Biasing Techniques | Analog and Digital Electronics - Electrical Engineering (EE) PDF Download

Introduction

Bipolar transistors 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 voltage divider configuration achieves the correct voltages by the use of resistors in certain patterns. By selecting the proper resistor values, stable current levels can be achieved that vary only little over temperature and with transistor properties such as β.

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 (V_ce) and the collector current (I_c) with no input signal applied.

Biasing Circuit Requirements

A bias network is selected to stabilize the operating point of the transistor, by reducing the following effects of device variability, temperature, and voltage changes:

• The gain of a transistor can vary significantly between different batches, which results in widely different operating points for sequential units in serial production or after replacement of a transistor.
• Due to the Early effect, the current gain is affected by the collector–emitter voltage.
• Both gain and base–emitter voltage depend on the temperature.
• The leakage current also increases with temperature.

A bias circuit may be composed of only resistors, or may include elements such as temperature-dependent resistors, diodes, or additional voltage sources, depending on the range of operating conditions expected.

A half-wave output is not problematic for some applications. Some applications may require this very kind of amplification, because it is possible to operate an amplifier in modes other than full-wave reproduction and specific applications require different ranges of reproduction, thus it is useful to describe the degree to which an amplifier reproduces the input waveform by designating it according to class. Amplifier class operation is categorized with alphabetical letters: A, B, C, and AB.

For Class A operation, the entire input waveform is faithfully reproduced.

Amplifier Class

Class A

Operation can only be obtained when the transistor spends its entire time in the active mode, never reaching either cutoff or saturation. To achieve this, sufficient DC bias voltage is usually set at the level necessary to drive the transistor exactly halfway between cutoff and saturation. This way, the AC input signal will be perfectly “centered” between the amplifier’s high and low signal limit levels.

Class A: The amplifier output is a faithful reproduction of the input.

Class B

Operation is what we had the first time an AC signal was applied to the common-emitter amplifier with no DC bias voltage. The transistor spent half its time in active mode and the other half in cutoff with the input voltage too low (or even of the wrong polarity!) to forward-bias its base-emitter junction.

Class B: Bias is such that half (180°) of the waveform is reproduced.

By itself, an amplifier operating in class B mode is not very useful. In most circumstances, the severe distortion introduced into the waveshape by eliminating half of it would be unacceptable. However, class B operation is a useful mode of biasing if two amplifiers are operated as a push-pull pair, each amplifier handling only half of the waveform at a time:

Class B push pull amplifier: Each transistor reproduces half of the waveform. Combining the halves produces a faithful reproduction of the whole wave.

Transistor Q1 “pushes” (drives the output voltage in a positive direction with respect to ground), while transistor Q2 “pulls” the output voltage (in a negative direction, toward 0 volts with respect to ground). Individually, each of these transistors is operating in class B mode, active only for one-half of the input waveform cycle. Together, however, both functions as a team to produce an output waveform identical in shape to the input waveform.

A decided advantage of class B (push-pull) amplifier design over the class A design is greater output power capability. With a class A design, the transistor dissipates considerable energy in the form of heat because it never stops conducting current. At all points in the wave cycle, it is in the active (conducting) mode, conducting substantial current and dropping substantial voltage. There is substantial power dissipated by the transistor throughout the cycle. In a class B design, each transistor spends half the time in cutoff mode, where it dissipates zero power (zero current = zero power dissipation). This gives each transistor a time to “rest” and cool while the other transistor carries the burden of the load. Class A amplifiers are simpler in design but tend to be limited to low-power signal applications for the simple reason of transistor heat dissipation.

Class AB

Another class of amplifier operation known as class AB is somewhere between class A and class B: the transistor spends more than 50% but less than 100% of the time conducting current.

If the input signal bias for an amplifier is slightly negative (opposite of the bias polarity for class A operation), the output waveform will be further “clipped” than it was with class B biasing, resulting in an operation where the transistor spends most of the time in cutoff mode:

Class C

Class C: Conduction is for less than a half cycle (< 180°).

At first, this scheme may seem utterly pointless. After all, how useful could an amplifier be if it clips the waveform as badly as this? If the output is used directly with no conditioning of any kind, it would indeed be of questionable utility. However, with the application of a tank circuit (parallel resonant inductor-capacitor combination) to the output, the occasional output surge produced by the amplifier can set in motion a higher-frequency oscillation maintained by the tank circuit. This may be likened to a machine where a heavy flywheel is given an occasional “kick” to keep it spinning:

Class C amplifier driving a resonant circuit.

Called class C operation, this scheme also enjoys high power efficiency since the transistor(s) spend the vast majority of time in the cutoff mode, where they dissipate zero power. The rate of output waveform decay (decreasing oscillation amplitude between “kicks” from the amplifier) is exaggerated here for the benefit of illustration. Because of the tuned tank circuit on the output, this circuit is usable only for amplifying signals of definite, fixed amplitude. A class C amplifier may be used in an FM (frequency modulation) radio transmitter. However, the class C amplifier may not directly amplify an AM (amplitude modulated) signal due to distortion.

Class D

Another kind of amplifier operation, significantly different from Class A, B, AB, or C, is called Class D. It is not obtained by applying a specific measure of bias voltage as are the other classes of operation, but requires a radical re-design of the amplifier circuit itself. It is a little too early in this chapter to investigate exactly how a class D amplifier is built, but not too early to discuss its basic principle of operation.

A class D amplifier reproduces the profile of the input voltage waveform by generating a rapidly-pulsing square wave output. The duty cycle of the output waveform (time “on” versus total cycle time) varies with the instantaneous amplitude of the input signal. The plots in (Figure below demonstrate this principle.

Class D amplifier: Input signal and unfiltered output.

The greater the instantaneous voltage of the input signal, the greater the duty cycle of the output square-wave pulse. If there can be any goal stated of the class D design, it is to avoid active-mode transistor operation. Since the output transistor of a class D amplifier is never in the active mode, only cutoff or saturated, there will be little heat energy dissipated by it. This results in very high power efficiency for the amplifier. Of course, the disadvantage of this strategy is the overwhelming presence of harmonics on the output. Fortunately, since these harmonic frequencies are typically much greater than the frequency of the input signal, these can be filtered out by a low-pass filter with relative ease, resulting in an output more closely resembling the original input signal waveform. Class D technology is typically seen where extremely high power levels and relatively low frequencies are encountered, such as in industrial inverters (devices converting DC into AC power to run motors and other large devices) and high-performance audio amplifiers.

A term you will likely come across in your studies of electronics is something called quiescent, which is a modifier designating the zero input condition of a circuit. Quiescent current, for example, is the amount of current in a circuit with zero input signal voltage applied. Bias voltage in a transistor circuit forces the transistor to operate at a different level of collector current with zero input signal voltage than it would without that bias voltage. Therefore, the amount of bias in an amplifier circuit determines its quiescent values.

Quiescent Current of Amplifiers

In a class A amplifier, the quiescent current should be exactly half of its saturation value (halfway between saturation and cutoff, cutoff by definition being zero). Class B and Class C amplifiers have quiescent current values of zero since these are supposed to be cut-off with no signal applied. Class AB amplifiers have very low quiescent current values, just above cutoff. To illustrate this graphically, a “load line” is sometimes plotted over a transistor’s characteristic curves to illustrate its range of operation while connected to a load resistance of specific value shown in the figure below.

Example load line drawn over transistor characteristic curves from Vsupply to saturation current.

A load line is a plot of collector-to-emitter voltage over a range of collector currents. At the lower-right corner of the load line, voltage is at maximum and current is at zero, representing a condition of cutoff. At the upper-left corner of the line, voltage is at zero while current is at a maximum, representing a condition of saturation. Dots marking where the load line intersects the various transistor curves represent realistic operating conditions for those base currents given.

Quiescent operating conditions may be shown on this graph in the form of a single dot along the load line. For a class A amplifier, the quiescent point will be in the middle of the load line as in (Figure below.)

Quiescent point (dot) for class A.

In this illustration, the quiescent point happens to fall on the curve representing a base current of 40 µA. If we were to change the load resistance in this circuit to a greater value, it would affect the slope of the load line, since a greater load resistance would limit the maximum collector current at saturation, but would not change the collector-emitter voltage at cutoff. Graphically, the result is a load line with a different upper-left point and the same lower-right point as in

Load line resulting from increased load resistance.

Note how the new load line doesn’t intercept the 75 µA curve along its flat portion as before. This is very important to know because the non-horizontal portion of a characteristic curve represents a condition of saturation. Having the load line intercept the 75 µA curve outside of the curve’s horizontal range means that the amplifier will be saturated at that amount of base current. Increasing the load resistor value is what caused the load line to intercept the 75 µA curve at this new point, and it indicates that saturation will occur at a lesser value of base current than before.

With the old, lower-value load resistor in the circuit, a base current of 75 µA would yield a proportional collector current (base current multiplied by β). In the first load line graph, a base current of 75 µA gave a collector current almost twice what was obtained at 40 µA, as the β ratio would predict. However, collector current increases marginally between base currents 75 µA and 40 µA, because the transistor begins to lose sufficient collector-emitter voltage to continue to regulate collector current.

To maintain linear (no-distortion) operation, transistor amplifiers shouldn’t be operated at points where the transistor will saturate; that is, where the load line will not potentially fall on the horizontal portion of a collector current curve. We’d have to add a few more curves to the graph in Figure below before we could tell just how far we could “push” this transistor with increased base currents before it saturates.

More base current curves shows saturation detail.

It appears in this graph that the highest-current point on the load line falling on the straight portion of a curve is the point on the 50 µA curve. This new point should be considered the maximum allowable input signal level for class A operation. Also for class A operation, the bias should be set so that the quiescent point is halfway between this new maximum point and cutoff are shown in Figure below.

New quiescent point avoids saturation region.

Now that we know a little more about the consequences of different DC bias voltage levels, it is time to investigate practical biasing techniques. DC voltage source (battery) connected in series with the AC input signal to bias the amplifier for whatever desired class of operation. In real life, the connection of a precisely-calibrated battery to the input of an amplifier is simply not practical. Even if it were possible to customize a battery to produce just the right amount of voltage for any given bias requirement, that battery would not remain at its manufactured voltage indefinitely. Once it started to discharge and its output voltage drooped, the amplifier would begin to drift toward class B operation.

Take this circuit, illustrated in the common-emitter section for SPICE simulation, for instance, in the figure below.

Impractical base battery bias.

That 2.3-volt “Vbias” battery would not be practical to include in a real amplifier circuit. A far more practical method of obtaining bias voltage for this amplifier would be to develop the necessary 2.3 volts using a voltage divider network connected across the 15-volt battery. After all, the 15-volt battery is already there by necessity, and voltage divider circuits are easy to design and build. Let’s see how this might look in the figure below.

Voltage divider bias.

If we choose a pair of resistor values for R2 and R3 that will produce 2.3 volts across R3 from a total of 15 volts (such as 8466 Ω for R2 and 1533 Ω for R3), we should have our desired value of 2.3 volts between base and emitter for biasing with no signal input. The only problem is, this circuit configuration places the AC input signal source directly in parallel with R3 of our voltage divider. This is not acceptable, as the AC source will tend to overpower any DC voltage dropped across R3. Parallel components must have the same voltage, so if an AC voltage source is directly connected across one resistor of a DC voltage divider, the AC source will “win” and there will be no DC bias voltage added to the signal.

One way to make this scheme work, although it may not be obvious why it will work, is to place a coupling capacitor between the AC voltage source and the voltage divider as in Figure below.

Coupling capacitor prevents voltage divider bias from flowing into signal generator.

The capacitor forms a high-pass filter between the AC source and the DC voltage divider, passing almost all of the AC signal voltage on the transistor while blocking all DC voltage from being shorted through the AC signal source. This makes much more sense if you understand the superposition theorem and how it works. According to superposition, any linear, bilateral circuit can be analyzed in a piecemeal fashion by only considering one power source at a time, then algebraically adding the effects of all power sources to find the final result. If we were to separate the capacitor and R2—R3 voltage divider circuit from the rest of the amplifier, it might be easier to understand how this superposition of AC and DC would work.

With only the AC signal source in effect, and a capacitor with arbitrarily low impedance at the signal frequency, almost all the AC voltage appears across R3:

Due to the coupling capacitor’s very low impedance at the signal frequency, it behaves much like a piece of wire, thus it can be omitted for this step in superposition analysis.

With only the DC source in effect, the capacitor appears to be an open circuit, and thus neither it nor the shorted AC signal source will have any effect on the operation of the R2—R3 voltage divider in the figure below.

The capacitor appears to be an open circuit as far at the DC analysis is concerned

Combining these two separate analyses in Figure below, we get a superposition of (almost) 1.5 volts AC and 2.3 volts DC, ready to be connected to the base of the transistor.

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$Ib=\frac{V}{R}$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 = β I_b. Collector current and emitter current are related by I_c = α I_e 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 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,$Ib=\frac{V}{-}$Advantages:

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

Disadvantages:

• In this circuit, to keep I_c independent of β the following condition must be met:$Ic=\beta Ib=\frac{\beta }{(}\approx \frac{(}{V}$which is approximately the case if$(\beta +1)Re\gg Rb.$

• 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.