P228 - Annex

How Negative Impedance Reduces Distortion

It's not entirely intuitive as to how negative impedance can remove transformer saturation distortion.  There are several factors that have to be considered, and they are interactive.

When a transformer's flux exceeds the limit for the core material used, a point is reached where an increase in signal voltage vs. magnetic flux is no longer a linear function.  At low levels, if the voltage is doubled, so is the flux density, but saturation literally means that the core cannot support additional magnetic flux.

The flux density is a function of the voltage across the primary winding, and the current through the winding.  At low frequencies, the inductance of the primary becomes insufficient to prevent significant current flow, so the magnetising current increases as the frequency is reduced.

Once the magnetising current is high enough to cause core saturation, the waveform becomes distorted.  This happens because the current is non-linear, and that causes the voltage developed across the winding's resistance to be non-linear as well.  If the transformer used a superconductor for the primary and was driven from a zero ohm signal source (with very high current available), there would be no distortion.

Alas, this is not viable, so we have to use materials that exist.  Using a NIC we can cancel the winding resistance, if not fully, at least well enough to make a significant difference to the low-frequency distortion.  To understand how this works requires (in part) a thought experiment.

Figure 1 - B-H Curve For Magnetic Materials

A more-or-less typical 'B-H' curve is shown above.  'B' is flux density in Tesla, and 'H' is magnetising force or magnetic field strength in ampere/metres (A/m).  Past the knee of the curve, applying a greater magnetising force fails to elicit a corresponding increase in flux density - the material is saturated.  This is the root cause of transformer distortion.  Hysteresis (shown exaggerated) is a measure of the reluctance of the material to change.  B_r is remanence - the core material's ability to retain magnetism after the magnetising force has been removed.  For audio transformers, hysteresis and remanence need to be as low as possible.  This is influenced by the core material itself.

Consider a transformer driven from a zero ohm source.  Quite obviously, no load can cause voltage distortion from a true zero ohm source, so the applied voltage is a sinewave (the defacto standard for AC analysis).  However, the current through a saturating transformer is not sinusoidal - it's distorted.  Unfortunately, simulators are pretty bad at giving a true representation of transformer saturation, but Fig. 1 shows what the simulator produces.  Compare this with Fig. 4 in the main article and you can see the similarity.

Figure 2 - Voltage & Current With A Partially Saturated Core

The simulation above shows the highly non-linear saturation current in a transformer.  The distorted current causes a distorted voltage to be impressed across the primary winding, and that's passed through to the secondary.  Remembering that the voltage from a zero ohm source cannot be distorted by any load, if the primary winding resistance is cancelled by using negative impedance, the transformer will 'see' a zero ohm source.  Transformers are voltage devices, and in an ideal transformer, current is only needed to supply the secondary load - transformer action is not affected by the current.

For example, all mains transformers will be operated with partial saturation at no load and full rated voltage.  While the current waveform is seriously distorted, the output voltage waveform is still sinusoidal - an almost perfect replica of the primary voltage.  The low winding resistance and very low mains impedance create a low impedance source.

In theory, the combination of winding resistance and an equal negative impedance drive will have no distortion at all, because the transformer is driven from an effectively zero ohm source.  However, we're dealing with real components that are imperfect.  This annex could easily become an article in its own right, but it's hoped that this simplified explanation goes some way to helping readers to understand the principles.  It's not intuitive, but it is real - at least within the limits imposed by the circuitry.