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Proper modelling of astronomical receivers is vital: it describes the systematic errors in the raw data, guides the receiver design process, and assists data calibration. In this paper, we describe a method of analytically modelling the full signal and noise behaviour of arbitrarily complex radio receivers. We use electrical scattering matrices to describe the signal behaviour of individual components in the receiver, and noise correlation matrices to describe their noise behaviour. These are combined to produce the full receiver model. We apply this approach to a specified receiver architecture: a hybrid of a continuous comparison radiometer and correlation polarimeter designed for the C-Band All-Sky Survey. We produce analytic descriptions of the receiver Mueller matrix and noise temperature, and discuss how imperfections in crucial components affect the raw data. Many of the conclusions drawn are generally applicable to correlation polarimeters and continuous comparison radiometers. [ABSTRACT FROM AUTHOR]

Fermi has provided the largest sample of γ-ray-selected blazars to date. In this work we use a complete sample of flat spectrum radio quasars (FSRQs) detected during the first year of operation to determine the luminosity function (LF) and its evolution with cosmic time. The number density of FSRQs grows dramatically up to redshift ∼0.5-2.0 and declines thereafter. The redshift of the peak in the density is luminosity dependent, with more luminous sources peaking at earlier times; thus the LF of γ-ray FSRQs follows a luminosity-dependent density evolution similar to that of radio-quiet active galactic nuclei. Also, using data from the Swift Burst Alert Telescope we derive the average spectral energy distribution (SED) of FSRQs in the 10 keV-300 GeV band and show that there is no correlation between the luminosity at the peak of the γ-ray emission component and its peak frequency. Using this luminosity-independent SED with the derived LF allows us to predict that the contribution of FSRQs to the Fermi isotropic γ-ray background is 9.3+1.6– 1.0% (±3% systematic uncertainty) in the 0.1-100 GeV band. Finally we determine the LF of unbeamed FSRQs, finding that FSRQs have an average Lorentz factor of γ = 11.7+3.3– 2.2, that most are seen within 5° of the jet axis, and that they represent only ∼0.1% of the parent population. [ABSTRACT FROM AUTHOR]