ENGI 242/ELEC 222
Updated 23 February 2005
Voltage Divider Bias
ENGI 242
ELEC 222
BJT Biasing 3
For the Voltage Divider Bias Configurations
• Draw Equivalent Input circuit
• Draw Equivalent Output circuit
• Write necessary KVL and KCL Equations
• Determine the Quiescent Operating Point
– Graphical Solution using Load lines
– Computational Analysis
• Design and test design using a computer simulation
23 February 2005
Voltage Divider Bias
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Voltage-divider bias configuration
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Voltage Divider Input Circuit Approximate Analysis
This method is valid only if R2 ≤ .1 β RE
Under these conditions RE does not significantly load R2 and it may be ignored:
IB << I1 and I2 and I1 ≅ I2 Therefore:
⎛ R2 ⎞
VB = VCC ⎜
⎟
⎝ R1+R2 ⎠
We may apply KVL to the input, which gives us:
-VB + VBE + IE RE = 0
Solving for IE we get:
IE =
VB - VBE
RE
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Voltage Divider Bias
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Input Circuit Exact Analysis
This method is always valid must be used when R2 > .1 β RE
Perform Thevenin’s Theorem
Open the base lead of the transistor, and the Voltage Divider bias circuit is:
⎛ R2 ⎞
VTH = VCC ⎜
⎟
⎝ R1+R2 ⎠
Calculate RTH
We may apply KVL to the input, which gives us:
-VTH + IB RTH + VBE + IE RE = 0
Since IE = (β + 1) IB
RTH
+ VBE + IE RE = 0
β+1
Solving for IE we obtain:
-VTH + IE
IE =
VTH - VBE
RTH
+ RE
β+1
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Redrawing the input circuit for the network
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Voltage Divider Bias
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Determining VTH
⎛ R2 ⎞
VTH = VCC ⎜
⎟
⎝ R1 + R2 ⎠
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Determining RTH
RTH =
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Voltage Divider Bias
R1 R2
R1 + R2
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The Thévenin Equivalent Circuit
Note that VE = VB – VBE and IE = (β + 1)IB
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Input Circuit Exact Analysis
We may apply KVL to the input, which gives us:
-VTH + IB RTH + VBE + IE RE = 0
Since IE = (β + 1) IB
RTH
+ VBE + IE RE = 0
β+1
Solving for IE we obtain:
-VTH + IE
IE =
VTH - VBE
RTH
+ RE
β+1
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Voltage Divider Bias
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Collector-Emitter Loop
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Collector-Emitter (Output) Loop
Applying Kirchoff’s voltage law:
- VCC + IC RC + VCE + IE RE = 0
Assuming that IE ≅ IC and solving for VCE: IC = VCC - VCE
RC + RE
Solve for VE:
V E = IE R E
Solve for VC:
VC = VCC - IC RC
or
VC = VCE + IE RE
Solve for VB:
23 February 2005
Voltage Divider Bias
VB = VCC - IB RB
or
VB = VBE + IE RE
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Voltage Divider Bias Example 1
VCC = 22V
R1 = 39kΩ
R2 = 3.9kΩ
RC = 10kΩ
RE = 1.5kΩ
β = 140
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Voltage Divider Bias Example 2
VCC = 18V
R1 = 39kΩ
R2 = 8.2kΩ
RC = 3.3kΩ
RE = 1kΩ
β = 120
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Voltage Divider Bias
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Voltage Divider Bias Example 3
VCC = 16V
R1 = 62kΩ
R2 = 9.1kΩ
RC = 3.9kΩ
RE = .68kΩ
β = 80
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Design of CE Amplifier with Voltage Divider Bias
1.
2.
3.
4.
5.
6.
7.
8.
Select a value for VCC
Determine the value of β from spec sheet or family of curves
Select a value for ICQ
Let VCE = ½ VCC (typical operation, 0.4 VCC ≤ VC ≤ 0.6 VCC )
Let VE = 0.1 VCC (for good operation, 0.1 VCC ≤ VE ≤ 0.2 VCC )
Calculate RE and RC
Let R2 ≤ 0.1 β RE (for this calculation, use low value for β)
Calculate R1
⎛ VCC - VB ⎞
R1 = R2 ⎜
⎟
VB
⎝
⎠
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Voltage Divider Bias
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CE Amplifier Design
• Design a Common Emitter Amplifier with Voltage Divider
Bias for the following parameters:
VCC = 24V
IC = 5mA
VE = .1VCC
VC = .55VCC
β = 135
Voltage Divider Bias
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CE Amplifier Design
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CE Amplifier Design Voltage Divider Bias
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Voltage Divider Bias
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Collector Feedback Bias
ENGI 242
ELEC 222
BJT Biasing 4
For the Collector Feedback Bias Configuration:
• Draw Equivalent Input circuit
• Draw Equivalent Output circuit
• Write necessary KVL and KCL Equations
• Determine the Quiescent Operating Point
– Graphical Solution using Loadlines
– Computational Analysis
• Design and test design using a computer simulation
23 February 2005
Voltage Divider Bias
ENGI 242/ELEC 222
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11
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Updated 23 February 2005
DC Bias with Collector (Voltage) Feedback
Another way to improve the stability of a bias circuit is to add a feedback path
from collector to base
In this bias circuit the Q-point is only slightly dependent on the transistor β
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Base – Emitter Loop Solve for IB
Applying Kirchoff’s voltage law: -VCC + IC′RC + IBRB + VBE + IERE = 0
Note: IC′ = IE = IC + IB
Since IE = (β + 1) IB then: -VCC + (β + 1)IB RC + IBRB + VBE (β + 1)IBRE = 0
Simplifying and solving for IB: IB =
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Voltage Divider Bias
VCC - VBE
RB + (β + 1) (RC + RE)
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Base – Emitter Loop Solve for IE
Applying Kirchoff’s voltage law: -VCC + IERC + IBRB + VBE + IERE = 0
Since IE = (β + 1) IB then:
Simplifying and solving for IE: IE =
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RB
+ VBE + IERE = 0
(β + 1)
VCC - VBE
-VCC + IE RC + IE
RB
+ (RC + RE)
(β + 1)
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Collector Emitter Loop
Applying Kirchoff’s voltage law:
Since IC′ = IE and IE = (β + 1) IB:
Solving for VCE:
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Voltage Divider Bias
IE RE + VCE + IC′RC – VCC = 0
IE(RC + RE) + VCE – VCC =0
VCE = VCC – IE (RE + RC)
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Network Example
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Network Example
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Voltage Divider Bias
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Collector feedback with RE = 0Ω
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Design of CE Amplifier with Collector Feedback Bias
1.
2.
3.
4.
5.
6.
Select a value for VCC
Determine the value of β from spec sheet or family of curves
Select a value for IEQ
Let VCE = ½ VCC (typical operation, 0.4 VCC ≤ VC ≤ 0.6 VCC )
Let VE = 0.1 VCC (for good operation, 0.1 VCC ≤ VE ≤ 0.2 VCC )
Calculate RE, RC and RB
.1VCC
IE
VCC - VCQ
VCC - .6VCC
.4VCC
RC =
=
; RC =
IE
IE
IE
VCC - IERC - VBE - IERE
VCC - IE (RC + RE) - 0.7V
RB =
;
RB =
IE
IE
β +1
β +1
VE = .1VCC
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Voltage Divider Bias
RE =
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Common Emitter Bias
with Dual Supplies
Voltage Divider Bias with Dual Power Supply
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Voltage Divider Bias
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Voltage Divider Bias with Dual Power Supply
Input Circuit
Find VTH and RTH
⎛ R2 ⎞
VTH1 = VCC ⎜
⎟
⎝ R1 + R2 ⎠
(Note VEE is negative)
⎛ R1 ⎞
VTH2 = - VEE ⎜
⎟
⎝ R1 + R2 ⎠
VTH = VTH1 + VTH2
⎛ R2 ⎞
⎛ R1 ⎞
VTH = VCC ⎜
⎟ - VEE ⎜
⎟
⎝ R1 + R2 ⎠
⎝ R1 + R2 ⎠
R1 R2
RTH =
R1 + R2
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Voltage Divider Bias with Dual Power Supply
Output Circuit
-VCC + ICRC + VCE + IERE - VEE = 0
If we assume IE ≅ IC (when β > 100)
VCC + VEE - VCE
RC + RE
If we use the exact solution IC = αIE
IC =
VCC + VEE - VCE
RE
RC +
α
β
where α =
β +1
IC =
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Voltage Divider Bias
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Voltage Divider Bias with Dual Power Supply
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PSpice Simulation
Voltage Divider Bias
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PSpice Bias Point Simulation
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PSpice Simulation for DC Bias
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Voltage Divider Bias
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PSpice Simulation for DC Sweep
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PSpice Simulation for DC Sweep
The response of VC demonstrates rises rapidly towards
the Q Point and then increases gradually towards a
maximum value
The response of VCE demonstrates that it
reaches a peak value near the Q point and
then decreases
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Voltage Divider Bias
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PSpice Simulation for AC Sweep
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PSpice Simulation for AC Sweep
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Voltage Divider Bias
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