DC Bias. Graphical Analysis. Script

Transcription

1 Course: B.Sc. Applied Physical Science (Computer Science) Year & Sem.: Ist Year, Sem - IInd Subject: Electronics Paper No.: V Paper Title: Analog Circuits Lecture No.: 3 Lecture Title: Analog Circuits - Transistor Bias Circuits Script Hello friends in the last lecture we talked about the basic operation of BJT as an amplifier and as a switch. Then we talked about photo-transistor and finally the transistor categories and packaging. In today s lecture, we shall discuss the transistor bias circuits. As you learned previously, a transistor must be properly biased in order to operate as an amplifier. DC biasing is used to establish fixed dc values for the transistor currents and voltages called the dc operating point or Q-point. This discussion would lay the foundation for the study of amplifiers, and other circuits that require proper biasing. After we complete this discussion you would be able to determine the dc operating point of a linear amplifier, analyze a voltage-divider biased circuit and analyze an emitter and base bias circuits. DC Bias Bias establishes the dc operating point or 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. Figure here shows the effects of proper and improper dc biasing of an inverting amplifier. In this figure, the output signal is an amplified replica of the input signal except that it is inverted, which means that it is 180 degrees out of phase with the input. The output signal swings equally above and below the dc bias level of the output, V DC(out). Improper biasing can cause distortion in the output signal, as illustrated in parts (b) and (c) of figure. Part (b) illustrates limiting of the positive portion of the output voltage as a result of a Q-point being too close to cutoff. Part (c) shows limiting of the negative portion of the output voltage as a result of a dc operating point being too close to saturation. Graphical Analysis The transistor in figure here 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 particular transistor are shown in part (b) of figure; we will use these curves to graphically illustrate the effects of dc bias.

2 Here we shall assign 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 µa, as shown in figure. Since I C = β DC I B, the collector current is 20 ma, as indicated in figure, and V CE = V CC I C R C, Substituting the values of V CC and I C R C, V CE = 10V (20mA) (220 Ω) and is equal to 10V 4.4V = 5.6V This Q-point is shown on the graph of figure as Q 1. Next, as shown in figure, V BB is increased to produce an I B of 300 µa and an I C of 30 ma.

3 Then, V CE becomes, 10V (30mA) (220 Ω) and is equal to 10V 6.6V = 3.6V. The Q-point for this condition is indicated by Q 2 on the graph. Finally, as in Figure here, V BB is increased to give an I B of 400 µa and an I C of 40 ma. Then V CE becomes, 10V (40mA) (220 Ω) and is equal to 10V 8.8V = 1.2V Q 3 is the corresponding Q-point on the graph. DC Load Line The dc operation of a transistor circuit can be described graphically using a dc load line. This is 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 figure. The load line is determined by the external circuit (V CC and R C ), not the transistor itself, which is described by the characteristic curves. The equation for I C becomes as shown here: 1 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, which is. The point at which the load line intersects a characteristic curve represents the Q-point for that particular value of I B.

4 Linear Operation The region along the load line including all points between saturation and cutoff is generally known as the linear region of the transistor s operation. As long as the transistor is operated in this region, the output voltage is ideally a linear reproduction of the input. Figure here shows an example of the linear operation of a transistor. AC quantities are indicated by lowercase italic subscripts. Assume a sinusoidal voltage, V in, is superimposed on V BB, causing the base current to vary sinusoidally above 100µ A and below its Q-point value of 300mA. This, in turn, causes the collector current to vary 10 ma above and below its Q-point value of 30 ma. As a result of the variation in collector current, the collector-to-emitter voltage varies 2.2 V above and below its Q-point value of 3.4 V. Point A on the load line in 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. VOLTAGE -DIVIDER BIAS Now we will discuss a method of biasing a transistor for linear operation using a singlesource resistive voltage divider. This is the most widely used biasing method. After completing this section, you should be able to define the term stiff voltage-divider, calculate currents and voltages in a voltage-divider biased circuit, explain the loading effects in voltage-divider bias, describe how dc input resistance at the transistor base affects the bias and finally apply Thevenin s theorem to the analysis of voltage-divider bias. Up to this point a separate dc source, V BB, was used to bias the base-emitter junction because it could be varied independently of V CC and it helped to illustrate transistor operation. A more practical bias method is to use V CC as the single bias source, as shown in figure.

5 To simplify the schematic, the battery symbol is omitted and replaced by a line termination circle with a voltage indicator V CC as shown. 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. Two current paths are between point A and ground: one through R 2 and the other through the base-emitter junction of the transistor and R E. Generally, voltage-divider bias circuits are designed so that the base current is much smaller than the current I 2 through R 2. In this case, the voltage-divider circuit is very straightforward to analyze because the loading effect of the base current can be ignored. A voltage divider in which the base current is small compared to the current in R 2 is said to be a stiff voltage divider because the base voltage is relatively independent of different transistors and temperature effects. To analyze a voltage-divider circuit in which I B is small compared to I 2, first calculate the voltage on the base using the unloaded voltagedivider rule as given here. Once you know the base voltage, you can find the voltages and currents in the circuit, as shown here: V E =V B - V BE And I C is approximately equal to I E = V E / R E Then, V C = V CC - I C R C Once you know V C and V E, you can determine V CE by this equation: V CE =V C - V E The basic analysis developed in this example is all that is needed for most voltage-divider circuits, but there may be cases where you need to analyze the circuit with more accuracy. Ideally, a voltage-divider circuit is stiff, which means that the transistor does not appear as a significant load. All circuit design involves trade-offs; and one trade-off is that stiff voltage dividers require smaller resistors, which are not always desirable because of potential loading effects on other circuits and added power requirements. If the circuit designer wanted to raise the input resistance, the divider string may not be stiff; and more detailed analysis is required to calculate circuit parameters. To determine if the divider is stiff, you need to examine the dc input resistance looking in at the base as shown in figure here.

6 Loading Effects of Voltage-Divider Bias The dc input resistance of the transistor is proportional to β, so it will change for different transistors. When a transistor is operating in its linear region, the emitter current I E is β. 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. The effective load on the voltage divider is given by the following formula: β You can quickly estimate the loading effect by comparing to the resistor R2 in the voltage divider. As long as is at least ten times larger than R 2, the loading effect will be 10% or less and the voltage divider is stiff. If 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 to evaluate the circuit. First, let s get an equivalent base-emitter circuit for the circuit in figure here using Thevenin s theorem.

7 Looking out from the base terminal, the bias circuit can be redrawn as shown in figure (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 given by this equation and the resistance is given by this equation: The Thevenin equivalent of the bias circuit, connected to the transistor base, is shown in part (c) of the figure. Applying Kirchhoff s voltage law around the equivalent base-emitter loop gives V TH - V RTH - V BE - V RE = 0 Substituting, using Ohm s law, and solving for V TH, V TH = I B R TH + V BE + I E R E Substituting I E / β DC for I B we get the equation as shown Then solving for I E, we get the equation as shown here: 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. Voltage-Divider Biased PNP Transistor As you know, a pnp transistor requires bias polarities opposite to the npn. This can be accomplished with a negative collector supply voltage, as in figure (a), or with a positive emitter supply voltage, as in figure (b).

8 In a schematic, the pnp is often drawn upside down so that the supply voltage is at the top of the schematic and ground at the bottom, as in figure (c). The analysis procedure is the same as for an npn transistor circuit using Thevenin s theorem and Kirchhoff s voltage law, as demonstrated in the following steps with reference to the figure here. For figure (a), applying Kirchhoff s voltage law around the base-emitter circuit gives this equation where, V TH V CC R TH = The base current is then I B = The equation for I E then becomes as shown here: For the figure in part (b) the analysis is like this - V TH + I B R TH - V BE + I E R E - V EE = 0 V TH = V EE R TH = I B = The equation for I E thus becomes as shown here EMMITER BIAS Emitter bias provides excellent bias stability in spite of changes in β or temperature. It uses both a positive and a negative supply voltage. To obtain a reasonable estimate of the key dc values in an emitter-biased circuit, analysis is quite easy. In an npn circuit, such as shown in figure here, the small base current causes the base voltage to be slightly below ground.

9 The emitter voltage is one diode drop less than this. The combination of this small drop across R B and V BE forces the emitter to be at approximately -1 V. Using this approximation; you can obtain the emitter current as, I E = Where, V EE is entered as negative value in this equation. You can apply the approximation that I C I E to calculate the collector voltage. V C =V CC I C R C The approximation that V E -1V is useful for troubleshooting because you won t need to perform any detailed calculations. As in the case of voltage-divider bias, there is a more rigorous calculation for cases where you need a more exact result. The approximation that V E -1V and the neglect of β DC may not be accurate enough for design work or detailed analysis.

10 In this case, Kirchhoff s voltage law can be applied as follows to develop a more detailed formula for I E. Kirchhoff s voltage law applied around the base-emitter circuit in part (a) of figure here, which has been redrawn in part (b) for analysis, gives the following equation: V EE + V RB + V BE + V RE = 0 Substituting, using Ohm s law, V EE + I B R B + V BE + I E R E = 0 Substituting for I B and transposing V EE, R B + I E R E + V BE = -V EE Factoring out I E and solving for I E, we get this equation: The emitter voltage with respect to ground is V E = V EE + I E R E The base voltage with respect to ground is V B = V E + V BE The collector voltage with respect to ground is V C = V CC - I C R C So friends here we come to the end of our discussion in this lecture and therefore we sum up. The purpose of biasing a circuit is to establish a proper stable dc operating point called the Q- point. The Q-point of a circuit is defined by specific values for I C and V CE. These values are called the coordinates of the Q-point. A dc load line passes through the Q-point on a transistor s collector curves intersecting the vertical axis at approximately I C(sat) and the horizontal axis at V CE(off). Loading effects are neglected for a stiff voltage divider. Voltagedivider bias provides good Q-point stability with a single-polarity supply voltage. It is the most common bias circuit. Emitter bias generally provides good Q-point stability but requires both positive and negative supply voltages. So that is it for today thank you very much.