The X-ray emission from bright active galactic nuclei (AGNs) is believed to originate in a hot corona lying above a cold, geometrically thin accretion disk. A highly concentrated corona located within $sim10$ gravitational radii above the black hole is inferred from observations. Based on the accretion of interstellar medium/wind, a disk corona model has been proposed in which the corona is well coupled to the disk by radiation, thermal conduction, as well as by mass exchange citep{Liu2015, Qiao2017}. Such a model avoids artificial energy input to the corona and has been used to interpret the spectral features observed in AGN. In this work, it is shown that the bulk emission size of the corona is very small for the extended accretion flow in our model. More than 80% of the hard X-ray power is emitted from a small region confined within 10 Schwarzschild radii around a non-spinning black hole, which is expected to be even smaller accordingly for a spinning black hole. Here, the corona emission is more extended at higher Eddington ratios. The compactness parameter of the corona, $l={Lover R}{sigma_{rm T}over m_{rm e} c^3}$, is shown to be in the range of 1-33 for Eddington ratios of 0.02 - 0.1. Combined with the electron temperature in the corona, this indicates that electron--positron pair production is not dominant in this regime. A positive relation between the compactness parameter and photon index is also predicted. By comparing the above model predictions with observational features, we find that the model is in agreement with observations.
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