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| [[Bipolar transistor]] [[amplifiers]] must be properly [[Biasing (electronics)|biased]] to operate correctly. In circuits made with individual devices (discrete circuits), biasing networks consisting of [[resistor]]s are commonly employed. Much more elaborate biasing arrangements are used in [[integrated circuits]], for example, [[bandgap voltage reference]]s and [[current mirror]]s.
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| 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 [[direct current|DC]] collector–emitter voltage (''V''<sub>ce</sub>) and the collector current (''I''<sub>c</sub>) with no input signal applied. The term is normally used in connection with devices such as [[transistors]]. | |
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| ==Bias circuit requirements==
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| ===Signal requirements for Class A amplifiers===
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| For analog operation of a [[Class_A_amplifier#Class_A|Class A amplifier]], the Q-point is placed so the transistor stays in '''[[Bipolar junction transistor#Regions of operation|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.
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| The Q-point should be stable; in particular, it should be insensitive to variations in transistor parameters (for example, should not shift if transistor is replaced by another of the same type), variations in temperature, variations in power supply voltage and so forth.
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| The circuit must also be practical; both easily implemented and cost-effective.
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| ===Thermal considerations===
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| At constant current, the voltage across the emitter–base junction ''V''<sub>BE</sub> of a bipolar transistor ''decreases'' 2 mV (silicon) and 1.8mV (germanium) for each 1 °C rise in temperature (reference being 25 °C). By the [[Ebers–Moll model]], if the base–emitter voltage ''V''<sub>BE</sub> is held constant and the temperature rises, the current through the base–emitter diode ''I''<sub>B</sub> will increase, and thus the collector current ''I''<sub>C</sub> 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]]'''.<ref name=Sedra>
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| {{cite book
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| |author=A.S. Sedra and K.C. Smith
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| |title=Microelectronic Circuits
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| |year= 2004
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| |pages=p. 397, Figure 5.17, and p.&nb₡sp;1245
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| |publisher=Oxford University Press
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| |edition=5th
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| |location=New York
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| |isbn=0-19-514251-9
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| |nopp=yes}}
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| </ref> There are several approaches to mitigate bipolar transistor thermal runaway. For example,
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| * [[Negative feedback]] can be built into the biasing circuit so that increased collector current leads to decreased base current. Hence, the increasing collector current throttles its source.
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| * [[Heat sink]]s can be used that carry away extra heat and prevent the base–emitter temperature from rising.
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| * The transistor can be biased so that its collector is normally less than half of the power supply voltage, which implies that collector–emitter power dissipation is at its maximum value. Runaway is then impossible because increasing collector current leads to a decrease in dissipated power; this notion is known as the ''half-voltage principle.''
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| The circuits below primarily demonstrate the use of negative feedback to prevent thermal runaway.
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| == Types of bias circuit for Class A amplifiers ==
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| The following discussion treats five common biasing circuits used with Class A bipolar transistor amplifiers:
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| # Fixed bias
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| # Collector-to-base bias
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| # Fixed bias with emitter resistor
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| # Voltage divider bias
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| # Emitter bias
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| === Fixed bias (base bias) ===
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| [[Image:Fixed bias.PNG|thumb|right|Fixed bias (Base bias)]]
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| This form of biasing is also called ''base bias''. 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.
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| In the given circuit,
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| :V<sub>cc</sub> = I<sub>B</sub>R<sub>B</sub> + V<sub>be</sub>
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| Therefore,
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| :I<sub>B</sub> = (V<sub>cc</sub> - V<sub>be</sub>)/R<sub>B</sub>
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| For a given transistor, V<sub>be</sub> does not vary significantly during use. As V<sub>cc</sub> is of fixed value, on selection of R<sub>B</sub>, the base current I<sub>B</sub> is fixed. Therefore this type is called ''fixed bias'' type of circuit.
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| Also for given circuit,
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| :V<sub>cc</sub> = I<sub>C</sub>R<sub>C</sub> + V<sub>ce</sub>
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| Therefore,
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| :V<sub>ce</sub> = V<sub>cc</sub> - I<sub>C</sub>R<sub>C</sub>
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| The [[Bipolar_junction_transistor#Transistor 'alpha' and 'beta'|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.
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| Because
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| :I<sub>C</sub> = βI<sub>B</sub>
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| we can obtain I<sub>C</sub> as well. In this manner, operating point given as (V<sub>ce</sub>,I<sub>C</sub>) can be set for given transistor.
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| '''Merits:'''
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| * It is simple to shift the operating point anywhere in the active region by merely changing the base resistor (R<sub>B</sub>).
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| * A very small number of components are required.
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| '''Demerits:'''
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| * The collector current does not remain constant with variation in temperature or power supply voltage. Therefore the operating point is unstable.
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| * Changes in V<sub>be</sub> will change I<sub>B</sub> and thus cause I<sub>E</sub> to change. This in turn will alter the gain of the stage.
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| * When the transistor is replaced with another one, considerable change in the value of β can be expected. Due to this change the operating point will shift.
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| * For small-signal transistors (e.g., not power transistors) with relatively high values of β (i.e., between 100 and 200), this configuration will be prone to [[thermal runaway]]. In particular, the [[Amplifier#Stability_factor|stability factor]], which is a measure of the change in collector current with changes in reverse [[saturation current]], is approximately β+1. To ensure [[Amplifier#Stability_factor|absolute stability]] of the amplifier, a stability factor of less than 25 is preferred, and so small-signal transistors have large stability factors.{{citation needed|date=March 2010}}
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| '''Usage:'''
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| 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 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.
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| === Collector-to-base bias ===
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| [[Image:Collector to base bias.PNG|thumb|right|Collector-to-base bias]]
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| This configuration employs [[negative feedback]] to prevent [[thermal runaway]] and stabilize the operating point. In this form of biasing, the base resistor <math>R_{\text{B}}</math> is connected to the collector instead of connecting it to the DC source <math>V_{\text{cc}}</math>. So any thermal runaway will induce a voltage drop across the <math>R_{\text{C}}</math> resistor that will throttle the transistor's base current.
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| From [[Kirchhoff's voltage law]], the voltage <math>V_{\text{R}_{\text{b}}}</math> across the base resistor <math>R_{\text{b}}</math> is
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| :<math>V_{\text{R}_{\text{b}}} = V_{\text{cc}} \, - \, \mathord{\overbrace{(I_{\text{c}} + I_{\text{b}}) R_{\text{c}}}^{\text{Voltage drop across } R_{\text{c}}}} \, - \, \mathord{\overbrace{V_{\text{be}}}^{\text{Voltage at base}}}.</math>
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| By the [[Ebers–Moll model]], <math>I_{\text{c}} = \beta I_{\text{b}}</math>, and so
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| :<math>V_{\text{R}_{\text{b}}} = V_{\text{cc}} - (\overbrace{\beta I_{\text{b}}}^{I_{\text{c}}} + I_{\text{b}}) R_{\text{c}} - V_{\text{be}} = V_{\text{cc}} - I_{\text{b}} (\beta + 1) R_{\text{c}} - V_{\text{be}}.</math>
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| From [[Ohm's law]], the base current <math>I_{\text{b}} = V_{\text{R}_{\text{b}}} / R_{\text{b}}</math>, and so
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| :<math>\overbrace{I_{\text{b}} R_{\text{b}}}^{V_{\text{R}_{\text{b}}}} = V_{\text{cc}} - I_{\text{b}} (\beta + 1) R_{\text{c}} - V_{\text{be}}.</math>
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| Hence, the base current <math>I_{\text{b}}</math> is
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| :<math>I_{\text{b}} = \frac{ V_{\text{cc}} - V_{\text{be}} }{ R_{\text{b}} + ( \beta + 1 ) R_{\text{c}} }</math>
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| If <math>V_{\text{be}}</math> is held constant and temperature increases, then the collector current <math>I_{\text{c}}</math> increases. However, a larger <math>I_{\text{c}}</math> causes the voltage drop across resistor <math>R_{\text{c}}</math> to increase, which in turn reduces the voltage <math>V_{\text{R}_{\text{b}}}</math> across the base resistor <math>R_{\text{b}}</math>. A lower base-resistor voltage drop reduces the base current <math>I_{\text{b}}</math>, which results in less collector current <math>I_{\text{c}}</math>. Because an increase in collector current with temperature is opposed, the operating point is kept stable.
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| '''Merits:'''
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| * Circuit stabilizes the operating point against variations in temperature and β (i.e. replacement of transistor)
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| '''Demerits:'''
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| *In this circuit, to keep <math>I_{\text{c}}</math> independent of <math>\beta</math>, the following condition must be met:
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| ::<math>I_{\text{c}} = \beta I_{\text{b}} = \frac { \beta (V_{\text{cc}} - V_{\text{be}})}{R_{\text{b}} + R_{\text{c}} + \beta R_{\text{c}}} \approx \frac{(V_{\text{cc}} - V_{\text{be}})}{R_{\text{c}}}</math>
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| which is the case when
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| ::<math>\beta R_{\text{c}} \gg R_{\text{b}}.</math>
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| *As <math>\beta</math>-value is fixed (and generally unknown) for a given transistor, this relation can be satisfied either by keeping <math>R_{\text{c}}</math> fairly large or making <math>R_{\text{b}}</math> very low.
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| ** If <math>R_{\text{c}}</math> is large, a high <math>V_{\text{cc}}</math> is necessary, which increases cost as well as precautions necessary while handling.
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| ** If <math>R_{\text{b}}</math> is low, the reverse bias of the collector–base region is small, which limits the range of collector voltage swing that leaves the transistor in active mode.
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| * The resistor <math>R_{\text{b}}</math> causes an [[alternating current|AC]] feedback, reducing the [[voltage gain]] of the amplifier. This undesirable effect is a trade-off for greater [[Q-point]] stability.
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| '''Usage:'''
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| The feedback also decreases the input impedance of the amplifier as seen from the base, which can be advantageous.
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| Due to the gain reduction from feedback, this biasing form is used only when the trade-off for stability is warranted.
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| === Fixed bias with emitter resistor ===
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| [[Image:Fixed bias with emitter resistor.PNG|thumb|right|Fixed bias with emitter resistor]]
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| 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
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| V<sub>Rb</sub> = V<sub>CC</sub> - I<sub>e</sub>R<sub>e</sub> - V<sub>be</sub>.
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| From [[Ohm's law]], the base current is
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| I<sub>b</sub> = V<sub>Rb</sub> / R<sub>b</sub>.
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| The way feedback controls the bias point is as follows. If V<sub>be</sub> is held constant and temperature increases, emitter current increases. However, a larger I<sub>e</sub> increases the emitter voltage V<sub>e</sub> = I<sub>e</sub>R<sub>e</sub>, which in turn reduces the voltage V<sub>Rb</sub> across the base resistor. A lower base-resistor voltage drop reduces the base current, which results in less collector current because I<sub>c</sub> = β I<sub>B</sub>. Collector current and emitter current are related by I<sub>c</sub> = α I<sub>e</sub> with α ≈ 1, so the increase in emitter current with temperature is opposed, and the operating point is kept stable.
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| Similarly, if the transistor is replaced by another, there may be a change in I<sub>C</sub> (corresponding to change in β-value, for example). By similar process as above, the change is negated and operating point kept stable.
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| For the given circuit,
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| I<sub>B</sub> = (V<sub>CC</sub> - V<sub>be</sub>)/(R<sub>B</sub> + (β+1)R<sub>E</sub>).
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| '''Merits:'''
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| The circuit has the tendency to stabilize operating point against changes in temperature and β-value.
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| '''Demerits:'''
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| *In this circuit, to keep I<sub>C</sub> independent of β the following condition must be met:
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| ::<math>I_C = \beta I_B = \frac { \beta (V_{CC} - V_{be})}{R_B+ ( \beta+1) R_E} \approx \frac {(V_{CC} - V_{be})}{R_E}</math>
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| which is approximately the case if
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| ::( β + 1 )R<sub>E</sub> >> R<sub>B</sub>.
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| *As β-value is fixed for a given transistor, this relation can be satisfied either by keeping R<sub>E</sub> very large, or making R<sub>B</sub> very low.
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| ** If R<sub>E</sub> is of large value, high V<sub>CC</sub> is necessary. This increases cost as well as precautions necessary while handling.
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| ** If R<sub>B</sub> is low, a separate low voltage supply should be used in the base circuit. Using two supplies of different voltages is impractical.
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| *In addition to the above, R<sub>E</sub> causes ac feedback which reduces the voltage gain of the amplifier.
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| '''Usage:'''
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| 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.
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| Collector-Stabilized Biasing
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| === Voltage divider biasing ===
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| '''[[Image:Voltage divider bias.PNG|thumb|right|Voltage divider bias]]'''
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| ''The voltage divider is formed using external resistors'' R<sub>1</sub> and R<sub>2</sub>. The voltage across R<sub>2</sub> forward biases the emitter junction. By proper selection of resistors R<sub>1</sub> and R<sub>2</sub>, 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.
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| In this circuit the base voltage is given by:
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| <math>V_B = \ </math> voltage across <math>R_2 \ </math> <math>= V_{cc} \frac{R_2}{(R_1+R_2)} - I_B \frac{R_1 R_2}{(R_1+R_2)}</math><br />
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| :<math>\approx V_{cc} \frac{R_2}{(R_1+R_2)}</math> provided <math>I_B << I_2 = V_B / R_2 \ </math>.
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| Also <math>V_B = V_{be} + I_ER_E \ </math>
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| For the given circuit,
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| ::<math> I_B =\frac
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| {
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| \frac
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| {V_{CC}}{1+R_1/R_2}
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| - V_{be}
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| }
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| {( \beta + 1)R_E + R_1 \parallel R_2 } .</math>
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| '''Merits:'''
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| * Unlike above circuits, only one dc supply is necessary.
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| * Operating point is almost independent of β variation.
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| * Operating point stabilized against shift in temperature.
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| '''Demerits:'''
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| *In this circuit, to keep I<sub>C</sub> independent of β the following condition must be met:
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| ::<math>I_C = \beta I_B = \beta \frac
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| {
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| \frac
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| {V_{CC}}{1+R_1/R_2}
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| - V_{be}
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| }
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| {( \beta + 1)R_E + R_1 \parallel R_2 } \approx \frac
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| { \frac {V_{CC}}{1+R_1/R_2}- V_{be}}
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| {R_E} , </math>
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| which is approximately the case if
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| ::<math>( \beta + 1 ) R_E >> R_1 \parallel R_2</math>
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| where R<sub>1</sub> || R<sub>2</sub> denotes the [[Series and parallel circuits|equivalent resistance]] of R<sub>1</sub> and R<sub>2</sub> connected in parallel.
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| *As β-value is fixed for a given transistor, this relation can be satisfied either by keeping R<sub>E</sub> fairly large, or making R<sub>1</sub>||R<sub>2</sub> very low.
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| ** If R<sub>E</sub> is of large value, high V<sub>CC</sub> is necessary. This increases cost as well as precautions necessary while handling.
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| ** If R<sub>1</sub> || R<sub>2</sub> is low, either R<sub>1</sub> is low, or R<sub>2</sub> is low, or both are low. A low R<sub>1</sub> raises V<sub>B</sub> closer to V<sub>C</sub>, reducing the available swing in collector voltage, and limiting how large R<sub>C</sub> can be made without driving the transistor out of active mode. A low R<sub>2</sub> lowers V<sub>be</sub>, reducing the allowed collector current. Lowering both resistor values draws more current from the power supply and lowers the input resistance of the amplifier as seen from the base.
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| * AC as well as DC feedback is caused by R<sub>E</sub>, which reduces the AC voltage gain of the amplifier. A method to avoid AC feedback while retaining DC feedback is discussed below.
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| '''Usage:'''
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| The circuit's stability and merits as above make it widely used for linear circuits.
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| ==== Voltage divider with AC bypass capacitor ====
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| [[Image:Voltage divider with cap.PNG|thumb|right|Voltage divider with capacitor]]
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| The standard voltage divider circuit discussed above faces a drawback - AC feedback caused by resistor R<sub>E</sub> reduces the gain. This can be avoided by placing a capacitor (C<sub>E</sub>) in parallel with R<sub>E</sub>, as shown in circuit diagram.
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| === Emitter bias ===
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| [[Image:Emitter bias.PNG|thumb|right|Emitter bias]]
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| 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<sub>EE</sub> is used to forward-bias the emitter junction through R<sub>E</sub>. The positive supply V<sub>CC</sub> 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.
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| We know that,
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| V<sub>B</sub> - V<sub>E</sub> = V<sub>be</sub>
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| If R<sub>B</sub> is small enough, base voltage will be approximately zero. Therefore emitter current is,
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| I<sub>E</sub> = (V<sub>EE</sub> - V<sub>be</sub>)/R<sub>E</sub>
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| The operating point is independent of β if R<sub>E</sub> >> R<sub>B</sub>/β
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| '''Merit:'''
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| Good stability of operating point similar to voltage divider bias.
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| '''Demerit:'''
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| This type can only be used when a split (dual) power supply is available.
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| ==Class B and AB amplifiers==
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| ===Signal requirements===
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| [[Electronic amplifier#Class_B|Class B]] and [[Electronic amplifier#Class_AB|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<sub>c</sub> with no signal is just conducting (about 1% of maximum possible value). Class AB bias is when the collector current I<sub>c</sub> is about 1/4 of maximum possible value.
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| The class AB [[push–pull output]] amplifier circuit below could be the basis for a moderate-power audio amplifier.
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| <center>[[Image:Amplifier Circuit Small.svg|500px|A practical amplifier circuit]]<br>
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| <div class="references-small">A practical amplifier circuit</div></center>
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| 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 [[diode]]s 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).
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| 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.
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| 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.
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| <!-- ===Thermal considerations and over current protection=== -->
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| == See also ==
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| * [[Biasing (electronics)]]
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| * [[Small signal model]]
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| * [[Bipolar junction transistor]]
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| * [[MOSFET]]
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| ==References==
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| {{reflist|30em}}
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| == Further reading ==
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| {{refbegin}}
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| * {{cite book|last1=Patil|first1=P.K.|last2=Chitnis|first2=M.M.|title=Basic Electricity and Semiconductor Devices|publisher=Phadke Prakashan|year=2005}}
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| {{refend}}
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| == External links ==
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| * [http://www.answers.com/topic/bias-technology?cat=technology#Sci-Tech_Encyclopedia Bias] – from Sci-Tech Encyclopedia
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| * [http://www.tpub.com/neets/book7/25d.htm Electrical Engineering Training Series: Types of bias]
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| [[Category:Electronic engineering]]
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