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Current-transformer excitation admittance represents the secondary-referred magnetic-core response as a complex ratio between current-transformer excitation current and the induced secondary electric potential difference at a stated frequency:For a passive parallel loss-and-magnetization model, $G\ge 0$ is the in-phase conductance and $B>0$ the inductive susceptance magnitude. NIST's equivalent circuit separates this excitation response from leakage and external current-transformer burden.^[ref]

In an original linear model with parallel core-loss electrical resistance $R_c$ and magnetizing inductance $L_m$,Thus $R_c=1/G$ and $L_m=1/(\omega B)$ when those parameters are positive. For stipulated $G=0.001\mathrm{S}$, $B=0.005\mathrm{S}$ and $f=50\mathrm{Hz}$, the corresponding values are $R_c=1000\Omega$ and $L_m\approx 0.6366\mathrm{H}$.

At $E_s=2\mathrm{V}$ RMS, the excitation phasor is $I_e=0.002-0.010i\mathrm{A}$, with magnitude about $10.20\mathrm{mA}$. Mean power in the modeled loss branch is $G|E_s{|}^2=4\mathrm{mW}$. The quadrature current also has physical significance even though it supplies no mean power in this ideal sinusoidal branch.

The admittance can be inferred from a measured complex transfer if the circuit assumptions are known. Let $H=I_s/(I_p/K_n)$, with consistent secondary polarity, and let $Z_t$ be winding-plus-burden impedance. The current balance givesWith the current-transformer ratio correction factor and secondary-leading phase $\alpha$, $H=e^{i\alpha }/\mathrm{RCF}$, so the same inversion isMagnitude-only ratio data cannot determine both $G$ and $B$ without additional information.

A real core is nonlinear, so the effective fundamental ratio can change with excitation amplitude, frequency, waveform and magnetic history. A parameter inferred from a small perturbation about one operating state need not equal the full-signal ratio at another. NIST explicitly notes nonlinear magnetizing impedance and current/burden dependence.^[ref] A proposed check measures ratio and phase at several known burdens, compares the inferred admittance values, and tests whether one local model describes them before applying it outside that range.

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, defineNIST distinguishes this factor from ratio correction, which is $\mathrm{RCF}-1$, and from the separately measured phase displacement.^[ref] Correcting amplitude does not remove current-transformer phase displacement.

With the inferred-primary error convention ${ϵ}_I=(K_n{I}_s-I_p)/I_p$, the exact relationship isFor an original example, $K_n=200$, $I_s=2.49\mathrm{A}$ and $\mathrm{RCF}=500/498\approx 1.004016$ give $I_p=500\mathrm{A}$. Using nominal scaling alone gives 498 A. The approximate correction $1-{ϵ}_I=1.004$ 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 givesFor a correction inferred from uncertain ${ϵ}_I$, its local sensitivity is $d\mathrm{RCF}/d{ϵ}_I=-(1+{ϵ}_I{)}^{-2}$. The GUM supplies the general sensitivity-and-covariance propagation rule used here.^[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 isThe correction at the mean error is instead one. Convexity of the reciprocal on $1+{ϵ}_I>0$ 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.

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 asA 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 isNIST distinguishes marked ratio, true ratio, ratio correction and ratio correction factor in its terminology section.^[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 ${ϵ}_I=-0.004=-0.4\%$. The correction factor is $500/498\approx 1.004016$. 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 $Z_t$,This original linearized model gives amplitude error approximately $-\mathrm{Re}(Y_e{Z}_t)$ and phase shift approximately $-\mathrm{Im}(Y_e{Z}_t)$ when $|Y_e{Z}_t|\ll 1$. 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.^[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.

Oskars Petersons worked on electrical metrology at the National Institute of Standards and Technology. With John D. Ramboz, Petersons coauthored the 1991 report describing NIST's laboratory current transformer calibration service. The report treats current ratio and current-transformer phase displacement as distinct measurement results.^[ref]

A current transformer allows a secondary electric current to represent a larger or smaller primary current. Its marked ratio is a nominal conversion, whereas the measured ratio can differ. The report expresses the measured ratio as the marked ratio multiplied by the current-transformer ratio correction factor, and uses a secondary-leading sign convention for the reported phase displacement.^[ref]

An original calculation illustrates the distinction. A marked ratio of $200$ A:$5$ A gives $K_n=40$. If the current-transformer ratio correction factor is $1.0002$, the measured magnitude ratio is $K=40.008$. A secondary reading of 5 A then represents 200.04 A under those stated conditions, rather than exactly 200 A.

Magnitude alone is not a full alternating-current description. If the secondary phasor leads the primary by $\beta$ and their magnitude ratio is $K$, a consistent convention isThe magnitude correction and phase rotation address different errors. A measurement system can reproduce one accurately while requiring correction of the other. The joint report's calibration circuits, including compensated current comparators, give these distinctions an apparatus-level setting rather than leaving them as ideal-transformer identities.^[ref]