Feed-Forward Error Correction

October 11, 2018

Feed-Forward Error Correction

Benchmark AHB2 Power Amplifier featuring Feed-Forward Error Correction Benchmark HPA4 Headphone Amplifier featuring Feed-Forward Error Correction

The Benchmark AHB2 power amplifier and HPA4 headphone amplifier both feature feed-forward error correction. This correction system is an important subset of the patented THX-AAA™ (Achromatic Audio Amplifier) technology. It is one of the systems that keeps these Benchmark amplifiers virtually distortion free when driving heavy loads. It is also the reason that these amplifiers can support 500 kHz bandwidths without risk of instability when driving reactive loads. The feed-forward system also helps to drive the output stage through the push-pull crossover region while providing a wide-bandwidth correction signal that virtually eliminates crossover distortion.

Feedback Error Correction

Feedback is a fundamental building block in audio amplifiers and in most any electrical or mechanical system. The basic concept is that a system output can be compared to a reference input in order to drive the output toward the reference.

Feedback drives the output toward the reference to reduce the difference between the reference and the output. The difference between the reference and the output is the error signal (or distortion) that we are attempting to minimize.

Combined use of Feedback and Feed-Forward Correction

I should point out that the Benchmark amplifiers use feed-forward correction in combination with traditional feedback correction. These two systems compliment each other in Benchmark amplifiers. To understand this interaction, lets look at a familiar example:

Cruise Control - a Feedback System

Cruise ControlThe cruise control in your car is a feedback system. The speed of the car (output) is compared to the desired speed (reference input) to control the engine power. An increase in power will result in an increase in speed and when the desired speed is reached, the power will be reduced. If the cruise control is well designed, it will respond to changes in loading (hills) while maintaining a nearly constant speed. If the cruise control is not well designed it may tend to over accelerate and then decelerate more than necessary causing an oscillation above and below the desired speed. Even with a well-designed cruise control, the onset of a hill will cause a slight loss in speed while the system works to recover. There is always a time delay in a feedback system. This is the loop response time. The mass of the car, the power of the engine, the transmission gear ratio, and the gain of the speed control are all factors in the response (and stability) of the system.

Feed-Forward Error Correction

If you are not using the cruise control, you may see a hill coming and press the accelerator in anticipation of the need for more power. Your eyesight enables you to feed more power to the engine before the hill begins to slow the car. In a way, you are providing feed-forward error correction.

Combined Feed-Forward and Feedback Correction

It is likely that there have have been times when you pressed the accelerator while the cruise control was on. You saw a hill coming and gave the accelerator a little nudge to help maintain a constant speed. You pressed the accelerator to overcome the slow response time of the cruise control (feedback) system. Your feed-forward correction was summed with the feedback from the cruise control system in order to control the engine power. If this was balanced skillfully, your car did not slow down at the onset of the hill. You provided a feed-forward correction signal before the cruise control detected a loss of speed. In doing so, you proved the benefit of adding some feed-forward correction to a feedback control system.

Feedback is Applied to an Input and is Recursive

Feedback control networks monitor a system output and apply a correction signal to an input earlier in the system. This feedback network forms a recursive loop. When the correction signal reaches the system output, the error at the output should be reduced. Any remaining error is fed back to the input to further correct the output. If the feedback system is well designed, the error will null toward zero after multiple passes through the loop. If the feedback system is not well designed, it may overshoot or oscillate instead of nulling toward zero error.

The Recursive Correction Process

To understand the recursive correction process, let's go back to the cruise control example: Our car starts going up a hill and the speed begins to drop. The control system begins to sense the drop in speed but the car continues to lose speed before the loop can increase the engine power. The speed may drop 5 MPH before the engine power is increased enough to prevent a further loss of speed. The feedback loop continues to call for more power until the speed set point is reached. Once the set point is reached, the feedback loop begins to reduce the power to the engine. Ideally, the cruise control will back off the power before the speed overshoots the set point.

Feedback Loops Can Have Stability Problems

Some cruise controls have a tendency to slightly overshoot the set point. If the cruise control in your car tends to overshoot, you may notice that this tendency gets worse at lower speeds, especially when the transmission is in a lower gear. As I said earlier, the mass of the car, the power of the engine, the transmission gear ratio, and the gain of the speed control are all factors in the response (and stability) of the system.

In our example, if the first overshoot is greater than the original 5 MPH undershoot, the speed control system is unstable. If so, each successive overshoot or undershoot will get worse. I remember driving a 1970's vintage full-size car that had a cruise control. I engaged it at 35 MPH on a hilly country road. The cruise control system went into oscillation causing the car to accelerate and slow by ever increasing amounts until I tapped the brake pedal to disengage the control loop. This hilarious, and potentially dangerous behavior was caused by the unusual operating conditions. The cruise control on this 1970's car was designed to be stable at highway speeds, but had not been designed to be stable on hilly roads at low speeds.

In an audio amplifier, the output loading can impact the response and stability of the feedback loop. Capacitive loads are usually the most problematic. Amplifier designers have to make compromises in order to maintain stability with anticipated loading. These compromises include limiting the bandwidth of the amplifier and/or reducing its use of feedback.

Feed-Forward Correction is Added to An Output and is not Recursive

A feed-forward system measures errors in an early part of the system and applies a correction in a later part of the system. If it is a true feed-forward system, the correction is not fed back to the stage that is causing the error. It is added after the output of the stage that is causing the error. This means that there is no recursion. There is no control loop. There are no loop stability problems, because there is no feedback loop. A change in system loading will not put the system into oscillation.

Feed-Forward Correction in an Audio Amplifier

The Benchmark AHB2 power amplifiers and HPA4 headphone amplifiers each have two amplifiers that run in parallel. The first amplifier is the main amplifier. This amplifier delivers the bulk of the output power. You could say it does the "dirty work" or the "heavy lifting". The second amplifier is the feed-forward correction amplifier. This amplifier is a clean, high-speed,  low-power amplifier that cleans up the mess made by the amplifier that is doing the heavy lifting. The correction amplifier puts the finishing touches on the output to cancel any distortion produced by the main amplifier. This cancellation is extremely fast and is entirely non recursive.

Changes in system loading will change the amount of distortion produced by the main amplifier, but this will be removed by the correction amplifier without creating any change in the stability of the system. As a result, the AHB2 and HPA4 amplifiers can support a 500 kHz bandwidth without risk of stability problems when driving reactive loads.

Furthermore, the feed-forward correction keeps the output clean when the amplifier is heavily loaded. If the loading increases the distortion produced by the main amplifier, the correction amplifier removes it. As a result, the THD produced by Benchmark amplifiers does not increase with loading. The unloaded THD matches the loaded THD. This is shown in the following plot below.

THD Does Not Increase when Benchmark Amplifiers are Heavily Loaded

The following graph shows the 1 kHz THD produced by the AHB2 amplifier with no load and with a 6-Ohm load. The amplifier was running in mono mode, so this is equivalent to simultaneously driving two 3-Ohm loads in stereo. Notice that the THD is virtually identical with or without this heavy load! This immunity to load changes demonstrates the effectiveness of the feed-forward system. Also notice that the THD measures -120 dB (0.0001%) at 477 Watts into 6 Ohms. The extra "clean up" provided by the feed-forward correction amplifier really pays off.

If you look at a similar plot for a conventional power amplifier, you will see that THD increases significantly as the load impedance decreases. Traditional amplifiers will produce more distortion when driving 4 Ohms than when driving 8 Ohms. Traditional amplifiers will also produce more distortion when running in monoblock configuration.

The stair steps in the graph below are due to the measurement limitations of the AP2722 test station. The presence of these stair steps indicates that the THD produced by the amplifier is very near the residual THD produced by the test station.

Clean First-Watt Performance

The magenta curve shows the output power as it was swept from 1.3 Watts to the 477 Watt onset of clipping. At 1.3 Watts, the red and green curves show that THD is an astonishing 140 dB below the amplifier's peak output! The AHB2 has extraordinary performance in the first watt where most listening occurs. This clean low-power performance can be seen from the following scope traces that compare the AHB2 to a conventional class-AB amplifier:

Most of the distortion produced by the traditional amplifier (lower photo) is due to push-pull crossover distortion transients that could not be fully removed by the traditional feedback network around the amplifier's output stage.

Push-Pull Output Stage

Class-AB amplifiers use complimentary devices to "push" the output high and "pull" the output low. The simplified diagram below is a class-B output stage. A class-AB stage adds a biasing network that attempts to keep both devices turned on while transitioning through the crossover between push and pull operation. The diagram shows the severe distortion that can result from having a dead zone where both devices are simultaneously turned off. This dead-zone is a characteristic of class-B amplifiers (which are rarely used for this reason). The illustration is included here because it helps to shows why some distortion occurs at the crossover between push and pull modes. The distortion shown in the scope photos above is much less than the distortion that would be produced by a class-B output stage, but the distortion produced by the traditional class-AB amplifier is clearly visible in the lower photo.

Push-Pull Crossover Distortion

In a traditional amplifier great care must be taken in the design of the output stage in order to minimize the need for feedback error correction. Biasing of the push-pull crossover region is critical, and output devices must be carefully matched. Push-pull switching transients often produce frequencies that exceed the bandwidth of the feedback loop around the output stage. When this happens, the transients are not removed by the feedback system.

Speaker loads and temperature variations can upset the precise biasing and device matching, resulting in an increase in distortion as the load impedance decreases. As stated above, this characteristic is evident when comparing THD into 8 Ohms with THD into 4 Ohms.

Feed-Forward Correction can Remove Crossover Distortion

In the Benchmark amplifiers, the feed-forward amplifier has enough bandwidth to correct the transients that are produced by the main amplifier. This keeps the output clean under heavy loads and temperature variations. The biasing of the main amplifier is not critical to the performance of the full system. Biasing errors just make the correction amplifier work a bit harder. It doesn't take much power to do the cleanup, so the correction amplifier just takes care of the additional errors. The feed-forward correction amplifier makes the system self correcting when changes in loading or temperature occur.

Benchmark AHB2 - Inside View

Summary

Feedback systems are an important part of most audio devices. Feedback can be used to reduce the distortion produced by an amplifier. Feedback is a recursive process and this makes it subject to stability issues. Feedback loops have a delayed response; some error must occur before the correction process gets started.

Feed-forward correction can replace or supplement a feedback system. Feed-forward correction is non-recursive and this makes it inherently stable. Feed-forward correction remains stable and effective when the output loading changes.

Benchmark amplifiers use a combination of feedback and feed-forward correction. The feed-forward correction amplifier adds a correction signal at the final output of the amplifier. Feed-forward correction is especially useful when correcting the performance of the high-power output stage in a power amplifier. Benchmark amplifiers use feed-forward correction to provide a final wide-bandwidth correction to compensate for distortion produced by the main output stage. This correction is applied with a small auxiliary amplifier. The main and auxiliary amplifiers are passively summed to the final output.

This combined system produces an amplifier with extremely low distortion. It maintains this low distortion under all load conditions, and it maintains stability when driving difficult loads. The unloaded and fully-loaded THD plots are nearly identical, demonstrating the effectiveness of this combined error-correction system.

Benchmark HPA4 Headphone Amplifier with Feed-Forward Error Correction

Benchmark HPA4 Headphone Amplifier featuring Feed-Forward Error Correction

Benchmark AHB2 Power Amplifier with Feed-Forward Error Correction

Benchmark AHB2 Power Amplifier featuring Feed-Forward Error Correction



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