We present the results of the analysis of the broad-band spectrum of C
ygnus X-1 from 3.0 to 200 keV, using data from a 10-ks observation by
the Rossi X-ray Timing Explorer (RXTE). The spectrum can be well descr
ibed phenomenologically by an exponentially cut-off power law with a p
hoton index Gamma = 1.45(-0.02)(+0.01) (a value considerably harder th
an is typically found), e-folding energy E-f = 162(-8)(+9) keV, plus a
deviation from a power law that formally can be modelled as a thermal
blackbody with temperature kT(BB) = 1.2(-0.1)(+0.0) keV, Although the
3-30 keV portion of the spectrum can be fitted with a reflected power
law with Gamma = 1.81 +/- 0.01 and covering fraction f = 0.35 +/- 0.0
2, the quality of the fit is significantly reduced when the HEXTE data
in the 30-100 keV range are included, as there is no observed softeni
ng in the power law within this energy range. As a physical descriptio
n of this system, we apply the accretion disc corona models of Dove, W
ilms & Begelman, in which the temperature of the corona is determined
self-consistently. A spherical corona with a total optical depth tau =
1.6 +/- 0.1 and an average temperature kT(C) = 87 +/- 5 keV, surround
ed by an exterior cold disc, does provide a good description of the da
ta (chi(red)(2) = 1.55). These models deviate from the data by up to 7
per cent in the 5-10 keV range, and we discuss possible reasons for t
hese discrepancies. However, considering how successfully the spherica
l corona reproduces the 10-200 keV data, such 'photon-starved' coronal
geometries seem very promising for explaining the accretion processes
of Cygnus X-1.