In this chapter, the characteristics of the propagation of waves in superconducting waveguides are investigated. To compute the propagation constant, the complex conductivity of the superconductor is incorporated into the set of characteristic equations which describes the propagation constant of waves in the waveguide. An important outcome from this analysis is that superconducting waveguides are shown to behave like a lossless waveguide, exhibiting literally lossless behaviour at frequencies above the cutoff and below the gap frequency. Above the gap frequency, however, the waveguide loses its superconductivity, giving attenuation which increases in correspond to frequencies. The result suggests strongly that superconducting waveguides can be applied in receiver systems to minimize the loss of propagating signals.
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Wave guiding structures such as circular and rectangular waveguides and microstrip transmission lines are widely used in telecommunication receiver systems to channel and couple signals to the mixer circuits. In order to ensure that the received signal is converted in the mixer circuit with minimum loss, accurate and versatile mathematical formulations are used as a guide to compute and predict the losses in the guiding structures.
Figure 1 shows the functional block diagram of a typical heterodyne receiver which comprises a receiving antenna, a local oscillator LO, a mixer circuit, an intermediate frequency IF amplifier, and a spectrometer (Chattopadhyay et al., 2002; Kraus, 1986; Yeap, Tham, Nisar, & Loh, 2013). The RF signal from the antenna is directed down to the receiver system via mirrors and beam waveguides (Paine, Papa, Leombruno, Zhang, Blundell, 1994). At the front-end of the receiver system, the RF signal is channeled and coupled to a mixer circuit via hollow waveguides and microstrips. A heterodyne mixer is commonly implemented to down convert the RF signal to an intermediate frequency IF signal. After going through multiple stages of amplification, the IF signal is fed to a data analysis system such as an acousto-optic spectrometer. The data analysis system will be able to perform Fourier transformation and record spectral information about the input signal.
Figure 1. Block diagram of a heterodyne receiver
The front-end receiver noise temperature TR is determined by a number of factors. These include the mixer noise temperature TM, the conversion loss CLoss, the noise temperature of the first IF amplifier TIF, and the coupling efficiency between the IF port of the junction and the input port of the first IF amplifier 
. Walker et al. (1992) has performed a comparison among different waveguide receivers. In their analysis, it is found that the value of TR for the 230 GHz system is a factor of 3 to 4 less than that achieved with the 492 GHz system. The decrease in system performance at 492 GHz is due to the increase of CLoss and TM by a factor of approximately 3.
Since the input power level of the telecommunication signal could be quite small, i.e. of the order of 10–18 to 10–20 W (Shankar, 1986), it is therefore of primary importance to minimize the conversion loss CLoss of the mixer circuit. One way is to ensure that the energy of the LO and, in particular, the RF signals is channeled and coupled from the waveguides to the mixer circuit in a highly efficient manner. To minimize the loss of the propagating signals, the availability of a highly efficient wave guiding structure is, of course, central to the development of the receiver circuits.
Although most waveguides implemented in radio receivers are made of copper, the attenuation level exhibited in standard metallic waveguides such as copper may actually degrade the detection of signals at such weak intensity (Winters and Rose, 1991). Superconducting waveguides, on the other hand, feature low transmission losses and dispersion level below the gap frequency fg. A theoretical study is, therefore, performed in this chapter to analyze the propagation of electromagnetic waves in superconducting waveguides.