Amplifier linearization

In amplifiers designating amplifier linearization is a form of error correction ( English error correction ), the nonlinear distortion by measuring the deviation, which then serve as correction signals compensated . When mixed with the transmission signal, there is ideally a complete elimination of all distortions.

Basic idea

The minimization of non-linear distortions through negative feedback requires a high loop gain . The increasing gain goes hand in hand with a greater risk of instability of the control loop and therefore requires fast electronics. The error correction, on the other hand, only requires a gain of one for the measurement of the error signal.

Feedforward

Feedforward

The signal flow diagram for a feedforward error correction illustrates the concept very well. The difference between the input and output signals from the transmission element G ₁ forms the correction signal . The transmission element G ₂ acts as a power amplifier for the correction signal. When the faulty signal is applied, a low-distortion output signal results.

${\displaystyle G_{gesamt}=\left(1-\beta \cdot G_{1}\right)\cdot G_{2}+G_{1}}$

The element β reverses the amplification of the input signal by G ₁ , so it corresponds to its reciprocal value. The correction signal needs the same gain as the main signal, so G _{2 has} the same gain factor as G ₁ .

${\displaystyle G_{1}\approx {\frac {1}{\beta }}\ \land \ G_{2}\approx G_{1}\ \Rightarrow \ G_{2}={\frac {1}{\beta }}}$

The requirement G ₂ = 1 / β enables the following transformations:

${\displaystyle G_{gesamt}=\left(1-\beta \cdot G_{1}\right)\cdot {\frac {1}{\beta }}+G_{1}}$

${\displaystyle G_{gesamt}={\frac {1}{\beta }}-G_{1}+G_{1}={\frac {1}{\beta }}}$

The distortions introduced by the non-linearity of G ₁ are completely reduced . Since there is no signal feedback whatsoever, natural oscillations are excluded.

Error feedback

Active error feedback

Error feedback type A

The adjacent arrangement contains a negative feedback loop, but viewed as a whole it is the error correction principle. The control loop of G ₂ and β regulates until the deviation of the output signal from the input signal approaches zero and thus compensates for the deviations introduced by G ₁ .

${\displaystyle G_{gesamt}=\left(G_{1}+G_{2}\right)\cdot {\frac {1}{1+G_{2}\cdot \beta }}}$

${\displaystyle G_{2}\rightarrow \infty \land G_{2}\gg G_{1}\Rightarrow G_{gesamt}\approx {\frac {1}{\beta }}}$

So that only linearity errors are corrected:

${\displaystyle G_{1}\approx {\frac {1}{\beta }}}$

This structure preserves the stability problems known from negative feedback. Shifting the loop to G ₂ offers advantages because the correction signal has a significantly smaller amplitude and G ₂ can therefore be interpreted differently than G ₁ .

Error feedback type B

In the second variant of the error feedback principle, only G ₁ acts as a power amplifier. Due to the corresponding transfer behavior of G ₂ , the error correction is limited to the lower frequency range and therefore the risk of oscillation is minimized. Only a single power-amplified signal is present at the output, there is no need to add output signals, which reduces losses, feedback and output resistance.

${\displaystyle G_{gesamt}={\frac {G_{1}\cdot \left(1+G_{2}\right)}{1+G_{1}\cdot G_{2}\cdot \beta }}}$

${\displaystyle G_{2}\ \rightarrow \ \infty \ \land \ G_{2}\gg G_{1}\ \Rightarrow \ G_{gesamt}\approx {\frac {1}{\beta }}}$

So that only linearity errors are corrected:

${\displaystyle G_{1}\approx {\frac {1}{\beta }}}$

Hawksford

Hawksford error feedback

The most unusual variant made Malcolm Hawksford popular for audio amplifiers. Understanding how it works is not trivial. Here is a brief summary of the mathematical derivation:

Summarize the parallel structure from G ₁ , β and the lower addition point:

${\displaystyle 1-G_{1}\cdot \beta }$

Dissolve circular structure from G ₂ and the above parallel structure:

${\displaystyle {\frac {1}{1-G_{2}\cdot \left(1-G_{1}\cdot \beta \right)}}}$

To remove the output signal from the parallel structure, move the node behind G ₁ to the front and then merge it with the circular structure ( displacement rules ):

${\displaystyle G_{gesamt}=G_{1}\cdot G_{\circ }}$

${\displaystyle G_{gesamt}=G_{1}\cdot {\frac {1}{1-G_{2}\cdot \left(1-G_{1}\cdot \beta \right)}}}$

${\displaystyle G_{2}=1\ \Rightarrow \ G_{gesamt}={\frac {1}{\beta }}}$

So that only linearity errors are corrected:

${\displaystyle G_{1}\approx {\frac {1}{\beta }}}$

It has proven to be particularly advantageous that G ₂ only requires a low gain of one. This increases the stability of the circuit against natural vibrations.

Note: The equations are only suitable for stability analysis in the case of low distortions, as G _{1 is} non-linear and the LZI conditions are therefore not fully met.

Current dumping

Current dumping

Amplifiers with the concept of current dumping also belong to the category of error correction. The dumper is a class B push-pull amplifier, while the G ₂ amplifier is a low-distortion class A amplifier and delivers only one hundredth of the output power of the dumper.

Patent pending and granted by PJ Walter in 1975.

NDFL

Nested differenciating feedback loops (nested differentiating feedback loops) are a development by Edward M. Cherry, through which the phase accuracy is maintained even with rapidly changing signals.

Applications

General for the linearization of analog circuits. Examples for this are:

• Amplifier (electrical engineering)
• Audio amplifier
• Operational amplifier

literature

• | Author = John Vanderkooy, Stanley P. Lipshitz

  |Titel=Feedforward Error Correction in Power Amplifiers
  |Sammelwerk=Journal of the Audio Engineering Society
  |(JAES)
  |Band=28
  |Nummer=1/2
  |Datum=1980
  |Seiten=2–16
  |Online=Abstract
  |Abruf=2013-01-08}

• Edward M. Cherry, Nested Diffenciating Feedback Loops in Simple Audio Power Amplifieres , JAES, Vol. 30, No. 5, May 1982, p. 295 ff

Web links

• Malcolm Hawksford
  • Distortion Correction in Audio Power Amplifiers (PDF file)
  • Distortion Correction Circuits for Audio Amplifiers (PDF file)
  • Towards a Generalization of Error Correction Amplifiers (PDF file; 895 kB)
• A MOSFET Power Amplifier with (Hawksfork) Error Correction, cordellaudio.com
• paX, power amplifier eXperimental by Jan Didden
  Described in detail in the April 2008 + May 2008 issues of Elektor (fee required)

Radio technology:

• An Adaptive Feedforward Amplifier Application for 5.8 GHz , Engin Kurt and Osman Palamutcuogullari (PDF file; 485 kB)
• Balanced error correction for power amplifiers , Warren Guthrie (PDF file; 541 kB)

Individual evidence

1. ↑ Patent US3970953 . ‌