Introduction to the Feed-Forward Linearization of RF Power Amplifiers

In wireless communications systems, it’s critically important for power amplifiers to be both highly efficient and highly linear. Efficiency is key for reducing energy consumption, extending battery lifespan, and simplifying thermal management. Linearity, on the other hand, is vital to guarantee that the amplified signals exhibit minimal distortion. However, power amplifiers designed to maximize efficiency suffer from considerable nonlinearity.

There are several different power amplifier linearization techniques available. Distortion in amplifiers has been a problem since the dawn of telephone communications, so some of them have been around for quite a long time. For example, Harold Black patented the feed-forward and feedback circuit techniques in 1928 and 1937, respectively. Originally intended to minimize distortion in repeater amplifiers, both techniques have since been employed to linearize RF power amplifiers.

In this article, we’ll discuss the feed-forward linearization technique. Figure 1 shows the basic block diagram of a feed-forward power amplifier (PA) system.

 

Figure 1. Basic feed-forward power amplifier topology. Image used courtesy of Steve Arar

 

As we can see, the feed-forward arrangement actually requires two amplifiers. This topology determines the distortion signal added by the main amplifier and subtracts it from the system’s output to enhance the overall linearity. Let’s explore how this circuit works.

The input is applied to two different paths. In the upper path, the input is amplified by the main power amplifier. The output of a nonlinear amplifier can be viewed as the sum of a linear replica of the input signal and an error signal caused by nonlinearity. Therefore, the voltage at node m can be expressed as:

$$V_m ~=~ A_v V_{in}~+~V_d$$

Equation 1.

 

where:

A_v is the voltage gain of the power amplifier

V_d is the error signal produced by the amplifier’s nonlinearity.

The vertical branch in the block diagram attenuates the total output of the nonlinear PA by a factor of A_v to produce the voltage at node n. From Equation 1, we have:

$$V_n ~=~ V_{in}~+~ \frac{V_d}{A_v}$$

Equation 2.

 

Subtracting the input V_in from V_n, we obtain the attenuated version of the distortion signal at node p:

$$V_p ~=~ \frac{V_d}{A_v}$$

Equation 3.

 

The two paths from the input to the first subtractor form a loop that eliminates the input signal at node p. This is known as the signal cancellation loop.

Next, the voltage at node p is applied to an error amplifier with a gain of A_v, generating a voltage of V_q = V_d. This gives us the distortion signal, V_d. Finally, V_q is subtracted from V_m to produce the output voltage:

$$V_{out} ~=~ A_v V_{in}$$

Equation 4.

 

Although the amplifier is nonlinear, the overall output is a linear replica of the input. The second loop of the feed-forward PA system is called the error cancellation loop.

 

The Error Amplifier

Any tracking errors introduced by the amplifier in the second loop appear uncompensated at the output. Therefore, the distortion properties of the error amplifier determine the overall linearity of the system.

At the output of the first subtractor, the signal is canceled and we’re left with only the distortion component. Assuming that this residual signal is small, the error amplifier is less subject to distortion than the main amplifier. However, the distortion components rise quickly as the signal amplitude grows. For example, the third-order distortion in an amplifier produces distortion components that expand cubically with the input signal amplitude.

For that reason, although it’s typically the main amplifier that determines the power rating of the system as a whole, the power capability of the error amplifier is also an important design consideration. It’s influenced by several different parameters, including:

• The attenuation incorporated in the signal path from the input to the first subtractor.
• The AM-PM distortion of the main amplifier.

For more information on this aspect of feed-forward PA design, please refer to “RF Power Amplifiers for Wireless Communications” by Steve Cripps.

The error amplifier should also provide enough output power to overcome the loss from the output combiner. Typically, this requires sizing the error amplifier comparably to the main power amplifier, which can increase the system’s cost and decrease its efficiency.

 

Gain and Phase Match are Mandatory

Let’s return for a moment to Figure 1. For our previous analysis of this circuit to be valid, the paths leading to the subtractors must have perfect phase match and their associated components must have perfect gain match. For example, signal cancellation can’t take place if the two paths from the input to the first subtractor exhibit different delays.

Accurate gain and phase tracking are required over frequency, temperature, and time. Beyond that, recall that amplifiers introduce some delay to a signal path. We therefore need to incorporate two delay blocks to equalize the delay of the corresponding paths. This is illustrated in Figure 2.

 

Figure 2. Addition of delay elements to the circuit in Figure 1. Image used courtesy of Steve Arar

 

In the above diagram, the delay block τ₁ compensates for the phase shift caused by the main amplifier and the attenuator. Similarly, the delay block τ₂ compensates for the phase shift introduced by the error amplifier. Delay blocks can be constructed with passive lumped-element networks or transmission lines.

Keep in mind, however, that these blocks lead to power dissipation and a decrease in the amplifier’s efficiency. Designing wideband delay blocks also presents a significant challenge.

 

Practical Implementations

Figure 3 shows a more practical implementation of the feed-forward PA.

 

Figure 3. The block diagram of a practical feed-forward power amplifier. Image (modified) used courtesy of William F. Egan

 

Here, directional couplers are strategically utilized to sample and route the signal at critical nodes within the circuit as required. The coefficients c_n and c_n′ represent the coupling factors and main-line gains, respectively, of each coupler.

Unlike the previous circuit we examined, this arrangement lacks a distinct attenuator block in the signal cancellation loop. Instead, attenuation results from the directional couplers placed within the loop.

 

Feed-Forward PA System With Vector Modulators

Figure 4 illustrates another variant of the feed-forward PA system. In this circuit, two vector modulators (VM) are placed before the main amplifier (MA) and the error amplifier (EA).

 

Figure 4. A feed-forward PA utilizing vector modulators. Image used courtesy of Richard N. Braithwaite

 

A vector modulator is a device that can control both the amplitude and phase of an RF signal. It splits the signal into two components, referred to as the in-phase and quadrature components, that are 90 degrees out of phase with each other. By adjusting these components, the vector modulators in Figure 4 match the gain and phase of the loops.

 

Adaptive Feed-Forward Systems

Adaptive feed-forward PAs monitor the linearity performance of the system and adjust the loop parameters accordingly. Figure 5 shows the simplified block diagram of an adaptive feed-forward power amplifier.

 

Figure 5. The block diagram of a pilot-assisted feed-forward PA. Image used courtesy of Richard N. Braithwaite

 

In this example, a pilot tone is introduced before the main amplifier. The pilot signal is treated as an unwanted distortion within the feed-forward circuitry. Ideally, it shouldn’t appear at the final output. This provides us with a means of assessing the amplifier’s linearity performance.

After that, a variety of algorithms exist to optimize performance by fine-tuning the signal cancellation and error cancellation loops. These algorithms seek to determine the control parameters that will minimize the residual distortion.Utilizing an adaptive feed-forward system enables us to achieve lower distortion levels lower than would otherwise be possible.

 

Advantages and Disadvantages

The feed-forward technique has several advantages when compared to feedback methods. For one thing, it can correct for both amplitude and phase errors. Far more important, however, is that a feed-forward PA system is inherently stable even when its building blocks exhibit a substantial phase shift. This stability arises from the fact that the output isn’t fed back to the input.

Another significant benefit of the feed-forward method is its wide bandwidth. Such wideband power amplifiers are essential for multi-carrier wireless communications, including those utilized by wireless base stations. It’s also a relatively low-noise linearization technique. The noise from the main amplifier is ideally nullified in the same way as the distortion.

This brings us to another benefit of feed-forward systems: they correct the distortion error almost instantaneously. As a result, they aren’t influenced by the memory effect normally associated with power amplifiers. The memory effect is a phenomenon where the PA's output is influenced by the history of the input signal. It compromises the efficacy of predistortion linearization techniques, as we’ll discuss in future articles.

In summary, feed-forward PA systems offer the following benefits:

• Can correct for both phase and amplitude.
• Inherently stable despite phase shifts.
• Wide bandwidth.
• Low noise.
• Immune to memory effects.

However, they also come with a number of drawbacks. As we mentioned earlier, the incorporation of analog delay elements necessitates the use of passive devices like microstrip lines. Power loss in these devices is a critical concern. Additionally, the construction of the output subtractor demands the use of a low-loss component—for example, a high-frequency transformer—to ensure efficiency.

 

Wrapping Up

The feed-forward linearization method operates on the principle of distortion signal cancellation. It achieves this by determining the distortion signal and then subtracting it from the nonlinear power amplifier's output, thereby correcting the signal. Feed-forward systems are well suited for applications that demand a wide bandwidth, making them vital components of mobile communications networks.

 

This article is Part 1 in a series on linearization techniques and nonlinearity in RF systems. Below is a complete list of articles in this series:

1. Introduction to the Feed-Forward Linearization of RF Power Amplifiers
2. Using Analog Predistortion for RF Power Amplifier Linearization
3. Improving RF Power Amplifier Linearity With Digital Predistortion
4. Introduction to the Memory Effect in RF Power Amplifiers
5. Using the 1 dB Compression Point to Characterize RF System Nonlinearity
6. Understanding Intermodulation Distortion and the Third-Order Intercept Point in RF Systems
7. A Guide to Calculating IM3 and IP3 for Nonlinear RF Circuits
8. Understanding Dynamic Range and Spurious-Free Dynamic Range in RF Systems
9. Understanding the Third-Order Intercept Point of a Cascaded System
10. Dynamic Nonlinearity in RF Power Amplifiers: Insights From Two-Tone Testing