  We have analyzed the proton form factor data by using a number of
phenomenological parameterizations (models) and extracting the proton electric
and magnetic radii. To this end we performed a global fit to all available form
factor data, with the virtual photon momentum squared $Q^2$ from $0.0002$ to
nearly 10 GeV$^2$ for electric form factor and from $0.015$ to 31 GeV$^2$ for
magnetic one. Special attention was given to the small structure shown by the
form factor data near $Q^2 = 0.2$ GeV$^2$. It was found that different models
yield different structures with different numbers of minimum at this
kinematics. Since the slope of form factor in the limit of $Q^2\to 0$ is
influenced by this structure, the extracted proton radii are consequently
different for different models. Our finding recommends that future experiments
should focus on this kinematics instead of low $Q^2$. Experimental data with
accuracies comparable to those of the latest data at low $Q^2$ would clearly
help to clarify the effect of this structure on the proton charge radius.
Interestingly, most of the extracted proton charge radii were found to be
closer to the value obtained from the muonic hydrogen atom spectroscopy.
