Basic Electronics | Transistor Bias Circuits

• 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.

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_DCI_B, the collector current is 20 mA as indicated, and

This Q-point is shown on the graph of Fig. 3(a) as Q₁.

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 Q₂ on the graph.

Finally, V_BB is increased to give an I_B of 400 A and an I_C of 40 mA.

Q₃ is the corresponding Q-point on the graph in Fig. 3(c).

• 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 V_CE = V_CC, and a y intercept of V_CC/R_C, which is 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.

• 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_CQ, and I_BQ are DC Q-point values with no input sinusoidal voltage applied.

• 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 R₁ and R₂. V_CC is the DC collector supply voltage.

• Since I_B << I₂, the voltage-divider circuit analysis is straightforward because the loading effect of I_Bcan be ignored (stiff voltage divider).

• To analyze a voltage-divider circuit in which IB is small compared to I₂, first calculate V_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.

• 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_DCI_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 R₂, the loading effect will be 10% or less and the voltage divider is considered stiff.

• If R_IN(BASE) is less than ten times R₂, it should be combined in parallel with R₂.

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 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 V_E ≈ -1 V is useful for troubleshooting to circumvent detailed calculations.

• Kirchhoff’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_E with respect to ground is

• V_B with respect to ground is

• V_C with respect to ground is

• 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_BR_B for V_RB and solving for I_B,

• Kirchhoff’s voltage law applied around the collector circuit in Fig. 9 gives the equation: V_CC - I_CR_C - V_CE = 0. Solving for V_CE,

• Substituting the expression for I_B into I_C=β_DCI_B yields

Q-Point Stability of Base Bias

• A variation in β_DC causes I_C, and as a result, V_CE to change, thus changing the Q-point of the transistor; making the base bias circuit extremely beta-dependent and unpredictable.

• β_DC varies with temperature and I_C. 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.

• 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 V_B =V_E+V_BE. This increase in V_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 I_E, you can write Kirchhoff’s voltage law (KVL) around the base circuit.

• Substituting I_E/β_DC for I_B, I_E is equal to

• While emitter-feedback bias is better for linear circuits than base bias, it is still dependent on β_DC and is not as predictable as voltage-divider 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_DC and V_BE. This dependency can be minimized by making R_C >> R_B/β_DC and V_CC>>V_BE.

• As the temperature goes up, β_DC goes up and V_BEgoes down. The increase in DC acts to increase I_C. The decrease in V_BEacts to increase I_B which, in turn also acts to increase I_C.

• As I_C tries to increase, V_RC also tries to increase. This tends to reduce V_C and therefore V_RB, 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.