# Basic Electronics | Transistor Bias Circuits

## DC Bias

Bias establishes the DC operating point (Q-point) for proper linear operation of an amplifier.

If an amplifier is not biased with correct DC voltages on the input and output, it can go into saturation or cutoff when an input signal is applied.

In Fig. 1(a), the output is an amplified replica of the input signal but inverted, which means that it is out of phase with the input. The output signal swings equally above and below the DC bias level of the output, V

_{DC(out)}.Fig. 1(b) and (c) illustrate the distortion in the output signal caused by improper biasing.

Fig. 1(b) shows the limiting of the positive portion of the output as a result of a Q-point being too close to cutoff. Fig.1(c) shows limiting of the negative portion of the output with a Q-point too close to saturation.

## Graphical Analysis

The transistor in Fig. 2(a) is biased with V_{CC} and V_{BB} to obtain certain values of I_{B}, I_{C}, I_{E}, and V_{CE}. The collector characteristic curves for this transistor are shown in Fig. 2(b); which graphically illustrate the effects of DC bias.

We assign three values to I_{B} and observe what happens to I_{C} and V_{CE}. First, V_{BB} is adjusted to produce an I_{B} of 200 A as shown in Fig. 3(a). Since I_{C} =β_{DC}I_{B}, the collector current is 20 mA as indicated, and

This Q-point is shown on the graph of Fig. 3(a) as * Q_{1}*.

Next, as shown in Fig. 3(b), V_{BB} is increased to produce an I_{B} of 300 A and an I_{C} of 30 mA.

The Q-point for this condition is indicated by * Q_{2 }*on the graph.

Finally, V_{BB} is increased to give an I_{B} of 400 A and an I_{C} of 40 mA.

* Q_{3}* is the corresponding Q-point on the graph in Fig. 3(c).

## DC Load Line

describes graphically the DC operation of a transistor circuit

a straight line drawn on the characteristic curves from the saturation value where I

_{C }= I_{C(sat)}on the y-axis to the cutoff value where V_{CE }= V_{CC}on the x-axis, as shown in Fig. 4(a)determined by the external circuit (V

_{CC}and R_{C}), not the transistor itself

In Fig. 3, the equation for I_{C} is

This is the equation of a straight line with a slope of * -1/R_{C}*, an x intercept of

**, and a y intercept of**

*V*_{CE }= V_{CC}**, which is**

*V*_{CC}/R_{C}**.**

*I*_{C(sat)}The point at which the load line intersects a characteristic curve represents the Q-point for that particular value of I_{B}. Fig. 4(b) illustrates the Q-point on the load line for each value of I_{B} in Fig. 3.

## Linear Operation

The region along the load line including all points between saturation and cutoff is the linear region of the transistor’s operation.

In this region, the output voltage is ideally a linear reproduction of the input.

Figure 5 shows an example of the linear operation of a transistor. AC quantities are indicated by lowercase italic subscripts.

A sinusoidal voltage, V

_{in}, is superimposed on V_{BB}, causing I_{B}to vary sinusoidally above and below its Q-point value of*300 A*. This causes I_{C}to vary*10 mA*above and below its Q-point value of*30 mA*.As a result of the variation I

_{C}, V_{CE}varies*2.2 V*above and below its Q-point value of*3.4 V*.Point A on the load line in Fig. 5 corresponds to the positive peak of the sinusoidal input voltage. Point B corresponds to the negative peak, and point Q corresponds to the zero value of the sine wave.

*V*,_{CEQ}*I*, and_{CQ}*I*are DC Q-point values with no input sinusoidal voltage applied._{BQ }

## Voltage-Divider Bias

A more practical bias method is to use V

_{CC}as the single bias source, as shown in Fig. 6. To simplify the schematic, the battery symbol is omitted and replaced by a line termination circle with a voltage indicator (V_{CC}).

A DC bias voltage at the base of the transistor can be developed by a resistive voltage divider that consists of R

_{1}and R_{2}. V_{CC}is the DC collector supply voltage.Since

*I*, the voltage-divider circuit analysis is straightforward because the loading effect of_{B}<< I_{2}*I*can be ignored (stiff voltage divider)._{B}To analyze a voltage-divider circuit in which IB is small compared to

*I*, first calculate V_{2}_{B}using the unloaded voltage-divider rule:

- Once you know V
_{B}, you can find the voltages and currents in the circuit, as follows:

- Once you know V
_{C}and V_{E}, you can determine V_{CE}.

If the input resistance is raised, the voltage divider may not be stiff; and more detailed analysis is required to calculate circuit parameters.

## Loading Effects of Voltage-Divider Bias

The DC input resistance of the transistor is proportional to β

_{DC}so it will change for different transistors.When a transistor is operating in its linear region, I

_{E }= β_{DC}I_{B}.When the emitter resistor is viewed from the base circuit, the resistor appears to be larger than its actual value because of the DC current gain in the transistor. That is,

As long as R

_{IN(BASE) }is at least ten times larger than R_{2}, the loading effect will be 10% or less and the voltage divider is considered stiff.If R

_{IN(BASE)}is less than ten times R_{2}, it should be combined in parallel with R_{2}.

**Thevenin’s Theorem Applied to Voltage-Divider Bias**

To analyze a voltage-divider biased transistor circuit for base current loading effects, we will apply Thevenin’s theorem.

For the circuit in Fig. 7(a), looking out from the base terminal, the bias circuit can be redrawn as shown in Fig. 7(b).

Apply Thevenin’s theorem to the circuit left of point A, with V_{CC} replaced by a short to ground and the transistor disconnected from the circuit. The voltage at point A with respect to ground is

and the resistance is

The Thevenin equivalent of the bias circuit, connected to the transistor base, is shown in the box in Fig. 7(c). Applying Kirchhoff’s voltage law around the equivalent base-emitter loop gives

Using Ohm’s law, and solving for V_{TH},

Substituting *I _{E}/β_{DC}* for

*I*,

_{B}Solving for *I _{E}*,

If *R _{TH}/β_{DC}* is small compared to R

_{E}, the result is the same as for an unloaded voltage divider.

Voltage-divider bias is widely used because reasonably good bias stability is achieved with a single supply voltage.

## Emitter Bias

Emitter bias provides excellent bias stability in spite of changes in or temperature. It uses both a positive and a negative supply voltage.

In an NPN circuit shown in Fig. 8, the small I

_{B}causes V_{B}to be slightly below ground. V_{E}_{}is one diode drop less than this.

The combination of the small drop across R

_{B}and V_{BE}forces the emitter to be at approximately -1 V. Using this approximation,

- V
_{EE}is entered as a negative value in this equation.

- You can apply the approximation that to calculate
:**V**_{C}

The approximation that

is useful for troubleshooting to circumvent detailed calculations.**V**_{E }≈ -1 VKirchhoff’s voltage law can be applied to develop a more accurate formula for I

_{E}for detailed analysis.Kirchhoff’s voltage law applied around the base-emitter circuit in Fig. 8(a), which has been redrawn in part (b) for analysis, gives:

- Substituting I
_{B }I**≈**_{E}/β_{DC},

- Solving for
**I**,_{E}

- Voltages with respect to ground are indicated by a single subscript.
**V**with respect to ground is_{E}

**V**with respect to ground is_{B }

**V**with respect to ground is_{C}

## Base Bias

This method of biasing is common in switching circuits. Fig. 9 shows a base-biased transistor.

- The analysis of this circuit for the linear region shows that it is directly dependent on β
_{DC}. Starting with Kirchhoff’s voltage law around the base circuit,

- Substituting
**I**for_{B}R_{B}**V**and solving for_{RB}**I**,_{B}

- Kirchhoff’s voltage law applied around the collector circuit in Fig. 9 gives the equation:
. Solving for**V**_{CC }- I_{C}R_{C }- V_{CE }= 0**V**,_{CE}

- Substituting the expression for
**I**into_{B}**I**yields_{C}=β_{DC}I_{B}

**Q-Point Stability of Base Bias**

A variation in

**β**causes_{DC}**I**, and as a result,_{C}**V**to change, thus changing the Q-point of the transistor; making the base bias circuit extremely beta-dependent and unpredictable._{CE}

**β**varies with temperature and_{DC}**I**. Also, there is a large spread of values from one transistor to another of the same type due to manufacturing variations. Thus, base bias is rarely used in linear circuits._{C}

## Emitter-Feedback Bias

If an emitter resistor is added to a base-bias circuit, the result is emitter-feedback bias, as shown in Fig. 10.

The idea is to help make base bias more predictable with negative feedback, which negates any attempted change in I

_{C}with an opposing change in V_{B}.If I

_{C}tries to increase, V_{E}increases, causing an increase in V_{B}because. This increase in V**V**_{B}=V_{E}+V_{BE}_{B}reduces the voltage across R_{B}, thus reducing I_{B}and keeping I_{C}from increasing. A similar action occurs if I_{C}tries to decrease.

To calculate

, you can write Kirchhoff’s voltage law (KVL) around the base circuit.**I**_{E}

- Substituting
for*I*/β_{E}_{DC},*I*_{B}is equal to**I**_{E}

- While emitter-feedback bias is better for linear circuits than base bias, it is still dependent on
*β*and is not as predictable as voltage-divider bias._{DC}

## Collector-Feedback Bias

In Fig. 11, R

_{B}is connected to the collector rather than to V_{CC}, as it was in the base bias arrangement. V_{C}provides the bias for the base-emitter junction. The negative feedback creates an “offsetting” effect that keeps the Q-point stable.

If I

_{C}tries to increase, it drops more voltage across R_{C}, thereby causing V_{C }to decrease. When V_{C }decreases, there is a decrease in voltage across R_{B}, which decreases I_{B}.The decrease in I

_{B}produces less I_{C}which, in turn, drops less voltage across R_{C}and thus offsets the decrease in V_{C}.

**Analysis of a Collector-Feedback Bias Circuit**

By Ohm’s law, **I _{B}** can be expressed as

Assuming that I_{C }>> I_{B}, V_{C }≈ V_{CC }- I_{C }R_{C}. Also, *I _{B}=I_{C} /β_{DC}* . Substituting for V

_{C}in the equation I

_{B}=(V

_{C}-V

_{BE})/R

_{B},

Solving for I_{C} ,

Since the emitter is ground, V_{CE}=V_{C}.

**Q-Point Stability Over Temperature**

I

_{C}is dependent to some extent on*β*and V_{DC}_{BE}. This dependency can be minimized by making R_{C }>> R_{B}/*β*and V_{DC}_{CC}>>V_{BE}.As the temperature goes up,

*β*goes up and V_{DC}_{BE}goes down. The increase in DC acts to increase I_{C}. The decrease in V_{BE}acts to increase I_{B}which, in turn also acts to increase I_{C}.As I

_{C}tries to increase, V_{R}_{C}also tries to increase. This tends to reduce V_{C}and therefore V_{R}_{B}, thus reducing I_{B}and offsetting the attempted increase in I_{C}and decrease in V_{C}.The result is that the collector-feedback circuit maintains a relatively stable Q-point. The reverse action occurs when the temperature decreases.

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