  Precision calibration of the instruments poses challenges to experiments
probing the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn
and the Epoch of Reionization (z~30-6). Both single antenna and interferometers
are being used to search for the signal and in both types, systematic
calibration is the leading source of error. Though many aspects of calibration
have been studied, the overlap between the two types of instruments has
received less attention. In this paper, we investigate sky based calibration of
total power measurements. Comparing a HERA dish and an EDGES style antenna we
hope to obtain a holistic understanding of the role auto-correlations might
play in an interferometer and what role the sky might play in calibrating a
total power instrument. Using simulations we study various scenarios such as
time variable gain, incomplete sky calibration model, and primary beam model.
We find that temporal gain drifts, sky model incompleteness, and beam
inaccuracies cause biases in the receiver gain amplitude and the receiver
temperature estimates. In some cases, these biases mix spectral structure
between beam and sky resulting in spectrally variable gain errors. Applying the
calibration method to data from HERA and EDGES we find good agreement with
calibration via the more standard methods and deviations consistent with beam
and sky errors similar in scale to those simulated. While we show that it is
possible to partially mitigate biases due to model inaccuracies by
incorporating a time-dependent gain model in calibration, the resulting errors
on calibration products are larger and more correlated. Completely addressing
these biases, as in the case of interferometer sky calibration, will require a
more accurate sky model and primary beam models.
