Bipolar transistor biasing
Bipolar transistors must be properly biased to operate correctly. In circuits made with individual devices (discrete circuits), biasing networks consisting of resistors are commonly employed. Much more elaborate biasing arrangements are used in integrated circuits, for example, bandgap voltage references and current mirrors. The voltage divider configuration achieves the correct voltages by the use of resistors in certain patterns. By selecting the proper resistor values, stable current levels can be achieved that vary only little over temperature and with transistor properties such as β. The operating point of a device, also known as "bias point", "quiescent point , or Q-point", is the point on the output characteristics that shows the DC collector–emitter voltage ("V") and the collector current ("I") with no input signal applied. Bias circuit requirements. The bias circuit stabilizes the operating point of the transistor for variations in transistor characteristics and operating temperature. The gain of a transistor can vary significantly between different batches, which results in widely different operating points for sequential units in serial production or after replacement of a transistor. Due to the Early effect, the current gain is affected by the collector–emitter voltage. Both gain and base–emitter voltage  depend on the temperature. The leakage current also increases with temperature. A bias network is selected to reduce effects of device variability, temperature, and voltage changes. A bias circuit may be composed of only resistors, or may include elements such as temperature-dependent resistors, diodes, or additional voltage sources, depending on the range of operating conditions expected. Signal requirements for class-A amplifiers. For analog operation of a class-A amplifier, the Q-point is placed so the transistor stays in active mode (does not shift to operation in the saturation region or cut-off region) when input is applied . For digital operation, the Q-point is placed so the transistor does the contrary – switches from the "on" (saturation) to the "off" (cutoff) state. Often, the Q-point is established near the center of the active region of a transistor characteristic to allow similar signal swings in positive and negative directions. Thermal considerations. At constant current, the voltage across the emitter–base junction "V" of a bipolar transistor "decreases" by 2 mV (silicon) and 1.8 mV (germanium) for each 1 °C rise in temperature (reference being 25 °C). By the Ebers–Moll model, if the base–emitter voltage  V is held constant and the temperature rises, the current through the base–emitter diode "I" will increase, and thus the collector current "I" will also increase. Depending on the bias point, the power dissipated in the transistor may also increase, which will further increase its temperature and exacerbate the problem. This deleterious positive feedback results in thermal runaway. There are several approaches to mitigate bipolar transistor thermal runaway. For example, Types of bias circuit for class-A amplifiers. The following discussion treats five common biasing circuits used with class-A bipolar transistor amplifiers: Fixed bias (base bias). This form  of biasing is also called "base bias or fixed resistance biasing". In the example image on the right, the single power source (for example, a battery) is used for both collector and base of a transistor, although separate batteries can also be used. In the given circuit, Therefore, For a given transistor, V does not vary significantly during use. As V is of fixed value, on selection of R, the base current I is fixed. Therefore, this type is called "fixed bias" type of circuit. Also, for the given circuit, Therefore, The common-emitter current gain of a transistor is  an important parameter in circuit design, and is specified on the data sheet for a particular transistor. It is denoted as β on this page. Because we can obtain I as well. In this manner, operating point given as (V,I) can be set for given transistor. Advantages: Disadvantages: Usage: Due to the above inherent drawbacks, fixed bias is rarely used in linear circuits (i.e., those circuits which use the transistor as a current source). Instead, it is often used in circuits where the transistor is used as a switch. However, one application of fixed bias is to achieve crude  automatic gain control in the transistor by feeding the base resistor from a DC signal derived from the AC output of a later stage. Collector feedback bias. This configuration employs negative feedback to prevent thermal runaway and stabilize the operating point. In this form of biasing, the base resistor formula_1 is connected to the collector instead of connecting it to the DC source formula_2. So any thermal runaway will induce a voltage drop across the formula_3 resistor that will throttle the transistor's base current. From Kirchhoff's voltage law, the voltage formula_4 across the base resistor formula_1 is By  the Ebers–Moll model, formula_7, and so From Ohm's law, the base current formula_9, and so Hence, the base current formula_11 is If formula_13 is held constant and temperature increases, then the collector current formula_14 increases. However, a larger formula_14 causes the voltage drop across resistor formula_16 to increase, which in turn reduces the voltage formula_4 across the base resistor formula_1. A lower base-resistor voltage drop reduces the base current formula_11, which results in less collector current formula_14. Because an increase in collector current with temperature is opposed, the operating point is kept stable. Advantages: Disadvantages: which is  the case when Usage: The negative feedback also increases the input impedance of the amplifier as seen from the base, which can be advantageous. Due to the gain reduction from feedback, this biasing form is used only when the trade-off for stability is warranted. Fixed bias with emitter resistor. The fixed bias circuit is modified by attaching an external resistor to the emitter. This resistor introduces negative feedback that stabilizes the Q-point. From Kirchhoff's voltage law, the voltage across the base resistor is From Ohm's law, the base current is The way feedback controls the bias  point is as follows. If V is held constant and temperature increases, emitter current increases. However, a larger I increases the emitter voltage V = IR, which in turn reduces the voltage V across the base resistor. A lower base-resistor voltage drop reduces the base current, which results in less collector current because I = β I. Collector current and emitter current are related by I = α I with α ≈ 1, so the increase in emitter current with temperature is opposed, and the operating point is kept stable. Similarly, if the transistor is replaced by another, there  may be a change in I (corresponding to change in β-value, for example). By similar process as above, the change is negated and operating point kept stable. For the given circuit, Advantages: The circuit has the tendency to stabilize operating point against changes in temperature and β-value. Disadvantages: which is approximately the case if Usage: The feedback also increases the input impedance of the amplifier when seen from the base, which can be advantageous. Due to the above disadvantages, this type of biasing circuit is used only with careful consideration of the trade-offs involved. Collector-Stabilized Biasing . Voltage divider biasing or emitter bias. "The voltage divider is formed using external resistors" R and R. The voltage across R forward biases the emitter junction. By proper selection of resistors R and R, the operating point of the transistor can be made independent of β. In this circuit, the voltage divider holds the base voltage fixed independent of base current, provided the divider current is large compared to the base current. However, even with a fixed base voltage, collector current varies with temperature (for example) so an emitter resistor is added to stabilize the Q-point, similar to the  above circuits with emitter resistor. The voltage divider configuration achieves the correct voltages by the use of resistors in certain patterns. By manipulating the resistors in certain ways you can achieve more stable current levels without having β value affect it too much. In this circuit the base voltage is given by: formula_40 voltage across formula_41 formula_42 Also formula_45 For the given circuit, Advantages: Disadvantages: which is approximately the case if where R || R denotes the equivalent resistance of R and R connected in parallel. Usage: The circuit's stability and merits as above make it widely used for  linear circuits. Voltage divider with AC bypass capacitor. The standard voltage divider circuit discussed above faces a drawback – AC feedback caused by resistor R reduces the gain. This can be avoided by placing a capacitor (C) in parallel with R, as shown in circuit diagram. The result is that the DC operating point is well controlled, while the AC-gain is much higher (approaching β), rather than the much lower (but predictable) value of formula_49 without the capacitor. Emitter bias. When a split supply (dual power supply) is available, this biasing circuit is the most effective, and provides zero bias  voltage at the emitter or collector for load. The negative supply V is used to forward-bias the emitter junction through R. The positive supply V is used to reverse-bias the collector junction. Only two resistors are necessary for the common collector stage and four resistors for the common emitter or common base stage. We know that, V − V = V If R is small enough, base voltage will be approximately zero. Therefore, emitter current is, Ie = (V − V)/R The operating point is independent of β if Re » R/β Advantages: Disadvantages: This type can only  be used when a split (dual) power supply is available. Class-B and AB amplifiers. Signal requirements. Class B and AB amplifiers employ 2 active devices to cover the complete 360 deg of input signal flow. Each transistor is therefore biased to perform over approximately 180 deg of the input signal. Class B bias is when the collector current I with no signal is just conducting (about 1% of maximum possible value). Class-AB bias is when the collector current I is about 1/4 of maximum possible value. The class-AB push–pull output amplifier circuit below could be the  basis for a moderate-power audio amplifier. A practical amplifier circuit Q3 is a common emitter stage that provides amplification of the signal and the DC bias current through D1 and D2 to generate a bias voltage for the output devices. The output pair are arranged in class-AB push–pull, also called a complementary pair. The diodes D1 and D2 provide a small amount of constant voltage bias for the output pair, just biasing them into the conducting state so that crossover distortion is minimized. That is, the diodes push the output stage into class-AB mode (assuming that  the base-emitter drop of the output transistors is reduced by heat dissipation). This design automatically stabilizes its operating point, since overall feedback internally operates from DC up through the audio range and beyond. The use of fixed diode bias requires the diodes to be both electrically and thermally matched to the output transistors. If the output transistors conduct too much, they can easily overheat and destroy themselves, as the full current from the power supply is not limited at this stage. A common solution to help stabilize the output device operating point is to include some emitter resistors, typically  an ohm or so. Calculating the values of the circuit's resistors and capacitors is done based on the components employed and the intended use of the amplifier.