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The ABCs of Device Biasing
Motorola, Wireless Infrastructure Systems Division
This tutorial article covers the most common modes of amplifier operation. Each mode of operation has distinct characteristics associated with it and, therefore, the modes are delineated into individual classes. Each class has distinct device parameter advantages that make it particularly suit an application. Each class also has certain disadvantages that may limit its use in a particular application or eliminate its use in a particular marketplace. The classes of operation of the most widely used transistors in today's applications are class A, B, AB and C mode. Other modes of operation exist, including high efficiency switching modes such as D, E, F and S. However, these modes are not covered here. The interested reader may research the topic further in several available sources.2,6,7,8
The differences between modes of operation affect parameters such as gain and power. However, the most significant factors affected are efficiency and linearity. Certain modes offer high efficiency but suffer from poor linearity. Other modes have excellent efficiency but lack the required linearity performance. There are also modes that offer a combination of both parameters to varying degrees. As always the designer is faced with a trade-off situation, and the final choice of operation will depend upon the system specifications.
The first step in RF circuit design is setting the DC bias level. Figure 1 shows one of the simplest bias circuits, the resistive divider used to bias the active device. The bias voltage, Vbias , is determined by the ratio of the two resistors. For the enhancement-mode MOSFET the bias voltage sets the voltage between the gate and source of the device, which, in turn, determines the amount of current through the drain of the device. For the bipolar junction transistor (BJT) case, the bias voltage sets the amount of current entering the device through the base, ib , which, in turn, determines the amount of current through the device collector. This method of directly applying voltage to the nodes of the active device is acceptable at low frequencies; however, with RF signals a more complex bias circuit is necessary.
Figure 2 shows the DC bias circuit for high frequency applications. The DC voltages applied at the gate and drain of the device cannot be applied directly. A high impedance component is used to ensure the complete RF signal passes through the device and not back through the DC bias circuit. The inductor, DCFEED, is seen as a high impedance element to the RF signal, allowing most of the information to pass through the device and not travel through the inductor along the DC bias path. Since the inductor is not an ideal open circuit (infinite impedance), some RF signal passes through the inductor. This RF signal is then directed along a low impedance path to ground through the RF shunt capacitor.
The DC signal applied at the point labeled Vbias sees a low impedance path through the inductor. The shunt capacitor to ground is seen as a high impedance or open circuit, so little or no DC signal is lost along this path. The RF input signal is applied to port 1 and passes through the low impedance capacitor to the gate of the device. The DC signal that passes through the inductor sees the DC blocking capacitor as a high impedance path, thus the term DC blocking capacitor. This capacitor prevents the DC signal from passing through the capacitor and back along the RF signal path.
In order to understand the different classes of device operation, the basic workings of a transistor must be understood. Figure 3 shows the transfer function of a transistor. The transfer curve is broken up into four distinct regions. In the first region, a small signal is applied, but it is not large enough to activate the device. This region is called the cutoff region, and the transistor is not conducting any current. The transistor conducts current to amplify a signal only after the device is turned on. The point at which there is a large enough bias to turn the transistor on is called the point of conduction and is represented by point A on the transfer curve. After the device is turned on, or activated, the output signal is roughly related to the input signal by a factor of two. This region is known as the square law (or transition) region. In the transition region, the device is in transition from an off state to the linear state. This region is represented by the input signal between points A and B. If the applied input voltage exceeds point B, then the transistor enters the linear portion of operation. This portion of the transfer characteristic is the most useful since the output signal is an accurate representation of the input signal except for a scaling factor. The linear region is represented when the input bias is between points B and C. Large input voltages greater than point C cause the transistor to enter the saturation region. The saturation region is where a large change in input signal will result in a small change in output signal.
The conduction angle refers to the amount of a full period of the sinusoidal input an active device conducts (amplifies) at the output. Class A is biased so that the input sine wave signal is applied optimally at the center of the linear region of operation. Figure 4 shows that the applied input signal is located in the linear portion of the transfer characteristic. For a sinusoidal information-bearing signal, the output is conducting for the full range (or 360°) of the input signal. Figure 5 shows that the conduction angle for class A is 360°. This condition means that a device biased at class A is fully on and there is DC current draw even when there is no applied RF signal. Class A operation is also entirely in the linear region, making the output signal an accurate representation of the input signal.
Class B is biased with the operating point right on the point of conduction. Figure 6 shows that class B is biased so that the positive slope of the sine wave input signal enters the conducting region of the device. Class B is characterized as being on for exactly one-half the input signal period (or 180°), as shown in Figure 7 . Since the transition region is nonlinear, some of the signal is distorted near the point of conduction. Class B is rarely used in practical applications because of the large crossover distortion. Since the device is only on half the time, half the signal is missing.
Several alternatives are available to accurately represent the input signal at the output. First, an LC resonant circuit can be designed to recreate the missing signal. Secondly, a push- pull circuit configuration, shown in Figure 8 , can be used. In a push-pull circuit the RF signal is applied to two devices. One of the devices is active on the positive voltage swing and off during the negative voltage swing. The other device works in the opposite manner so that there are two devices, each conducting half the time, and the full signal is represented. However, because of the transition region, the distortion between one device turning off and the other turning on is usually not acceptable.
There are two methods to realize the push-pull configuration. Another push-pull configuration is shown in Figure 9 , where a balun is used. A balun (balanced-unbalanced) component accomplishes two things. First, it acts as a power splitter, equally dividing the power between the two output ports. Second, the balun outputs one port in phase and the second port as an inverted signal. The signals are fed to the same type of transistor. Since the signals are out of phase, only one device is on at a time. This configuration is easier to manufacture since only one type of device is processed.
An alternative biasing scheme is class AB. Class AB is biased between class A and class B (as the name implies), and exhibits linear benefits approaching the class A device and efficiency close to that of the class B device. Figures 10 and 11 show the class AB transfer curve and conduction angle. The actual performance is based on whether the device is biased closer to the class A or class B level of operation. Class C is biased below the turn-on level of the device. When the input signal is on the positive voltage swing, part of the signal is enough to reach the point of conduction, and the device turns on. Therefore, only the peaks of the input signal are amplified and are available at the output. This operation mode is highly efficient and produces high peak power but extremely poor linear amplification. This mode operates for less than one-half cycle. Figures 12 and 13 show class C operation. Table 1 lists the conduction angle vs. class of operation.
One of the defining characteristics of an amplifier is its efficiency. The power conversion efficiency of an amplifier is defined as the amount of RF power delivered to the load compared to the amount of DC power supplied to the amplifier. The method for calculating efficiency is
Pdc =Idc total power supply voltage
The reason efficiency is so important is the thermal characteristics. For example, Pdc = 10 W, Prf = 5 W and, using Equation 1, = 50 percent. However, the other 50 percent, or 5 W, is dissipated as heat. The less efficient the amplifier, the more heat must be dissipated; therefore, the larger the heat sink needs to be to dissipate the heat. This heat must be properly dissipated and, therefore, the heat sink design is critical for reliability considerations. If the heat sink is not adequate, the device will heat excessively to beyond safety limits and fail prematurely.
The maximum theoretical efficiency of a class A device is 50 percent. This specification implies that, at its best, a class A device dissipates 1 W in heat for every 1 W of RF output power. In practice, class A devices are anywhere from a few percent to 30 percent efficient. Theoretically, class B devices can be shown to be p /4 or 78.5 percent efficient. In reality, class B is somewhere between 10 and 50 percent. This savings is a real advantage in many situations, and class B can be used for much higher power amplification than class A. Class B has no current when no RF is applied, and the current increases as the RF drive level is increased. Therefore, the efficiency increases with drive level with a class B device. As the name implies, the efficiency for class AB theoretically ranges from 50 to 78.5 percent. Class AB has some DC current draw with zero RF, but also exhibits higher efficiency with drive level. Theoretically, class C amplifiers show 80 to 100 percent efficiency. Class C devices are highly efficient amplifiers that are excellent for high power high efficiency applications. Table 2 lists these results.
From earlier observations, class A operation is on the linear portion of the transfer characteristic and has the highest linearity of all classes of amplifier operation. One measure of linearity is the two-tone intermodulation distortion (IMD) test. Two continuous-wave tones of equal amplitude but different frequencies are applied to the input of the amplifier. At the output, the amplified fundamental tones are present in addition to several harmonic frequencies.
Both harmonics and IMD products exist at the output. The first odd intermodulation product is the third order (IMD3). For a class A amplifier, the fundamental and harmonics will be a linear function of the power. The fundamental frequency, or first-order tone, will back off 1 dB of output power for every 1 dB of input power reduction. The third-order (IMD3) tones will back off 3 dB of output power for every 1 dB of input power reduction. In theory, these two products will meet and cross at a single point as the input power is increased.3
The third-order intercept point, IP3, is the theoretical intersection of the fundamental tone and the third-order tone, and is a measure of linearity. The greater the IP3 level, the better the linearity of the device. Because of the linear nature of the class A device, the IMD3 at any input power level can be calculated. There will be a 2 dB improvement for every decibel reduction from IP3, as shown in Figure 14 . For example, for an IP3 = 40 dBm (10 W), if the input power is reduced by 10 dB, the output power of the fundamental will be 30 dBm (40 ? 10 dBm), while the third order will be 10 dBm (40 ? 30 dBm). The IMD3 for a 10 dB back off should improve by 20 dBc, which can be seen in the graph. Class B is biased only partially in the linear portion of the transfer curve. The use of push-pull circuits recovers half of the input signal, yet the crossover distortion due to the transition region makes the use of class B rare.
For linearity purposes, class AB is used with the push-pull circuit configuration to improve linearity compared to class B operation and efficiency compared to class A operation. Class C designs are not linear and cannot be used if the output signal must be an accurate representation of the input signal. Table 3 lists linearity vs. efficiency characteristics.
The gain of the amplifier is affected by the mode of operation. Class A designs offer the highest gain of any of the modes of operation. Class B designs can be shown to lose up to 6 dB of gain1 compared to class A designs. The gain of a class AB design falls somewhere between the highest gain at class A and 6 dB from that point near the class B bias point. Class C gain is even further reduced from class B. Table 4 lists these gain characteristics. If efficiency is important in a particular application, then some gain may be sacrificed with the use of a non-class A design. Table 5 lists a summary of the four operating class traits.
Certain applications demand very high linearity; these are best suited for class A designs. Amplitude-modulated signals depend on class A designs since the information is contained in the amplitude of the signal. Audio amplifiers also must be very linear but usually cannot afford the inefficiencies of a class A design. Typically, a class AB push-pull configuration is used to improve efficiency while maintaining a high level of linearity. Class C designs are used with extremely high power applications because of their high efficiency. A class C design can provide high peak power to certain applications that do not require high linearity specifications. Satellite communication systems rely on class C operation.
Hopefully this article has provided a basic understanding of DC biasing of devices, including the common modes of operation and their advantages and disadvantages. The concept of conduction angle associated with each mode of operation was discussed, along with the trade-offs between efficiency and linearity.
This article provided an overview of the basics of device biasing for the junior engineer. The author is in no way an expert in this field, and the derivations of many formulas and equations are left to the interested reader in the bibliography for additional research.1?5 *
1.? J.L.B. Walker, High-power GaAs FET Amplifiers , Artech House, Norwood, MA, 1993.
2.? S.C. Cripps, RF Power Amplifiers for Wireless Communications , Artech House, Norwood, MA, 1999.
3.? N. Dye and H. Granberg, Radio Frequency Transistors , Butterworth-Heinemann, Stoneham, MA, 1993.
4.? G. Gonzalez, Microwave Transistor Amplifiers , Prentice-Hall, Englewood Cliffs, NJ, 1984.
5.? N. Pothecary, Feedforward Linear Power Amplifiers , Artech House, Norwood, MA, 1999.
6. G. Breed, "Classes of Power Amplification," RF Design , August 1993.
7.? G. Breed, "Transistor Biasing Fundamentals," RF Design , June 1993.
8. J.L.B. Walker, "Understanding the Basics of FET Operating Classes," Microwaves & RF , August 1996.
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