Predistortion circuits can improve the linearity of power amplifiers (PAs) and other devices used in communications systems. An amplifying predistorter, for example, employs the nonlinear distortion components of a preamplifier to correct the distortion of a following nonlinear device, such as a PA, rather than using separate nonlinear elements such as diodes or field-effect transistors (FETs). Amplifying predistortion, which can be considered a generalization of feedforward (FF) technique, can be used to improve amplifier efficiency while reducing cost and size compared to traditional FF methods. The approach can be adapted to systems with frequency upconverters as well as to systems with broadband electro-optic devices.

FF systems date from the early 20th century,^1,2 but their application in high-frequency systems began with the work of Seidel et al.³ Since then, numerous FF systems have been reported in the literature for modern applications.^4-6 An example of amplifying predistortion (APD) can be found in ref. 7, where a driver amplifier is used to generate distortion to correct the distortion of the main PA. In this example, discussed in relationship to Class AB devices and operating over a narrow bandwidth, modest (9 dB) suppression of intermodulation distortion (IMD) was achieved.

APD is an attractive for several reasons. It does not suffer from the bandwidth restriction of a typical digital predistorter. In fact, it has been successfully applied to linearize devices spanning more than an octave. In addition, the APD approach has the following advantages over a conventional FF system:

1. Losses due to the delay line and couplers at the output are eliminated.
2. The error amplifier is of substantially lower power than used with a traditional FF system.
3. Since delay elements are not at the output, they need not exhibit low loss; compact, low-cost delay lines can therefore be used.
4. The method is amenable to adaptive linearization to correct for aging, drift, and temperature effects.
5. It is possible to linearize devices with inputs having a different nature than the outputs. Examples include a millimeter-wave amplifier preceded by a frequency upconverter and electro-optical transducers such as lasers or electro-optic modulators.

For practical application of APD, it would be useful to estimate the amount of IMD suppression that can be achieved by this technique compared to high-performance FF techniques. By treating the APD approach as a generalized form of FF, it may be possible to arrive at some estimates. Figure 1(b) shows a basic block diagram for the APD scheme; it bears a superficial resemblance to the FF system shown in Fig. 1(a).

However, unlike an FF system where the distortion generated by a given device is canceled at its output, in an APD a second device (A3, the driver stage) is used as an additional source for distortion components. The distortion from A3 is fed with the correct magnitude and phase at the input of power stage A1 in order to cancel the distortion components generated by A1. If A1 is removed from the circuit, the distortion from the path consisting of A2 does not completely cancel the distortion from the main path as in a FF scheme. But the extra gain of A2 helps generate more distortion than necessary compared to a FF scheme, and this extra distortion cancels the distortion from the power stage (A1). For this reason, this technique can be called the over-compensated feedforward (OCFF) technique.

In order to develop a simplified OCFF analysis approach, fifth- and higher-order distortion components will be neglected, a reasonable assumption for Class A amplifiers and certain electro-optic components. It will also be assumed that the imaginary part of the devices' nonlinear transfer function is negligible.^8,9

Referring to Fig.1(b), the following parameters can be defined as:

P₁ = the input power (two-tone excitation) at the input port of A3 (in dBm/tone);

IM3_A1 and IM3_A3 = the two-tone third-order intermodulation components at the outputs of A1 and A3, respectively (in dBm);

IP3_A1 and IP3_A3 = the output third-order intercepts of A1 and A3, respectively (in dBm);

G_A1, G_A2, and G_A3 = the gain of A1, A2, and A3, respectively (in dB);

L = the loss of the main path, which is comprised of the insertion losses of couplers C1 and C2 and the loss through delay line D1 (in dB).

At point A of Fig.1(b), following the definition of third-order intercept point:

At point B, the intermodulation voltage signal from the main path is:

and the intermodulation voltage signal from the shunt path at point B is:

where:

G_shunt = the gain in the shunt path comprised of G_A2 minus coupling losses in C1 and C2 and insertion loss in hybrid coupler H1.

If the delays in the main and shunt paths are identical, the phasors V₁ and V₂ would be in opposite phase, provided that gain G_A2 exceeds some minimum value. In that case, the resultant voltage at point B can be expressed as:

At point C, the intermodulation voltage signal from A1 alone can be expressed as:

Referring the above signal to the point B results in:

which can be converted to voltage to obtain:

Cancellation of the distortion phasors requires that:

From Eqs. 2, 4, and 5, it is possible to solve for G_shunt to get: