RF Power Amplification 101: Waveform Basics
High-power RF generation is required not only by various wireless communication applications, such as 4G and 5G cellular and satellite, but also by radar for airspace and weather monitoring, radar and communication jamming, imaging, DC/DC conversion, and even RF heating.
This power is delivered by the RF power amplifier (PA), the final stage of amplification before the antenna, with each application placing on the PA its own set of requirements in terms of frequency, bandwidth, load, power, efficiency, and linearity.
In communications, for instance, significant RF power may be needed to enable the transmission range goal to be met. A typical cellular communications application must deliver good signal coverage and high-speed data transfer with as little battery power consumption as possible. This interplay of requirements results in design tradeoffs between spectral efficiency, linearity, and power efficiency.
This RF power can be generated using any of a wide variety of techniques or amplifier modes of operation or classes. Each class differs in terms of the amount of time the transistor conducts and the shape of its output voltage and current waveforms, as well as the resulting unique set of tradeoffs.
This article is the first in a series that aims to refresh these considerations. We begin with a primer on basic waveform shapes and consider the power and efficiency they represent.
Three basic waveforms
Let’s take a closer look at three basic waveforms: the sine wave (A), square wave (B), and the half-rectified sine or half-sine wave (C) (Figure 1). The waveforms have the same 1 GHz frequency, and the same amplitude, oscillating from zero 0 to 2 for a magnitude of 1. They can represent either the voltage or the current of an ideal transistor in an RF Power Amplifier.
The sinusoidal waveform ‘A’ is a representation of a DC component and a single fundamental frequency with no harmonics, wherein harmonics are waves with a frequency that is a positive integer multiple of the fundamental.
Sinusoidal waves, along with a DC offset, can be used as building blocks that describe an approximation of any periodic waveform. Waveforms ‘B’ and ‘C’ shown in the figure can be deconstructed into a sinusoid at the fundamental frequency or first harmonic and higher-order harmonic components.
The ideal square wave is a special case of a pulse wave with a duty cycle — the ratio of the high duration or period to the total period of the wave — of 50%. In an ideal square wave, there is an instantaneous transition between the minimum or low state (trough) and maximum or high state (crest) values without any under- or overshoots.
Similarly, the half-sine wave has harmonic components at even-integer multiples of the fundamental frequency to infinity.
While these harmonics will determine the final shape of the composite time-domain waveform, for the purpose of our discussion on power and efficiency, it is the DC and the fundamental frequency components that are of interest.
Looking at the composite waveforms, even though all three waveforms have the same amplitude, the square wave “hides” inside it a fundamental sinusoid that is of a higher amplitude than that of waveform ‘A’ (Figure 2).
Similarly, deconstructing the half-rectified sine wave reveals that, while the fundamental sinusoid has the same amplitude as waveform ‘A’, its DC component has a lower value:
Where Imax represents the maximum value in the current waveform.
Looking at it from another perspective, one might say that for the same DC value as waveform ‘A’, the half-rectified sine wave would produce a larger RF swing.
Calculating power and efficiency
A power amplifier uses the DC supply power to amplify the RF input. The supplied DC power is a product of the DC voltage and current. The power amplifier efficiency is defined as the ratio of the RF output power at the fundamental frequency over the supplied DC power:
For a sinusoid like that at the fundamental frequency, the root mean square voltage and current are obtained by dividing the respective voltage or current magnitude by the square root of 2. RF power, therefore, is given by:
Efficiency (%) can then be written as:
Assumption of idealities
This discussion has assumed ideal waveforms enabled by an ideal transistor. What that means is that we have assumed the transistors behave as perfect switches.
The characteristics shown in Figure 3 illustrates that when the gate-source voltage Vgs completely closes the channel, the drain current Ids is abruptly pinched off with no leakage. This ideal switch also exhibits an equally abrupt saturation point when increases in Vgs do not increase Ids.
In the next article, we continue to use these idealities to illustrate the amplification mechanism and introduce the key amplifier classes — A, B, C, F, and inverse-F — for RF applications.
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