4 Linear Power Amplifiers

4 Linear power amplifiers Linear amplifiers are the core of most electronic signal processing, and RF transmitters are no exception. Linear circuitry always operates with the transistor as a controlled current source (CCS). We can state both that a linear amplifier operates as a CCS, and the converse that with CCS operation we have a linear amplifier. With a century of history, the design of linear power amplifiers is covered extensively in the literature [4-1] and will not be repeated here. In this chapter, the points about linear RF power amplifiers that are most important to their application in DPS architectures are described. 4.1 Overview The entire objective of any linear amplifier is to provide an output signal y(t) that is proportionally scaled from the input signal x(t). The constant of proportionality is called the gain of the amplifier. Mathematically we write this as ytðÞ¼axðÞ t ; ð4:1Þ where the proportionality constant a is the amplifier gain. In the real world, the relationship in (4.1) is an ideal goal that is never precisely reached. How hard we must work to make our amplifier approximate this ideal performance more closely is dependent on the signal type we are to amplify, and the output performance specifications we need to meet. In general, the greater the signal order is [4-2], which is the number of possible information values that can be transmitted in any signal symbol, the more precise the amplifier linearity performance must be. It is very important to be clear that the concept of a linear amplifier is a port-based specification, as shown in Figure 4-1. What the actual circuitry is within the amplifier, and how it precisely operates, does not matter. It is very common to implement a linear amplifier function using linear circuitry. But this is not necessary at all. What is a requirement, though, is that the input and output signals be essentially sinusoidal in wave shape. All communications signals used are of the narrowband type, which simply means that the bandwidth occupied by the signal is much less than the center frequency of the signal. This definition includes any power present around the harmonics of the signal center frequency. Fourier theory clearly states that any signal that is narrowband is also sinusoidal in wave shape. Therefore, if the amplifier block of Downloaded from https:/www.cambridge.org/core. University College London, on 23 Apr 2017 at 18:33:28, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781107416215.005 Overview 45 SignalIN SignalOUT Figure 4-1 Amplifier linearity is only measured at the amplifier ports. 20 10 0 −10 −20 −30 −40 Output Power (dBm); Gain (dB) −50 −60 −60 −50 −40 −30 −20 −10 0 10 Input Power (dBm) Figure 4-2 Amplifier gain is typically not constant for all values of the input signal, shown here evaluated for an example amplifier transfer function (solid line) with its corresponding slope gain (dotted line) and ratiometric gain (dashed line). See Section 4.1.4 for details on the two gain measures used here. Figure 4-1 contains nonlinear circuitry, to be a legitimate amplifier it must also contain circuitry to guarantee that the output signal is narrowband. This particularly applies to so-called switch-based or switch-mode amplifiers, such as class S [2-4]. Any actual amplifier exhibits a nonconstant gain as the input signal varies. A typical example of this gain variation is presented in Figure 4-2. Here we see both gain expansion, where the gain increases from its very small signal value, and also gain compression, where the gain is below its value at very small signal operation. The two different measures of gain shown in Figure 4-2 are defined in Section 2.2 and detailed in Section 4.1.4. Both gain expansion and gain compression lead to signal distortion. Gain expansion typically arises from using reduced quiescent current biasing usually adopted for power savings. Gain expansion is not experienced as often when class A biasing is used. Compression effects As the output signal from any amplifier approaches the maximum value it can attain, a deviation from linear behavior, called compression, occurs. Compression describes how Downloaded from https:/www.cambridge.org/core. University College London, on 23 Apr 2017 at 18:33:28, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781107416215.005 46 4 Linear power amplifiers Figure 4-3 Definition of compression points using a simulated amplifier voltage transfer function. the output from an amplifier does not reach the expected full value if that amplifier remained operating linearly. One measure of compression is the output level where the measured output power is 1 dB below what we expect it to be from the linearity extension from very small signal conditions. This is the power at P1dB, the 1 dB output compression point. We can similarly measure P3dB, the 3 dB output compression point. And, of course, any other output compression value. Three measures of output compression are shown in Figure 4-3. For this particular transfer function, the input values where the actual output is 1 dB, 2 dB, and 3 dB below the ideal linear response (dashed line) are shown. The onset of waveform distortion is much sooner, near to the normalized input voltage of 0.6 V. In Figure 4-3, we note that the 3 dB output compression point (P3dB) is very close to the onset of output clipping. This is not always true for all amplifiers. Each amplifier needs to be individually characterized. From Section 2.3.3 and Figure 2-6, we note that for a perfectly linearized amplifier, often called a “soft limiter” because of its finite gain, the onset of clipping is essentially 2 dB below the output power saturation. This is a completely different measure from the present discussion surrounding Figure 4-3, because here we have a reverse-looking (PSAT – 2 dB) measurement instead of the forward-looking measurements of the output compression points (decibels below ideal linear projection). Therefore, there is no equivalence of the output compression value at power saturation. We can only say that we know that output power saturation is reached when the ratiometric gain is dropping decibel for decibel with further increases of the input power. In this region, the compression point is also increasing decibel for decibel with further increases of the input power. Sizing the design of any power amplifier is a key decision on any project. The primary requirement is that the power amplifier must be able to provide the absolute maximum output power that the signal envelope can attain when the transmitter is at maximum power. This follows from Figure 2-6, which shows that any amplifier is an output power limited device. The design is driven by PEP, not average signal power. Setting PSAT = PEP may still not be sufficient for some applications. Section 4.1.5 shows that at PSAT the amplifier output waveform is essentially square, severely Downloaded from https:/www.cambridge.org/core. University College London, on 23 Apr 2017 at 18:33:28, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781107416215.005 Overview 47 clipping off any signal peak from the input sinusoidal waveform. For several mod- ulation types, this signal distortion due to clipping is unacceptable. For these signals, it is necessary to set PEP at a lower output power than PSAT, possibly at P1 dB. Whatever the reduction is, this type of operation is called output back-off (OBO) where (in dB) OBO = PSAT – PEPMAX dB. 4.1.1 Bias classes and their waveforms For completeness, here is a very brief review of linear amplifier bias class definitions. These include class A, class B, and the various intermediate bias conditions of class AB. Class C is included because it definitely is a controlled current source (CCS) amplifier. Finally a discussion of the two-device push-pull amplifier is included with particular attention to its operation as the device bias transitions from deep class AB through class B and into class C. Controlled current source (CCS) CCS amplifiers are the fundamental designs taught in engineering school, and date from the beginning of amplifier design one century ago. The differences among them are set by what bias is applied to the transistor controlling element, as shown in Figure 4-4. Class A requires that current flows through the transistor at all times. All of the other classes require that current flow be interrupted during some fraction of each RF signal cycle. Class A Class A amplifiers are the original amplifier circuit. After allowing for the output DC offset, the RF output signal is directly proportional to the input signal. If there is no input signal, a current called the quiescent current continues to flow through the RF transistor. This quiescent current must be greater than the maximum negative excursion of signal current, to ensure that device current will always flow as required for this class. Figure 4-5 illustrates several signal currents for class A operation. Along with the DC (a) (b) Figure 4-4 Biasing of CCS amplifiers: (a) control characteristic view (depletion FET example); (b) load line view. Downloaded from https:/www.cambridge.org/core. University College London, on 23 Apr 2017 at 18:33:28, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms.

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