
2
3
4
5
0
Vi
RC
VCC
Vo
RB Vo(Volts)
Vi (Volts)
* The key challenges in realizing this amplifier in practice are
- adjusting the input DC bias to ensure that the BJT remains in the linear(active) region with a certain bias value of IC .
- mixing the input DC bias with the signal voltage.
* The first issue is addressed by using a suitable biasing scheme, and the secondby using “coupling” capacitors.
M. B. Patil, IIT Bombay
![Page 15: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/15.jpg)
BJT amplifier: a simple biasing scheme
15 V
1 k
VCC
RBRC
“Biasing” an amplifier ⇒ selection of component values for a certain DC value of IC(i.e., when no signal is applied).
Equivalently, we may bias an amplifier for a certain DC value of VCE , since IC andVCE are related: VCE + ICRC = VCC .
As an example, for RC = 1 k, β = 100, let us calculate RB which will giveIC = 3.3 mA, assuming the BJT to be operating in the active mode.
IB =IC
β=
3.3 mA
100= 33µA =
VCC − VBE
RB
→ RB =14.3V
33µA= 430 kΩ .
M. B. Patil, IIT Bombay
![Page 16: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/16.jpg)
BJT amplifier: a simple biasing scheme
15 V
1 k
VCC
RBRC
“Biasing” an amplifier ⇒ selection of component values for a certain DC value of IC(i.e., when no signal is applied).
Equivalently, we may bias an amplifier for a certain DC value of VCE , since IC andVCE are related: VCE + ICRC = VCC .
As an example, for RC = 1 k, β = 100, let us calculate RB which will giveIC = 3.3 mA, assuming the BJT to be operating in the active mode.
IB =IC
β=
3.3 mA
100= 33µA =
VCC − VBE
RB
→ RB =14.3V
33µA= 430 kΩ .
M. B. Patil, IIT Bombay
![Page 17: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/17.jpg)
BJT amplifier: a simple biasing scheme
15 V
1 k
VCC
RBRC
“Biasing” an amplifier ⇒ selection of component values for a certain DC value of IC(i.e., when no signal is applied).
Equivalently, we may bias an amplifier for a certain DC value of VCE , since IC andVCE are related: VCE + ICRC = VCC .
As an example, for RC = 1 k, β = 100, let us calculate RB which will giveIC = 3.3 mA, assuming the BJT to be operating in the active mode.
IB =IC
β=
3.3 mA
100= 33µA =
VCC − VBE
RB
→ RB =14.3V
33µA= 430 kΩ .
M. B. Patil, IIT Bombay
![Page 18: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/18.jpg)
BJT amplifier: a simple biasing scheme
15 V
1 k
VCC
RBRC
“Biasing” an amplifier ⇒ selection of component values for a certain DC value of IC(i.e., when no signal is applied).
Equivalently, we may bias an amplifier for a certain DC value of VCE , since IC andVCE are related: VCE + ICRC = VCC .
As an example, for RC = 1 k, β = 100, let us calculate RB which will giveIC = 3.3 mA, assuming the BJT to be operating in the active mode.
IB =IC
β=
3.3 mA
100= 33µA =
VCC − VBE
RB
→ RB =14.3V
33µA= 430 kΩ .
M. B. Patil, IIT Bombay
![Page 19: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/19.jpg)
BJT amplifier: a simple biasing scheme
15 V
1 k
VCC
RBRC
“Biasing” an amplifier ⇒ selection of component values for a certain DC value of IC(i.e., when no signal is applied).
Equivalently, we may bias an amplifier for a certain DC value of VCE , since IC andVCE are related: VCE + ICRC = VCC .
As an example, for RC = 1 k, β = 100, let us calculate RB which will giveIC = 3.3 mA, assuming the BJT to be operating in the active mode.
IB =IC
β=
3.3 mA
100= 33µA =
VCC − VBE
RB
→ RB =14.3V
33µA= 430 kΩ .
M. B. Patil, IIT Bombay
![Page 20: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/20.jpg)
BJT amplifier: a simple biasing scheme (continued)
15 V
1 k
VCC
RBRC
With RB = 430 k, we expect IC = 3.3 mA, assuming β = 100.
However, in practice, there is a substantial variation in the β value (even for the sametransistor type). The manufacturer may specify the nominal value of β as 100, but theactual value may be 150, for example.
With β = 150, the actual IC is,
IC = β ×VCC − VBE
RB= 150×
(15− 0.7)V
430 k= 5 mA ,
which is significantly different than the intended value, 3.3 mA.
⇒ need a biasing scheme which is not so sensitive to β.
M. B. Patil, IIT Bombay
![Page 21: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/21.jpg)
BJT amplifier: a simple biasing scheme (continued)
15 V
1 k
VCC
RBRC
With RB = 430 k, we expect IC = 3.3 mA, assuming β = 100.
However, in practice, there is a substantial variation in the β value (even for the sametransistor type). The manufacturer may specify the nominal value of β as 100, but theactual value may be 150, for example.
With β = 150, the actual IC is,
IC = β ×VCC − VBE
RB= 150×
(15− 0.7)V
430 k= 5 mA ,
which is significantly different than the intended value, 3.3 mA.
⇒ need a biasing scheme which is not so sensitive to β.
M. B. Patil, IIT Bombay
![Page 22: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/22.jpg)
BJT amplifier: a simple biasing scheme (continued)
15 V
1 k
VCC
RBRC
With RB = 430 k, we expect IC = 3.3 mA, assuming β = 100.
However, in practice, there is a substantial variation in the β value (even for the sametransistor type). The manufacturer may specify the nominal value of β as 100, but theactual value may be 150, for example.
With β = 150, the actual IC is,
IC = β ×VCC − VBE
RB= 150×
(15− 0.7)V
430 k= 5 mA ,
which is significantly different than the intended value, 3.3 mA.
⇒ need a biasing scheme which is not so sensitive to β.
M. B. Patil, IIT Bombay
![Page 23: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/23.jpg)
BJT amplifier: a simple biasing scheme (continued)
15 V
1 k
VCC
RBRC
With RB = 430 k, we expect IC = 3.3 mA, assuming β = 100.
However, in practice, there is a substantial variation in the β value (even for the sametransistor type). The manufacturer may specify the nominal value of β as 100, but theactual value may be 150, for example.
With β = 150, the actual IC is,
IC = β ×VCC − VBE
RB= 150×
(15− 0.7)V
430 k= 5 mA ,
which is significantly different than the intended value, 3.3 mA.
⇒ need a biasing scheme which is not so sensitive to β.
M. B. Patil, IIT Bombay
![Page 24: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/24.jpg)
BJT amplifier: improved biasing scheme
3.6 k
1 k
10 k
2.2 k
10 V
IB
VCC
RE
RC
R1IC
IER2
IB VCC
VCC R2
R1
IC
IE
RC
RE
IB
IE
IC
VCCRTh
VThRE
RC
VTh =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V , RTh = R1 ‖ R2 = 1.8 k
Assuming the BJT to be in the active mode,
KCL: VTh = RTh IB + VBE + RE IE = RTh IB + VBE + (β + 1) IB RE
→ IB =VTh − VBE
RTh + (β + 1)RE, IC = β IB =
β (VTh − VBE )
RTh + (β + 1)RE.
For β = 100, IC=1.07 mA.
For β = 200, IC=1.085 mA.
M. B. Patil, IIT Bombay
![Page 25: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/25.jpg)
BJT amplifier: improved biasing scheme
3.6 k
1 k
10 k
2.2 k
10 V
IB
VCC
RE
RC
R1IC
IER2
IB VCC
VCC R2
R1
IC
IE
RC
RE
IB
IE
IC
VCCRTh
VThRE
RC
VTh =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V , RTh = R1 ‖ R2 = 1.8 k
Assuming the BJT to be in the active mode,
KCL: VTh = RTh IB + VBE + RE IE = RTh IB + VBE + (β + 1) IB RE
→ IB =VTh − VBE
RTh + (β + 1)RE, IC = β IB =
β (VTh − VBE )
RTh + (β + 1)RE.
For β = 100, IC=1.07 mA.
For β = 200, IC=1.085 mA.
M. B. Patil, IIT Bombay
![Page 26: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/26.jpg)
BJT amplifier: improved biasing scheme
3.6 k
1 k
10 k
2.2 k
10 V
IB
VCC
RE
RC
R1IC
IER2
IB VCC
VCC R2
R1
IC
IE
RC
RE
IB
IE
IC
VCCRTh
VThRE
RC
VTh =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V , RTh = R1 ‖ R2 = 1.8 k
Assuming the BJT to be in the active mode,
KCL: VTh = RTh IB + VBE + RE IE = RTh IB + VBE + (β + 1) IB RE
→ IB =VTh − VBE
RTh + (β + 1)RE, IC = β IB =
β (VTh − VBE )
RTh + (β + 1)RE.
For β = 100, IC=1.07 mA.
For β = 200, IC=1.085 mA.
M. B. Patil, IIT Bombay
![Page 27: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/27.jpg)
BJT amplifier: improved biasing scheme
3.6 k
1 k
10 k
2.2 k
10 V
IB
VCC
RE
RC
R1IC
IER2
IB VCC
VCC R2
R1
IC
IE
RC
RE
IB
IE
IC
VCCRTh
VThRE
RC
VTh =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V , RTh = R1 ‖ R2 = 1.8 k
Assuming the BJT to be in the active mode,
KCL: VTh = RTh IB + VBE + RE IE = RTh IB + VBE + (β + 1) IB RE
→ IB =VTh − VBE
RTh + (β + 1)RE, IC = β IB =
β (VTh − VBE )
RTh + (β + 1)RE.
For β = 100, IC=1.07 mA.
For β = 200, IC=1.085 mA.
M. B. Patil, IIT Bombay
![Page 28: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/28.jpg)
BJT amplifier: improved biasing scheme
3.6 k
1 k
10 k
2.2 k
10 V
IB
VCC
RE
RC
R1IC
IER2
IB VCC
VCC R2
R1
IC
IE
RC
RE
IB
IE
IC
VCCRTh
VThRE
RC
VTh =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V , RTh = R1 ‖ R2 = 1.8 k
Assuming the BJT to be in the active mode,
KCL: VTh = RTh IB + VBE + RE IE = RTh IB + VBE + (β + 1) IB RE
→ IB =VTh − VBE
RTh + (β + 1)RE, IC = β IB =
β (VTh − VBE )
RTh + (β + 1)RE.
For β = 100, IC=1.07 mA.
For β = 200, IC=1.085 mA.
M. B. Patil, IIT Bombay
![Page 29: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/29.jpg)
BJT amplifier: improved biasing scheme
3.6 k
1 k
10 k
2.2 k
10 V
IB
VCC
RE
RC
R1IC
IER2
IB VCC
VCC R2
R1
IC
IE
RC
RE
IB
IE
IC
VCCRTh
VThRE
RC
VTh =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V , RTh = R1 ‖ R2 = 1.8 k
Assuming the BJT to be in the active mode,
KCL: VTh = RTh IB + VBE + RE IE = RTh IB + VBE + (β + 1) IB RE
→ IB =VTh − VBE
RTh + (β + 1)RE, IC = β IB =
β (VTh − VBE )
RTh + (β + 1)RE.
For β = 100, IC=1.07 mA.
For β = 200, IC=1.085 mA.
M. B. Patil, IIT Bombay
![Page 30: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/30.jpg)
BJT amplifier: improved biasing scheme
3.6 k
1 k
10 k
2.2 k
10 V
IB
VCC
RE
RC
R1IC
IER2
IB VCC
VCC R2
R1
IC
IE
RC
RE
IB
IE
IC
VCCRTh
VThRE
RC
VTh =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V , RTh = R1 ‖ R2 = 1.8 k
Assuming the BJT to be in the active mode,
KCL: VTh = RTh IB + VBE + RE IE = RTh IB + VBE + (β + 1) IB RE
→ IB =VTh − VBE
RTh + (β + 1)RE, IC = β IB =
β (VTh − VBE )
RTh + (β + 1)RE.
For β = 100, IC=1.07 mA.
For β = 200, IC=1.085 mA.
M. B. Patil, IIT Bombay
![Page 31: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/31.jpg)
BJT amplifier: improved biasing scheme
3.6 k
1 k
10 k
2.2 k
10 V
IB
VCC
RE
RC
R1IC
IER2
IB VCC
VCC R2
R1
IC
IE
RC
RE
IB
IE
IC
VCCRTh
VThRE
RC
VTh =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V , RTh = R1 ‖ R2 = 1.8 k
Assuming the BJT to be in the active mode,
KCL: VTh = RTh IB + VBE + RE IE = RTh IB + VBE + (β + 1) IB RE
→ IB =VTh − VBE
RTh + (β + 1)RE, IC = β IB =
β (VTh − VBE )
RTh + (β + 1)RE.
For β = 100, IC=1.07 mA.
For β = 200, IC=1.085 mA.
M. B. Patil, IIT Bombay
![Page 32: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/32.jpg)
BJT amplifier: improved biasing scheme (continued)
1.8 V
6 V
1.1 V
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
With IC = 1.1 mA, the various DC (“bias”) voltages are,
VE = IE RE ≈ 1.1 mA× 1 k = 1.1V ,
VB = VE + VBE ≈ 1.1V + 0.7V = 1.8V ,
VC = VCC − IC RC = 10V − 1.1 mA× 3.6 k ≈ 6V ,
VCE = VC − VE = 6− 1.1 = 4.9V .
M. B. Patil, IIT Bombay
![Page 33: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/33.jpg)
BJT amplifier: improved biasing scheme (continued)
1.8 V
6 V
1.1 V
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
With IC = 1.1 mA, the various DC (“bias”) voltages are,
VE = IE RE ≈ 1.1 mA× 1 k = 1.1V ,
VB = VE + VBE ≈ 1.1V + 0.7V = 1.8V ,
VC = VCC − IC RC = 10V − 1.1 mA× 3.6 k ≈ 6V ,
VCE = VC − VE = 6− 1.1 = 4.9V .
M. B. Patil, IIT Bombay
![Page 34: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/34.jpg)
BJT amplifier: improved biasing scheme (continued)
1.8 V
6 V
1.1 V
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
With IC = 1.1 mA, the various DC (“bias”) voltages are,
VE = IE RE ≈ 1.1 mA× 1 k = 1.1V ,
VB = VE + VBE ≈ 1.1V + 0.7V = 1.8V ,
VC = VCC − IC RC = 10V − 1.1 mA× 3.6 k ≈ 6V ,
VCE = VC − VE = 6− 1.1 = 4.9V .
M. B. Patil, IIT Bombay
![Page 35: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/35.jpg)
BJT amplifier: improved biasing scheme (continued)
1.8 V
6 V
1.1 V
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
With IC = 1.1 mA, the various DC (“bias”) voltages are,
VE = IE RE ≈ 1.1 mA× 1 k = 1.1V ,
VB = VE + VBE ≈ 1.1V + 0.7V = 1.8V ,
VC = VCC − IC RC = 10V − 1.1 mA× 3.6 k ≈ 6V ,
VCE = VC − VE = 6− 1.1 = 4.9V .
M. B. Patil, IIT Bombay
![Page 36: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/36.jpg)
BJT amplifier: improved biasing scheme (continued)
1.8 V
6 V
1.1 V
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
With IC = 1.1 mA, the various DC (“bias”) voltages are,
VE = IE RE ≈ 1.1 mA× 1 k = 1.1V ,
VB = VE + VBE ≈ 1.1V + 0.7V = 1.8V ,
VC = VCC − IC RC = 10V − 1.1 mA× 3.6 k ≈ 6V ,
VCE = VC − VE = 6− 1.1 = 4.9V .
M. B. Patil, IIT Bombay
![Page 37: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/37.jpg)
BJT amplifier: improved biasing scheme (continued)
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
A quick estimate of the bias values can be obtained by ignoring IB (which is fair if β islarge). In that case,
VB =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V .
VE = VB − VBE ≈ 1.8V − 0.7V = 1.1V .
IE =VE
RE=
1.1V
1 k= 1.1 mA.
IC = α IE ≈ IE = 1.1 mA.
VCE = VCC − IC RC − IE RE = 10V − (3.6 k× 1.1 mA)− (1 k× 1.1 mA) ≈ 5V .
M. B. Patil, IIT Bombay
![Page 38: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/38.jpg)
BJT amplifier: improved biasing scheme (continued)
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
A quick estimate of the bias values can be obtained by ignoring IB (which is fair if β islarge). In that case,
VB =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V .
VE = VB − VBE ≈ 1.8V − 0.7V = 1.1V .
IE =VE
RE=
1.1V
1 k= 1.1 mA.
IC = α IE ≈ IE = 1.1 mA.
VCE = VCC − IC RC − IE RE = 10V − (3.6 k× 1.1 mA)− (1 k× 1.1 mA) ≈ 5V .
M. B. Patil, IIT Bombay
![Page 39: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/39.jpg)
BJT amplifier: improved biasing scheme (continued)
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
A quick estimate of the bias values can be obtained by ignoring IB (which is fair if β islarge). In that case,
VB =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V .
VE = VB − VBE ≈ 1.8V − 0.7V = 1.1V .
IE =VE
RE=
1.1V
1 k= 1.1 mA.
IC = α IE ≈ IE = 1.1 mA.
VCE = VCC − IC RC − IE RE = 10V − (3.6 k× 1.1 mA)− (1 k× 1.1 mA) ≈ 5V .
M. B. Patil, IIT Bombay
![Page 40: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/40.jpg)
BJT amplifier: improved biasing scheme (continued)
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
A quick estimate of the bias values can be obtained by ignoring IB (which is fair if β islarge). In that case,
VB =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V .
VE = VB − VBE ≈ 1.8V − 0.7V = 1.1V .
IE =VE
RE=
1.1V
1 k= 1.1 mA.
IC = α IE ≈ IE = 1.1 mA.
VCE = VCC − IC RC − IE RE = 10V − (3.6 k× 1.1 mA)− (1 k× 1.1 mA) ≈ 5V .
M. B. Patil, IIT Bombay
![Page 41: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/41.jpg)
BJT amplifier: improved biasing scheme (continued)
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
A quick estimate of the bias values can be obtained by ignoring IB (which is fair if β islarge). In that case,
VB =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V .
VE = VB − VBE ≈ 1.8V − 0.7V = 1.1V .
IE =VE
RE=
1.1V
1 k= 1.1 mA.
IC = α IE ≈ IE = 1.1 mA.
VCE = VCC − IC RC − IE RE = 10V − (3.6 k× 1.1 mA)− (1 k× 1.1 mA) ≈ 5V .
M. B. Patil, IIT Bombay
![Page 42: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/42.jpg)
BJT amplifier: improved biasing scheme (continued)
2.2 k 1 k
3.6 k10 k
10 V
IB
VCC
RE
IER2
RC
R1
IC
A quick estimate of the bias values can be obtained by ignoring IB (which is fair if β islarge). In that case,
VB =R2
R1 + R2VCC =
2.2 k
10 k + 2.2 k× 10V = 1.8V .
VE = VB − VBE ≈ 1.8V − 0.7V = 1.1V .
IE =VE
RE=
1.1V
1 k= 1.1 mA.
IC = α IE ≈ IE = 1.1 mA.
VCE = VCC − IC RC − IE RE = 10V − (3.6 k× 1.1 mA)− (1 k× 1.1 mA) ≈ 5V .
M. B. Patil, IIT Bombay
![Page 43: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/43.jpg)
Adding signal to bias
VCC
RC
RE
R1
R2
vB
CB
vs
* As we have seen earlier, the input signal vs(t) = V sin ωt (for example) needs tobe mixed with the desired bias value VB so that the net voltage at the base isvB(t) = VB + V sin ωt.
* This can be achieved by using a coupling capacitor CB .
* Let us take a simple circuit to illustrate how a coupling capacitor works.
M. B. Patil, IIT Bombay
![Page 44: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/44.jpg)
Adding signal to bias
VCC
RC
RE
R1
R2
vB
CB
vs
* As we have seen earlier, the input signal vs(t) = V sin ωt (for example) needs tobe mixed with the desired bias value VB so that the net voltage at the base isvB(t) = VB + V sin ωt.
* This can be achieved by using a coupling capacitor CB .
* Let us take a simple circuit to illustrate how a coupling capacitor works.
M. B. Patil, IIT Bombay
![Page 45: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/45.jpg)
Adding signal to bias
VCC
RC
RE
R1
R2
vB
CB
vs
* As we have seen earlier, the input signal vs(t) = V sin ωt (for example) needs tobe mixed with the desired bias value VB so that the net voltage at the base isvB(t) = VB + V sin ωt.
* This can be achieved by using a coupling capacitor CB .
* Let us take a simple circuit to illustrate how a coupling capacitor works.
M. B. Patil, IIT Bombay
![Page 46: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/46.jpg)
Adding signal to bias
VCC
RC
RE
R1
R2
vB
CB
vs
* As we have seen earlier, the input signal vs(t) = V sin ωt (for example) needs tobe mixed with the desired bias value VB so that the net voltage at the base isvB(t) = VB + V sin ωt.
* This can be achieved by using a coupling capacitor CB .
* Let us take a simple circuit to illustrate how a coupling capacitor works.
M. B. Patil, IIT Bombay
![Page 47: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/47.jpg)
Coupling capacitor: example
C
A
i3i1 i2
vCR2
R1vs(t) V0 (DC)
Let vA be the instantaneous node voltage at A. KCL gives,
−i1 + i3 + i2 = 0→ −CdvC
dt+
vA
R1+
vA − V0
R2= 0.
−Cd(vs − vA)
dt+
vA
R1+
vA − V0
R2= 0. (1)
Let vA = VA + va(t), where VA = constant (DC).
In sinusoidal steady state, Eq. (1) can be split into two equations, one with only DCterms and the other with only sinusoidal terms.
−Cd(−VA)
dt+
VA
R1+
VA − V0
R2= 0, and −C
d(vs − va)
dt+
va
R1+
va
R2= 0.
M. B. Patil, IIT Bombay
![Page 48: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/48.jpg)
Coupling capacitor: example
C
A
i3i1 i2
vCR2
R1vs(t) V0 (DC)
Let vA be the instantaneous node voltage at A. KCL gives,
−i1 + i3 + i2 = 0→ −CdvC
dt+
vA
R1+
vA − V0
R2= 0.
−Cd(vs − vA)
dt+
vA
R1+
vA − V0
R2= 0. (1)
Let vA = VA + va(t), where VA = constant (DC).
In sinusoidal steady state, Eq. (1) can be split into two equations, one with only DCterms and the other with only sinusoidal terms.
−Cd(−VA)
dt+
VA
R1+
VA − V0
R2= 0, and −C
d(vs − va)
dt+
va
R1+
va
R2= 0.
M. B. Patil, IIT Bombay
![Page 49: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/49.jpg)
Coupling capacitor: example
C
A
i3i1 i2
vCR2
R1vs(t) V0 (DC)
Let vA be the instantaneous node voltage at A. KCL gives,
−i1 + i3 + i2 = 0→ −CdvC
dt+
vA
R1+
vA − V0
R2= 0.
−Cd(vs − vA)
dt+
vA
R1+
vA − V0
R2= 0. (1)
Let vA = VA + va(t), where VA = constant (DC).
In sinusoidal steady state, Eq. (1) can be split into two equations, one with only DCterms and the other with only sinusoidal terms.
−Cd(−VA)
dt+
VA
R1+
VA − V0
R2= 0, and −C
d(vs − va)
dt+
va
R1+
va
R2= 0.
M. B. Patil, IIT Bombay
![Page 50: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/50.jpg)
Coupling capacitor: example
C
A
i3i1 i2
vCR2
R1vs(t) V0 (DC)
Let vA be the instantaneous node voltage at A. KCL gives,
−i1 + i3 + i2 = 0→ −CdvC
dt+
vA
R1+
vA − V0
R2= 0.
−Cd(vs − vA)
dt+
vA
R1+
vA − V0
R2= 0. (1)
Let vA = VA + va(t), where VA = constant (DC).
In sinusoidal steady state, Eq. (1) can be split into two equations, one with only DCterms and the other with only sinusoidal terms.
−Cd(−VA)
dt+
VA
R1+
VA − V0
R2= 0, and −C
d(vs − va)
dt+
va
R1+
va
R2= 0.
M. B. Patil, IIT Bombay
![Page 51: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/51.jpg)
Coupling capacitor: example
C
A
i3i1 i2
vCR2
R1vs(t) V0 (DC)
Let vA be the instantaneous node voltage at A. KCL gives,
−i1 + i3 + i2 = 0→ −CdvC
dt+
vA
R1+
vA − V0
R2= 0.
−Cd(vs − vA)
dt+
vA
R1+
vA − V0
R2= 0. (1)
Let vA = VA + va(t), where VA = constant (DC).
In sinusoidal steady state, Eq. (1) can be split into two equations, one with only DCterms and the other with only sinusoidal terms.
−Cd(−VA)
dt+
VA
R1+
VA − V0
R2= 0, and −C
d(vs − va)
dt+
va
R1+
va
R2= 0.
M. B. Patil, IIT Bombay
![Page 52: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/52.jpg)
Coupling capacitor: example (continued)
C
A
i3i1 i2
vCR2
R1vs(t) V0 (DC)
SincedVA
dt= 0 (VA being constant), we get
VA
R1+
VA − V0
R2= 0, and
va
(1
R1+
1
R2
)= C
d(vs − va)
dt.
In other words, the original circuit can be thought of as
AND
C
AA
(DC circuit) (AC circuit)
C
A
i3i1 i2
vC
R1
R2 R2 R2
R1R1vs(t) vs(t)V0V0
We can get VA from the first circuit, va(t) from the second, and then combine them
to get the actual vA(t): vA(t) = VA + va(t)
M. B. Patil, IIT Bombay
![Page 53: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/53.jpg)
Coupling capacitor: example (continued)
C
A
i3i1 i2
vCR2
R1vs(t) V0 (DC)
SincedVA
dt= 0 (VA being constant), we get
VA
R1+
VA − V0
R2= 0, and
va
(1
R1+
1
R2
)= C
d(vs − va)
dt.
In other words, the original circuit can be thought of as
AND
C
AA
(DC circuit) (AC circuit)
C
A
i3i1 i2
vC
R1
R2 R2 R2
R1R1vs(t) vs(t)V0V0
We can get VA from the first circuit, va(t) from the second, and then combine them
to get the actual vA(t): vA(t) = VA + va(t)
M. B. Patil, IIT Bombay
![Page 54: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/54.jpg)
Coupling capacitor: example (continued)
C
A
i3i1 i2
vCR2
R1vs(t) V0 (DC)
SincedVA
dt= 0 (VA being constant), we get
VA
R1+
VA − V0
R2= 0, and
va
(1
R1+
1
R2
)= C
d(vs − va)
dt.
In other words, the original circuit can be thought of as
AND
C
AA
(DC circuit) (AC circuit)
C
A
i3i1 i2
vC
R1
R2 R2 R2
R1R1vs(t) vs(t)V0V0
We can get VA from the first circuit, va(t) from the second, and then combine them
to get the actual vA(t): vA(t) = VA + va(t)
M. B. Patil, IIT Bombay
![Page 55: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/55.jpg)
Capacitors in an amplifier circuit
* Split the original circuit into two circuits:
- DC circuit: replace each capacitor with an open circuit, each AC voltage
source with a short circuit.
- AC circuit: replace each DC voltage source with a short circuit.
* Analyse the two circuits separately.
* Combine the results of the two circuits to obtain the net instantaneous voltagesand currents.
* The procedure described above also applies to a nonlinear circuit such as a BJTamplifier IF the “small-signal approximation” is satisfied. We will soon see whatthat means.
M. B. Patil, IIT Bombay
![Page 56: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/56.jpg)
Capacitors in an amplifier circuit
* Split the original circuit into two circuits:
- DC circuit: replace each capacitor with an open circuit, each AC voltage
source with a short circuit.
- AC circuit: replace each DC voltage source with a short circuit.
* Analyse the two circuits separately.
* Combine the results of the two circuits to obtain the net instantaneous voltagesand currents.
* The procedure described above also applies to a nonlinear circuit such as a BJTamplifier IF the “small-signal approximation” is satisfied. We will soon see whatthat means.
M. B. Patil, IIT Bombay
![Page 57: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/57.jpg)
Capacitors in an amplifier circuit
* Split the original circuit into two circuits:
- DC circuit: replace each capacitor with an open circuit, each AC voltage
source with a short circuit.
- AC circuit: replace each DC voltage source with a short circuit.
* Analyse the two circuits separately.
* Combine the results of the two circuits to obtain the net instantaneous voltagesand currents.
* The procedure described above also applies to a nonlinear circuit such as a BJTamplifier IF the “small-signal approximation” is satisfied. We will soon see whatthat means.
M. B. Patil, IIT Bombay
![Page 58: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/58.jpg)
Capacitors in an amplifier circuit
* Split the original circuit into two circuits:
- DC circuit: replace each capacitor with an open circuit, each AC voltage
source with a short circuit.
- AC circuit: replace each DC voltage source with a short circuit.
* Analyse the two circuits separately.
* Combine the results of the two circuits to obtain the net instantaneous voltagesand currents.
* The procedure described above also applies to a nonlinear circuit such as a BJTamplifier IF the “small-signal approximation” is satisfied. We will soon see whatthat means.
M. B. Patil, IIT Bombay
![Page 59: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/59.jpg)
Common-emitter amplifier
couplingcapacitor
couplingcapacitor
bypasscapacitor
loadresistor
vs
CB
CC
CE
VCC
RL
RE
R2
R1
RC
DC circuit
VCC
RER2
R1
RC
AND
AC circuit
vs
CB
CC
CE
RL
RE
R2
R1
RC
* The coupling capacitors ensure that the singal source and the load resistor donot affect the DC bias of the amplifier. (We will see the purpose of CE a littlelater.)
* This enables us to bias the amplifier without worrying about what load it isgoing to drive.
M. B. Patil, IIT Bombay
![Page 60: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/60.jpg)
Common-emitter amplifier
couplingcapacitor
couplingcapacitor
bypasscapacitor
loadresistor
vs
CB
CC
CE
VCC
RL
RE
R2
R1
RC
DC circuit
VCC
RER2
R1
RC
AND
AC circuit
vs
CB
CC
CE
RL
RE
R2
R1
RC
* The coupling capacitors ensure that the singal source and the load resistor donot affect the DC bias of the amplifier. (We will see the purpose of CE a littlelater.)
* This enables us to bias the amplifier without worrying about what load it isgoing to drive.
M. B. Patil, IIT Bombay
![Page 61: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/61.jpg)
Common-emitter amplifier
couplingcapacitor
couplingcapacitor
bypasscapacitor
loadresistor
vs
CB
CC
CE
VCC
RL
RE
R2
R1
RC
DC circuit
VCC
RER2
R1
RC
AND
AC circuit
vs
CB
CC
CE
RL
RE
R2
R1
RC
* The coupling capacitors ensure that the singal source and the load resistor donot affect the DC bias of the amplifier. (We will see the purpose of CE a littlelater.)
* This enables us to bias the amplifier without worrying about what load it isgoing to drive.
M. B. Patil, IIT Bombay
![Page 62: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/62.jpg)
Common-emitter amplifier
couplingcapacitor
couplingcapacitor
bypasscapacitor
loadresistor
vs
CB
CC
CE
VCC
RL
RE
R2
R1
RC
DC circuit
VCC
RER2
R1
RC
AND
AC circuit
vs
CB
CC
CE
RL
RE
R2
R1
RC
* The coupling capacitors ensure that the singal source and the load resistor donot affect the DC bias of the amplifier. (We will see the purpose of CE a littlelater.)
* This enables us to bias the amplifier without worrying about what load it isgoing to drive.
M. B. Patil, IIT Bombay
![Page 63: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/63.jpg)
Common-emitter amplifier
couplingcapacitor
couplingcapacitor
bypasscapacitor
loadresistor
vs
CB
CC
CE
VCC
RL
RE
R2
R1
RC
DC circuit
VCC
RER2
R1
RC
AND
AC circuit
vs
CB
CC
CE
RL
RE
R2
R1
RC
* The coupling capacitors ensure that the singal source and the load resistor donot affect the DC bias of the amplifier. (We will see the purpose of CE a littlelater.)
* This enables us to bias the amplifier without worrying about what load it isgoing to drive.
M. B. Patil, IIT Bombay
![Page 64: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/64.jpg)
Common-emitter amplifier: AC circuit
CB
CC
CE
RL
RE
R2vs
R1
RC
RL
vs
R2
R1
RC
vsRL
R2R1
RC
* The coupling and bypass capacitors are “large” (typically, a few µF ), and atfrequencies of interest, their impedance is small.
For example, for C = 10µF , f = 1 kHz,
ZC =1
2π × 103 × 10× 10−6= 16 Ω,
which is much smaller than typical values of R1, R2, RC , RE (a few kΩ).
⇒ CB , CC , CE can be replaced by short circuits at the frequencies of interest.
* The circuit can be re-drawn in a more friendly format.
* We now need to figure out the AC description of a BJT.
M. B. Patil, IIT Bombay
![Page 65: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/65.jpg)
Common-emitter amplifier: AC circuit
CB
CC
CE
RL
RE
R2vs
R1
RC
RL
vs
R2
R1
RC
vsRL
R2R1
RC
* The coupling and bypass capacitors are “large” (typically, a few µF ), and atfrequencies of interest, their impedance is small.
For example, for C = 10µF , f = 1 kHz,
ZC =1
2π × 103 × 10× 10−6= 16 Ω,
which is much smaller than typical values of R1, R2, RC , RE (a few kΩ).
⇒ CB , CC , CE can be replaced by short circuits at the frequencies of interest.
* The circuit can be re-drawn in a more friendly format.
* We now need to figure out the AC description of a BJT.
M. B. Patil, IIT Bombay
![Page 66: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/66.jpg)
Common-emitter amplifier: AC circuit
CB
CC
CE
RL
RE
R2vs
R1
RC
RL
vs
R2
R1
RC
vsRL
R2R1
RC
* The coupling and bypass capacitors are “large” (typically, a few µF ), and atfrequencies of interest, their impedance is small.
For example, for C = 10µF , f = 1 kHz,
ZC =1
2π × 103 × 10× 10−6= 16 Ω,
which is much smaller than typical values of R1, R2, RC , RE (a few kΩ).
⇒ CB , CC , CE can be replaced by short circuits at the frequencies of interest.
* The circuit can be re-drawn in a more friendly format.
* We now need to figure out the AC description of a BJT.
M. B. Patil, IIT Bombay
![Page 67: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/67.jpg)
Common-emitter amplifier: AC circuit
CB
CC
CE
RL
RE
R2vs
R1
RC
RL
vs
R2
R1
RC
vsRL
R2R1
RC
* The coupling and bypass capacitors are “large” (typically, a few µF ), and atfrequencies of interest, their impedance is small.
For example, for C = 10µF , f = 1 kHz,
ZC =1
2π × 103 × 10× 10−6= 16 Ω,
which is much smaller than typical values of R1, R2, RC , RE (a few kΩ).
⇒ CB , CC , CE can be replaced by short circuits at the frequencies of interest.
* The circuit can be re-drawn in a more friendly format.
* We now need to figure out the AC description of a BJT.
M. B. Patil, IIT Bombay
![Page 68: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/68.jpg)
Common-emitter amplifier: AC circuit
CB
CC
CE
RL
RE
R2vs
R1
RC
RL
vs
R2
R1
RC
vsRL
R2R1
RC
* The coupling and bypass capacitors are “large” (typically, a few µF ), and atfrequencies of interest, their impedance is small.
For example, for C = 10µF , f = 1 kHz,
ZC =1
2π × 103 × 10× 10−6= 16 Ω,
which is much smaller than typical values of R1, R2, RC , RE (a few kΩ).
⇒ CB , CC , CE can be replaced by short circuits at the frequencies of interest.
* The circuit can be re-drawn in a more friendly format.
* We now need to figure out the AC description of a BJT.
M. B. Patil, IIT Bombay
![Page 69: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/69.jpg)
Common-emitter amplifier: AC circuit
CB
CC
CE
RL
RE
R2vs
R1
RC
RL
vs
R2
R1
RC
vsRL
R2R1
RC
* The coupling and bypass capacitors are “large” (typically, a few µF ), and atfrequencies of interest, their impedance is small.
For example, for C = 10µF , f = 1 kHz,
ZC =1
2π × 103 × 10× 10−6= 16 Ω,
which is much smaller than typical values of R1, R2, RC , RE (a few kΩ).
⇒ CB , CC , CE can be replaced by short circuits at the frequencies of interest.
* The circuit can be re-drawn in a more friendly format.
* We now need to figure out the AC description of a BJT.
M. B. Patil, IIT Bombay
![Page 70: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/70.jpg)
BJT amplifier: basic operation
C
B
E
1.1
0 0.2 0.4 0.6 0.8 1
t (msec)
0.9
0.7
0.5
vBE
iCiB
iE
i C(m
A)
V0 = 0.65 V,
vBE(t) = V0 + Vm sinωt
f = 1 kHz
Vm = 10 mV
Vm = 5 mV
Vm = 2 mV
* As the vBE amplitude increases, the shape of iC (t) deviates from a sinusoid→ distortion.
* If vbe(t), i.e., the time-varying part of vBE , is kept small, iC varies linearlywith vBE . How small? Let us look at this in more detail.
M. B. Patil, IIT Bombay
![Page 71: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/71.jpg)
BJT amplifier: basic operation
C
B
E
1.1
0 0.2 0.4 0.6 0.8 1
t (msec)
0.9
0.7
0.5
vBE
iCiB
iE
i C(m
A)
V0 = 0.65 V,
vBE(t) = V0 + Vm sinωt
f = 1 kHz
Vm = 10 mV
Vm = 5 mV
Vm = 2 mV
* As the vBE amplitude increases, the shape of iC (t) deviates from a sinusoid→ distortion.
* If vbe(t), i.e., the time-varying part of vBE , is kept small, iC varies linearlywith vBE . How small? Let us look at this in more detail.
M. B. Patil, IIT Bombay
![Page 72: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/72.jpg)
BJT amplifier: basic operation
C
B
E
1.1
0 0.2 0.4 0.6 0.8 1
t (msec)
0.9
0.7
0.5
vBE
iCiB
iE
i C(m
A)
V0 = 0.65 V,
vBE(t) = V0 + Vm sinωt
f = 1 kHz
Vm = 10 mV
Vm = 5 mV
Vm = 2 mV
* As the vBE amplitude increases, the shape of iC (t) deviates from a sinusoid→ distortion.
* If vbe(t), i.e., the time-varying part of vBE , is kept small, iC varies linearlywith vBE . How small? Let us look at this in more detail.
M. B. Patil, IIT Bombay
![Page 73: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/73.jpg)
BJT: small-signal model
C
B
E
vBE
iCiB
iE vBE
iC
iB
α iE
iE
Let vBE (t) = VBE + vbe(t) (bias+signal), and iC (t) = IC + ic (t).
Assuming active mode, iC (t) = α iE (t) = α IES
[exp
(vBE (t)
VT
)− 1
].
Since the B-E junction is forward-biased, exp
(vBE (t)
VT
) 1, and we get
iC (t) = α IES exp
(vBE (t)
VT
)= α IES exp
(VBE + vbe(t)
VT
)= α IES exp
(VBE
VT
)× exp
(vbe(t)
VT
)If vbe(t) = 0, iC (t) = IC (the bias value of iC ), i.e.,
IC = α IES exp
(VBE
VT
)⇒ iC (t) = IC exp
(vbe(t)
VT
).
M. B. Patil, IIT Bombay
![Page 74: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/74.jpg)
BJT: small-signal model
C
B
E
vBE
iCiB
iE vBE
iC
iB
α iE
iE
Let vBE (t) = VBE + vbe(t) (bias+signal), and iC (t) = IC + ic (t).
Assuming active mode, iC (t) = α iE (t) = α IES
[exp
(vBE (t)
VT
)− 1
].
Since the B-E junction is forward-biased, exp
(vBE (t)
VT
) 1, and we get
iC (t) = α IES exp
(vBE (t)
VT
)= α IES exp
(VBE + vbe(t)
VT
)= α IES exp
(VBE
VT
)× exp
(vbe(t)
VT
)If vbe(t) = 0, iC (t) = IC (the bias value of iC ), i.e.,
IC = α IES exp
(VBE
VT
)⇒ iC (t) = IC exp
(vbe(t)
VT
).
M. B. Patil, IIT Bombay
![Page 75: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/75.jpg)
BJT: small-signal model
C
B
E
vBE
iCiB
iE vBE
iC
iB
α iE
iE
Let vBE (t) = VBE + vbe(t) (bias+signal), and iC (t) = IC + ic (t).
Assuming active mode, iC (t) = α iE (t) = α IES
[exp
(vBE (t)
VT
)− 1
].
Since the B-E junction is forward-biased, exp
(vBE (t)
VT
) 1, and we get
iC (t) = α IES exp
(vBE (t)
VT
)= α IES exp
(VBE + vbe(t)
VT
)= α IES exp
(VBE
VT
)× exp
(vbe(t)
VT
)
If vbe(t) = 0, iC (t) = IC (the bias value of iC ), i.e.,
IC = α IES exp
(VBE
VT
)⇒ iC (t) = IC exp
(vbe(t)
VT
).
M. B. Patil, IIT Bombay
![Page 76: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/76.jpg)
BJT: small-signal model
C
B
E
vBE
iCiB
iE vBE
iC
iB
α iE
iE
Let vBE (t) = VBE + vbe(t) (bias+signal), and iC (t) = IC + ic (t).
Assuming active mode, iC (t) = α iE (t) = α IES
[exp
(vBE (t)
VT
)− 1
].
Since the B-E junction is forward-biased, exp
(vBE (t)
VT
) 1, and we get
iC (t) = α IES exp
(vBE (t)
VT
)= α IES exp
(VBE + vbe(t)
VT
)= α IES exp
(VBE
VT
)× exp
(vbe(t)
VT
)If vbe(t) = 0, iC (t) = IC (the bias value of iC ), i.e.,
IC = α IES exp
(VBE
VT
)⇒ iC (t) = IC exp
(vbe(t)
VT
).
M. B. Patil, IIT Bombay
![Page 77: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/77.jpg)
BJT: small-signal model
C
B
E
vBE
iCiB
iE vBE
iC
iB
α iE
iE
iC (t) = IC exp
(vbe(t)
VT
)= IC
[1 + x + x2 + · · ·
], x = vbe(t)/VT .
If x is small, i.e., if the amplitude of vbe(t) is small compared to the thermal voltage VT , we get
iC (t) = IC
[1 +
vbe(t)
VT
].
We can now see that, for |vbe(t)| VT , the relationship between iC (t) and vbe(t) is linear, as wehave observed previously.
iC (t) = IC + ic (t) = IC
[1 +
vbe(t)
VT
]⇒ ic (t) =
IC
VT
vbe(t)
M. B. Patil, IIT Bombay
![Page 78: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/78.jpg)
BJT: small-signal model
C
B
E
vBE
iCiB
iE vBE
iC
iB
α iE
iE
iC (t) = IC exp
(vbe(t)
VT
)= IC
[1 + x + x2 + · · ·
], x = vbe(t)/VT .
If x is small, i.e., if the amplitude of vbe(t) is small compared to the thermal voltage VT , we get
iC (t) = IC
[1 +
vbe(t)
VT
].
We can now see that, for |vbe(t)| VT , the relationship between iC (t) and vbe(t) is linear, as wehave observed previously.
iC (t) = IC + ic (t) = IC
[1 +
vbe(t)
VT
]⇒ ic (t) =
IC
VT
vbe(t)
M. B. Patil, IIT Bombay
![Page 79: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/79.jpg)
BJT: small-signal model
C
B
E
vBE
iCiB
iE vBE
iC
iB
α iE
iE
iC (t) = IC exp
(vbe(t)
VT
)= IC
[1 + x + x2 + · · ·
], x = vbe(t)/VT .
If x is small, i.e., if the amplitude of vbe(t) is small compared to the thermal voltage VT , we get
iC (t) = IC
[1 +
vbe(t)
VT
].
We can now see that, for |vbe(t)| VT , the relationship between iC (t) and vbe(t) is linear, as wehave observed previously.
iC (t) = IC + ic (t) = IC
[1 +
vbe(t)
VT
]⇒ ic (t) =
IC
VT
vbe(t)
M. B. Patil, IIT Bombay
![Page 80: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/80.jpg)
BJT: small-signal model
C
B
E
vBE
iCiB
iE vBE
iC
iB
α iE
iE
iC (t) = IC exp
(vbe(t)
VT
)= IC
[1 + x + x2 + · · ·
], x = vbe(t)/VT .
If x is small, i.e., if the amplitude of vbe(t) is small compared to the thermal voltage VT , we get
iC (t) = IC
[1 +
vbe(t)
VT
].
We can now see that, for |vbe(t)| VT , the relationship between iC (t) and vbe(t) is linear, as wehave observed previously.
iC (t) = IC + ic (t) = IC
[1 +
vbe(t)
VT
]⇒ ic (t) =
IC
VT
vbe(t)
M. B. Patil, IIT Bombay
![Page 81: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/81.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE vBE
rπgm vbe
iC
iB
α iE
iE
The relationship, ic (t) =IC
VTvbe(t) can be represented by a VCCS, ic (t) = gm vbe(t),
where gm = IC/VT .
For the base current, we have,
iB(t) = IB + ib(t) =1
β[IC + ic (t)]
→ ib(t) =1
βic (t) =
1
βgm vbe(t)→ vbe(t) = (β/gm) ib(t).
The above relationship is represented by a resistance, rπ = β/gm, connected betweenB and E.
The resulting model is called the π-model for small-signal description of a BJT.
M. B. Patil, IIT Bombay
![Page 82: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/82.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE vBE
rπgm vbe
iC
iB
α iE
iE
The relationship, ic (t) =IC
VTvbe(t) can be represented by a VCCS, ic (t) = gm vbe(t),
where gm = IC/VT .
For the base current, we have,
iB(t) = IB + ib(t) =1
β[IC + ic (t)]
→ ib(t) =1
βic (t) =
1
βgm vbe(t)→ vbe(t) = (β/gm) ib(t).
The above relationship is represented by a resistance, rπ = β/gm, connected betweenB and E.
The resulting model is called the π-model for small-signal description of a BJT.
M. B. Patil, IIT Bombay
![Page 83: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/83.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE vBE
rπgm vbe
iC
iB
α iE
iE
The relationship, ic (t) =IC
VTvbe(t) can be represented by a VCCS, ic (t) = gm vbe(t),
where gm = IC/VT .
For the base current, we have,
iB(t) = IB + ib(t) =1
β[IC + ic (t)]
→ ib(t) =1
βic (t) =
1
βgm vbe(t)→ vbe(t) = (β/gm) ib(t).
The above relationship is represented by a resistance, rπ = β/gm, connected betweenB and E.
The resulting model is called the π-model for small-signal description of a BJT.
M. B. Patil, IIT Bombay
![Page 84: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/84.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE vBE
rπgm vbe
iC
iB
α iE
iE
The relationship, ic (t) =IC
VTvbe(t) can be represented by a VCCS, ic (t) = gm vbe(t),
where gm = IC/VT .
For the base current, we have,
iB(t) = IB + ib(t) =1
β[IC + ic (t)]
→ ib(t) =1
βic (t) =
1
βgm vbe(t)→ vbe(t) = (β/gm) ib(t).
The above relationship is represented by a resistance, rπ = β/gm, connected betweenB and E.
The resulting model is called the π-model for small-signal description of a BJT.
M. B. Patil, IIT Bombay
![Page 85: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/85.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE vBE
rπgm vbe
iC
iB
α iE
iE
* The transconductance gm depends on the biasing of the BJT, sincegm = IC/VT . For IC = 1 mA, VT ≈ 25 mV (room temperature),gm = 1 mA/25 mV = 40 mf.
* rπ also depends on IC , since rπ = β/gm = β VT /IC . For IC = 1 mA,VT ≈ 25 mV , β = 100, rπ = 2.5 kΩ.
* Note that the small-signal model is valid only for small vbe (compared to VT ), aswe have seen earlier.
M. B. Patil, IIT Bombay
![Page 86: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/86.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE vBE
rπgm vbe
iC
iB
α iE
iE
* The transconductance gm depends on the biasing of the BJT, sincegm = IC/VT . For IC = 1 mA, VT ≈ 25 mV (room temperature),gm = 1 mA/25 mV = 40 mf.
* rπ also depends on IC , since rπ = β/gm = β VT /IC . For IC = 1 mA,VT ≈ 25 mV , β = 100, rπ = 2.5 kΩ.
* Note that the small-signal model is valid only for small vbe (compared to VT ), aswe have seen earlier.
M. B. Patil, IIT Bombay
![Page 87: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/87.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE vBE
rπgm vbe
iC
iB
α iE
iE
* The transconductance gm depends on the biasing of the BJT, sincegm = IC/VT . For IC = 1 mA, VT ≈ 25 mV (room temperature),gm = 1 mA/25 mV = 40 mf.
* rπ also depends on IC , since rπ = β/gm = β VT /IC . For IC = 1 mA,VT ≈ 25 mV , β = 100, rπ = 2.5 kΩ.
* Note that the small-signal model is valid only for small vbe (compared to VT ), aswe have seen earlier.
M. B. Patil, IIT Bombay
![Page 88: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/88.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE
rπgm vbe
0
1
0 1 2 3 4 5
I C(m
A)
VCE (V)
CB
E
rπgm vbe
ro
* In the above model, note that ic is independent of vce .
* In practice, ic does depend on vce because of the Early effect, anddIC
dVCE≈ constant = 1/ro , where ro is called the output resistance.
* A more accurate model includes ro as well.
M. B. Patil, IIT Bombay
![Page 89: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/89.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE
rπgm vbe
0
1
0 1 2 3 4 5I C
(mA)
VCE (V)
CB
E
rπgm vbe
ro
* In the above model, note that ic is independent of vce .
* In practice, ic does depend on vce because of the Early effect, anddIC
dVCE≈ constant = 1/ro , where ro is called the output resistance.
* A more accurate model includes ro as well.
M. B. Patil, IIT Bombay
![Page 90: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/90.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE
rπgm vbe
0
1
0 1 2 3 4 5I C
(mA)
VCE (V)
CB
E
rπgm vbe
ro
* In the above model, note that ic is independent of vce .
* In practice, ic does depend on vce because of the Early effect, anddIC
dVCE≈ constant = 1/ro , where ro is called the output resistance.
* A more accurate model includes ro as well.
M. B. Patil, IIT Bombay
![Page 91: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/91.jpg)
BJT: small-signal model
C
B
E
B C
E
vBE
iCiB
iE
rπgm vbe
0
1
0 1 2 3 4 5I C
(mA)
VCE (V)
CB
E
rπgm vbe
ro
* In the above model, note that ic is independent of vce .
* In practice, ic does depend on vce because of the Early effect, anddIC
dVCE≈ constant = 1/ro , where ro is called the output resistance.
* A more accurate model includes ro as well.
M. B. Patil, IIT Bombay
![Page 92: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/92.jpg)
BJT: small-signal model
C
B
E
CB
E
Cπ
iC
iE
iB
rb
rπgm vbe
ro
Cµ
* A few other components are required to make the small-signal model complete:rb: base spreading resistanceCπ : base charging capacitance + B-E junction capacitanceCµ: B-C junction capacitance
* The capacitances are typically in the pF range. At low frequencies, 1/ωC islarge, and the capacitances can be replaced by open circuits.
* Note that the small-signal models we have described are valid in the activeregion only.
M. B. Patil, IIT Bombay
![Page 93: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/93.jpg)
BJT: small-signal model
C
B
E
CB
E
Cπ
iC
iE
iB
rb
rπgm vbe
ro
Cµ
* A few other components are required to make the small-signal model complete:rb: base spreading resistanceCπ : base charging capacitance + B-E junction capacitanceCµ: B-C junction capacitance
* The capacitances are typically in the pF range. At low frequencies, 1/ωC islarge, and the capacitances can be replaced by open circuits.
* Note that the small-signal models we have described are valid in the activeregion only.
M. B. Patil, IIT Bombay
![Page 94: EE101: BJT circuits (Part 1) - ee.iitb.ac.insequel/ee101/ee101_bjt_2.pdf · EE101: BJT circuits (Part 1) M. B. Patil ... BJT ampli er: basic operation E C C ... BJT ampli er biasing:](https://reader034.vdocuments.mx/reader034/viewer/2022042503/5ac10cd37f8b9ae45b8ce961/html5/thumbnails/94.jpg)
BJT: small-signal model
C
B
E
CB
E
Cπ
iC
iE
iB
rb
rπgm vbe
ro
Cµ
* A few other components are required to make the small-signal model complete:rb: base spreading resistanceCπ : base charging capacitance + B-E junction capacitanceCµ: B-C junction capacitance
* The capacitances are typically in the pF range. At low frequencies, 1/ωC islarge, and the capacitances can be replaced by open circuits.
* Note that the small-signal models we have described are valid in the activeregion only.
M. B. Patil, IIT Bombay