= Current-transformer ratio correction factor
{title2=$\mathrm{RCF}$}
The <current-transformer ratio correction factor> multiplies a nominally scaled secondary-current indication to recover primary-current magnitude under stated calibration conditions. If $K_n$ is the marked primary-to-secondary ratio and $K=I_p/I_s$ is the true magnitude ratio, define
$$
\mathrm{RCF}=\frac K{K_n},\qquad I_p=K_nI_s\,\mathrm{RCF}.
$$
NIST distinguishes this factor from ratio correction, which is $\mathrm{RCF}-1$, and from the separately measured phase displacement.<A Calibration Service for Current Transformers by John D. Ramboz and Oskars Petersons>[§1.3, printed pp.5–6, marked/true ratio and ratio correction definitions]{ref} Correcting amplitude does not remove <current-transformer phase displacement>.
With the inferred-primary error convention $\epsilon_I=(K_nI_s-I_p)/I_p$, the exact relationship is
$$
\mathrm{RCF}=\frac1{1+\epsilon_I}.
$$
For an original example, $K_n=200$, $I_s=2.49\,\mathrm A$ and $\mathrm{RCF}=500/498\approx1.004016$ give $I_p=500\,\mathrm A$. Using nominal scaling alone gives 498 A. The approximate correction $1-\epsilon_I=1.004$ would instead give 499.992 A, leaving a small second-order difference.
A calibration correction has its own <measurement uncertainty>. Treating $K_n$ as an exact label and retaining correlation, first-order propagation gives
$$
\frac{u^2(I_p)}{I_p^2}\simeq
\frac{u^2(I_s)}{I_s^2}+\frac{u^2(\mathrm{RCF})}{\mathrm{RCF}^2}
+\frac{2\operatorname{cov}(I_s,\mathrm{RCF})}{I_s\,\mathrm{RCF}}.
$$
For a correction inferred from uncertain $\epsilon_I$, its local sensitivity is $d\mathrm{RCF}/d\epsilon_I=-(1+\epsilon_I)^{-2}$. The GUM supplies the general sensitivity-and-covariance propagation rule used here.<Guide to the expression of uncertainty in measurement by JCGM>[§§5.1.3 and 5.2.2, equations 11 and 13]{ref}
Nonlinearity also affects averaging. Suppose a stipulated error takes values $+0.01$ and $-0.01$ with equal probabilities. Its mean is zero, but the mean correction factor is
$$
\tfrac12\left(\frac1{1.01}+\frac1{0.99}\right)
=\frac1{1-0.01^2}\approx1.00010001.
$$
The correction at the mean error is instead one. Convexity of the reciprocal on $1+\epsilon_I>0$ explains this <Jensen's inequality> effect. It is an illustrative probability model, not a claim about random drift of a particular transformer.
A correction factor should therefore travel with its current level, <frequency>, <current-transformer burden> and uncertainty information. A proposed check repeats the ratio comparison at selected operating conditions and tests whether one retained correction remains adequate. Applying more displayed digits cannot replace that validation.
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