Superconductivity is a phenomenon occurring in certain materials generally at very low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field (the Meissner effect). It was discovered by Heike Kamerlingh Onnes in 1911. Applying the principle of S uper conductivity in microwave and millimeter-wave (mm-wave) regions, components with superior performance can be fabricated. Major problem during the earlier days was the that the cryogenic burden has been perceived as too great compared to the performance advantage that could be realized. There were very specialized applications, such as low-noise microwave and mm-wave mixers and detectors, for the highly demanding radio astronomy applications where the performance gained was worth the effort and complexity. With the discovery of high temperature superconductors like copper oxide, rapid progress was made in the field of microwave superconductivity.

Microwave Superconductivity
According to BCS theory cooper pairs are formed during superconducting state and it is having energy slightly less than the normal there exist a superconducting energy gap between normal electrons and cooper pairs. The band gap E' related to transition temperature by relation,
E (at t=0K) =3.52*Kb*Tc
Where Kb Boltzman's constant
Tc Critical temperature and
3.52 is a constant for ideal superconductor and may vary from 3.2 to 3.6 for most superconductors.
If a microwave or a millimeter wave photon with energy greater than superconducting energy gap incident on a sample and is absorbed by the cooper pair, it will be broken with two normal electron created above the energy gap and zero resistance property is lost by material. This property is shown in fig below. For ideal with a transition temperature of Tc = 1K, the frequency of the mm wave photon with energy equal to superconducting energy gap at T=0K would be about 73GHz. For practical superconductors the photon energy corresponding to energy gap would scale with Tc. For niobium (Tc=9.2K) the most common material in LTS devices and circuits, the frequency of radiation corresponding to energy gap is about 670GHz.

The zero resistance property of the superconductor is true for dc (f=0). For finite frequencies there are finite but usually very small electrical losses. The origin of these losses at non zero frequency is due to the presence of two type of charge carriers in the superconductor. Although cooper pairs move without resistance, the carriers in normal state, those above energy gap behave as electrons in normal conductor. As long as the operating frequency is below energy gap the equivalent circuit for the superconductor is simply the parallel combination of resistor and inductor, where resistor indicate normal electrons and inductor the cooper pairs. These two carriers contribute separately to the screening of fields.

The characteristic decay length of fields into a super conductor as determined by cooper pair current is superconducting penetration depth. The penetration depth get larger with increased temperature but only slightly close to Tc