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A Comparison of VariousBipolar Transistor Biasing CircuitsApplication Note 1293
IntroductionThe bipolar junction transistor(BJT) is quite often used as a lownoise amplifier in cellular, PCS,and pager applications due to itslow cost. With a minimal numberof external matching networks,the BJT can quite often producean LNA with RF performanceconsiderably better than anMMIC. Of equal importance is theDC performance. Although thedevices RF performance may bequite closely controlled, the
variation in device dc parameterscan be quite significant due tonormal process variations. It isnot unusual to find a 2 or 3 to 1ratio in device h FE . Variation inhFE from device to device willgenerally not show up as a
difference in RF performance. Inother words, two devices withwidely different h FE s can havesimilar RF performance as long asthe devices are biased at the same
VCE and I C. This is the primary purpose of the bias network, i.e.,to keep V CE and I C constant as thedc parameters vary from device todevice.
Quite often the bias circuitry isoverlooked due to its apparent
simplicity. With a poorly designedfixed bias circuit, the variation inIC from lot to lot can have thesame maximum to minimum ratioas the h FE variation from lot tolot. With no compensation, as h FEis doubled, I C will double. It is thetask of the dc bias circuit tomaximize the circuits tolerance
to h FE variations. In addition,transistor parameters can varyover temperature causing a driftin I C at temperature. The low
power supply voltages typicallyavailable for handheldapplications also make it moredifficult to design a temperaturestable bias circuit.
One solution to the biasingdilemma is the use of activebiasing. Active biasing oftenmakes use of an IC or even just aPNP transistor and a variety of resistors, which effectively sets
VCE and I C regardless of variations in device h FE . Althoughthe technique of active biasingwould be the best choice for the
control of device to device variability and over temperature variations, the cost associatedwith such an arrangement isusually prohibitive.
Other biasing options include various forms of passive biasing. Various passive biasing circuitswill be discussed along with theiradvantages and disadvantages.
Various BJT Passive Bias Circuits
Passive biasing schemes usuallyconsist of two to five resistors
properly arranged about thetransistor. Various passive biasingschemes are shown in Figure 1.The simplest form of passivebiasing is shown as Circuit #1 inFigure 1. The collector current I Cis simply h FE times the base
RCRB
VBB VCC
Figure 1A. Circuit #1 Non-stabilized BJT Bias Network
current I B. The base current isdetermined by the value of R B.The collector voltage V CE isdetermined by subtracting the
voltage drop across resistor R C
from the power supply voltage VCC . As the collector current is varied, the V CE will change basedon the voltage drop across R C.
Varying h FE will cause I C to varyin a fairly direct manner. Forconstant V CC and constant V BE ,IC will vary in direct proportionto h FE . As an example, as h FE isdoubled, collector current, I C,will also double. Bias circuit #1
provides no compensation for variation in device h FE .
Bias circuit #2 provides voltagefeedback to the base currentsource resistor R B. The basecurrent source is fed from the
voltage V CE as opposed to thesupply voltage V CC . The value of the base bias resistor R B iscalculated based upon nominal
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RCRBVCC
Figure 1B. Circui t #2Voltage Feedback BJT Bias Network
RCRB1
RB2
RB
VCC
Figure 1C. Circuit #3Voltage Feedback with Current Source BJTBias Network
RCRB1
RB2
VCC
Figure 1D. Circuit #4Voltage Feedback with Voltage Source BJT Bias Network
Figure 1E. Circuit #5Emitter Feedback BJT Bias Network
device V BE and the desired V CE .Collector resistor R C has both I Cand I B flowing through it. Theoperation of this circuit is bestexplained as follows. An increasein h FE will tend to cause I C toincrease. An increase in I C causesthe voltage drop across resistorRC to increase. The increase in
voltage across R C causes V CE todecrease. The decrease in V CEcauses I B to decrease because the
potential difference across base
bias resistor R B has decreased.This topology provides a basicform of negative feedback whichtends to reduce the amount thatthe collector current increases ashFE is increased.
Bias circuit #3 has been quiteoften written up in past literaturebut predominately when very high
VCC (>15 V) and V CE (>12 V) has
been used[1]
. The voltage dividernetwork consisting of R B1 andRB2 provides a voltage dividerfrom which resistor R B isconnected. Resistor R B thendetermines the base current. I Btimes h FE provides I C. The voltagedrop across R C is determined bythe collector current I C, the biascurrent I B, and the currentconsumed by the voltage dividerconsisting of R B1 and R B2 . Thiscircuit provides similar voltage
feedback to bias circuit #2.
Bias circuit #4 is similar to biascircuit #3 with the exception thatthe series current source resistorRB is omitted. This circuit is seenquite often in bipolar poweramplifier design with resistor R B2replaced by a series silicon powerdiode providing temperaturecompensation for the bipolar
device. The current flowingthrough resistor R B1 is shared byboth resistor R B2 and the emitterbase junction V BE . The greater thecurrent through resistor R B2 , thegreater the regulation of theemitter base voltage V BE .
Bias circuit #5 is the customarytextbook circuit for biasing BJTs.
A resistor is used in series withthe device emitter lead to provide
voltage feedback. This circuit
ultimately provides the bestcontrol of h FE variations fromdevice to device and overtemperature. The onlydisadvantage of this circuit is thatthe emitter resistor must be
properly bypassed for RF. Thetypical bypass capacitor quiteoften has internal lead inductancewhich can create unwantedregenerative feedback. The
RB1
RB2
VCC
RE
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feedback quite often createsdevice instability. Despite the
problems associated with usingthe emitter resistor technique, thisbiasing scheme generally providesthe best control on h FE and over
temperature variations.
The sections that follow beginwith a discussion of the BJTmodel and its temperaturedependent variables. From thebasic model, various equationsare developed to predict thedevice s behavior over h FE andtemperature variations. Thisarticle is an update to the originalarticle written by Kenneth Richterof Hewlett-Packard [2] and
Hewlett-Packard ApplicationNote 944-1 [3] .
BJT ModelingThe BJT is modeled as twocurrent sources as shown inFigure 2. The primary currentsource is h FE IB. In parallel is asecondary current source I CBO(1+ h FE ) which describes theleakage current flowing through areverse biased PN junction. I CBOis typically 1x10 -7 A @ 25 C for an
Agilent Technologies HBFP-0405transistor. V ' BE is the internalbase emitter voltage with h ierepresenting the equivalentHybrid PI input impedance of thetransistor. h ie is also equal tohFE / IC where = 40 @ +25 C.
VBE will be defined as measuredbetween the base and emitterleads of the transistor. It isequivalent to V' BE + I B h ie . VBE isapproximately 0.78 V @ 25 C forthe HBFP-0405 transistor.
The device parameters that havethe greatest change astemperature is varied consist of hFE , V' BE , and I CBO . Thesetemperature dependent variableshave characteristics which are
process dependent and fairly wellunderstood. h FE typically
Figure 2. Gummel Poon model of BJT with Voltage Feedback and Constant Base CurrentSource Network
increases with temperature at therate of 0.5% / C. V' BE has atypical negative temperaturecoefficient of -2 mV / C. Thisindicates that V BE decreases 2 mVfor every degree increase intemperature. I CBO typicallydoubles for every 10 C rise intemperature. Each one of these
parameters contributes to the netresultant change in collectorcurrent as temperature is varied.
For each bias network shown inFigure 1, several sets of simplifiedcircuit equations have beengenerated to allow calculation of the various bias resistors. Theseare shown in Figures 3, 4, 5, 6, and7. Each of the bias resistor valuesis calculated based on variousdesign parameters such as desiredIC, VCE , power supply voltage V CCand nominal h FE . I CBO and h ie areassumed to be zero for the basiccalculation of resistor values.
Additional designer providedinformation is required for thethree circuits that utilize the
voltage divider consisting of R B1and R B2 . In the case of the biasnetwork that uses voltagefeedback with current source, thedesigner must pick the voltage
across R B2 (VRB2 ) and the biascurrent through resistor R B2which will be termed I RB2 .
Choose V CE > VRB2 > VBE
Suggest V RB2 = 1.5 V
Suggest I RB2 to be about 10% of I C
The voltage feedback with a voltage source network and theemitter feedback network alsorequire that the designer chooseIRB2 . As will be learned later, theratio of I C to I RB2 is an importantratio that plays a major part inbias stability.
An equation was then developedfor each circuit that calculatescollector current, I C, based onnominal bias resistor values andtypical device parametersincluding h FE , ICBO , and V' BE .MATHCAD version 7 was used tohelp develop the I C equation.
Although the I C equation startsout rather simply, it develops intoa rather lengthy equation for someof the more complicated circuits.MATHCAD helped to simplify thetask.
RB1
RB2
VCE
V'BE
VBE
IBB + IB
IC
RC
C
VCC
ICBO (1 + hFE)hFEIB
hie
E
B
IBB
IB
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RCRB
RB =
+ ICBO (1 + hFE)IC =hFE (VCC - V'BE)
VBB VCC
IBRC =
VCC - VCEVCC - VBEIC
hie + RB
Figure 3. Equations for Non-stabilized BiasNetwork
Figure 4. Equations for Voltage Feedback Bias Network
Figure 5. Equations for Voltage Feedback with Current Source Bias Network
RCRBVCC
RB =
I =hFE (VCC - V'BE) + ICBO (1 + hFE) (hie + RB + RC)
IBRC =
VCC - VCEVCE - VBEIC + IB
hie + RB + RC (1 + hFE)
RB =
RB1 =
IC =
IBRC =
VCC - VCEVRB2 - VBEIC + IB2 + IB
RCRB1
RB2
RB
VCC
IB2 + IB
VCE - VRB2RB2 = IB2
VRB2
-V'BE (RB1 + RB2 + RC) -RB2 [RC ICBO (1 + hFE) -VCC](RB + h ie) (RB1 + RB2 + RC) + RB2 (hFE RC + RC + RB1)
hFE + ICBO (1 + hFE)
Designer must choose IB2
and VRB2
such that VCE
> VRB2
> VBE
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Figure 6. Equations for Voltage Feedback with Voltage Source Bias Network
Figure 7. Equations for Emitter Feedback Bias Network
Pick IB2 to be 10% of IC
IC =
RE
=
1 +
VCC - VCE
IC
R2 =VRB2 VRB2 = V'BE + (IB + IC) REIB2
R1 =VCC - IB2 R2
IB2 + IB
hFER1
hFE
RER2
R1
R2R1
hFERE
hFE
REhFE
R1+ RE + RE +
R1(R2 hFE)
R1(R2 hFE)
hie +
hFE1
-
- --
-+--
+ +
R2
R1R2
R1hFE
RE-hFE1 hie
RB1
RB2
VCC
RB3
hFE1
V'BE hie ICBO- hie ICBO ICBO- RE ICBO V'BE -
R2R1 RE ICBO hie ICBO
R2
R1 hie ICBO
ICBO ICBO-R1 ICBO-VCC
RCRB1
Designer must choose I B2
RB2
VCC
RB2 = IB2RC =
RB1 =
VCC - VCE
VCE - (IB2 RB2)
VBE
IC =
IC + IB + IB2
IB + IB2
hFE
hFE
-RC
hFE
RC
hFERB2
RC
RB2
ICBO -RC ICBO+RB2RB1
hFE
RB1
RB1RB2
RB1RB1
(RB2 hFE)RC RC V'BE
(RB2 hFE)RC
(RB2 hFE)
RB1(RB2 hFE)
hie ICBO hie ICBO ICBO-RB1 ICBO
V'BE hie ICBO1
+
+ -
+
hie ICBO- hie ICBO-VCC
hFE1 hieRC + hie + hie +
-- --
- hie ICBO+ V'BE -
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Design example using the AgilentHBFP-0405 BJTThe HBFP-0405 transistor will beused as a test example for each of the bias circuits. The AgilentHBFP-0405 is described in an
application note[4]
as a low noiseamplifier for 1800 to 1900 MHzapplications. The HBFP-0405 willbe biased at a V CE of 2.7 Volts anda drain current I C of 5 mA. A
power supply voltage of 3 voltswill be assumed. The nominal h FEof the HBFP-0405 is 80. Theminimum is 50 while themaximum is 150. The calculatedbias resistor values for each biascircuit are described in Table 1.
With the established resistor values, I C is calculated based on
minimum and maximum h FE . The performance of each bias circuitwith respect to h FE variation isshown in Table 2. Bias circuit #1
clearly has no compensation for varying h FE allowing I C toincrease 85% as h FE is taken to itsmaximum. Circuit #2 with verysimple collector feedback offersconsiderable compensation due toh FE variations allowing anincrease of only 42%. Surprisingly,circuit #3 offers very littleimprovement over circuit #2.Circuit #4 provides considerableimprovement in h FE control byonly allowing a 9% increase in I C.
Circuit #4 offers an improvementover the previous circuits by
providing a stiffer voltage sourceacross the base emitter junction.
As will be shown later, this circuithas worse performance over
temperature as compared tocircuits #2 and #3. However, whenboth h FE and temperature areconsidered, circuit #4 will appearto be the best performer for agrounded emitter configuration.
As expected, circuit #5 providesthe best control on I C with
varying h FE allowing only a 5.4%increase in I C. Results are verymuch power supply dependentand with higher V CC , results may
vary significantly.
Voltage Feedback Voltage FeedbackResistor Non-stabilized Voltage Feedback w/Current Source w/Voltage Source Emitter Feedback
Bias Network Bias Network Bias Network Bias Network Bias NetworkRC 140 138 126 126
RB 30770 19552 11539
RB1 889 2169 2169
RB2 3000
1560
2960
RE 138
Table 1. Bias resistor values for HBFP-0405 biased at V CE= 2 V, VCC= 2.7 V, IC = 5 mA, hFE= 80 for the various bias networks
Table 2. Summary of IC variation vs. h FEfor various bias networks for the HBFP-0405VCC= 2.7 V, VCE= 2 V, IC = 5 mA, TJ = +25C
Voltage Feedback Voltage FeedbackBias Non-stabilized Voltage Feedback w/Current Source w/Voltage Source Emitter FeedbackCircuit Bias Network Bias Network Bias Network Bias Network Bias NetworkIC (mA) @ 3.14 3.63 3.66 4.53 4.70minimumhFE
IC (mA) 5.0 5.0 5.0 5.0 5.0@ typicalhFEIC (mA) @ 9.27 7.09 6.98 5.44 5.27maximumhFEPercentage +85% +42% +40% +9% +5.4%change in -37% -27% -27% -9% -6%IC fromnominal IC
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BJT Performance overTemperatureSince all three temperaturedependent variables (I CBO , h FE ,and V' BE ) exist in the I C equation,then differentiating the I C
equation with respect to each of the parameters provides insightinto their effect on I C. The partialderivative of each of the three
parameters represents a stabilityfactor. The various stabilityfactors and their calculation areshown in Table 3. Each circuitthen has three distinctly differentstability factors which are thenmultiplied times a correspondingchange in either V' BE , h FE , orICBO and then summed. These
changes or deltas in V' BE , h FE ,and I CBO are calculated based on
variations in these parametersdue to manufacturing processes.
A comparison of each circuit sstability factors will certainly
provide insight as to which circuitcompensates best for each
parameter. MATHCAD was again pushed into service to calculatethe partial derivatives for eachdesired stability factor. Thestability factors for each circuitare shown in Table 4.
Table 3. Calculation of the Stability Factors and their combined effect on I C
The change in collector currentfrom the nominal design value at25 C is then calculated by takingeach stability factor and
multiplying it times thecorresponding change in each parameter. Each product is thensummed to determine theabsolute change in collectorcurrent.
As an example, the collectorcurrent of the HBFP-0405 will beanalyzed as temperature isincreased from +25 C to +65 C.For the HBFP-0405, I CBO istypically 100 nA @ +25 C and
typically doubles for every 10 Ctemperature rise. Therefore, I CBOwill increase from 100 nA to1600 nA at +65 C. The differenceor ICBO will be 1600 - 100 =1500 nA. The 1500 nA will then bemultiplied times its correspondingICBO Stability factor.
V' BE @ 25C was measured at0.755 V for the HBFP-0405. Since
V' BE has a typical negativetemperature coefficient of -2 mV / C, V' BE will be 0.675 V @ +65 C.The difference in V' BE will thenbe 0.675 - 0.755 = -0.08 V.
The -0.08 V will then be multipliedtimes its corresponding V' BEstability factor.
hFE is typically 80 @ +25 C andtypically increases at a rate of 0.5% / C. Therefore, h FE willincrease from 80 to 96 @ +65 Cmaking hFE equal to 96 - 80 = 16.
Again the is multiplied times itscorresponding stability factor.
Once all stability terms areknown, they can be summed togive the resultant change incollector current from thenominal value at +25 C. The
results of the stability analysis areshown in Table 5. The non-stabilized circuit #1 allows I C toincrease about 27% while circuits2 and 3 show a 19 to 20% increasein I C. Somewhat surprising is thefact that circuit #4 shows a nearly30% increase in I C withtemperature. In looking at thecontribution of the individualstability factors for circuit #4, onefinds that V' BE is the majorcontributor. This is probably dueto the impedance of the R B1 andRB2 voltage divider workingagainst V' BE . It is also interesting
ICBO= hFE, V'BE = constantIC
ICBO
V'BE = ICBO, hFE = constantIC
V'BE
hFE = ICBO, V'BE = constantIC
hFE
IC = SICBO ICBO+ SV'BE V'BE+ ShFE hFE
First calculate the stabilityfactors for V' BE, ICBO, and hFE.Then, to find the change incollector current at any temperature,multiply the change from 25 C ofeach temperature dependent variablewith its corresponding stabilityfactor and sum.
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to note that both circuit #2 and #3have very similar performanceover temperature. Both offer asignificant improvement overcircuit #1 and #4. As expected,circuit #5 offers the best
performance over temperature bynature of emitter feedback.Emitter feedback can be usedeffectively if the resistor can beadequately RF bypassed without
producing stability problems.
The degree of control that eachbias circuit has on controlling I Cdue to h FE variations and theintrinsic temperature dependent
parameters has a lot to due withhow the bias circuit is designed.
Increasing the voltage differentialbetween V CE and V CC canenhance the circuits ability tocontrol I C. In handsetapplications, this becomesdifficult with 3 volt batteries as
power sources. The current that isallowed to flow through the
various bias resistors can alsohave a major effect on I C control.
In order to analyze the variousconfigurations, an AppCADmodule was generated. AppCADwas created by Bob Myers of the
Agilent Technologies WSD Applications Department and isavailable free of charge via the
Agilent web site. AppCADconsists of various modulesdeveloped to help the RF designerwith microstrip, stripline,detector, PIN diode, MMICbiasing, RF amplifier, transistorbiasing and system levelcalculations, just to name a few.The AppCAD BJT biasing moduleallows the designer to fine tuneeach bias circuit design foroptimum performance. AppCADalso allows the designer to inputdevice variation parameters
peculiar to a certainmanufacturer s semiconductor
process. A sample screen showing
a typical bias circuit is shown inFigure 8. The data from AppCADis used to create the graphs in thefollowing sections.
The first exercise is to graphically
show the percentage change in I C versus h FE . AppCAD is used tocalculate the resistor values foreach of the five bias networks.The HBFP-0405 transistor isbiased at a V CE of 2 V, I C of 5 mA,and V CC of 2.7 V. Various valuesof h FE are substituted into
AppCAD. The results are shownin Figure 9. The data clearlyshows that the Emitter Feedbackand Voltage Feedback with
Voltage Source networks are
superior to the remaining circuitswith regards to controlling h FE atroom temperature. Thesenetworks provide a 4:1improvement over the other two
Voltage Feedback networks.
AppCAD is then used to simulatea temperature change fromT J = -25 C to +65 C holding h FEconstant. Whereas the originalMatchcad analysis assumed thatTC = T J , AppCAD takes intoaccount that T J is greater than T C.
AppCAD calculates the thermalrise based on dc power dissipatedand the thermal impedance of thedevice. The results of the analysisare shown in Figure 10.Somewhat surprising was the factthat the Voltage Feedback with
Voltage Source network performed nearly as poorly as thenon-stabilized circuit. This is dueto V BE decreasing withtemperature and the bias circuittrying to keep V BE constant. Thisis why power bipolar designerswill utilize a silicon diode in placeof R B2 so that the bias voltage willtrack the V BE of the transistor.Depending on the impedance of the voltage divider network, V BEcould actually rise causing I C toincrease. The Emitter Feedback
network performed very well asexpected. The simple VoltageFeedback network appeared to beoptimum when one considers thesimplicity of the circuit.
Bias networks 3 through 5 makeuse of an additional resistor thatshunts some of the total powersupply current to ground.Properly chosen, this additionalbias current can be used to assistin controlling I C over temperatureand h FE variations from device todevice. AppCAD is set up suchthat the designer can make a fewdecisions regarding the amount of bias resistor current that isallowed to flow from the power
supply. AppCAD is again used toanalyze each bias circuit.
The graphs in Figures 11 and 12 plot the percentage change in I C versus the ratio of I C to I RB1 .IRB1 is the current flowingthrough resistor RB1 which is thesummation of base current I B andcurrent flowing through resistorRB2. The maximum permissibleratio of I C to I RB1 is limited by thehFE of the transistor. Figure 11represents the worst casecondition where I C increases atmaximum h FE and highesttemperature. Figure 12 shows theopposite scenario where lowest I Cresults from lowest h FE andlowest temperature. The
percentage change is certainlymore pronounced at high h FE andhigh temperature.
Some of the actual predictedresults are somewhat surprising.However, as expected, the biasnetwork with emitter resistorfeedback offers the best
performance overall. For a ratioof I C to I RB1 of 10 to 1 or less, theresultant change in collectorcurrent is less than 20%. The
Voltage Feedback with VoltageSource network provides its best
(continues on page 15)
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Figure 8. Agilent Technologies AppCAD module for BJT Biasing
Figure 9. Percent Change in Quiescent Collector Current vs. h FE for the HBFP-0405
VCC= 2.7 V, VCE= 2 V, IC = 5 mA, TJ = +25C
50 70 90 110 130 150
NON-STABILIZED
VOLTAGE FEEDBACK
VOLTAGE FEEDBACK W/CURRENT SOURCE
VOLTAGE FEEDBACK W/VOLTAGE SOURCE
EMITTER FEEDBACK
hFE
-40-20
0
20
40
60
80
100
P E R C E N T D E V I A T I O N F R O M
A
Q U I E S C E N T C O L L E C T O R C U R R E N T
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Figure 10. Percent Change in Quiescent Collector Current vs. Temperature for the HBFP-0405
VCC= 2.7 V, VCE= 2 V, IC = 5 mA, TJ = +25C
Figure 11. Percent Change in Quiescent Collector Current vs. Ratio of I C to IRB1for Maximum hFEand +65 C for the HBFP-0405
VCC= 2.7 V, VCE= 2 V, IC = 5 mA, TJ = +25C
Figure 12. Percent Change in Quiescent Collector Current vs. Ratio of I C to IRB1for Minimum hFEand TJ = -25C for the HBFP-0405
VCC= 2.7 V, VCE= 2 V, IC = 5 mA
-25 -15 -5 5 15 25 35 45 55 65TEMPERATURE (C)
-40
-30
-20
-10
0
10
20
30
P E R C E N T C H A N G E F R O M
A
Q U I E S C E N T C O L L E C T O R C U R R E N T
NON-STABILIZED
VOLTAGE FEEDBACK
VOLTAGE FEEDBACK W/CURRENT SOURCE
VOLTAGE FEEDBACK W/VOLTAGE SOURCE
EMITTER FEEDBACK
1 10 100
NON-STABILIZED
VOLTAGE FEEDBACK
VOLTAGE FEEDBACK W/CURRENT SOURCE
VOLTAGE FEEDBACK W/VOLTAGE SOURCE
EMITTER FEEDBACK
RATIO OF IC TO IRB1
020
40
60
80
100
120
140
P E R C E N T C H A N G E F R O M
I C ( + )
MAXIMUM hFEAND +65 C
1 10 100RATIO OF IC TO IRB1
MINIMUM hFEAND -25C
020
40
60
80
100
120
140
P E R C E N T C H A N G E F R O M
I C ( - )
NON-STABILIZED
VOLTAGE FEEDBACK
VOLTAGE FEEDBACK W/CURRENT SOURCE
VOLTAGE FEEDBACK W/VOLTAGE SOURCE
EMITTER FEEDBACK
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Table 4.Stability Factors for Non-stabilized Bias Network #1
Table 4.Stability Factors for Voltage Feedback Bias Network #2
Collector current at any temperature (I C)
ICBOStability factor
hFE (VCC - V'BE)(hie + RB)
hie + RB
hie + RB
-hFE
+ ICBO (1 + hFE)
ICBO=
1 + hFE
hFE, V'BE = ConstantIC
ICBO
V'BEStability factor
V'BE = ICBO, hFE = ConstantIC
V'BE
hFEStability factor
hFE = ICBO, V'BE = ConstantIChFE
VCC - V'BE+ ICBO
Collector current at any temperature (I C)
ICBOStability factor
hFE (VCC - V'BE) + ICBO (1 + hFE) A
hie + RB + RC (1 + hFE)
hie + RB + RC (1 + hFE)
hie + RB + RC (1 + hFE)
(hFE RC + RB + h ie + RC)2
hFE
RC
+ RB
+ hie
+ RC
RC hFE (VCC - V'BE+ A ICBO) + A ICBO
-hFE
ICBO=
(1 + hFE) A
hFE, V'BE = constantIC
ICBO
V'BEStability factor
V'BE = ICBO, hFE = constantIC
V'BE
hFEStability factor
hFE = ICBO, V'BE = constantI
ChFE
VCC - V'BE+ A ICBO
Where:
A = hie + RB + RC
-
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Table 4.Stability Factors for Voltage Feedback with Current Source Bias Network #3
Collector current at any temperature (I C)
ICBOStability factor
(RB + h ie) A + RB2 (hFE RC + RC + RB1)
RB2 hFE RC (1 + hFE)A (RB + h ie)+ RB2 (hFE RC + RC + RB1)
(RB + h ie) A + RB2 (hFE RC + RC + RB1)
B + RB2 [RC ICBO (1 + hFE) -VCC+ hFE RC ICBO]
-hFE A
ICBO= hFE, V'BE = constantIC
ICBO
V'BEStability factor
V'BE = ICBO, hFE = constantIC
V'BE
hFEStability factor
hFE = ICBO, V'BE = constantIC
hFE
Where:
- V'BE A - RB2 [RC ICBO (1 + hFE) -VCC]+ ICBO (1 + hFE)hFE
(1 + hFE) -
hFE {RB2 RC [(-RB2 VCC + B) + RB2 RC ICBO (1 + hFE)]}D2
D
+ ICBO
A = RB1 + RB2 + RC
B = V'BE (RB1 + RB2 + RC)
C = (RB + h ie) (RB1 + RB2 + RC)
D = (RB + h ie) (RB1 + RB2 + RC) + RB2 (hFE RC + RC + RB1)
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Table 4.Stability Factors for Voltage Feedback with Voltage Source Bias Network #4
Collector current at any temperature (I C)
ICBOStability factor
ICBO= hFE, V'BE = constantIC
ICBO
V'BEStability factor
V'BE = ICBO, hFE = constantIC
V'BE
hFEStability factor
hFE = ICBO, V'BE = constantIC
hFE
Where:
C2
C
C
C
C
1
A =
ICBO (-A) + ICBO hie (-B) + D - VCC
ICBO A + ICBO hie B - D + VCC
hie B + A
-RCRB2
-RB1RB2
-RC -
RB1
- 1
hFE2 hFE2
RB1
RB2
RB1RB2
ICBO + ICBO hie E
-RC -RB1
hFE2 hFE2+ h ie E
RC
RC
hFE+ RC +
RB1hFE
hFE
1hFE2
+ RB1
RChFE
+RB1hFE
+ h ie
B =
RCRB2 hFE
RB1
C = RC +
D =
E =
RCRB2
V'BE V'BE+ V'BE
RCRB2 hFE
-RCRB2 hFE2
RB2 hFE
RB1RB2 hFE
- -
+
+
+
1hFE
+
+ 1+ + +RB2
RB1RB2 hFE2
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Table 4.Stability Factors for Emitter Feedback Bias Network #5
Collector current at any temperature (I C)
ICBOStability factor
ICBO= hFE, V'BE = constantIC
ICBO
V'BEStability factor
V'BE = ICBO, hFE = constantIC
V'BE
hFEStability factor
hFE = ICBO, V'BE = constantIC
hFE
Where:
C2
C
C
C
C
A =
hie A + B
R1R2
R1R2
-
-
R1
R1
R2 hFE2
- 1
1
- 1hFE2
ICBO E + hie ICBO
ICBO B + hie ICBO A - D
hFE2hFE2
1hFE
+ RE
+ RE
RE
REhFE2R1
RE
RE
V'BE
R1R2 hFE
R1R2 hFE
-
hie ICBO (-A) + ICBO (-B) + D
-R1
R2 hFE2- 1
hFE2
hie + E
+ 1+
R1R2
+
+
+
+ ++
hFE
B =
C =
D = V'BE
E =
R1R2
R1R2
+R1R2
- -R1R2
+R1R2
hFE
REhFE
+R1hFE
REhFE
+REhFE
-RE
+R1hFE
hie
- VCC
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performance at an I C to I RB1 ratiobetween 6 and 10 with a worstcase change of 41% in collectorcurrent.
To complete the comparison, twoadditional points representing the
Non-Stabilized and the VoltageFeedback networks have beenadded to the graphs. They areshown as single points becauseonly the base current is inaddition to the collector current.The Non-stabilized network has a+129% change while the VoltageFeedback network has anincrease of 74.5%. It is alsointeresting to note that the
Voltage Feedback with CurrentSource network really offers no
benefit over the simpler VoltageFeedback network.
ConclusionThis paper has presented thecircuit analysis of four commonlyused stabilized bias networks andone non-stabilized bias networkfor the bipolar junction transistor.In addition to the presentation of the basic design equations for the
bias resistors for each network,an equation was presented forcollector current in terms of biasresistors and device parameters.The collector current equationwas then differentiated withrespect to the three primarytemperature dependent variablesresulting in three stability factorsfor each network. These stabilityfactors plus the basic collectorcurrent equation give the designerinsight as to how best bias any
bipolar transistor for best performance over h FE andtemperature variations. The basicequations were then integratedinto an AppCAD module
providing the circuit designer aneasy and effective way to analyzebias networks for bipolartransistors.
Table 5. Bias Stability Analysis at +65 C using the HBFP-0405VCC= 2.7 V, VCE= 2 V, IC = 5 mA
#1 Non- #2 Voltage #3 Voltage #4 Voltage #5 EmitterBias Circuit Stabilized Feedback Feedback Feedback Feedback
w/Current
SourceICBOStability Factor 81 52.238 50.865 19.929 11.286
V BE Stability Factor -2.56653x 10-3 -2.568011x10-3 -3.956x10-3 -0.015 -6.224378x10-3
hFEStability Factor 6.249877x10-5 4.031x10-5 3.924702x10-5 1.537669x10-5 8.707988x10-6
IC due to I CBO (mA) 0.120 0.078 0.076 0.030 0.017
IC due to V BE (mA) 0.210 0.205 0.316 1.200 0.497
IC due to h FE (mA) 0.999 0.645 0.628 0.246 0.140
Total IC (mA) 1.329 0.928 1.020 1.476 0.654
Percentage change in
IC from nominal IC 26.6% 18.6% 20.4% 29.5% 13.1%
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www.agilent.com/semiconductorsFor product information and a complete list ofdistributors, please go to our web site.
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Data subject to change.Copyright 2003 Agilent Technologies, Inc.January 22, 20035988-6173EN
References.1. A Cost-Effective AmplifierDesign Approach at 425 MHzUsing the HXTR-3101 SiliconBipolar Transistor , Hewlett-Packard Application Note 980,
2/81 (out of print).
2. Richter, Kenneth. Design DCStability Into Your TransistorCircuits , Microwaves, December1973, pp 40-46.
3. Microwave Transistor BiasConsiderations , Hewlett-Packard
Application Note 944-1, 8/80, (outof print).
4. 1800 to 1900 MHz Amplifier
using the HBFP-0405 and HBFP-0420 Low Noise Silicon BipolarTransistors , Hewlett-Packard
Application Note 1160, (11/98), publication number 5968-2387E.
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