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Modern digital communication systems provide improved spectral efficiency, clarity, and fade resistance when compared to analog FM systems. Spectral efficiency is a key factor because higher efficiency means more radio channels can occupy a given bandwidth. As such, code-division multiple access (CDMA) systems have been designed for maximum spectral efficiency in two ways:

• A large number of channels are transmitted on the same frequency, using orthogonal codes.

• The bands are spaced closely so that unused spectra is very small.

Both factors are set for maximum spectral efficiency but result in competing requirements. The signal structure causes a large peak-to-average signal power ratio, typically above 10 dB. So, transmitters must be capable of high peak power and must have low spectral regrowth to control adjacent channel interference. As such, transmit power amplifier distortion requirements are becoming increasingly stringent.

These increased requirements have resulted in the need for improved linearization techniques optimized for low distortion. A new approach to this is called balanced error correction (BEC).

Distortion results from non-linear voltage transfer, often described by the Taylor series expansion:

Where V_i(t) is the input and V_o(t) is the output.

This model is useful over narrow frequency ranges, where the system has relatively constant gain and phase transfer. However, wider frequency ranges require a more complex model. The odd-order terms in (1) result in intermodulation distortion (IMD) close to the desired signal. Even-order terms cause distortion an octave or more away. The third-order term dominates spectral regrowth in non-linearized amplifiers with an IS-95 waveform¹. UMTS requires even higher spectral purity, so third-order dominance is even greater.

A linearized power amplifier (LPA) produces higher power than is normally realized, without higher distortion. This results in improved efficiency and reduced power stage complexity (less silicon).

A key metric in such a design is the amount of distortion cancellation provided. The amount of cancellation is a function of both linearization and the allowed distortion. However, high cancellation is not always better because it can limit the practical bandwidth and may require extreme network accuracy.

As such, techniques must be evaluated with the intended waveform both from the point of view of the required bandwidth and the ultimate distortion limits.

After further discussion, a series of simulations illustrate the main points. Note that the simulations fall short of exact system models because the Taylor series only includes two terms and the waveforms have only two tones. Even so, the simplicity of the simulations allows valuable insight into system fundamental limits and capabilities.

An LPA can be separated into a simple amplifier (SA) and linearization circuitry. A traditional feed-forward amplifier (FFA) is shown in Figure 1.

Three metrics compare the SA to the LPA when operated at the maximum power within distortion limits. They are:

• Efficiency improvement
• Power improvement
• Distortion cancellation

The amount of cancellation determines how accurate the linearization technique must be. As mentioned earlier, high cancellation can translate to high production costs and reduced operating bandwidth. Therefore, lower cancellation will be more practical to implement.

The practical bandwidth is a function of the needed cancellation and tolerances for the cancellation circuitry. High cancellation is easy over a narrow band; wider ranges are more difficult.

For example, achieving 20 dB cancellation over 10% bandwidth is relatively difficult, requiring better than 0.5 dB and 5° of ripple.

The main linearization techniques are power back-off (or SA), FFA and pre-distortion (PD). BEC is a hybrid of PD and FFA. The last three active techniques have practical limitations due to accuracy requirements and fundamental limitations caused by second-order regrowth factors.

Here, the output power is lowered to reduce IMD. Figure 4 shows the results of a simulated SA (shown in Figure 3) based on the model in (1) where B = 1.0 and D = 0.1. (Only third-order distortion is included because it normally dominates.) In the simulations, 0 dB/V output is referred to 1 V peak for each of the two tones, as show in (2).

The third-order distortion decreases three times faster than desired signals and distortion is controlled with lower output power. Here, the SA power must be less than -14 dB/V to achieve -50 dBc distortion.

Feed-forward amplification (see Figure 1) is well-established². In Figure 1, a sample of the distortion is separated, amplified and summed, out-of-phase, back to the output. Vector modulators (VM 1, 2) adjust the network for optimum phase and gain. The antipodal cancellation signal can reduce distortion as determined by network accuracy. The cancellation signal is derived from the main amplifier distortion, so there is some compensation for variations in distortion level and gain ripple of the main amplifier. Even so, cancellation is usually limited to about 20 dB for narrow bandwidths and phase/gain ripple limits cancellation to about 15 dB over a 10% bandwidth.

FFA limits cancellation caused by distortion of the cancellation signal (in the error amplifier). To demonstrate, an FFA amplifier (see Figure 7) was simulated using the same model for the previous SA, with two identical amplifiers (B=1.0, D=0.1) and a 10 dB coupler summing the error path to the main path with 0.46 dB of main path loss (intrinsic in the 10 dB error coupler).

Figures 5 through 7 show the results with a two-tone input at 50 and 70 MHz.

The FFA can operate at -3 dB/V prior to exceeding -50 dBc, but requires two amplifiers. The main amplifier supplies -2 dB/V desired signal and the error amplifier supplies -25 dB/V cancellation power.

When amplifying low distortion signals, the error amplifier operates well below maximum power. Other combinations of error amplifier capacity and coupling coefficient can reduce the apparent waste of silicon. However, the error amplifier will always be operated well below maximum power.

High cancellation requires closed-loop controls as shown in red in Figure 8. The system uses VM₁ to minimize power at the sum node (Det 1) and VM₂ to compensate for changes in the error amp by monitoring Det 1 and Det 2. Input and output powers are monitored with Det 3 and Det 4. The adjustments stop when signals are out of appropriate ranges.

Closed loop control will compensate for gain and phase offsets. However, performance over a given frequency range will still require holding the accuracy in Figure 2.

This technique (see Figure 9) adds a cancellation signal to the input of the SA, resulting in an antipodal cancellation signal at the SA output. Adaptive PD has been in use for years³.

The simple model cancels only third-order terms. More complex systems include higher-order odd terms.

There is no output delay line or distortion-summing coupler, so there is less output loss. Still, PD exhibits limitations similar to those of the FFA. The cancellation signal must attain the required accuracy (see Figure 2). Unfortunately, the PD system does not have the same intrinsic ripple compensation as the FFA. As such, without closed loop controls, the PD system will exhibit reduced cancellation due to gain ripple and variations in distortion over frequency.

Similar to the FFA, the cancellation signal re-distorts in the SA and reduces system effectiveness. Figures 10 and 11 show simulation results for a two-tone input 50 and 70 MHz:

To achieve better than -50 dBc distortion, the system must operate at lower than -7.5 dB/V output.

An effective PD system requires accurate distortion models of the SA. However, the SA will change over temperature, voltage, time and frequency. So, a wideband and accurate PD is practically realized with closed loop control (see Figure 12).

The digital, adaptive PD system samples the output signal and uses adaptive filter technology to digitally predistort the baseband signal prior to modulation. The added complexity allows the PD coefficients to be altered as needed for slowly varying distortion characteristics of the SA. The PD coefficients can be a function of frequency (within the operating bandwidth of the linearization circuitry). Note that the downconverter must still maintain the required ripple (refer back to Figure 2).

In BEC, a predistortion signal is derived from one of several identical amplifiers. The predistortion is summed with the input signal and applied to multiple error amplifiers (two in the example of Figure 13). The amplitude of the predistortion signal is adjusted to compensate for the total distortion from all amplifiers. For optimal efficiency, each amplifier is coupled to the output proportional to the actual available desired signal power. For example, if the output delay line adds 1 dB of loss, the output coupler is designed for 1 dB reduced coupling to the main amplifier.

Using balanced error correction fundamental limits, which are similar to the FFA, the cancellation signal can re-distort in the SA and thereby reduce system effectiveness. Figures 14 and 15 show the results of a computer simulation of a BEC system with a two-tone input, 50 and 70 MHz. To achieve better than -50 dBc distortion, the system must operate at lower than -2.5 dB/V output.

The BEC requires the same accuracy as FFA but also has the same ripple compensation because the cancellation signal is based on a sample of actual distortion. The models show less cancellation needed for BEC than for FFA. To adjust for temperature and aging, the BEC may require closed loop controls.

Closed loop BEC requires controls almost identical to the FFA (see Figure 16). One exception is that a different principle is used to adjust VM₂. An unbalanced hybrid coupler is used to sum the “error” and main signals. Power at the “isolated” port of the hybrid will be minimized when the system has correct gain and phase balance. So Det 5 is used to adjust the phase of VM₂ and Det 3 is used to adjust the phase of VM₁. The SA gain variations are compensated with the VM's by monitoring power levels at the SA inputs and outputs.

In all cases, the cancellation signal is redistorted in the error amplifier or SA. So, all of the active techniques add new products and have reduced cancellation as the output power increases.

Table 1 summarizes the key simulation results. The FFA supplies the most power per SA, but it also requires high cancellation. The PD system and BEC require relatively low cancellation with slightly lower power per SA.

The BEC has the same low accuracy requirements as the PD, but uses the same type of simple (and mature) control system as the FFA. The implication is that BEC is better adapted to wide-bandwidth (multicarrier) systems and requires less accuracy. Showing such promise, a test bed was assembled.

The system in Figure 16 was assembled and tested with an IS-95 forward-link test signal. Evaluation focused around comparing the BEC system to the SA characteristics. Figure 17 charts efficiency and adjacent channel power rejection (ACPR) at 885 KHz offset from the center as measured in a 30 KHz bandwidth.

The BEC improves efficiency by about 50% near IS-95 spec limits (-45 dB ACPR) by allowing the amplifiers to operate about 3.5 dB higher. The BEC system cancels distortion by 7 to 10 dB above 42 dbm, with cancellation decreasing at higher power. Below 42 dBm, the ACPR measurement was equipment-limited.

Figure 18 shows the SA output spectrum superimposed with a BEC system. It is operated with SAs at the same power when producing an IS-95 forward-link test waveform and a 3GPP Model 1 (64 carriers).

The test bed (see Figure 21) can operate, multicarrier, over the 2140 to 2170 MHz range and uses static settings in that range. Unfortunately, the sampling coupler exhibited high ripple (5 dB) from 2110 to 2140 MHz, so adaptive control is required. It is expected to achieve full 2110 to 2170 MHz multicarrier capability and 0.5 dB lower output combiner loss on the next pass. Figure 19 shows performance vs. frequency.

The test bed demonstrates that BEC can make substantial efficiency improvements over wide frequency ranges. Simple, established techniques combined with low accuracy requirements make BEC attractive. The technology can be applied in many places where FFA amplification is presently employed by modifying network transfer functions.

1. Wu et al., “Linear RF Power Amplifier Design for CDMA Signals: A Spectrum Analysis Approach,” Microwave Journal, Dec. 1998 pp. 22-40.

2. Jean Yamas, “An HF Dynamic Range Amplifier Using Feedforward Techniques,” RF Design, July 1987, pp. 50-59.

3. Guthrie et al., U.S. Patent 5,838,195, Reduction of Second Order Harmonic Distortion in High Power TWT Amplifiers.

4. Guthrie, U.S. Patent 6,359,509, Balanced error correction amplifier and method of removing distortion from an amplified signal.

5. Guthrie, U.S. Patent 6,348,838, Optimal power combining for balanced error correction amplifier.

Warren Guthrie works for Netcom in Wheeling, Il. Guthrie specializes in signal processing and radio communication systems and has completed coursework toward a Ph.D. in that specialization. He is manager of the advanced development group at Netcom. He may be reached at warren@netcominc.com