Dear transformer and tube audio fans,
Here’s a brief tutorial I wrote about the parasitic properties of transformers, where no engineer can escape from.
Fig 1 : A simplified schematic of the parasitic components of transformers
Ohmic losses, (Rpri, Rsec)
These are the ohmic resistances of the primary and secondary coils. Their main impact is power loss, which is an important aspect for power transfer, most importantly in output transformers. It is less paramount for voltage coupling devices, such as interstage or input transformers.
Leakage inductance, (Ls)
This one is the result of the lack of magnetic coupling between the primary and secondary coils. It is influenced by the coil geometry, the interleaving configuration and the number of turns(squared). It contributes to a roll-off in the high-frequency domain with the formation of an RL filter together with the transformer’s reflected load Rload.
Parralel capacitance, (Cp)
Also known as shunt capacitance, this is the overall capacitive value parallel to the transformer. It is influenced by coil geometry, interleaving configuration, dielectric type used, its thickness, and the connection strategy of windings. Cp limits high-frequency bandwidth by forming an RC filter together with the driving impedance Rgen.
Series capacitance, (Cs)
This one is formed by the capacitance between the primary and secondary layers. The increase of Cs also goes together with an increase of Cp. Series capacitance itself doesn’t limit high-frequency bandwidth, but results in a parallel RLC tank together with leakage inductance (Ls)
Cp/Ls resonance.
The first resonant frequency we should pay attention to, is a series RLC tank, formed by the parallel capacitance Cp and the leakage inductance Ls. It gives off a characteristic peaking in the high-frequency region and it should be way above the audio band. Its quality (Q) factor value is naturally decreased by loading the transformer, or by increasing the drive impedance.
Cs/Ls resonance.
A second resonant frequency, in some cases more evil than the first one, is a parallel RLC tank and it is created from the series capacitance and the leakage inductance. It forms a characteristic “dip” in the high frequency region and it also should be way above the audio band. In this case, the quality (Q) factor is increased with loading and the drive impedance.
Secondary leakage inductance and resonances.
This one is caused by unequal currents circulating through secondary layers and is problematic mostly in output transformers. It forms additional resonances as well and can cause a first order roll-off. The transformer designer should equalize secondary currents by all means necessary in order to achieve best performance.
Fig 2 : Maximized excitation condition for both resonances. Observe both the peak and dip.
Controlling parasitic components
It lies in the hands and mind of the engineer to minimize and distribute these evil components in a mostly harmless way for each specific situation. Although their influence in my opinion is very little compared to the materials used, I believe every audio transformer should have the best as possible electrical parameters.
Like most things in high-fidelity audio, building a transformer is an art of compromises and EVERY aspect plays in
