Power-amplifier (PA) distortion must be minimized in any broadcast application to prevent interference with adjacent channels. Distortion can be present in the form of amplifier clipping, intermodulation distortion (IMD), and memory effects. For some communications standards, such as Brazil’s ISDB-T standard, which is based on orthogonal frequency- division-multiplex (OFDM) modulation, excessive phase distortion in the transmit amplifiers can disrupt proper system operation. But by the use of proper models and linearization techniques, it is possible to minimize PA distortion even in demanding OFDM-based communications systems.

All PAs suffer from some distortion, independent of input signal level and device technology, since transistors are not ideal linear components.¹ The three basic types of distortion are amplitude, frequency, and phase distortion. Amplitude distortion is caused by amplifier gain compression (P1dB), which is device dependent. During amplifier clipping, unwanted harmonics are generated, a form of frequency distortion. The magnitude of these harmonics is increased with the amount of signal clipping, consequently increasing the amplifier’s overall distortion.

PA phase distortion in power amplifiers is caused mainly by memory effects from a variety of factors, including device bias conditions, transistor transit-time, and thermal effects. Operating an amplifier with significant backoff can minimize phase distortion but with degradation of amplifier efficiency. One method for minimizing amplifier phase distortion while maintaining efficiency is the use of linearization techniques.

Linear Equipamentos Eletronicos S/A began research on power amplifier (PA) linearization some years ago. Initial results for AM/AM analysis were obtained by inferring that the transfer function of a PA’s output voltage had third-order nonlinear dependence with respect to the input signal. Although the numerical approach adopted for this analysis was efficient in this particular case, it did not compensate for the nonlinear effects of amplitude-modulation/ phase-modulation (AM/PM) distortion.^{2, 3} References 4 and 5 provide examples of models that can compensate for these and other distortions; in ref. 5, for example, a study was performed involving several practical models. An accurate model represents the first step for implementing an efficient predistortion system. Using the parallel model described in ref. 5, Linear Equipamentos Eletronicos obtained good results, compensating for both AM/ AM distortion, AM/PM distortion, and memory effects.

Communications systems based on OFDM techniques can employ signals with thousands of carriers, as in standard ISDB-T systems. The carrier combination can generate a reasonable number of voltage spikes in the time domain, depending on its phase. The magnitude of these peaks can be measured through a figure of merit, the peak to average ratio (PAR), which is defined by:

PAR = 20log(|X_peak|/X_av)

where X_peak and X_av are the maximum and average values (in V), respectively, of a signal under test.

The X_peak value can be measured in the time domain using an oscilloscope with sufficient bandwidth. The X_av value can be measured using a wattmeter and then converting the value to voltage, assuming a 50-Ohm load. The PAR from some commonly used signals are: 3 (dB) for a continuous wave (CW) signal, 3.5 to 4 dB for a QPSK signal, and approximately 12 dB for the ISDB-T standard OFDM signal. This implies that, if a Class AB PA has a 1-dB compression point at +10 dBm (Fig. 1), an OFDM signal per the ISDB-T standard can be boosted without compression using this amplifier with input levels to -2 dBm. This indicates that all amplifiers used in the ISDB-T transmitter chain require a large backoff compared to amplifiers used in analog broadcast transmitters.

Amplifier gain compression results from the IMD characteristics of the amplifier’s transistors, with major influence of the third-harmonic component.6 Intermodulation can be easily measured when more than one carrier is used as a PA input signal, such as using a test signal consisting of two-tones with equal amplitude. When a two-tone test signal is applied to an amplifier, it is possible to observe several IMD components in the output spectrum generated due to the nonlinear behavior of the transistors (Fig. 2).

In an ISDB-T standard OFDM signal with thousands of carriers, distortion can appear as multiple distortion signals (Fig. 3). The bandwidth of the distortion is related to the signal bandwidth. Thus, if a signal has a bandwidth of 5.6 MHz at the fundamental frequency, the bandwidth of the second-order distortion will be 2 x 5.6 = 11.2 MHz, the third-order distortion will have a bandwidth of 3 x 5.6 MHz, and so on. Odd-order distortion lies within the fundamental zone, requiring a different treatment than for even-order ones. These lie outside the fundamental zone and at the DC zone, and can be removed by means of filters.⁷

One way to avoid PA IMD is through backoff techniques, although this increases transmission costs by the need for an increased number of PAs for a required transmit power. The approach does guarantee high quality of the transmitted ISDB-T signal, measured by the modulation error ratio (MER, in dB),⁸ by which excellent levels are over 40 dB. Unfortunately, if high backoff values are used, the PA efficiency is degraded. As a result, a tradeoff between backoff (or high MER values) and PA efficiency must be established.

In a system with memory effects, the condition of the output signal is dependent upon the past states of the input signal. The extent of the memory effects can be estimated through observation of the first-order Volterra kernel. The amount of memory is defined as the time between the origin of the kernel until the point where it passes through zero, and is directly dependent on the bandwidth of the transmitted signal.⁹

An RF PA has a complex structure with many different types of memory effects. These can be classified¹⁰ as low-frequency (kHz to MHz) effects (such as thermal effects, trapping effects, the influence of biasing circuits, and the influence of AGC loops) and high-frequency (GHz) effects (such as transistor transit time and reactance parasitic and group delay from matching networks).

Such memory effects are mixed together (nonlinearly coupled) in a PA and the problem of estimating behavioral models becomes very difficult.¹¹ A general classification of memory effects, in linear and nonlinear form, can be found in ref. 12. A memoryless system is one in which the output signal envelope follows the variations of the input signal envelope. Matching networks are the origin of linear memory, and nonlinear memories are generated in the nonlinear dynamic interactions of the input signal. A practical RF PA output signal has both linear and nonlinear memory, and an ISDB-T OFDM signal that occupies a bandwidth of 5.7 (MHz) and as many as 8,000 carriers will cause more memory effects in a PA than an analog signal, which has only three carriers.

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