= Current-transformer excitation current
{title2=$I_e$}
A <current-transformer excitation current> is the part of the secondary-referred input current needed for the magnetic core's response and losses rather than delivered to the external secondary circuit. In an ideal <current transformer> this contribution is neglected. In a real equivalent circuit it helps explain both <current-transformer ratio error> and <current-transformer phase displacement>.
Choose terminal polarities so ideal current reproduction is in phase. Let $K_n$ be the nominal primary-to-secondary ratio, $I_0=I_p/K_n$ the secondary-referred input phasor, and $I_s$ the measured secondary phasor. The current balance is
$$
I_0=I_s+I_e.
$$
Represent the excitation branch locally by <current-transformer excitation admittance> $Y_e$ and induced secondary phasor $E_s$. With total secondary winding-plus-burden impedance $Z_t$,
$$
I_e=Y_eE_s,\qquad E_s=I_sZ_t,\qquad
\frac{I_s}{I_0}=\frac1{1+Y_eZ_t}.
$$
The NIST treatment gives the corresponding magnetizing, leakage and burden equivalent circuit and shows how those impedances enter the complex ratio.<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}
For an original local model, write $Y_e=G-iB$ with $G,B>0$, and take $Z_t=R_t>0$. When $|Y_eR_t|\ll1$,
$$
\frac{I_s}{I_0}\simeq1-GR_t+iBR_t.
$$
The amplitude deficit is approximately $GR_t$, while the secondary lead is approximately $BR_t$ radians. For stipulated $G=0.001\,\mathrm S$, $B=0.005\,\mathrm S$ and $R_t=1\,\Omega$, these are about $0.1\%$ and 5 milliradians. At an induced $1\,\mathrm V$, the excitation components are 1 milliampere in phase and 5 milliamperes in quadrature; the real branch power is $G|E_s|^2=1\,\mathrm{mW}$.
An increased <current-transformer burden> raises the induced potential required for a given secondary current. The actual excitation response need not remain linear: core behavior, <frequency>, waveform and prior magnetic state can change the local parameters. The NIST equivalent-circuit discussion explicitly notes the nonlinear core 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 characterization varies a known connected burden and compares measured current ratio and phase, keeping the primary-current and frequency conditions recorded. A model that fits one operating point is not thereby validated through saturation or for arbitrary <harmonic components>. Separating excitation from load delivery explains why a turns ratio alone cannot specify practical measurement accuracy.
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