Bipolar transistor biasing

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Small signal bipolar transistor amplifiers must be properly biased to operate correctly. In circuits made with individual devices (discrete circuits), biasing networks consisting of discrete components such as resistors and capacitors are commonly employed. In integrated circuits much more elaborate biasing arrangements are used, for example, bandgap voltage references and current mirrors.

Contents 1 Requirements upon biasing circuit 2 Note on temperature dependence 3 Types of bias circuit 3.1 Fixed bias (base bias) 3.2 Collector-to-base bias 3.3 Fixed bias with emitter resistor 3.4 Voltage divider bias 3.4.1 Voltage divider with AC bypass capacitor 3.5 Emitter bias 4 References 5 Further reading 6 See also 7 External links

[edit] Requirements upon biasing circuit

The operating point of a device, also known as bias point or quiescent point (or simply Q-point), is the DC voltage and/or current which, when applied to a device, causes it to operate in a certain desired fashion.

1. For analog circuit operation, 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 "on" to "off" state. Often, Q-point is established near the center of active region of transistor characteristic to allow similar signal swings in positive and negative directions.
2. 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.
3. The circuit must be practical: easily implemented and cost-effective.

[edit] Note on temperature dependence

At constant current, the voltage across the emitter-base junction V_BE of a bipolar transistor decreases about 2 mV for each 1°C rise in temperature.^[1] Oppositely, if V_BE: is held constant and the temperature rises, I_C increases, also increasing the power consumed in the transistor, tending to further increase its temperature. Unless steps are taken to control this positive feedback of increased temperature → increased current → increased temperature, thermal runaway ensues.^[2] An electrical approach to avoid thermal runaway is to use negative feedback, as described in conjunction with some of the circuits below. A different approach is to use heat sinks that carry away the extra heat.

[edit] Types of bias circuit

The following discussion treats five common biasing circuits used with bipolar transistors:

1. Fixed bias
2. Collector-to-base bias
3. Fixed bias with emitter resistor
4. Voltage divider bias
5. Emitter 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 transistor, although separate batteries can also be used.

In the given circuit,

V_CC = I_BR_B + V_be

Therefore,

I_B = (V_CC - V_be)/R_B

For a given transistor, V_be does not vary significantly during use. As V_CC is of fixed value, on selection of R_B, the base current I_B is fixed. Therefore this type is called fixed bias type of circuit.

Also for given circuit,

V_CC = I_CR_C + V_ce

Therefore,

V_ce = V_CC - I_CR_C

From this equation we can obtain V_ce. Since I_C = βI_B, we can obtain I_C as well. In this manner, operating point given as (V_CE,I_C) can be set for given transistor.

Merits:

• It is simple to shift the operating point anywhere in the active region by merely changing the base resistor (R_B).
• Very few number of components are required.

Demerits:

• The collector current does not remain constant with variation in temperature or power supply voltage. Therefore the operating point is unstable.
• 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.

Usage:

Due to the above inherent drawbacks, fixed bias is rarely used in linear circuits, ie. those circuits which use the transistor as a current source. Instead it is often used in circuits where transistor is used as a switch.

[edit] Collector-to-base bias

In this form of biasing, the base resistor R_B is connected to the collector instead of connecting it to the battery V_CC. That means this circuit employs negative feedback to stabilize the operating point.

From Kirchhoff's voltage law, the voltage across the base resistor is

V_Rb = V_CC - (I_C + I_b)R_C - V_be.

From Ohm's law, the base current is

I_b = V_Rb / R_b.

The way feedback controls the bias point is as follows. If V_be is held constant and temperature increases, collector current increases. However, a larger I_C causes the voltage drop across resistor R_C to increase, which in turn reduces the voltage V_Rb across the base resistor. A lower base-resistor voltage drop reduces the base current, which results in less collector current, so increase in collector current with temperature is opposed, and operating point is kept stable.

For the given circuit,

I_B = (V_CC - V_be) / (R_B+βR_C).

Merits:

• Circuit stabilizes the operating point against variations in temperature and β (ie. replacement of transistor)

Demerits:

• In this circuit, to keep I_C independent of β the following condition must be met:

which is approximately the case if

β R_C >> R_B.

• As β-value is fixed for a given transistor, this relation can be satisfied either by keeping R_C fairly large, or making R_B very low.

• If R_C is of large value, high V_CC is necessary. This increases cost as well as precautions necessary while handling.
• If R_B is low, the reverse bias of the collector-base is small, which limits the range of collector voltage swing that leaves the transistor in active mode.

• The resistor R_B causes an ac feedback, reducing the voltage gain of the amplifier. This undesirable effect is a trade-off for greater Q-point stability.

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.

[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

V_Rb = V_CC - I_eR_e - V_be.

From Ohm's law, the base current is

I_b = V_Rb / R_b.

The way feedback controls the bias point is as follows. If V_be is held constant and temperature increases, emitter current increases. However, a larger I_e increases the emitter voltage V_e = I_eR_e, which in turn reduces the voltage V_Rb across the base resistor. A lower base-resistor voltage drop reduces the base current, which results in less collector current because I_c = ß I_B. Collector current and emitter current are related by I_c = α I_e with α ≈ 1, so increase in emitter current with temperature is opposed, and operating point is kept stable.

Similarly, if the transistor is replaced by another, there may be a change in I_C (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,

I_B = (V_CC - V_be)/(R_B + (β+1)R_E).

Merits:

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

Demerits:

• In this circuit, to keep I_C independent of β the following condition must be met:

which is approximately the case if

( β + 1 )R_E >> R_B.

• As β-value is fixed for a given transistor, this relation can be satisfied either by keeping R_E very large, or making R_B very low.

• If R_E is of large value, high V_CC is necessary. This increases cost as well as precautions necessary while handling.
• If R_B is low, a separate low voltage supply should be used in the base circuit. Using two supplies of different voltages is impractical.

• In addition to the above, R_E causes ac feedback which reduces the voltage gain of the amplifier.

Usage:

The feedback also increases the input impedance of the amplifier as 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.

[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:

voltage across

provided .

Also

For the given circuit,

Merits:

• Unlike above circuits, only one dc supply is necessary.
• Operating point is almost independent of β variation.
• Operating point stabilized against shift in temperature.

Demerits:

• In this circuit, to keep I_C independent of β the following condition must be met:

which is approximately the case if

where R₁ || R₂ denotes the equivalent resistance of R₁ and R₂ connected in parallel.

• As β-value is fixed for a given transistor, this relation can be satisfied either by keeping R_E fairly large, or making R₁||R₂ very low.

• If R_E is of large value, high V_CC is necessary. This increases cost as well as precautions necessary while handling.
• If R₁ || R₂ is low, either R₁ is low, or R₂ is low, or both are low. A low R₁ raises V_B closer to V_C, reducing the available swing in collector voltage, and limiting how large R_C can be made without driving the transistor out of active mode. A low R₂ lowers V_be, 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.

• AC as well as DC feedback is caused by R_E, which reduces the AC voltage gain of the amplifier. A method to avoid AC feedback while retaining DC feedback is discussed below.

Usage:

The circuit's stability and merits as above make it widely used for linear circuits.

[edit] Voltage divider with AC bypass capacitor

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

This capacitor is usually chosen to have a low enough reactance at the signal frequencies of interest such that R_E is essentially shorted at AC, thus grounding the emitter. Feedback is therefore only present at DC to stabilize the operating point. Of course, any AC advantages of feedback are lost.

Of course, this idea can be used to shunt only a portion of R_E, thereby retaining some AC feedback.

[edit] Emitter bias

When a split supply (dual power supply) is available, this biasing circuit is the most effective. The negative supply V_EE is used to forward-bias the emitter junction through R_E. The positive supply V_CC is used to reverse-bias the collector junction. Only three resistors are necessary.

We know that,

V_B - V_E = V_be

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

I_E = (V_EE - V_be)/R_E

The operating point is independent of β if R_E >> R_B/β

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.

[edit] References

1. ^ A.S. Sedra and K.C. Smith (2004). Microelectronic circuits, Fifth Edition, New York: Oxford University Press, p. 397 and Figure 5.17. ISBN 0-19-514251-9. 
2. ^ A.S. Sedra and K.C. Smith (2004). p. 1245. ISBN 0-19-514251-9. 

[edit] Further reading

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

[edit] See also

• Biasing (electronics)
• Small signal model
• Bipolar Junction Transistor
• MOSFET

[edit] External links

• Bias - from Sci-Tech Encyclopedia
• http://www.tpub.com/neets/book7/25d.htm