### Causes of Core Losses in Open Loop Transducers

The magnetic material and core design of a transducer, as well as the current amplitude versus frequency spectra, determine the level of core losses:

• eddy current losses are proportional to the square of three different parameters: the peak flux density in the core, the frequency of induction, and the lamination sheet thickness of the core

• hysteresis losses are proportional to frequency, core volume, and the square of peak flux density

For typical transducers, this leads to the following conclusions:

• these losses are directly proportional to the square of the flux density, which is directly related to the primary ampere-turns, implying core losses are theoretically proportional to the square of primary ampere-turns if no magnetic saturation occurs. When increasing sensitivity by using multiple primary turns, core losses are increased by the square of the turns

• core losses become significant at high frequencies and it is essential to limit the current amplitude at these frequencies to acceptable levels (dependent on ambient and maximum transducer temperatures); this implies not only limiting the maximum frequency of the fundamental current, but also harmonic content, since even a low amplitude signal may create unacceptable losses at high frequencies.

**Core Loss Rule-of-Thumb**

Core loss calculations are complex. As a "rule-of-thumb" judgment, it is possible to consider that core losses are minimized if the product "N • I • f" is kept as small as possible, where:

N = number of internal or external primary coil turns

I = primary current or amplitude of a current harmonic

f = frequency of the primary current or current harmonic

As a result, when one of the three factors is increased (i.e. the current), the iron losses are increased unless at least one of the two other factor is decreased (i.e. the frequency of the measured current and/or the number of primary turns). While this formula implies that the core losses will increase with an increase of any of these parameters, it is not intended to say that acceptable core losses are realized if the product of the three parameters is kept constant. For example, it is wrong to say that one can operate at twice the frequency if the Ampere-turns are cut in half. At a given frequency, it is nevertheless correct to assume that keeping constant the "N • I" product implies similar iron losses, though even the probable change on the primary conductor magnetic coupling may affect the iron losses value.

To conclude, trouble-free operation of a current transducer requires limiting the temperature rise to avoid overheating the internal components. Parameters affecting temperature rise go beyond core losses and include the primary busbar resistive losses, the losses of the electronics and the various thermal resistances. In particular, to keep losses constant requires to decrease the transducer primary current while the working frequency increases.

**Addressing Transducer Core Losses**

Often the adverse effects of core losses are not considered or cannot be predicted accurately during the initial design stages. Therefore many designers find themselves in a difficult situation when a design, or a specific application of that design, causes overheating of the transducer due to core losses. There are solutions to this problem, but a careful analysis of the tradeoff between reducing core losses and maintaining acceptable response time of the transducer is required.

Although the insertion loss of a transducer is extremely low, this impedance is in fact a combination of the resistance and inductance of the primary transducer coil. Placing a series resistor-capacitor in parallel with the primary (Figure 1) diverts the high frequency components of the current around the primary, significantly reducing core losses. This also removes these frequencies from the measurement path, increasing the response time.

Open loop transducer response is dependent on the transducer design and the magnetic coupling of the signal to be measured, as well as those not to be measured. The latter places some responsibility on the user to investigate the coupling effects and determine the appropriate placement of the primary and other conductors to optimize the response of the transducer in the application. Careful consideration of the cabling in and around the transducer usually resolves response time problems.

**For more information, please read the following:**

Characteristics of Closed Loop Current Transducers

Open Loop Hall Effect Current Transducers

Transducers - Basic Principles of Selection