CRMagnetics Catalog

Calculating Ratio Errors

152

UNDERSTANDING CURRENT TRANSFORMER RATIO ERROR AND EXCITATION CURVES

A current transformer follows all the standard physical laws for electrical transformers. The primary winding is usually a very low imped-

ance and therefore treated as a "brute force" constant current source. Faraday's law of ampere-turn balance states that the number of

turns in the primary winding times the primary current must equal the number of turns in the secondary winding times the secondary

current. Therefore, since the primary is a constant current source, the secondary becomes a constant current source proportional only to

the turns ratio.

Other factors come in to play that affect the basic Faraday's relationship, such as the non-linear properties of the core material, eddy cur-

rent, hysteresis and IR losses. As Figure 1 illustrates, the eddy current and hysteresis losses act to shunt current across the transformer

secondary and are defined as excitation losses I E . Since the excitation losses are non-linear, they are determined from an Excitation Curve

provided by the transformer's manufacturer. The I R losses act as a resistance R S in series with the secondary winding.

As Figure 2 illustrates, the secondary voltage E s is found on the vertical axis and the secondary exciting current I E can be found on the

horizontal axis. This exciting current can best be described as the current that contributes to the current transformation ratio error.

Power transformers use the terms "Load" and "Regulation" to describe their operation. Current transformers use the terms "Burden" and

"Accuracy" respectively to describe similar functions. Burden defines the connection made to the secondary winding to differentiate it from

the primary connection that is generally described as the Load. Current transformers use the term Accuracy to describe what would gener-

ally be considered Regulation with a power transformer. It is important to remember that Burden and Accuracy are interdependent; gen-

erally the lower the Burden resistance, the better the Accuracy.

Designs that have the current transformer separate from the instrumentation resistor R I need to consider transformer ratio error. An

example would be an ampere meter that uses an external current transformer. The transformer must have an accurately-defined current

ratio to allow for interchangeability with other transformers of the same rating.

Designs that have the current transformer as an integral part of the instrumentation can place less emphasis on ratio error and consider

more on the transformer's linearity. An example would be a printed circuit-board-mounted current transformer that inputs into an opera-

tional amplifier circuit. Ratio error can generally be minimized during calibration with adjustment to the offset and gain controls. The

major concern to the overall accuracy of the design would then be linearity of the transformer through out the operating range.

In practice, the designer must consider various factors in selecting a current transformer: since the secondary is operating as a constant

current source, a Burden resistor of lower value will provide improved accuracy but decrease instrumentation voltage (V=IR). As the

instrumentation voltage is increased with a high Burden resistor, the power dissipated may become a factor (P = I 2 R). Generally the

designer determines the lowest voltage the electronics can handle considering such parameters as circuit noise and gains. Then the value

of the burden resistor can be determined, knowing the characteristics of the current transformer and overall design requirements.

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