Signal Transformers#

The transformers for the sensing stage are handmade.

What we can act on is the number of turns, which has effect on:

  • transformation ratio

  • magnetizing impedance

In brief we need:

  • a certain transformation ratio to have an acceptable level for the ADC at the output;

  • a certain transformation ratio so that the downstream (i.e. resistors) has minimal influence on the upstream

  • high/low enough magnetizing impedance (high for voltage sensor and low for current sensor);

See here for the model of a transformer.

Design#

The design procedure is done following some basic rules that can be found in Fundamentals of Power Electronics [Erickson and Maksimović, 2020] Part III.

../../_images/RT_core_explication.png

Fig. 7 Main dimension in a toroidal core#

The reluctance of the core is given by

\[ \mathcal R = \frac{l_e}{\mu_0\mu_r A_e} \]

where \(l_e\) is the length of the magnetic path (i.e. average-circumference) and \(A_e\) the area of the cross-section perpendicular to the magnetic path. The magnetizing inductance is

\[ L_m=\frac{N^2}{\mathcal R} \]

where \(N\) is the number of turn of the side where we are interested to model the inductance. In brief:

\[ L_m=\underbrace{\frac{\mu_0\mu_r A_e}{l_e}}_{\text{fixed by the core}}{N^2} \]

The value of permeability in vacuum is \(\mu_0=1.256\times 10^{-6}\;\frac{N}{A^2}\), equivalently \(\mu_0=4\pi\times 10^{-7} \frac{H}{m} = 4\pi\times 10^{-4} \frac{H}{mm}\).

With the transformer we are in phase-advance

Built transformers with data#

Measure are obtained with the RLC measurement machine in GAEI Lab.

Available core#

The core that are available for transformers are:

<table with the cores>

core code

77206A7 (grey core big)

5977000301 (black core small)

5978002701 (black core medium)

B64290L0618X038 (blue core - CT)