**Introduction** - The Active Current Transformer has been around for over fifty years,
but has found limited application. This may be because most electronic
engineers look upon electromagnetics as a black art. In this instance,
the marriage of modern electronics and electromagnetism team up to produce
a superior product; that is, a current transformer with the transformation
ratio determined by the turns ratio, with negligible phase shift between
the primary and secondary currents, reduced core size, reduced sensitivity
to secondary (burden) changes, increased dynamic range, and non-reactive
primary.

**Theory of Operation** - A basic active transformer consists of a high gain amplifier and a transformer
as shown in the figure. The sense winding feeds a voltage, e, into the
input of the amplifier. The amplifier output is negatively fed back to
the transformer secondary to cancel out the primary flux changes. With
sufficient amplifier gain, e is essentially zero. In order for e to be zero, according to Faraday's Law, there must be
no flux change in the core. Faraday's Law states that the induced voltage,
e, is related to the rate of core flux, F, change and the number of turns,
N, in the sense coil:

(1)

Integrating both sides yields:

(2)

e is forced to zero by an ideal amplifier having infinite gain, therefore

(3)

The net core flux is the difference between the primary flux, Fp, and the secondary flux, Fs. Therefore the limits on the integral (3) are Fp and Fs.

Upon integrating equation (3), (4) is obtained:

Fp - Fs = 0 or Fp = Fs (4)

Flux is equal to the product of the flux density, B, and the core cross-sectional area:

Fp = Bp * Area & Fs = Bs * Area (5)

The core area is common to the primary and secondary, hence

Bp = Bs (6)

Magnetic flux density, B, is directly proportional to the magnetizing force, H, through the permeability factor, U. Equation (6) becomes:

UpHp = UsHs (7)

The core permeability is common to the primary and secondary, hence

Hp = Hs (8)

Ampere's Law provides a relationship between magnetizing force, H, and current, I. (ML is the mean length of the magnetic material)

& (9)

Substituting (9) into (8) and reducing, the following result is obtained:

NpIp = NsIs (10) or (11)

Equation (11) shows that an ideal (infinite amplifier gain) active transformer is equivalent to an ideal current transformer under the stated conditions. Even with finite amplifier gain, equation (11) is accurate to less than 10 parts per million. See Certificate of Calibration.

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