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**Topic 5 Bipolar Junction Transistors**

ECE 271 Electronic Circuits I Topic 5 Bipolar Junction Transistors Chap 5 - 1 NJIT ECE271 Dr. Serhiy Levkov

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**Chapter Goals Explore physical structure of bipolar transistor**

Understand bipolar transistor action and importance of carrier transport across base region Study terminal characteristics of BJT. Explore differences between npn and pnp transistors. Define four operation regions of BJT. Explore simplified models for each operation region. Study Q-point Biasing of BJT. Chap 5 - 2 NJIT ECE271 Dr. Serhiy Levkov

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**Bipolar Transistor: Physical Structure**

Consists of 3 alternating layers of n- and p-type semiconductor called emitter (E), base (B) and collector (C). Chap 5 - 3 NJIT ECE271 Dr. Serhiy Levkov

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**Bipolar Transistor: Physical Structure**

Consists of 3 alternating layers of n- and p-type semiconductor called emitter (E), base (B) and collector (C). Majority of current enters collector, crosses base region and exits through emitter. A small current also enters base terminal, crosses base-emitter junction and exits through emitter. Chap 5 - 4 NJIT ECE271 Dr. Serhiy Levkov

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**Bipolar Transistor: Physical Structure**

Consists of 3 alternating layers of n- and p-type semiconductor called emitter (E), base (B) and collector (C). Majority of current enters collector, crosses base region and exits through emitter. A small current also enters base terminal, crosses base-emitter junction and exits through emitter. Carrier transport in the active base region directly beneath the heavily doped (n+) emitter dominates i-v characteristics of BJT. Chap 5 - 5 NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor and pn-junctions**

Base-emitter voltage vBE and base-collector voltage vBC determine currents in transistor Chap 5 - 6 NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor and pn-junctions**

Base-emitter voltage vBE and base-collector voltage vBC determine currents in transistor They are said to be positive when they forward-bias their respective pn junctions. Chap 5 - 7 NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor and pn-junctions**

Base-emitter voltage vBE and base-collector voltage vBC determine currents in transistor They are said to be positive when they forward-bias their respective pn junctions. The terminal currents are collector current(iC ), base current (iB) and emitter current (iE). Chap 5 - 8 NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor and pn-junctions**

Base-emitter voltage vBE and base-collector voltage vBC determine currents in transistor They are said to be positive when they forward-bias their respective pn junctions. The terminal currents are collector current(iC ), base current (iB) and emitter current (iE). Primary difference between BJT and FET is that iB is significant while iG = 0. Chap 5 - 9 NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor: How it Works (common emitter)**

Left pn junction is forward biased – open. Right pn junction is reverse biased – closed. If those would be regular diodes – no current would exist btw emitter and collector. But the width of the base is very narrow, two back-to-back pn junctions are tightly coupled. Electrons injected from emitter into base region rush through it and are removed by collector, creating collector current IC. Some of the electrons will travel to the base, creating base current IB . Base current is usually quite smaller: where b is the common-emitter current gain usually is in the range 50 to 200. Thus transistor works as a current amplifier: Look for relationship btw iB and iC. Simulation: Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor: How it Works (common base)**

Left pn junction is forward biased – open. Right pn junction is reverse biased – closed. Similarly, since the width of the base is very narrow, electrons injected from emitter into the base region rush through it and are removed by collector, creating collector current IC. Some of the electrons will travel to the base, creating base current IB . Base current is usually quite small. Considering transistor as a super node: where is common-base current gain. Look for relationship btw iE and iC. Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Forward Characteristics**

BJT is almost symmetrical, except that usually emitter is more heavily doped then collector. Thus we consider two models: when BE is forward biased and BC is zero biased (forward characteristics) Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Forward Characteristics**

BJT is almost symmetrical, except that usually emitter is more heavily doped then collector. Thus we consider two models: when BE is forward biased and BC is zero biased (forward characteristics) when BC is forward biased and BE is zero biased (reverse characteristics). Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Forward Characteristics**

Forward transport current is Where IS is saturation current VT = kT/q =0.025 V at room temperature BJT is almost symmetrical, except that usually emitter is more heavily doped then collector. Thus we consider two models: when BE is forward biased and BC is zero biased (forward characteristics) when BC is forward biased and BE is zero biased (reverse characteristics). Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Forward Characteristics**

Forward transport current is Where IS is saturation current VT = kT/q =0.025 V at room temperature Base current: is forward common-emitter current gain BJT is almost symmetrical, except that usually emitter is more heavily doped then collector. Thus we consider two models: when BE is forward biased and BC is zero biased (forward characteristics) when BC is forward biased and BE is zero biased (reverse characteristics). Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Forward Characteristics**

Forward transport current is Where IS is saturation current VT = kT/q =0.025 V at room temperature Base current: is forward common-emitter current gain BJT is almost symmetrical, except that usually emitter is more heavily doped then collector. Thus we consider two models: when BE is forward biased and BC is zero biased (forward characteristics) when BC is forward biased and BE is zero biased (reverse characteristics). Emitter current is given by is forward common- base current gain Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Forward Characteristics**

Forward transport current is Where IS is saturation current VT = kT/q =0.025 V at room temperature Base current: is forward common-emitter current gain BJT is almost symmetrical, except that usually emitter is more heavily doped then collector. Thus we consider two models: when BE is forward biased and BC is zero biased (forward characteristics) when BC is forward biased and BE is zero biased (reverse characteristics). Emitter current is given by is forward common- base current gain In the forward active operation region: Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Reverse Characteristics**

Reverse transport current is Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Reverse Characteristics**

is reverse common-emitter current gain Reverse transport current is Base current is given by Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Reverse Characteristics**

is reverse common-emitter current gain Base currents in forward and reverse modes are different due to asymmetric doping levels in emitter and collector regions. Reverse transport current is Base current is given by Chap NJIT ECE271 Dr. Serhiy Levkov

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**npn Transistor Model: Reverse Characteristics**

is reverse common-emitter current gain Base currents in forward and reverse modes are different due to asymmetric doping levels in emitter and collector regions. Emitter current is given by Reverse transport current is is reverse common-base current gain Base current is given by In the reverse active operation region: Chap NJIT ECE271 Dr. Serhiy Levkov

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**pnp Transistor: Structure**

Voltages vEB and vCB are positive when they forward bias their respective pn junctions. Collector current and base current exit transistor terminals and emitter current enters the device. Chap NJIT ECE271 Dr. Serhiy Levkov

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**pnp Transistor: Forward Characteristics**

Base current is given by Emitter current is given by Forward transport current is Chap NJIT ECE271 Dr. Serhiy Levkov

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**pnp Transistor: Reverse Characteristics**

Base current is given by Emitter current is given by Reverse transport current is Chap NJIT ECE271 Dr. Serhiy Levkov

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**Operation Regions of Bipolar Transistors**

Binary Logic States Chap NJIT ECE271 Dr. Serhiy Levkov

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**i-v Characteristics of BJT (Recall MOSFET)**

Chap NJIT ECE271 Dr. Serhiy Levkov

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**i-v Characteristics of BJT (npn): Common-Emitter Output Characteristics**

Circuit to measure output characteristic: For iB = 0, transistor is cutoff. When iB > 0, and increases, iC also increases. For vCE > vBE, npn transistor is in forward-active region, iC = bF iB is independent of vCE. For vCE < vBE, transistor is in saturation (the voltage btw collector and emitter is small, base collector diode conducts). For vCE < 0, roles of collector and emitter reverse. npn For pnp, iC vs. vEC Chap NJIT ECE271 Dr. Serhiy Levkov

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**i-v Characteristics of BJT (pnp): Common-Emitter Output Characteristics**

Circuit to measure output characteristic: Chap NJIT ECE271 Dr. Serhiy Levkov

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**i-v Characteristics of BJT (npn): Common-Emitter Transfer Characteristic**

Defines relation between collector current and base-emitter voltage of transistor. Almost identical to transfer characteristic of pn junction diode Setting vBC = 0 in the collector-current expression yields Collector current expression has the same form as that of the diode equation Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Cutoff Region Model**

The full BJT model is the so called Gummel-Poon transport model, which is relatively complicated. For our purpose, it will be enough to use the simplified model. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Cutoff Region Model**

The full BJT model is the so called Gummel-Poon transport model, which is relatively complicated. For our purpose, it will be enough to use the simplified model. In cutoff region both junctions are reverse-biased, transistor is off state: vBE < 0, vBC < 0 If we assume that , where VT = kT/q = and -4kT/q = -0.1 V, then , and the transport model terminal current equations simplifies: Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Cutoff Region Model**

The full BJT model is the so called Gummel-Poon transport model, which is relatively complicated. For our purpose, it will be enough to use the simplified model. In cutoff region both junctions are reverse-biased, transistor is off state: vBE < 0, vBC < 0 If we assume that , where VT = kT/q = and -4kT/q = -0.1 V, then , and the transport model terminal current equations simplifies: As will be shown in the example (next slide) those currents are so small that for practical purposes, they are essentially zero. Thus, equivalent circuit: Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Cutoff Region Model (Example)**

Problem: Estimate terminal currents using simplified transport model Given data: IS = A, aF = 0.95, aR = 0.25, VBE = 0 V, VBC = -5 V Assumptions: Simplified transport model assumptions Analysis: From given voltages, we know that transistor is in cutoff. For practical purposes, all three currents are essentially zero. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region: Model**

In forward-active region, emitter-base junction is forward-biased and collector-base junction is reverse-biased: vBE > 0, vBC < 0 The simplified transport model terminal current equations: and Conclusion. All currents are independent of the base-collector voltage vBC . The collector current can be modeled as a current source that is controlled by the base-emitter voltage. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region: Circuit**

NL CVD Current in base-emitter diode is amplified by common-emitter current gain bF and appears at collector; base and collector currents are exponentially related to base-emitter voltage. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region: Circuit**

NL CVD Current in base-emitter diode is amplified by common-emitter current gain bF and appears at collector; base and collector currents are exponentially related to base-emitter voltage. For simplicity, base-emitter diode can be replaced by constant voltage drop model (VBE = 0.7 V) since it is forward-biased in forward-active region. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region: Circuit**

NL CVD Current in base-emitter diode is amplified by common-emitter current gain bF and appears at collector; base and collector currents are exponentially related to base-emitter voltage. For simplicity, base-emitter diode can be replaced by constant voltage drop model (VBE = 0.7 V) since it is forward-biased in forward-active region. Like with the diode, using NL model circuit, requires solving nonlinear diode equation in combination with other equations for the circuit in order to find vBE , iB and iC . Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region: Circuit**

NL CVD Current in base-emitter diode is amplified by common-emitter current gain bF and appears at collector; base and collector currents are exponentially related to base-emitter voltage. For simplicity, base-emitter diode can be replaced by constant voltage drop model (VBE = 0.7 V) since it is forward-biased in forward-active region. Like with the diode, using NL model circuit, requires solving nonlinear diode equation in combination with other equations for the circuit in order to find vBE , iB , iC , and iE . When using CVD model, vBE is postulated as 0.7V, and iB , iC , and iE are found in combination with other equations for the circuit. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region Model (Example 1)**

Problem: Estimate terminal currents and base-emitter voltage Given data: IS =10-16 A, aF = 0.95, VBC = VB - VC = -5 V, IE = 100 mA Assumptions: Simplified transport model assumptions, room temperature operation, VT = 25.0 mV Do example on the board Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region Model (Example 1)**

Problem: Estimate terminal currents and base-emitter voltage Given data: IS =10-16 A, aF = 0.95, VBC = VB - VC = -5 V, IE = 100 mA Assumptions: Simplified transport model assumptions, room temperature operation, VT = 25.0 mV Analysis: Current source forward-biases base-emitter diode, VBE > 0, VBC < 0, we know that transistor is in forward-active operation region. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region Model (Example 2)**

Problem: Estimate terminal currents, base-emitter and base-collector voltages. Given data: IS = A, aF = 0.95, VC = +5 V, IB = 100 mA Assumptions: Simplified transport model assumptions, room temperature operation, VT = 25.0 mV Do example on the board Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region Model (Example 2)**

Problem: Estimate terminal currents, base-emitter and base-collector voltages. Given data: IS = A, aF = 0.95, VC = +5 V, IB = 100 mA Assumptions: Simplified transport model assumptions, room temperature operation, VT = 25.0 mV Analysis: Current source causes base current to forward-bias base-emitter diode, VBE > 0, VBC <0, we know that transistor is in forward-active operation region. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region Model (Example 3)**

Problem: Find Q-point Given data: bF = 50, bR = 1 VBC = VB - VC = -9 V Assumptions: Forward-active region of operation, VBE = 0.7 V Do example on the board Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Forward-Active Region Model (Example 3)**

Problem: Find Q-point Given data: bF = 50, bR = 1 VBC = VB - VC = -9 V Assumptions: Forward-active region of operation, VBE = 0.7 V Analysis: Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Reverse-Active Region: Model**

In reverse-active region, base-collector junction is forward-biased and base-emitter junction is reverse-biased: vBE < 0, vBC > 0 The simplified transport model terminal current equations are: and Conclusion. All currents are independent of the base-collector voltage vBE . The emitter current can be modeled as a current source that is controlled by the base-collector voltage. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Reverse-Active Region: Circuit**

or CVD NL Current in base-collector diode is amplified by the gain bR and appears at collector; base and collector currents are exponentially related to base-collector voltage. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Reverse-Active Region: Circuit**

or CVD NL Current in base-collector diode is amplified by the gain bR and appears at collector; base and collector currents are exponentially related to base-collector voltage. Base-collector diode can be replaced by constant voltage drop model (VBC = 0.7 V) since it is forward-biased in reverse-active region. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Reverse-Active Region: Circuit**

or CVD NL Current in base-collector diode is amplified by the gain bR and appears at collector; base and collector currents are exponentially related to base-collector voltage. Base-collector diode can be replaced by constant voltage drop model (VBC = 0.7 V) since it is forward-biased in reverse-active region. Like with the diode, using NL model circuit, requires solving nonlinear diode equation in combination with other equations for the circuit in order to find vBC , iB , iC and iE . Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Reverse-Active Region: Circuit**

or CVD NL Current in base-collector diode is amplified by the gain bR and appears at collector; base and collector currents are exponentially related to base-collector voltage. Base-collector diode can be replaced by constant voltage drop model (VBC = 0.7 V) since it is forward-biased in reverse-active region. Like with the diode, using NL model circuit, requires solving nonlinear diode equation in combination with other equations for the circuit in order to find vBC , iB , iC and iE . When using CVD model, vBC is postulated as 0.7V, and iB , iC and iE are found in combination with other equations for the circuit. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Reverse-Active Region: Example**

Problem: Find Q-point Given data: bF = 50, bR = 1 VBE = VB - VE = -9 V. Combination of R and the voltage source forward biases base-collector junction. Do example on the board Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Reverse-Active Region: Example**

Problem: Find Q-point Given data: bF = 50, bR = 1 VBE = VB - VE = -9 V. Combination of R and the voltage source forward biases base-collector junction. Assumptions: Reverse-active region of operation, VBC = 0.7 V Analysis: Chap NJIT ECE271 Dr. Serhiy Levkov

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**Simplified Saturation Region Model**

In saturation region, both junctions are forward-biased, and the transistor operates with a relatively large current and a small voltage between collector and emitter. This is vCESAT - the saturation voltage for the npn BJT. No simplified expressions exist for terminal currents other than iC + iB = iE. They are determined by external circuit elements. Simplified Model Chap NJIT ECE271 Dr. Serhiy Levkov

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Nonideal BJT Behavior Junction Breakdown Voltages. If reverse voltage across either of the two pn junctions in the transistor is too large, the corresponding diode will break down. Minority Carrier Transport effects in the Base Region. Base transit time (associated with storing minority-carrier charge Q required to establish career gradient in base region) places upper limit on useful operating frequency of transistor. Diffusion Capacitance: for vBE and hence iC to change, charge stored in base region must also change. b-Cutoff Frequency, Transconductance and Transit Time - forward-biased diffusion and reverse-biased pn junction capacitances of BJT cause current gain to be frequency-dependent. Early Effect and Early Voltage - in a practical BJT, output characteristics have a positive slope in forward-active region; collector current is not independent of vCE. Chap NJIT ECE271 Dr. Serhiy Levkov

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Biasing for BJT Digital logic circuits and linear amplifiers use very different operating points of transistors. This circuit can be either a logic inverter or a linear amplifier depending on a choice of Q-point Chap NJIT ECE271 Dr. Serhiy Levkov

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Biasing for BJT Goal of biasing is to establish known Q-point which in turn establishes initial operating region of the transistor. For a BJT, the Q-point is represented by (IC, VCE) for an npn transistor or (IC, VEC) for a pnp transistor. In general, during circuit analysis, we use simplified mathematical relationships derived for a specified operation region, and the Early voltage is assumed to be infinite. Two practical biasing circuits used for a BJT are: Four-Resistor Bias network Two-Resistor Bias network The constant VBE is not practical because of very steep iv curve and strong dependence on temperature. Much better circuits are those of 4-resistor and 2-resistor biasing. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Two-Resistor Bias Network for BJT:**

Problem: Find Q-point for pnp transistor in 2-resistor bias circuit with given parameters. Given data: bF = 50, VCC = 9 V Assumptions: Forward-active operation region, VEB = 0.7 V Do example on the board Chap NJIT ECE271 Dr. Serhiy Levkov

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**Two-Resistor Bias Network for BJT:**

Problem: Find Q-point for pnp transistor in 2-resistor bias circuit with given parameters. Given data: bF = 50, VCC = 9 V Assumptions: Forward-active operation region, VEB = 0.7 V Analysis: Forward-active region operation is correct Q-point is : (6.01 mA, 2.88 V) Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT**

One of the best circuits for stabilizing the Q-point. R1 and R2 - a voltage divider used to establish a fixed voltage at the base . RE and RC a- define the emitter current and CE voltage. Do example on the board Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT**

One of the best circuits for stabilizing the Q-point. R1 and R2 - a voltage divider used to establish a fixed voltage at the base . RE and RC a- define the emitter current and CE voltage. Transform the left (input) part of the circuit with using Thevenin equivalent. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT**

Left loop: Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT**

Right loop: Left loop: Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT**

Right loop: All calculated currents are > 0 VBC = VBE - VCE = = V Hence, base-collector junction is reverse-biased, and assumption of forward-active region operation is correct. Left loop: F. A. region correct: Q-point is (201 mA, 4.32 V) Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT (load line analysis)**

Load-line for the circuit is: The two points needed to plot the load line are (0, 12 V) and (314 mA, 0). Resulting load line is plotted on common-emitter output characteristics. IB = 2.7 mA, intersection of corresponding characteristic with load line gives Q-point. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT: Design Objectives**

The input loop : Then: Also: Thus design objectives: The value of REQ is usually designed small, to neglect the voltage drop in it. Then IC , IE , are set by VEQ , VBE , RE Also, VEQ is designed to be large enough that small variations in the assumed value of VBE won’t affect IE. This implies that IB << IR2, so that IR1 = IR2. So base current doesn’t disturb voltage divider action. This implies that IB << IE, so that Q-point is independent of base current. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT: Design Objectives**

From the good engineering approximation for the 4 resistor biasing: From the input loop: The value of REQ is usually designed small, to neglect the voltage drop in it. Then IC , IE , are set by VEQ , VBE , RE Also, VEQ is designed to be large enough that small variations in the assumed value of VBE won’t affect IE. This implies that IB << IR2, so that IR1 = IR2. So base current doesn’t disturb voltage divider action. This implies that IB << IE, so that Q-point is independent of base current. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT: Design Guidelines**

Choose Thévenin equivalent base voltage Select R1 to set I1 = 9IB. Select R2 to set I2 = 10IB. RE is determined by VEQ and desired IC. RC is determined by desired VCE. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT: Design Example**

Problem: Design 4-resistor bias circuit with given parameters. Given data: IC = 750 mA, bF = 100, VCC = 15 V, VCE = 5 V Assumptions: Forward-active operation region, VBE = 0.7 V Analysis: Divide (VCC - VCE) equally between RE and RC. Thus, VE = 5 V and VC = 10 V Chap NJIT ECE271 Dr. Serhiy Levkov

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**Four-Resistor Bias Network for BJT Saturation region**

Consider the first example, where RC is replaced with 56 kOhm Do example on the board Chap NJIT ECE271 Dr. Serhiy Levkov

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**Tolerances - Worst-Case Analysis: Example (1)**

Typically, tolerance of discrete transistors is 10%. 5%, 1%. In IC – 30%. Power supply – (5-10)%. Current gain even more. Thus: the problem of tolerance analysis. Problem: Find worst-case values of IC and VCE. Given data: bFO = 75 with 50% tolerance, VA = 50 V, 5 % tolerance on VCC , 10% tolerance for each resistor. Analysis: To max IC , VEQ should be maximized, RE should be minimized and opposite for minimizing IC. Extremes of RE are: 14.4 kW and kW. To maximize VEQ, VCC and R1 should be maximized, R2 should be minimized and opposite for minimizing VEQ. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Tolerances - Worst-Case Analysis: Example (2)**

Extremes of VEQ are: 4.78 V and 3.31 V. Using these values, extremes for IC are: 283 mA and 148 mA. To maximize VCE , IC and RC should be minimized, and opposite for minimizing VEQ. Extremes of VCE are: 7.06 V and V The min is actually a saturated region, hence calculated values for VCE and IC actually not correct. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Tolerances - Monte Carlo Analysis**

In real circuits, it is unlikely that various components will reach their extremes at the same time, instead they will have some statistical distribution. Hence worst-case analysis over-estimates extremes of circuit behavior. In Monte Carlo analysis, values of each circuit parameter are randomly selected from possible distributions of parameters and used to analyze the circuit. Random parameter sets are generated, and the statistical behavior of circuit is built up from the analysis of many test cases. Chap NJIT ECE271 Dr. Serhiy Levkov

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**Tolerances - Monte Carlo Analysis: Example**

Full results of Monte Carlo analysis of 500 cases of the 4-resistor bias circuit yields mean values of 207 mA and 4.06 V for IC and VCE respectively which are close to values originally estimated from nominal circuit elements. Standard deviations are 19.6 mA and 0.64 V respectively. The worst-case calculations lie well beyond the extremes of the distributions Chap NJIT ECE271 Dr. Serhiy Levkov

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BJT SPICE Model Besides capacitances associated with the physical structure, additional components are: diode current iS and substrate capacitance CJS related to the large area pn junction that isolates the collector from the substrate and one transistor from the next. RB is resistance between external base contact and intrinsic base region. Collector current must pass through RC on its way to active region of collector-base junction. RE models any extrinsic emitter resistance in device. Chap NJIT ECE271 Dr. Serhiy Levkov

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**BJT SPICE Model Typical Values**

Saturation Current IS = 3x10-17 A Forward current gain BF = 100 Reverse current gain BR = 0.5 Forward Early voltage VAF = 75 V Base resistance RB = 250 W Collector Resistance RC = 50 W Emitter Resistance RE = 1 W Forward transit time TT = 0.15 ns Reverse transit time TR = 15 ns Chap NJIT ECE271 Dr. Serhiy Levkov

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