We present the results of detailed spectral studies of the ultra-compact low mass X-ray binary (LMXB) 4U 1820-30 carried out with the Rossi X-ray Timing Explorer (RXTE) during 1996-7. 4U 1820-30 is an ``atoll source X-ray burster (XRB) located in the globular cluster NGC 6624. It is known to have an 11 minute binary period and a ~176 day modulation in its 2--12 keV flux. Observations were made with the PCA and HEXTE instruments on RXTE at roughly one-month intervals to sample this long-term period and study flux-related spectral changes. There are clear correlations between our fitted spectral parameters and both the broad-band (2--50 keV) flux and the position in the color-color diagram, as described by the parameter S_a introduced by Mendez et al. (1999). In addition, we find a strong correlation between the position in the color-color diagram and the frequencies of the kilohertz quasi-periodic oscillations (kHz QPOs) reported by Zhang et al. (1998). This lends further support to the notion that evidence for the last stable orbit in the accretion disk of 4U 1820-30 has been observed. For a model consisting of Comptonization of cool photons by hot electrons plus an additional blackbody component, we report an abrupt change in the spectral parameters at the same accretion rate at which the kHz QPOs disappear. For a model consisting of a multicolor disk blackbody plus a cut-off power law, we find that the inner disk radius reaches a minimum at the same accretion rate at which the kHz QPO frequency saturates, as expected if the disk reaches the last stable orbit. Both models face theoretical and observational problems when interpreted physically for this system.
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