= John D. Ramboz
{c}
{tag=Metrology author}
\b[John D. Ramboz] is the first author, with <Oskars Petersons>, of NIST's 1991 account of a laboratory <current transformer> calibration service. The report describes ratio and phase measurements, their uncertainties and quality-control procedures for electrical measurement work.<A Calibration Service for Current Transformers by John D. Ramboz and Oskars Petersons>[Title page and Abstract]{ref} It is a primary technical record of the service and its measurement conventions.
The separation of magnitude and phase has a direct consequence for <electric power> measurements. Consider an original sinusoidal model with root-mean-square <electric potential difference> $V$, secondary current magnitude $I_s$, true current ratio $K$ and primary-current lag $\phi$. True active power is
$$
P=VKI_s\cos\phi.
$$
If the secondary leads the primary by $\beta$, simply multiplying the secondary signal by nominal ratio $K_n$ gives
$$
P_{\rm indicated}=VK_nI_s\cos(\phi-\beta),\qquad
\frac{P_{\rm indicated}}P=
\frac{K_n}{K}\frac{\cos(\phi-\beta)}{\cos\phi},
$$
provided $\cos\phi\ne0$. This uses the lead-positive <current-transformer phase displacement> convention stated in the report.<A Calibration Service for Current Transformers by John D. Ramboz and Oskars Petersons>[§1.3, printed pp.5–6]{ref}
With exact magnitude conversion $K_n=K$ and small $\beta$ in radians, the relative power error is approximately $\beta\tan\phi$. For stipulated $\beta=0.001$ rad and $\phi=60^{\circ}$, that term is about $0.173\%$. At $\phi=0$, its first-order value vanishes. Thus the same phase error can have different effects at different <power factors>.
This derivation is an explanatory example, not a reported performance test or an attribution of the calculation to Ramboz. It explains why a calibration report needs operating conditions, a sign convention and <measurement uncertainty>, in addition to a nominal transformer ratio. Precision in the current magnitude does not remove phase-dependent power error.
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