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Transcript of dc biasing
DC Biasing of BJTs
Outline:
Selection of operating point
Chapter 4. DC Biasing of BJTs
Various bias circuitsFixed bias
Voltage-divider biasEmitter bias
DC Biasing of BJTs
The dc and ac response are necessary to the analysis of a transistor amplifier.
Introduction
The amplified output ac power is the result of a transfer of energy from the applied dc supplies.
This is the processing of transferring a current from a low to high resistance:
transfer + resistor transistor
DC Biasing of BJTs
The superposition theorem is applicable and the the investigation of the dc conditions can be totally separated from the ac response.
However, while designing, the selection of parameters for the required dc level will affect the ac response and vice versa.
So the first step of designing is to chose a suitable operating point.
DC Biasing of BJTs
Some important basic relationships in the analysis:
IE = (β+1)IB IC
Then a network must be constructed that will establish the desired operating point.
VBE = 0.7V
IC = βIB
DC Biasing of BJTs
Figure: Transistor amplification circuit
DC Biasing of BJTs
Operating PointThe operating point is a fixed point on the characteristics and is also called quiescent point, denoted by Q-point.
The term biasing means the application of dcvoltages used to setup a fixed level of current and voltage.
This leads to an operating point in the region of characteristics employed for amplification.
DC Biasing of BJTs
The figure shows a general output device characteristic.The maximum ratings are indicated:
The maximum collector current ICmax
The maximum collector-to-emitter voltage VCEmax
The maximum power constraint defined by the curve PCmax
DC Biasing of BJTs
Or, the lifetime of device would be shortened or the device would be damaged.
The biasing circuit can be designed to set the device operation at any point within the active region.
The cutoff region, defined by IB 0A
The saturation region, defined by VCE VCE sat
DC Biasing of BJTs
No bias:
The chosen Q-point often depends on the intended use of the circuit. Some basic ideas about the operating point:
The device would initially be completely off and zero current through the device and zero voltage across it.
DC Biasing of BJTs
Small-voltage biasing:
This leads to that only part of the input signal is applied to the circuit. So this point is not suitable.
This point would allow some positive and negative variation of the output signal.
But the peak-to-peak value would be limited by the proximity of VCE = 0 and IC = 0.
DC Biasing of BJTs
Large-voltage biasing:
Operating at this point raises some concern about the nonlinearities introduced by rapid changing spacing between IB curves. It is preferable to operate where the gain of the device is fairly constant to ensure that the amplification over the entire swing of input signal is the same.
The operating point is shown in the figure.
DC Biasing of BJTs
Acceptable biasing:
Operating point is near the maximum voltage and power level.
The output voltage swing in the positive direction is thus limited.
If a signal is applied to the circuit, the device will vary in current and voltage from the operating point.
DC Biasing of BJTs
Then the device react to both the positive and negative excursions of the input signal.
The voltage and current will vary but not enough to drive the device into cutoff or saturation region.
It is also in the region of more linear spacing and therefore more linear operation.
DC Biasing of BJTs
Therefore, this point is the optimal operating point in terms of linear gain and largest possible voltage and current swing.
This is usually the desired condition for small-signal amplifier but not for power amplifier.
The latter will be covered in chapter 11.
DC Biasing of BJTs
Figure: Operating points
DC Biasing of BJTs
For the BJT to be biased in its linear or active operating region, the following must be true:
The b-c junction must be reversed-biased with reversed-bias voltage being any value within the maximum limits of the device.
The b-e junction must be forward-biased with a resulting forward-bias voltage of about 0.6 to 0.7 V.
DC Biasing of BJTs
Fixed-Bias CircuitThe fixed-bias circuit is the simplest transistor dc bias configuration, as shown in the figure (npn transistor).
Even thought npn transistor is employed, the analysis is also valid to pnp transistor if current directions and voltage polarities are changed.
DC Biasing of BJTs
For the dc analysis, the network can be isolated from the ac levels by replacing each capacitor with an open circuit.
Also the dc supply VCC can be separated into two supplies to permit a separation of input and output circuits.
All these are for analysis purpose only.
DC Biasing of BJTs
Consider first the base-emitter circuit loop.
Base-Emitter Loop
It’s obvious that:
So, we get the equation for current IB :
VCC = IB RB + VBE
B
BECCB R
VVI
DC Biasing of BJTs
The supply voltage VCC is a constant, which is chosen in advance. Also the b-e voltage VBE is a constant, which is approximately equal to 0.7V while in forward-biasing.
So the selection of a base resistor RB sets the level of base current for the operating point.
DC Biasing of BJTs
The collector-emitter loop is shown in the figure.
Collector-Emitter Loop
The magnitude of the collector current is related directly to IB through
Note that:IC = β IB
IB is controlled by the level of RB.
IC is related to IB by a constant β.
DC Biasing of BJTs
The magnitude of IC is not a function of the resistance RC .
Changing RC to any level will not affect IC or IB as long as the device remains in the active region.
However, RC will determine the magnitude of VCE , which will affect the position of Q-point.
DC Biasing of BJTs
The magnitude of VCE is obtained by
This states that the voltage across collector-emitter of a transistor is the supply voltage less the drop across RC.
VCC RB IB IC
VCE = VCC - IC RC
VCC RC , IC VCE
Q-point
DC Biasing of BJTs
Figure: Fixed-Bias Circuit
DC Biasing of BJTs
Example 4.1:
Determine the following for the fixed-bias configuration. 1. IBQ , ICQ and VCEQ.
2. VB , VC and VBC .
Solution:
1.B
BECCBQ R
VVI
DC Biasing of BJTs
BQCQ II
A08.4750 mA35.2
CCCCCEQ RIVV
)2.2()35.2(12 kmAV
V83.6
k
VV240
7.012 A08.47
DC Biasing of BJTs
2. VB
VC = VCE = 6.83V
VBC = VB - VC
= 0.7V – 6.83V = -6.13V
The negative voltage means that the junction is reverse-biased, as it should be for linear amplification.
= VBE = 0.7V
DC Biasing of BJTs
Figure: Example of fixed-bias circuit
50
DC Biasing of BJTs
Load-Line AnalysisNow we investigate how the network parameters define the possible range of Q-points and how the actual Q-point is determined.The network is shown in the figure.An output equation relates the variables ICand VCE in the following manner:
VCE =VCC - IC RC
DC Biasing of BJTs
On the other hand, the output characteristics of the transistor also relate the same two variables IC and VCE , as shown in the figure.
It is obvious that the relationship between variables IC and VCE is a linear one, i.e., a straight line.
So the solution of Q-point should satisfy both of the relationships simultaneously.
DC Biasing of BJTs
The output characteristics is ready here.
Then, for straight line, two points are sufficient to determine it. For the first point:
CCVICCCCCE VRIVVC
0
So the first point is (VCC ,0).For the other point :
C
CC
VVC
CECCC R
VR
VVICE
0
DC Biasing of BJTs
From the two points, we get the straight line.
The straight line is called a load line because the intersection on the vertical axis is defined by the applied load resistor RC.
So the second point is (0, VCC /R ).
By solving for the resulting level of IB, we can establish the actual Q-point.
DC Biasing of BJTs
If the level of IB is changed by varying the value of RB, the Q-point moves up or down the load line as shown in the figure.
If RC changed while VCC and IB are held, the load line will shift as shown in the figure.
If RC is fixed and VCC varied, the load line will shift as shown in the figure.
DC Biasing of BJTs
Figure: Biasing of a network
DC Biasing of BJTs
IB
Figure: Output characteristics & load-line
VCC/RC
VCC
Load-line
Q-point
DC Biasing of BJTs
IB increasing
Figure: Q-point moves as changing of RB .
VCC/RC
VCC
DC Biasing of BJTs
Figure: Load line shifts as changing of RC .VCC
RC1< RC2 <RC3
VCC/RC1
VCC/RC2
VCC/RC3
Constant IB
DC Biasing of BJTs
Figure: Load line shifts as changing of VCC .
VCC3< VCC2 <VCC1
VCC2
VCC2/RC
Constant IB
VCC1/RC
VCC1
VCC3/RC
VCC3
DC Biasing of BJTs
Example 4.3As shown in the figure, given the load line and the defined Q-point, determine the required values of VCC , RC and RBfor a fixed-bias configuration.Solution:From the figure, we can get that:
VCE = VCC = 20V at IC = 0 mA
DC Biasing of BJTs
So,
kmAI
VRVVC
CCC
CE
210
20
0
Also, we know that B
BECCB R
VVI
VVC
CCC
CER
VI0
And we know that
DC Biasing of BJTs
From the figure, we know that IB = 25μA.
B
BECCB I
VVR
So,
Briefly, we obtain that VCC = 20V, RC = 2kΩ and RB =772kΩ.
k772A
VV25
7.020
DC Biasing of BJTs
Figure: Output characteristics of example
VCC/RC
VCC
Q-point
DC Biasing of BJTs
Emitter Bias
In the dc bias network, an emitter resistor is added.
The analysis will be performed by examining b-e loop and c-e loop.
This will improve the stability level over that of the fixed-bias configuration.
DC Biasing of BJTs
Base-Emitter LoopThe base-emitter loop is shown in the figure.
Also, it is obvious that
VCC = IB RB +VBE + IE RE
We know that:
IE = (β+1) IB
Replacing IE with IB , we get
DC Biasing of BJTs
For the base-emitter circuit, the net voltage is VCC - VBE.
EB
BECCB RR
VVI)1(
The resistance level are RB + (β+1) RE .
This means that:
The resistor RE is reflected back to the input base circuit by a factor of (β+1) .
DC Biasing of BJTs
Collector-Emitter Loop
The c-e loop is shown in the figure.
Also, it is obvious that
VCC = IC RC +VCE + IE RE
We know that:
IE IC
Replacing IE with IC , we get
DC Biasing of BJTs
VE = IERE
VC = VCC - ICRC
Also, we get
VCE = VCC - IC (RC +RE )
and VB = VBE + VE
DC Biasing of BJTs
Figure: BJT Bias circuit with emitter resistor
DC Biasing of BJTs
Example 4.4As shown in the figure, given the parameters in the circuit, determine:
Solution:
1. IB , IC and VCE .
2. VC , VE , VB and VBC .
1. we know that:EB
BECCB RR
VVI)1(
DC Biasing of BJTs
BC II
So,
)1)(150(4307.020
kk
VVIB
kV
4813.19 A1.40
And)1.40()50( A mA01.2
Also, we know that VCE = VCC - IC (RC +RE ).
VCE = 20V – (2.01mA) (2kΩ +1kΩ )
= 20V –6.03V = 13.97V
DC Biasing of BJTs
2. VC = VCC - IC RC
= 20V – (2.01mA) (2kΩ) = 15.98V
VE = VC - VCE
= 15.98V - 13.97V = 2.01VOr
VE = IE RE IC RE
= (2.01mA) (1kΩ) = 2.01VVB = VBE + VE= 0.7V + 2.01V = 2.71V
DC Biasing of BJTs
VBC = VB - VC
= 2.71V - 15.98V = -13.27V
This means that b-c junction is reverse-biased, which is required by active region .
With a resistor connected to emitter, Q-point is more robust to variation of β. This is an improvement of the stability of the network. Example 4.5 gives a clear explanation.
DC Biasing of BJTs
Figure: Bias circuit of example 4.4
DC Biasing of BJTs
Load-Line AnalysisThe load-line analysis of emitter-bias network is only slightly different from that of fixed-bias configuration.
The level of IB determined by:
and denoted by IBQ .
EB
BECCB RR
VVI)1(
DC Biasing of BJTs
The collector-emitter loop equation that defines the load line is
VCE = VCC - IC (RC +RE ).
CCVIECCCCCE VRRIVVC
0
)(
EC
CC
VVEC
CECCC RR
VRRVVI
CE
0
Two intersections of the load line are obtained by
DC Biasing of BJTs
Figure: Load line for emitter bias configuration
VCC
EC
CCC RR
VI
IBQQ-point
DC Biasing of BJTs
Voltage-divider BiasAs shown in the figure, it is the voltage-divider bias configuration.
The advantage of it is that the variation of β due to temperature change will not lead to a dramatic change of Q-point.
We investigate this in exact and approximateapproaches.
DC Biasing of BJTs
Exact AnalysisFor the dc analysis, the b-e loop is shown in the figure.
RIN = R1 || R2
We use Thevenin equivalent circuit to simplify the network by introducing VIN and RIN .
where CCRIN VRR
RVV21
22
DC Biasing of BJTs
Then, in the b-e loop, we get
So, substituting IE = (β+1) IB , and solving for IB yields
VIN = IB RIN +VBE + IE RE
EIN
BEINB RR
VVI)1(
The resistor RE is reflected back to the input base circuit by a factor of (β+1) , the same as that in emitter-bias circuit.
DC Biasing of BJTs
Once IB is known, the remaining work is to get IC and VCE , in the same manner as in emitter-bias circuit.
The remaining equation for VE , VC and VBare also the same as obtained for the emitter-bias network.
IC = β IB
VCE = VCC - IC (RC +RE )
DC Biasing of BJTs
Figure: Voltage-divider bias configuration
DC Biasing of BJTs
Approximate AnalysisThe b-e loop of the voltage-divider can be represented as the network shown in the figure.The Ri is the equivalent resistance between base and ground for the transistor with an emitter resistor RE.And this reflected resistance
Ri = (β+1) RE
DC Biasing of BJTs
If Ri is much larger than R2, the current IBwill be much smaller than I2.
So the voltage across R2, which is actually VB, can be determined by
And I2 will be approximately equal to I1.
Or IB will be approximately equal to zero.
CCB VRR
RV21
2
DC Biasing of BJTs
The condition that should be satisfied to use the approximate approach is
Once VB is determined, then
β RE 10 R2
VE = VB - VBE
IE = VE / RE
ICQ IE
DC Biasing of BJTs
The level of VCE is determined as before,
Now, Q-point is determined.
VCEQ = VCC - ICQ (RC +RE )
Note that during the above derivations, β is not involved and IB is not calculated.
The Q-point (as determined by ICQ and VCE) is therefore independent of the value β.
DC Biasing of BJTs
Figure: Approximate method for Voltage-divider bias
DC Biasing of BJTs
Example 4.7 & 4.8Shown in the figure, it is the voltage-divider bias network. By exact & approximate methods, determine ICQ and VCEQ.
1. Solution of exact method:First, introduce equivalent circuit to left side of b-e loop.The equivalent power supply VIN is obtained by
DC Biasing of BJTs
RIN = R1 || R2
CCIN VRR
RV21
2
V
kkk 22
9.3399.3
V2
The equivalent resistance RIN is obtained by
kkkk
9.339)9.3()39(
k55.3
Also, from the equation discussed before, we get
EIN
BEINB RR
VVI)1(
DC Biasing of BJTs
)5.1)(1140(55.37.02
kk
VV A05.6
Then, we get
ICQ = β IBQ
VCE = VCC - IC (RC +RE )
A05.6140 mA85.0
)5.110)(85.0(22 kkmAV
V22.12
DC Biasing of BJTs
Figure: Example 4.7
DC Biasing of BJTs
2. Solution of approximate method:First, test the condition for approximation.
β RE 10 R2
(140) (1.5kΩ) 10 (3.9kΩ)
210kΩ 39kΩ (satisfied)Then, use the equation to get VB.
CCB VRR
RV21
2
V
kkk 22
9.3399.3
V2
DC Biasing of BJTs
Then
VE = VB - VBE = 2V – 0.7V = 1.3V
ICQ IE = VE / RE = 1.3V / 1.5kΩ
= 0.867mA
VCEQ = VCC - ICQ(RC +RE )
)5.110)(867.0(22 kkmAV
V03.12
DC Biasing of BJTs
From the results of the two different solutions, it’s obvious that ICQ and VCEQ are certainly close and one can be considered as accurate as the other.
The larger the level of Ri compared to R2, the closer is the approximate to the exact solution.
DC Biasing of BJTs
Figure: Example 4.8
DC Biasing of BJTs
Summary of Chapter 4
Calculation of operating point
Investigation of bias circuitsFixed biasEmitter bias
Load-line analysis
Voltage-divider biasExact & approximate methods