Microwave Superconductivity
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16-11-2010, 10:03 PM

1. Introduction
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 Superconductivity 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.
This topic describes the properties of superconductivity that can be exploited in microwave and mm-wave technologies to yield components with appreciable performance enhancement over conventional systems. Superconducting signal transmission lines can yield low attenuation, zero-dispersion signal transmission behavior for signals with frequency components less than about one tenth the superconducting energy gap. No other known microwave device technology can provide a similar behavior. Superconductors have also been used to make high speed digital circuits, josephsons junction and RF and microwave filters for mobile phone base stations.

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2. Superconductivity
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. Like ferromagnetism and atomic spectral lines superconductivity is a quantum mechanical phenomenon. The electrical resistivity of a metallic conductor decreases gradually as the temperature is lowered. The temperature at which the transition to superconducting state occurs is known as the critical temperature.

However, in ordinary conductors such as copper and silver, impurities and other defects impose a lower limit. Even near absolute zero a real sample of copper shows a non-zero resistance. The resistance of a superconductor, despite these imperfections, drops abruptly to zero when the material is cooled below its critical temperature. Superconductivity occurs in a wide variety of materials, including simple elements like tin and aluminium, various metallic alloys and some heavily-doped semiconductors. The common examples are niobium with Tc=9.2K. however superconductivity doesnot occur noble metals like gold ,silver etc and pure samples of ferromagnetic materials.
The major properties shown by the super conductors are zero electrical resistance and meissner effect.

2.1 Meissner effect:
The Meissner effect (also known as the Meissner-Ochsenfeld effect) is the expulsion of a magnetic field from a superconductor. Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside tin and lead samples. The samples, in the presence of an applied magnetic field, were cooled below what is called their superconducting transition temperature. Below the transition temperature the samples cancelled all magnetic field inside, which means they became perfectly diamagnetic. They detected this effect only indirectly; because the magnetic flux is conserved by a superconductor, when the interior field decreased the exterior field increased.

Fig2: meissner effect

The meissner experiment demonstrated for the first time that superconductors were more than just perfect conductors and provided a uniquely defining property of the superconducting state. In fig2 shown the first one represents the passing of magnetic field when T>Tc and second one shows meissner effect at T <Tc.

2.2 High temperature superconductivity (HTS):
The major problem associated with superconductivity in earlier days was the cryogenic burden or the difficulty in maintaining temperature below the critical temperature. High-temperature superconductors (abbreviated high-Tc or HTS) are materials that have a superconducting transition temperature (Tc) above 30 K, which was thought (1960-1980) to be the highest theoretically allowed Tc. The first high-Tc superconductor was discovered in 1986 by Karl Müller and Johannes Bednorz, for which they were awarded the Nobel Prize in Physics in 1987.
The interest towards superconductivity greatly increased after the discovery in 1986 of a class of copper oxide material that shows superconductivity at temperature near 40K.Rapid progress was made and the critical temperature pushed to approximately 90-120K for these oxide-based high temperature superconductors. Later hts was discovered in other materials like Lanthanum based cuprate perovskite material with transition temperature of 35K, yttrium based YBCO with transition temperature of 92K which was important because liquid nitrogen could then be used as a refrigerant. Later highest temperature superconductor was a ceramic material consisting of thallium, mercury, copper, barium, calcium, and oxygen, with Tc=138 K ,iron based family of superconductor, bismuth strontium calcium oxide or BSSCO with Tc=107K etc.

3. Theories of superconductivity:

Various theories have been developed to explain the principle of superconductivity.

3.1 Ginzburg–Landau theory:
In physics, Ginzburg–Landau theory is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity. Instead, it examines the macroscopic properties of a superconductor with the aid of general thermodynamic arguments. This theory is sometimes called phenomenological as it describes some of the phenomena of superconductivity without explaining the underlying microscopic mechanism.

3.2 BCS theory:
In 1957 Bardeen, Cooper and Robert Schrieffer came up with theory called the BCS theory of superconductivity. BCS theory is the first microscopic theory of superconductivity. In the BCS framework, superconductivity is a macroscopic effect which results from "condensation" of electron pairs, called Cooper pairs. These nearly behave as bosons which, at sufficiently low temperature, form a large Bose-Einstein condensate. At sufficiently low temperatures, electrons near the Fermi surface become unstable against the formation of cooper pairs. Cooper showed such binding will occur in the presence of an attractive potential, no matter how weak. In conventional superconductors, such binding is generally attributed to an electron-lattice interaction which is shown in fig 3(a) and 3(b)

Fig 3: The Electron-phonon interaction

An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite "spin", to move into the region of higher positive charge density. The two electrons are then held together with a certain binding energy. If this binding energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electron pair will stick together and resist all kicks, thus not experiencing resistance. Such a pair of electrons are known

as Cooper pairs. Coupling and interaction between electrons can be represented by Feynman diagram as in fig 4 shown below.
For each superconducting material there is critical temperature (Tc) and critical magnetic field (Hc) below which the material exhibits superconductivity or the cooper pair exists. In addition to these there is critical current density (Jc) which depends on metallurgy and physical condition of the specimen and it sets the upper limit on the current that can be induced in specimen before the onset of the generation of harmonic related signals that will degrade the performance of the superconducting microwave device. The graphical representation of the statement is shown in fig 5. The material shows superconductivity at points below the surface shown in fig.

4. Microwave superconductivity

According to BCS theory cooper pairs are formed during superconducting state and it is having energy slightly less than the normal electrons.so 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.

As operating temperature closer to Tc the band gap also reduces. Hence the superconductor will be more sensitive to temperature variations. So inorder to avoid this operating temperature must be less than 2/3 of Tc. Thus for high frequency application of superconducting materials the operating frequency of device should be 10% or less of the frequency corresponding to energy gap of the material and temperature must be less than 2/3Tc. For example in case of niobium (Tc=9.2K) the band gap is about 670 GHz and can be operated at a maximum frequency of 70GHz and temperature below 6K.

5. Superconductor microwave device technology
Superconducting materials are used for device fabrication since 1960. The major advantage is in the field of attenuation and dispersion compared to the copper transmission line. In case of copper transmission line the attenuation in the frequency range from 10MHz to about 100THz varies smoothly. However for a superconducting niobium-niobium oxide-niobium parallel plate transmission line operating near 4K, the attenuation at low frequency is less than copper and rises as frequency squared up to frequencies above 100GHz whereas magnitude remain below that of copper transmission line. For further increasing frequency the attenuation abruptly increases by about two order of magnitude at a frequency that corresponds to energy gap of niobium, approximately 670GHz. At still frequency attenuation follows square root frequency dependence for normal metal with magnitude about a factor of ten larger than copper at room temperature.
The phase velocity of signal increases with increasing frequency in a monotonic fashion through out frequency region for copper. However for superconducting transmission line the phase velocity is constant up to 100GHz. For further increase in frequency the phase velocity dips goes through minimum below 1000GHz and then increases with increase in frequency. Thus complex signals with frequency components can propagate along superconducting transmission line without dispersion.

6. Superconducting communication filters
The choice of resonator technology for microwave filter is influenced by the insertion loss and the selectivity. To achieve higher selectivity more number of resonators are required which increases the insertion loss. When conductor losses are dominant it is possible to drastically reduce the resonator size by using superconductors. Superconductivity can yield very high Q value resonator and filter at reduced volume compared with that realized using conventional technologies. The inherent advantage of the above property is that
• The volume of the entire system can be reduced.
• Due to low losses, highly complex filters with many poles can be built with low insertion loss.
• The cryogenic environment for the hts filter, Improves the performance of other components in the system like the low noise amplifier. Noise figure of the system is reduced.
• The interference problem can be minimized by the use of hts filter.
These characteristics have made HTS technology attractive to the wireless communications vendors, who frequently have strong interference problems, which can be minimized by the use of an HTS filter and the lower noise figure of the cryogenic system. The HTS filter system comprises a very high selectivity, low-loss HTS filter followed by an extremely low noise, cryogenically cooled semiconductor preamplifier. The hts filter circuit connects the base station antenna to the input of the base station receiver. Its purpose is to minimize the
degradation of signal-to-noise ratio (SNR) that occurs in the base station receiver as a natural consequence of detecting and extracting the information content of the desired signals. The hts filter accomplishes this by performing two circuit functions extremely well:

• Efficiently and effectively rejecting out-of-band interference and
• Amplifying in-band signals with extremely low added noise and high linearity.

6.1 Ultra selective HTS filter:

For example an ultra-sharp skirt filter that has 22 poles and 10 transmission zeros. The HTS filter is fabricated using thin film and microstrip technology. HTS thin film for filter application requires homogeneous large area double sided sided film with small surface resistance. HTS film is deposited on wafer substrate with acceptable microwave properties like MgO. The substrate must have
• Suitable crystalline structure
• Low microwave loss tangent
• Non reactive with HTS material
• Tolerable thermal expansion match with HTS.
The YBCO deposition is done by sputtering or organometallic chemical vapour deposition or pulsed laser deposition or thermal evaporation. Such a thin film is shown in figure.

Fig 7: HTS thin film

Advanced folded half wavelength resonator or clip resonators are used in the design of filter inorder to reduce the area of filter and to increase performance of filter. by clip resonator a reduction 54% area is obtained and 22 resonators can be accommodated in 2-in wafer. Due to small loss of HTS such a close arrangement of arms of resonator is possible and hence reduction in area. The clip resonator structure and the arrangement in filter is shown in fig.

Quadruplet coupling was used inorder to produce required number of transmission zeros near band edge.it used inorder to maximize the number of zeros while keeping the structure simple to design and tune. The coupling is shown in fig below

Fig 10: quadruplet coupling structure

The performance of the filter is able to surpass the performance of a 50-pole Chebyshev filter. The 22-pole filter is used to meet one of the existing 3G wireless bands; a 1950-MHz center frequency and a 20-MHz bandwidth. The comparison between the responses of the two filters, their insertion loss and group delays are shown below

The roll off is same for both filters in the initial portion. But due to the presence of zeros at transmission edge, the roll off become more steep up to 90dB level. Due to low losses the insertion loss curve is close to zero in the pass band of HTS filter. In HTS filter the curve is flat in wide region because of the distribution of poles near the band edges. The group delay is depending on the pole density. Since in HTS filter poles are distributed in band edges the group delay is low and flat in the passband. This minimizes dispersion of signal.

7. Superconducting digital microwave technology

Today the computers are operating at a speed of several GHz, so even the digital technology is penetrating into microwave range. Eventhough the conventional digital circuits are not able to operate in GHz range, the superconducting circuits work in low GHz range. An active device in this field is the two terminal Josephson junction, which has a trilayer SIS structure, where two superconducting layers are the terminals of the device. The device can work either in superconducting mode or in normal mode.
Assume that the junction is cooled through the superconducting transition temperature while there is no voltage applied to the device. If one now applies a current to the device, a supercurrent will flow through the device, and as the current is increased, the operating point will move vertical upward along the V=0 axis. When the current exceeds the critical current of the Josephson structure, the
device will switch into the normal state and a increase in voltage occurs.

If the applied current is then decreased, the operating point will move down along the finite voltage branch until the zero voltage point is reached at the origin of the current versus voltage curve, when the device will switch back into the superconducting state.

To produce digital circuit with josephson device one or more josephson junctions are embedded in an otherwise superconducting circuit, and the circuit is configured so that the Josephson junction(s) can be switched in and out of the normal state by the action of a control current flowing through a control electrode.
Because the Josephson device has zero resistance (and thus, zero loss) for a good portion of the operating cycle, Josephson digital circuits exhibit very low electrical losses. Josephson devices can switch at 770GHz range. Hence the josephson digital devices has got high speed, low loss and low figure of merit.
The superconductor digital technology is used in ADCs. The ADCs capable of digitization of signals up to 21GHz. Application of microwave frequency ADC is in microwave receiver with direct digitization at front end. So the amplifier and down converters at the front end of receiver can be removed and ADC can be used after LNA.

8. Superconductivity in High-Energy Physics

Microwave superconductivity is used in high energy particle accelerators like cyclotron, it consist of electromagnets at edge of vacuum chamber. The maximum speed of particle is limited by the magnetic field produced by magnet. Superconducting magnets provide much higher magnetic field than air core iron magnets. In order to increase the energy boost per transit superconducting cavities were used which reduce the losses in walls of the cavity.
The Large Hadron Collider by the European Organizations for Nuclear Research (CERN) in Geneva, Switzerland, has about 20 superconducting RF cavities along its 27-km circumference circular path. The next large particle accelerator, which is currently under development, is called the International Linear Collider (ILC), which will contain about 16,000 superconducting RF cavities along its 31-km linear path.

9. Conclusion

Superconductivity is one of the most exotic phenomena observed in nature and it can have an impressive impact on the performance of passive and active devices operating throughout the microwave and mm wave region of the spectrum. In these frequency ranges,
• The electrical losses are superconductors are significantly less than the losses for normal conducting metallization in device and component applications.
• Active superconducting Josephson device technology is inherently low loss and has demonstrated operation in excess of 700 GHz.

There has been much progress in the recent years to exploit superconductivity in selected microwave and mm-wave system. The HTS filters having low loss, sharp roll off have been designed for wireless communication systems to filter out of band interference and reduce noise. HTS found application in high energy particle accelerators, ADC’s etc.
In addition to advances in superconducting technology there have been gains in cryogenic refrigeration community that can provide energy efficient, reliable cryogenic refrigeration systems.

10. References

• Martin Nisenoff and Jeffrey M.Pond, “superconductors and microwaves”, IEEE microwave magazine, may 2009

• G. Tsuzuki, S. Ye, and S. Berkowitz, “Ultra-sensitive 22-pole, 10 transmission zero superconducting bandpass filter surpasses 50- pole Chebyhshev filter,” IEEE Trans. Microwave Theory Tech.

• Superconducting Microwave Filter Systems for Cellular Telephone Base Stations, IEEE Trans. Microwave Theory Tech., May 2004

• Superconductor Technologies, Inc., Santa Barbara, CA. [Online].
Available: http://www.suptech.com

• L. A. Abelson and G. L. Kerber, “Superconductor integrated circuit
fabrication technology,” Proc. IEEE, vol. 92, no. 10, pp. 1517–1531


11. Discussion:

• Why cooper pairs are having less energy than normal electrons?

Cooper pair is the name given to two electrons (or other fermions) that are bound together at low temperatures in a certain manner. Arbitrarily small attraction between electrons in a metal can cause a paired state of electrons to have a lower energy than the Fermi energy. Some energy of electron is lost during interaction and it results in lattice vibrations called phonons. This causes reduction in energy of cooper pairs.

• Is super conductor different from perfect conductor?

Superconductor is different from perfect conductor or ideal conductor. The meissner experiment demonstrated for the first time that superconductors were more than just perfect conductors and provided a uniquely defining property of the superconducting state.

• What are other cross-coupling structures?

In addition to quadruplet coupling, various coupling structures present like Canonical structure, trisection structure, canonical asymmetric structure etc.

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18-09-2011, 12:38 AM

Can u please upload a powerpoint presentation within 2-3 days....
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