= Current-transformer excitation admittance
{title2=$Y_e$}
<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>:
$$
Y_e=\frac{I_e}{E_s}=G-iB.
$$
For a passive parallel loss-and-magnetization model, $G\ge0$ 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>.<A Calibration Service for Current Transformers by John D. Ramboz and Oskars Petersons>[§1.2, printed pp.4–5, Figure 2 and equation 2]{ref}
In an original linear model with parallel core-loss <electrical resistance> $R_c$ and magnetizing <inductance> $L_m$,
$$
Y_e=\frac1{R_c}+\frac1{i\omega L_m}
=\frac1{R_c}-\frac{i}{\omega L_m}.
$$
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 $L_m\approx0.6366\,\mathrm H$.
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 gives
$$
H=\frac1{1+Y_eZ_t},\qquad
Y_e=\frac{H^{-1}-1}{Z_t},\quad Z_t\ne0.
$$
With the <current-transformer ratio correction factor> and secondary-leading phase $\alpha$, $H=e^{i\alpha}/\mathrm{RCF}$, so the same inversion is
$$
Y_e=\frac{\mathrm{RCF}\,e^{-i\alpha}-1}{Z_t}.
$$
Magnitude-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.<A Calibration Service for Current Transformers by John D. Ramboz and Oskars Petersons>[§1.2, printed pp.4–5]{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.
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