Bipolar transistor biasing

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Bipolar transistor amplifiers 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 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 (Vce) and the collector current (Ic) with no input signal applied. The term is normally used in connection with devices such as transistors.

Bias circuit requirements[edit]

Signal requirements for Class A amplifiers[edit]

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. 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. The circuit must also be practical; both easily implemented and cost-effective.

Thermal considerations[edit]

At constant current, the voltage across the emitter–base junction VBE 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 VBE is held constant and the temperature rises, the current through the base–emitter diode IB will increase, and thus the collector current IC 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.[1] There are several approaches to mitigate bipolar transistor thermal runaway. For example,

The circuits below primarily demonstrate the use of negative feedback to prevent thermal runaway.

Types of bias circuit for Class A amplifiers[edit]

The following discussion treats five common biasing circuits used with Class A bipolar transistor amplifiers:

  1. Fixed bias
  2. Collector-to-base bias
  3. Fixed bias with emitter resistor
  4. Voltage divider bias
  5. Emitter bias

Fixed bias (base bias)[edit]

Fixed bias (Base bias)

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.

In the given circuit,

Vcc = IBRB + Vbe

Therefore,

IB = (Vcc - Vbe)/RB

For a given transistor, Vbe does not vary significantly during use. As Vcc is of fixed value, on selection of RB, the base current IB is fixed. Therefore this type is called fixed bias type of circuit.

Also for given circuit,

Vcc = ICRC + Vce

Therefore,

Vce = Vcc - ICRC

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

IC = βIB

we can obtain IC as well. In this manner, operating point given as (Vce,IC) can be set for given transistor.

Merits:

Demerits:

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 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[edit]

Collector-to-base bias

This configuration employs negative feedback to prevent thermal runaway and stabilize the operating point. In this form of biasing, the base resistor R_{\text{B}} is connected to the collector instead of connecting it to the DC source V_{\text{cc}}. So any thermal runaway will induce a voltage drop across the R_{\text{C}} resistor that will throttle the transistor's base current.

From Kirchhoff's voltage law, the voltage V_{\text{R}_{\text{b}}} across the base resistor R_{\text{b}} is

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}}}.

By the Ebers–Moll model, I_{\text{c}} = \beta I_{\text{b}}, and so

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}}.

From Ohm's law, the base current I_{\text{b}} = V_{\text{R}_{\text{b}}} / R_{\text{b}}, and so

\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}}.

Hence, the base current I_{\text{b}} is

I_{\text{b}} = \frac{ V_{\text{cc}} - V_{\text{be}} }{ R_{\text{b}} + ( \beta + 1 ) R_{\text{c}} }

If V_{\text{be}} is held constant and temperature increases, then the collector current I_{\text{c}} increases. However, a larger I_{\text{c}} causes the voltage drop across resistor R_{\text{c}} to increase, which in turn reduces the voltage V_{\text{R}_{\text{b}}} across the base resistor R_{\text{b}}. A lower base-resistor voltage drop reduces the base current I_{\text{b}}, which results in less collector current I_{\text{c}}. Because an increase in collector current with temperature is opposed, the operating point is kept stable.

Merits:

Demerits:

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}}}

which is the case when

\beta R_{\text{c}} \gg R_{\text{b}}.

Usage: The feedback also decreases 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[edit]

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

VRb = VCC - IeRe - Vbe.

From Ohm's law, the base current is

Ib = VRb / Rb.

The way feedback controls the bias point is as follows. If Vbe is held constant and temperature increases, emitter current increases. However, a larger Ie increases the emitter voltage Ve = IeRe, which in turn reduces the voltage VRb across the base resistor. A lower base-resistor voltage drop reduces the base current, which results in less collector current because Ic = β IB. Collector current and emitter current are related by Ic = α Ie 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 IC (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,

IB = (VCC - Vbe)/(RB + (β+1)RE).

Merits:

The circuit has the tendency to stabilize operating point against changes in temperature and β-value.

Demerits:

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}

which is approximately the case if

( β + 1 )RE >> RB.

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[edit]

Voltage divider bias

The voltage divider is formed using external resistors R1 and R2. The voltage across R2 forward biases the emitter junction. By proper selection of resistors R1 and R2, 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.

In this circuit the base voltage is given by:

V_B = \ voltage across R_2 \ = V_{cc} \frac{R_2}{(R_1+R_2)} - I_B \frac{R_1 R_2}{(R_1+R_2)}

\approx V_{cc} \frac{R_2}{(R_1+R_2)} provided I_B << I_2 = V_B / R_2 \ .

Also V_B = V_{be} + I_ER_E \

For the given circuit,

 I_B =\frac  {  \frac  {V_{CC}}{1+R_1/R_2}  - V_{be} } {( \beta + 1)R_E + R_1 \parallel R_2 } .

Merits:

Demerits:

I_C = \beta I_B = \beta \frac  {   \frac  {V_{CC}}{1+R_1/R_2}  - V_{be} } {( \beta + 1)R_E + R_1 \parallel R_2 } \approx \frac  { \frac {V_{CC}}{1+R_1/R_2}- V_{be}} {R_E} ,

which is approximately the case if

( \beta + 1 ) R_E >> R_1 \parallel R_2

where R1 || R2 denotes the equivalent resistance of R1 and R2 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[edit]

Voltage divider with capacitor

The standard voltage divider circuit discussed above faces a drawback - AC feedback caused by resistor RE reduces the gain. This can be avoided by placing a capacitor (CE) in parallel with RE, as shown in circuit diagram.

Emitter bias[edit]

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 VEE is used to forward-bias the emitter junction through RE. The positive supply VCC 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,

VB - VE = Vbe

If RB is small enough, base voltage will be approximately zero. Therefore emitter current is,

IE = (VEE - Vbe)/RE

The operating point is independent of β if RE >> RB

Merit:

Good stability of operating point similar to voltage divider bias.

Demerit:

This type can only be used when a split (dual) power supply is available.

Class B and AB amplifiers[edit]

Signal requirements[edit]

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 Ic with no signal is just conducting (about 1% of maximum possible value). Class AB bias is when the collector current Ic 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
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.

See also[edit]

References[edit]

  1. ^ A.S. Sedra and K.C. Smith (2004). Microelectronic Circuits (5th ed.). New York: Oxford University Press. p. 397, Figure 5.17, and p.&nb₡sp;1245. ISBN 0-19-514251-9. 

Further reading[edit]

  • Patil, P.K.; Chitnis, M.M. (2005). Basic Electricity and Semiconductor Devices. Phadke Prakashan. 

External links[edit]