A Comparison of Various Bipolar Circuits Application Note 1293

Introduction The bipolar junction transistor to hFE variations. In addition, (BJT) is quite often used as a low transistor parameters can vary VBB VCC noise in cellular, PCS, over temperature causing a drift and pager applications due to its in IC at temperature. The low low cost. With a minimal number power supply voltages typically RB RC of external matching networks, available for handheld the BJT can quite often produce applications also make it more an LNA with RF performance difficult to design a temperature considerably better than an stable bias circuit. MMIC. Of equal importance is the DC performance. Although the One solution to the biasing device’s RF performance may be dilemma is the use of active quite closely controlled, the biasing. Active biasing often Figure 1A. Circuit #1 – variation in device dc parameters makes use of an IC or even just a Non-stabilized BJT Bias Network can be quite significant due to PNP transistor and a variety of normal process variations. It is , which effectively sets current IB. The base current is not unusual to find a 2 or 3 to 1 VCE and IC regardless of determined by the value of RB. ratio in device hFE. Variation in variations in device hFE. Although The collector voltage VCE is hFE from device to device will the technique of active biasing determined by subtracting the generally not show up as a would be the best choice for the voltage drop across RC difference in RF performance. In control of device to device from the power supply voltage other words, two devices with variability and over temperature VCC. As the collector current is widely different hFE’s can have variations, the cost associated varied, the VCE will change based similar RF performance as long as with such an arrangement is on the voltage drop across RC. the devices are biased at the same usually prohibitive. Varying hFE will cause IC to vary VCE and IC. This is the primary in a fairly direct manner. For purpose of the bias network, i.e., Other biasing options include constant VCC and constant VBE, to keep VCE and IC constant as the various forms of passive biasing. IC will vary in direct proportion dc parameters vary from device to Various passive biasing circuits to hFE. As an example, as hFE is device. will be discussed along with their doubled, collector current, IC, advantages and disadvantages. will also double. Bias circuit #1 Quite often the bias circuitry is provides no compensation for overlooked due to its apparent Various BJT Passive Bias Circuits variation in device hFE. simplicity. With a poorly designed Passive biasing schemes usually fixed bias circuit, the variation in consist of two to five resistors Bias circuit #2 provides voltage IC from lot to lot can have the properly arranged about the feedback to the base current same maximum to minimum ratio transistor. Various passive biasing source resistor RB. The base as the hFE variation from lot to schemes are shown in Figure 1. current source is fed from the lot. With no compensation, as hFE The simplest form of passive voltage VCE as opposed to the is doubled, IC will double. It is the biasing is shown as Circuit #1 in supply voltage VCC. The value of task of the circuit to Figure 1. The collector current IC the base bias resistor RB is maximize the circuit’s tolerance is simply hFE times the base calculated based upon nominal RB RC RB1 RC VCC VCC

RB2

Figure 1B. Circuit #2 – Voltage Feedback BJT Bias Network Figure 1D. Circuit #4 – Voltage Feedback with Voltage Source BJT Bias Network

RB1 RC V CC VCC

RB1

RB

RB2 R B2 RE

Figure 1C. Circuit #3 – Figure 1E. Circuit #5 – Voltage Feedback with Current Source BJT Emitter Feedback BJT Bias Network Bias Network

device VBE and the desired VCE. been used [1]. The voltage divider device. The current flowing Collector resistor RC has both IC network consisting of RB1 and through resistor RB1 is shared by and IB flowing through it. The RB2 provides a voltage divider both resistor RB2 and the emitter operation of this circuit is best from which resistor RB is base junction VBE. The greater the explained as follows. An increase connected. Resistor RB then current through resistor RB2, the in hFE will tend to cause IC to determines the base current. IB greater the regulation of the increase. An increase in IC causes times hFE provides IC. The voltage emitter base voltage VBE. the voltage drop across resistor drop across RC is determined by RC to increase. The increase in the collector current IC, the bias Bias circuit #5 is the customary voltage across RC causes VCE to current IB, and the current textbook circuit for biasing BJTs. decrease. The decrease in VCE consumed by the voltage divider A resistor is used in series with causes IB to decrease because the consisting of RB1 and RB2. This the device emitter lead to provide potential difference across base circuit provides similar voltage voltage feedback. This circuit bias resistor RB has decreased. feedback to bias circuit #2. ultimately provides the best This topology provides a basic control of hFE variations from form of negative feedback which Bias circuit #4 is similar to bias device to device and over tends to reduce the amount that circuit #3 with the exception that temperature. The only the collector current increases as the series current source resistor disadvantage of this circuit is that hFE is increased. RB is omitted. This circuit is seen the emitter resistor must be quite often in bipolar power properly bypassed for RF. The Bias circuit #3 has been quite amplifier design with resistor RB2 typical bypass capacitor quite often written up in past literature replaced by a series silicon power often has internal lead inductance but predominately when very high providing temperature which can create unwanted VCC (>15 V) and VCE (>12 V) has compensation for the bipolar regenerative feedback. The 2 feedback quite often creates IBB + IB device instability. Despite the RB1 problems associated with using IC the emitter resistor technique, this B IB C biasing scheme generally provides the best control on hFE and over temperature variations. hie VBE VCE IBB RC The sections that follow begin with a discussion of the BJT V'BE hFE IB ICBO (1 + hFE) model and its temperature RB2 dependent variables. From the VCC basic model, various equations are developed to predict the E device’s behavior over hFE and temperature variations. This Figure 2. Gummel Poon model of BJT with Voltage Feedback and Constant Base Current article is an update to the original Source Network article written by Kenneth Richter of Hewlett-Packard [2] and Hewlett-Packard Application increases with temperature at the across RB2 (VRB2) and the bias Note 944-1 [3]. rate of 0.5% / °C. V' BE has a current through resistor RB2 typical negative temperature which will be termed IRB2. BJT Modeling coefficient of -2 mV / °C. This The BJT is modeled as two indicates that VBE decreases 2 mV Choose VCE > VRB2 > VBE current sources as shown in for every degree increase in Figure 2. The primary current temperature. ICBO typically Suggest VRB2 = 1.5 V source is hFE IB. In parallel is a doubles for every 10°C rise in secondary current source ICBO temperature. Each one of these Suggest IRB2 to be about 10% of IC (1+ hFE) which describes the parameters contributes to the net current flowing through a resultant change in collector The voltage feedback with a reverse biased PN junction. ICBO current as temperature is varied. voltage source network and the is typically 1x10-7 A @ 25°C for an emitter feedback network also Agilent Technologies HBFP-0405 For each bias network shown in require that the designer choose transistor. V 'BE is the internal Figure 1, several sets of simplified IRB2. As will be learned later, the base emitter voltage with hie circuit equations have been ratio of IC to IRB2 is an important representing the equivalent generated to allow calculation of ratio that plays a major part in Hybrid PI input impedance of the the various bias resistors. These bias stability. transistor. hie is also equal to are shown in Figures 3, 4, 5, 6, and hFE / λ IC where λ = 40 @ +25°C. 7. Each of the bias resistor values An equation was then developed VBE will be defined as measured is calculated based on various for each circuit that calculates between the base and emitter design parameters such as desired collector current, IC, based on leads of the transistor. It is IC, VCE, power supply voltage VCC nominal bias resistor values and equivalent to V' BE + IB hie. VBE is and nominal hFE. ICBO and hie are typical device parameters approximately 0.78 V @ 25°C for assumed to be zero for the basic including hFE, ICBO, and V' BE. the HBFP-0405 transistor. calculation of resistor values. MATHCAD version 7 was used to help develop the IC equation. The device parameters that have Additional designer provided Although the IC equation starts the greatest change as information is required for the out rather simply, it develops into temperature is varied consist of three circuits that utilize the a rather lengthy equation for some hFE, V' BE, and ICBO. These voltage divider consisting of RB1 of the more complicated circuits. temperature dependent variables and RB2. In the case of the bias MATHCAD helped to simplify the have characteristics which are network that uses voltage task. process dependent and fairly well feedback with current source, the understood. hFE typically designer must pick the voltage

3 VBB VCC RB RC VCC

RB RC

VCC - VBE VCC - VCE VCE - VBE VCC - VCE RB = RC = RB = RC = IB IC IB IC + IB

• • • • hFE (VCC - V'BE) hFE (VCC - V'BE) + ICBO (1 + hFE) (hie + RB + RC) I = + I • (1 + h ) I = C h + R CBO FE • ie B hie + RB + RC (1 + hFE)

Figure 3. Equations for Non-stabilized Bias Figure 4. Equations for Voltage Feedback Bias Network Network

RB1 RC VCC

RB

RB2

VRB2 - VBE VCC - VCE RB = RC = IB IC + IB2 + IB

VCE - VRB2 VRB2 RB1 = RB2 = IB2 + IB IB2

Designer must choose IB2 and VRB2 such that VCE > VRB2 > VBE

• • • • -V'BE (RB1 + RB2 + RC) -RB2 [RC ICBO (1 + hFE) -VCC] I = • h + I • (1 + h ) C • • • FE CBO FE (RB + hie) (RB1 + RB2 + RC) + RB2 (hFE RC + RC + RB1)

Figure 5. Equations for Voltage Feedback with Current Source Bias Network

4 RB1 RC VCC

VBE VCC - VCE RB2 = RC = IB2 IC + IB + IB2 • VCE - (IB2 RB2) RB1 = RB2 IB + IB2

Designer must choose IB2

-R R C • • C RC RC RB1 - ICBO -RC ICBO + • V' - • • - • • - • • h R BE • ) hie ICBO hie ICBO ICBO -RB1 ICBO FE B2 (RB2 hFE RB2 hFE RB1 RB1 RB1 1 + • V' - • • - • • • • • BE • ) hie ICBO hie ICBO + V'BE - hie ICBO - hie ICBO -VCC RB2 (RB2 hFE RB2 hFE IC =

RC RC R RB1 1 + • B1 • • RC + • ) hie + + • ) hie + hie hFE (RB2 hFE hFE (RB2 hFE hFE

Figure 6. Equations for Voltage Feedback with Voltage Source Bias Network

VCC • VCC - VCE VCC - IB2 R2 RE = R1 = IB2 + IB RB1 1 IC 1 + hFE

Pick IB2 to be 10% of IC

RB2 R V B3 RB2 ) • R2 = VRB2 = V'BE + (IB + IC RE IB2

1 RE R1 R1 R1 - • • • • • + • V' - • • - - V'BE hie ICBO - hie ICBO - ICBO - RE ICBO BE • ) hie ICBO hFE hFE R2 (R2 hFE R2 R R R R • • 1 • E • 1 • • 1 • • hie ICBO - ICBO- RE ICBO - ICBO -R1 ICBO -VCC R2 hFE R2 hFE

IC =

1 RE R1 R1 RE R1 R1 • • •- + • R + hie + + RE + • ) hie + E hFE hFE (R2 hFE R2 hFE R2 hFE

Figure 7. Equations for Emitter Feedback Bias Network

5 Design example using the Agilent HBFP-0405 BJT The HBFP-0405 transistor will be minimum and maximum hFE. The providing a stiffer voltage source used as a test example for each of performance of each bias circuit across the base emitter junction. the bias circuits. The Agilent with respect to hFE variation is As will be shown later, this circuit HBFP-0405 is described in an shown in Table 2. Bias circuit #1 has worse performance over application note [4] as a low noise clearly has no compensation for temperature as compared to amplifier for 1800 to 1900 MHz varying hFE allowing IC to circuits #2 and #3. However, when applications. The HBFP-0405 will increase 85% as hFE is taken to its both hFE and temperature are be biased at a VCE of 2.7 Volts and maximum. Circuit #2 with very considered, circuit #4 will appear a drain current IC of 5 mA. A simple collector feedback offers to be the best performer for a power supply voltage of 3 volts considerable compensation due to grounded emitter configuration. will be assumed. The nominal hFE hFE variations allowing an As expected, circuit #5 provides of the HBFP-0405 is 80. The increase of only 42%. Surprisingly, the best control on IC with minimum is 50 while the circuit #3 offers very little varying hFE allowing only a 5.4% maximum is 150. The calculated improvement over circuit #2. increase in IC. Results are very bias resistor values for each bias Circuit #4 provides considerable much power supply dependent circuit are described in Table 1. improvement in hFE control by and with higher VCC, results may only allowing a 9% increase in IC. vary significantly. With the established resistor Circuit #4 offers an improvement values, IC is calculated based on over the previous circuits by

Table 1. Bias resistor values for HBFP-0405 biased at VCE = 2 V, VCC = 2.7 V, IC = 5 mA, hFE = 80 for the various bias networks Voltage Feedback Voltage Feedback Resistor Non-stabilized Voltage Feedback w/Current Source w/Voltage Source Emitter Feedback Bias Network Bias Network Bias Network Bias Network Bias Network RC 140 Ω 138 Ω 126 Ω 126 Ω RB 30770 Ω 19552 Ω 11539 Ω RB1 889 Ω 2169 Ω 2169 Ω RB2 3000 Ω 1560 Ω 2960 Ω RE 138 Ω

Table 2. Summary of IC variation vs. hFE for various bias networks for the HBFP-0405 VCC = 2.7 V, VCE = 2 V, IC = 5 mA, TJ = +25°C Voltage Feedback Voltage Feedback Bias Non-stabilized Voltage Feedback w/Current Source w/Voltage Source Emitter Feedback Circuit Bias Network Bias Network Bias Network Bias Network Bias Network IC (mA) @ 3.14 3.63 3.66 4.53 4.70 minimum hFE IC (mA) 5.0 5.0 5.0 5.0 5.0 @ typical hFE IC (mA) @ 9.27 7.09 6.98 5.44 5.27 maximum hFE Percentage +85% +42% +40% +9% +5.4% change in -37% -27% -27% -9% -6% IC from nominal IC

6 BJT Performance over Temperature Since all three temperature The change in collector current The -0.08 V will then be multiplied dependent variables (ICBO, hFE, from the nominal design value at times its corresponding V' BE and V'BE) exist in the IC equation, 25°C is then calculated by taking stability factor. then differentiating the IC each stability factor and equation with respect to each of multiplying it times the hFE is typically 80 @ +25°C and the parameters provides insight corresponding change in each typically increases at a rate of into their effect on IC. The partial parameter. Each product is then 0.5% / °C. Therefore, hFE will derivative of each of the three summed to determine the increase from 80 to 96 @ +65°C parameters represents a stability absolute change in collector making ∆ hFE equal to 96 - 80 = 16. factor. The various stability current. Again the ∆ is multiplied times its factors and their calculation are corresponding stability factor. shown in Table 3. Each circuit As an example, the collector then has three distinctly different current of the HBFP-0405 will be Once all stability terms are stability factors which are then analyzed as temperature is known, they can be summed to multiplied times a corresponding increased from +25°C to +65°C. give the resultant change in change in either V' BE, hFE, or For the HBFP-0405, ICBO is collector current from the ICBO and then summed. These typically 100 nA @ +25°C and nominal value at +25°C. The changes or deltas in V' BE, hFE, typically doubles for every 10°C results of the stability analysis are and ICBO are calculated based on temperature rise. Therefore, ICBO shown in Table 5. The non- variations in these parameters will increase from 100 nA to stabilized circuit #1 allows IC to due to manufacturing processes. 1600 nA at +65°C. The difference increase about 27% while circuits or ∆ ICBO will be 1600 - 100 = 2 and 3 show a 19 to 20% increase A comparison of each circuit’s 1500 nA. The 1500 nA will then be in IC. Somewhat surprising is the stability factors will certainly multiplied times its corresponding fact that circuit #4 shows a nearly provide insight as to which circuit ICBO Stability factor. 30% increase in IC with compensates best for each temperature. In looking at the parameter. MATHCAD was again V' BE @ 25°C was measured at contribution of the individual pushed into service to calculate 0.755 V for the HBFP-0405. Since stability factors for circuit #4, one the partial derivatives for each V' BE has a typical negative finds that V'BE is the major desired stability factor. The temperature coefficient of -2 mV / contributor. This is probably due stability factors for each circuit °C, V'BE will be 0.675 V @ +65°C. to the impedance of the RB1 and are shown in Table 4. The difference in V' BE will then RB2 voltage divider working be 0.675 - 0.755 = -0.08 V. against V' BE. It is also interesting

Table 3. Calculation of the Stability Factors and their combined effect on IC

∂IC h , V' = constant First calculate the stability ICBO = ∂ FE BE ICBO factors for V'BE, ICBO, and hFE. Then, to find the change in ∂IC collector current at any temperature, I , h = constant V'BE = CBO FE multiply the change from 25°C of ∂V'BE each temperature dependent variable ∂I with its corresponding stability C hFE = ICBO, V'BE = constant factor and sum. ∂hFE

∆IC = SICBO • ∆ICBO + SV'BE • ∆V'BE + ShFE • ∆hFE

7 to note that both circuit #2 and #3 a typical bias circuit is shown in network performed very well as have very similar performance Figure 8. The data from AppCAD expected. The simple Voltage over temperature. Both offer a is used to create the graphs in the Feedback network appeared to be significant improvement over following sections. optimum when one considers the circuit #1 and #4. As expected, simplicity of the circuit. circuit #5 offers the best The first exercise is to graphically performance over temperature by show the percentage change in IC Bias networks 3 through 5 make nature of emitter feedback. versus hFE. AppCAD is used to use of an additional resistor that Emitter feedback can be used calculate the resistor values for shunts some of the total power effectively if the resistor can be each of the five bias networks. supply current to ground. adequately RF bypassed without The HBFP-0405 transistor is Properly chosen, this additional producing stability problems. biased at a VCE of 2 V, IC of 5 mA, bias current can be used to assist and VCC of 2.7 V. Various values in controlling IC over temperature The degree of control that each of hFE are substituted into and hFE variations from device to bias circuit has on controlling IC AppCAD. The results are shown device. AppCAD is set up such due to hFE variations and the in Figure 9. The data clearly that the designer can make a few intrinsic temperature dependent shows that the Emitter Feedback decisions regarding the amount of parameters has a lot to due with and Voltage Feedback with bias resistor current that is how the bias circuit is designed. Voltage Source networks are allowed to flow from the power Increasing the voltage differential superior to the remaining circuits supply. AppCAD is again used to between VCE and VCC can with regards to controlling hFE at analyze each bias circuit. enhance the circuits’ ability to room temperature. These control IC. In handset networks provide a 4:1 The graphs in Figures 11 and 12 applications, this becomes improvement over the other two plot the percentage change in IC difficult with 3 volt batteries as Voltage Feedback networks. versus the ratio of IC to IRB1. power sources. The current that is IRB1 is the current flowing allowed to flow through the AppCAD is then used to simulate through resistor RB1 which is the various bias resistors can also a temperature change from summation of base current IB and have a major effect on IC control. TJ = -25°C to +65°C holding hFE current flowing through resistor constant. Whereas the original RB2. The maximum permissible In order to analyze the various Matchcad analysis assumed that ratio of IC to IRB1 is limited by the configurations, an AppCAD TC = TJ, AppCAD takes into hFE of the transistor. Figure 11 module was generated. AppCAD account that TJ is greater than TC. represents the worst case was created by Bob Myers of the AppCAD calculates the thermal condition where IC increases at Agilent Technologies WSD rise based on dc power dissipated maximum hFE and highest Applications Department and is and the thermal impedance of the temperature. Figure 12 shows the available free of charge via the device. The results of the analysis opposite scenario where lowest IC Agilent web site. AppCAD are shown in Figure 10. results from lowest hFE and consists of various modules Somewhat surprising was the fact lowest temperature. The developed to help the RF designer that the Voltage Feedback with percentage change is certainly with microstrip, stripline, Voltage Source network more pronounced at high hFE and detector, PIN diode, MMIC performed nearly as poorly as the high temperature. biasing, RF amplifier, transistor non-stabilized circuit. This is due biasing and system level to VBE decreasing with Some of the actual predicted calculations, just to name a few. temperature and the bias circuit results are somewhat surprising. The AppCAD BJT biasing module trying to keep VBE constant. This However, as expected, the bias allows the designer to fine tune is why power bipolar designers network with emitter resistor each bias circuit design for will utilize a silicon diode in place feedback offers the best optimum performance. AppCAD of RB2 so that the bias voltage will performance overall. For a ratio also allows the designer to input track the VBE of the transistor. of IC to IRB1 of 10 to 1 or less, the device variation parameters Depending on the impedance of resultant change in collector peculiar to a certain the voltage divider network, VBE current is less than 20%. The manufacturer’s semiconductor could actually rise causing IC to Voltage Feedback with Voltage process. A sample screen showing increase. The Emitter Feedback Source network provides its best

(continues on page 15) 8 Figure 8. Agilent Technologies’ AppCAD module for BJT Biasing

100 80 NON-STABILIZED 60 VOLTAGE FEEDBACK 40 VOLTAGE FEEDBACK W/CURRENT SOURCE 20 VOLTAGE FEEDBACK W/VOLTAGE SOURCE 0 EMITTER FEEDBACK -20

PERCENT DEVIATION FROM A -40 QUIESCENT COLLECTOR CURRENT 50 70 90 110 130 150 hFE

Figure 9. Percent Change in Quiescent Collector Current vs. hFE for the HBFP-0405

VCC = 2.7 V, VCE = 2 V, IC = 5 mA, TJ = +25°C

9 30 20 NON-STABILIZED 10 VOLTAGE FEEDBACK 0 VOLTAGE FEEDBACK W/CURRENT SOURCE -10 VOLTAGE FEEDBACK W/VOLTAGE SOURCE -20 EMITTER FEEDBACK -30 PERCENT CHANGE FROM A -40 QUIESCENT COLLECTOR CURRENT -25 -15 -5 5 15 25 35 45 55 65 TEMPERATURE (°C)

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 = +25°C

MAXIMUM hFE AND +65 °C 140 (+) C 120 NON-STABILIZED 100 VOLTAGE FEEDBACK 80 VOLTAGE FEEDBACK W/CURRENT SOURCE 60 VOLTAGE FEEDBACK W/VOLTAGE SOURCE 40 EMITTER FEEDBACK 20

PERCENT CHANGE FROM I 0 1 10 100 RATIO OF IC TO IRB1

Figure 11. Percent Change in Quiescent Collector Current vs. Ratio of IC to IRB1 for Maximum hFE and +65°C for the HBFP-0405

VCC = 2.7 V, VCE = 2 V, IC = 5 mA, TJ = +25°C

MINIMUM hFE AND -25 °C 140 (-) C 120 NON-STABILIZED 100 VOLTAGE FEEDBACK 80 VOLTAGE FEEDBACK W/CURRENT SOURCE 60 VOLTAGE FEEDBACK W/VOLTAGE SOURCE 40 EMITTER FEEDBACK 20

PERCENT CHANGE FROM I 0 1 10 100 RATIO OF IC TO IRB1

Figure 12. Percent Change in Quiescent Collector Current vs. Ratio of IC to IRB1 for Minimum hFE and TJ = -25°C for the HBFP-0405

VCC = 2.7 V, VCE = 2 V, IC = 5 mA

10 Table 4. Stability Factors for Non-stabilized Bias Network #1

Collector current at any temperature (IC) h • (V - V' ) FE CC BE • + ICBO (1 + hFE) (hie + RB)

I Stability factor CBO 1 + hFE ∂ IC h , V' = Constant ICBO = ∂ FE BE ICBO

V' Stability factor BE -hFE ∂ IC h + R I , h = Constant ie B V'BE = ∂ CBO FE V'BE

hFE Stability factor ∂ VCC - V'BE IC I , V' = Constant + ICBO hFE = ∂ CBO BE hie + RB hFE

Table 4. Stability Factors for Voltage Feedback Bias Network #2

Collector current at any temperature (IC) • • • hFE (VCC - V'BE) + ICBO (1 + hFE) A • hie + RB + RC (1 + hFE)

ICBO Stability factor • (1 + hFE) A ∂ IC h , V' = constant h + R + R • (1 + h ) ICBO = ∂ FE BE ie B C FE ICBO

V' Stability factor BE -hFE ∂ IC • I , h = constant hie + RB + RC (1 + hFE) V'BE = ∂ CBO FE V'BE

• h Stability factor VCC - V'BE + A ICBO FE - ∂ • IC hFE RC + RB + hie + RC I , V' = constant hFE = ∂ CBO BE hFE • • • • RC hFE (VCC - V'BE + A ICBO) + A ICBO • 2 (hFE RC + RB + hie + RC)

Where:

A = hie + RB + RC

11 Table 4. Stability Factors for Voltage Feedback with Current Source Bias Network #3

Collector current at any temperature (I ) C • • • • - V'BE A - RB2 [RC ICBO (1 + hFE) -VCC] hFE + I • (1 + h ) • • • CBO FE (RB + hie) A + RB2 (hFE RC + RC + RB1)

I Stability factor CBO R • h • R • (1 + h ) ∂ B2 FE C FE IC (1 + hFE) - h , V' = constant A • (R + h )+ R • (h • R + R + R ) ICBO = ∂ FE BE B ie B2 FE C C B1 ICBO

V'BE Stability factor • -hFE A ∂ IC • • • I , h = constant (RB + hie) A + RB2 (hFE RC + RC + RB1) V'BE = ∂ CBO FE V'BE

hFE Stability factor • • • • • • • hFE {RB2 RC [(-RB2 VCC + B) + RB2 RC ICBO (1 + hFE)]} ∂I – C  2 h = ICBO, V'BE = constant D FE ∂h FE • • • • • B + RB2 [RC ICBO (1 + hFE) -VCC + hFE RC ICBO] + I D CBO

Where:

A = RB1 + RB2 + RC • B = V'BE (RB1 + RB2 + RC) • C = (RB + hie) (RB1 + RB2 + RC) • • • D = (RB + hie) (RB1 + RB2 + RC) + RB2 (hFE RC + RC + RB1)

12 Table 4. Stability Factors for Voltage Feedback with Voltage Source Bias Network #4

Collector current at any temperature (IC) • • • ICBO (-A) + ICBO hie (-B) + D - VCC C

ICBO Stability factor • ∂ hie B + A IC h , V' = constant ICBO = ∂ FE BE C ICBO

V'BE Stability factor -R R C - B1 - 1 ∂ IC RB2 RB2 I , h = constant V'BE = ∂ CBO FE C V'BE

hFE Stability factor -R R ∂ C B1 • • IC I • - + ICBO hie E I , V' = constant CBO h 2 h 2 hFE = ∂ CBO BE FE FE hFE – C

• • • ICBO A + ICBO hie B - D + VCC -R R • C - B1 + h • E 2 2 2 ie C hFE hFE

Where:

RC RB1 A = + RC + + RB1 hFE hFE

R R RB1 RB1 1 C C + + + 1 B = • + + • RB2 hFE RB2 RB2 hFE RB2 hFE

R RB1 R R C = R + C • C B1 1 C + + hie • + • + hFE hFE RB2 hFE RB2 hFE hFE

RC RB1 D = • V' + • V' + V' R BE BE BE B2 RB2

-R R E = C --B1 1 • 2 • 2 2 RB2 hFE RB2 hFE hFE

13 Table 4. Stability Factors for Emitter Feedback Bias Network #5

Collector current at any temperature (IC) • • • hie ICBO (-A) + ICBO (-B) + D C

I Stability factor CBO • ∂ hie A + B IC h , V' = constant ICBO = ∂ FE BE C ICBO

V' Stability factor R BE - 1 - 1 ∂ R IC 2 I , h = constant V'BE = ∂ CBO FE C V'BE

hFE Stability factor R • • • - 1 1 ∂ ICBO E + hie ICBO - IC 2 R • h 2 I , V' = constant hFE 2 FE hFE = ∂ CBO BE – hFE C

I • B + h • I • A - D - 1 R1 CBO ie CBO • h • - + E ie 2 • 2 C2 hFE R2 hFE

Where:

R1 R1 1 A = • + + + 1 R2 hFE R2 hFE

R R R R R1 1 •- E 1 • E + R + + R B = + RE + E h 1 R2 hFE R2 hFE FE

R R R R R R • 1 1 E 1 • E 1 • 1 C = hie + • + + RE + + RE + hFE R2 hFE hFE R2 hFE R2 hFE

R 1 • D = V'BE + V'BE - VCC R2

-RE R R R E = - 1 • E - 1 2 2 2 hFE R2 hFE hFE

14 Table 5. Bias Stability Analysis at +65°C using the HBFP-0405 VCC = 2.7 V, VCE = 2 V, IC = 5 mA

#1 Non- #2 Voltage #3 Voltage #4 Voltage #5 Emitter Bias Circuit Stabilized Feedback Feedback Feedback Feedback w/Current Source

ICBO Stability 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 hFE Stability Factor 6.249877x10-5 4.031x10-5 3.924702x10-5 1.537669x10-5 8.707988x10-6

∆ IC due to ICBO (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 hFE (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%

Conclusion performance at an IC to IRB1 ratio This paper has presented the between 6 and 10 with a worst circuit analysis of four commonly case change of 41% in collector used stabilized bias networks and current. one non-stabilized bias network for the bipolar junction transistor. To complete the comparison, two In addition to the presentation of additional points representing the the basic design equations for the Non-Stabilized and the Voltage bias resistors for each network, Feedback networks have been an equation was presented for added to the graphs. They are collector current in terms of bias shown as single points because resistors and device parameters. only the base current is in The collector current equation addition to the collector current. was then differentiated with The Non-stabilized network has a respect to the three primary +129% change while the Voltage temperature dependent variables Feedback network has an resulting in three stability factors increase of 74.5%. It is also for each network. These stability interesting to note that the factors plus the basic collector Voltage Feedback with Current current equation give the designer Source network really offers no insight as to how best bias any benefit over the simpler Voltage bipolar transistor for best Feedback network. performance over hFE and temperature variations. The basic equations were then integrated into an AppCAD module providing the circuit designer an easy and effective way to analyze bias networks for bipolar .

15 References. 1. “A Cost-Effective Amplifier Design Approach at 425 MHz Using the HXTR-3101 Silicon Bipolar Transistor”, Hewlett- Packard Application Note 980, 2/81 (out of print).

2. Richter, Kenneth. “Design DC Stability Into Your Transistor Circuits”, Microwaves, December 1973, pp 40-46.

3. “Microwave Transistor Bias Considerations”, Hewlett-Packard Application Note 944-1, 8/80, (out of print).

4. “1800 to 1900 MHz Amplifier using the HBFP-0405 and HBFP- 0420 Low Noise Silicon Bipolar Transistors”, Hewlett-Packard Application Note 1160, (11/98), publication number 5968-2387E.

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