Biasing a Transistor

8/6/2019 Biasing a Transistor

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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


Figure 11. Percent Change in Quiescent Collector Current vs. Ratio of I C to IRB1for Maximum hFEand +65 C for the HBFP-0405


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



EMITTER FEEDBACK

1 10 100

NON-STABILIZED

VOLTAGE FEEDBACK



EMITTER FEEDBACK

RATIO OF IC TO IRB1

020

40

60

80

100

120

140


I C ( + )

MAXIMUM hFEAND +65 C

1 10 100RATIO OF IC TO IRB1

MINIMUM hFEAND -25C

020

40

60

80

100

120

140


I C ( - )

NON-STABILIZED

VOLTAGE FEEDBACK



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



hFE (VCC - V'BE) + ICBO (1 + hFE) A




(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'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



(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



V'BE

hFEStability factor


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




ICBO



V'BE

hFEStability factor


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




ICBO



V'BE

hFEStability factor


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


15/16

15

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%


16/16

www.agilent.com/semiconductorsFor product information and a complete list ofdistributors, please go to our web site.

For technical assistance call:

Americas/Canada: +1 (800) 235-0312 or(408) 654-8675

Europe: +49 (0) 6441 92460

China: 10800 650 0017

Hong Kong: (+65) 6271 2451

India, Australia, New Zealand: (+65) 6271 2394

Japan: (+81 3) 3335-8152(Domestic/International), or0120-61-1280(Domestic Only)

Korea: (+65) 6271 2194

Malaysia, Singapore: (+65) 6271 2054

Taiwan: (+65) 6271 2654

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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Biasing a Transistor

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