= Current-transformer ratio error
{title2=$\epsilon_I$}
<Current-transformer ratio error> quantifies the amplitude mismatch between primary <electric current> and the value inferred by multiplying secondary current by a nominal ratio. For positive RMS magnitudes $I_p,I_s$ and marked primary-to-secondary ratio $K_n$, define the inferred-primary fractional error as
$$
\epsilon_I=\frac{K_nI_s-I_p}{I_p}.
$$
A negative value means that nominal scaling underestimates the primary current. This explicitly states the error convention; a reported correction can have the opposite sign.
The true ratio is $K=I_p/I_s$. The <current-transformer ratio correction factor> used in NIST's report convention is
$$
\mathrm{RCF}=\frac K{K_n}=\frac1{1+\epsilon_I},\qquad
I_p=K_nI_s\,\mathrm{RCF}.
$$
NIST distinguishes marked ratio, true ratio, ratio correction and ratio correction factor in its terminology section.<A Calibration Service for Current Transformers by John D. Ramboz and Oskars Petersons>[§1.3, printed pp.5–6, definitions and equations 3–4]{ref} Error and correction are approximately negatives for small errors, but their exact fractional relationship is nonlinear.
For an original example, take $K_n=200$, a reference primary current of $500\,\mathrm A$, and secondary current $2.49\,\mathrm A$. Nominal scaling gives $498\,\mathrm A$, so $\epsilon_I=-0.004=-0.4\%$. The correction factor is $500/498\approx1.004016$. Multiplying the nominal indication by that factor recovers 500 A; simply adding 0.4% would leave a small second-order residual.
A simplified secondary-referred equivalent circuit makes burden dependence visible. Let $I_p/K_n$ divide between the measured secondary current and a <current-transformer excitation current>. With excitation admittance $Y_e$ and total secondary series impedance $Z_t$,
$$
\frac{I_s}{I_p/K_n}=\frac1{1+Y_eZ_t}.
$$
This original linearized model gives amplitude error approximately $-\operatorname{Re}(Y_eZ_t)$ and phase shift approximately $-\operatorname{Im}(Y_eZ_t)$ when $|Y_eZ_t|\ll1$. The core response can be nonlinear; the formula is not a universal calibration curve. NIST's equivalent circuit shows the separate magnetizing, leakage and burden terms that motivate such a model.<A Calibration Service for Current Transformers by John D. Ramboz and Oskars Petersons>[§1.2, printed pp.4–5, equation 2]{ref}
A proposed ratio test compares primary and secondary magnitudes against a reference at stated current, <frequency> and <current-transformer burden>. Record polarity and phase separately: a correct magnitude ratio does not establish a correct <active power> reading. The pair of ratio and <current-transformer phase displacement> measurements determines the relevant complex transfer at that operating point.
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