- Email: [email protected]
Microwave transmission through high-temperature superconducting waveguides
Physica C 372–376 (2002) 523–525 www.elsevier.com/locate/physc
Microwave transmission through high-temperature superconducting waveguides a,*,1
G. Yassin
, I. Barboy b,1, V. Dikovsky b, M. Kambara c, D.A. Cardwell c, S. Withington a, G. Jung b,2
a
b
Cavendish Astrophysics, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK Department of Physics, Ben Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel c IRC in Superconductivity, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK
Abstract Microwave transmission through HTSC circular waveguides close to the cutoff conditions has been investigated. Applicative consequences of a sharp decrease in the transmitted power observed in the vicinity of the superconducting transition are discussed. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction A common way of investigating electromagnetic properties of superconducting materials at microwave frequencies consists of inserting samples into bulk resonant cavities and measuring the Q factor of the loaded resonators at temperatures well below the critical temperature of the sample [1]. Frequently, thin film technology has also been employed to fabricate resonators in which the superconducting element constitutes an integral part of a microstrip or a coplanar thin film resonant structure [2]. The advantage and high sensitivity of all cavity methods is based on the fact that the mi*
Corresponding author. G.Y. visits to BGU and I.B. participation in EUCAS conference were supported by the president of Ben Gurion University, Prof. A. Braverman. 2 Also with Instytut Fizyki PAN, 02-668 Warszawa, Poland. 1
crowave signal bounces back and forth many times before it decays as a result of the losses in the cavity associated with the presence of the superconducting sample. In this paper we report our investigations of the influence of the superconducting transition in the waveguide walls on the propagation properties of a bulk superconducting circular waveguide. The experiments were performed at 15 GHz, and the waveguide dimensions were chosen such that in the normal state it only propagated the lowest order TE11 mode with a cutoff frequency close to 10.5 GHz. We have observed a sharp decrease in the transmitted power whenever the waveguide walls undergo the transition from the superconducting to normal state, or vice versa. Accurate measurement of attenuation change near cutoff may allow determination of the surface resistance of the superconducting material. In what follows we shall present preliminary results that illustrate the feasibility of this method.
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 0 7 8 4 - 0
524
G. Yassin et al. / Physica C 372–376 (2002) 523–525
2. Superconducting waveguides
3. Experimental investigation
The characteristic equation of a TE mode propagating along an ideal cylindrical waveguide is given by
Experiments were carried out using 50 mm long YBa2 Cu3 O7d (YBCO) cylindrical waveguide which was assembled from six disks, each of 16.3 mm inner diameter and 32 mm outer diameter, fabricated by top seeded melt growth technique. This involved placing a small single crystal NdBCO seed on the top surface of a sintered YBCO pellet and heating the arrangement above the peritectic decomposition temperature of YBCO. The partially decomposed sample was then cooled below its solidification temperature and processed isothermally for 48 h. The samples were additionally oxygenated in a separate process to enhance their superconducting properties. The disks were then machined flat and a cylindrical tube of internal diameter 16.3 mm was drilled ultrasonically at the center of each. The disks were finally re-oxygenated and the cylindrical waveguide was constructed by gluing the disks together with a conducting silver epoxy. The first measurements were dedicated to evaluating the superconducting properties of the discs. The critical temperature of each disc was determined by an inductive technique previously employed for evaluation of properties of active elements of superconducting fault current limiter [6]. The transition temperature of our discs was fairly homogenous and contained in the range 86– 90 K. However, only few discs demonstrated sharp superconducting transitions narrower than 2 K while the transition width of the majority of our elements extended over several degrees. We suspect that the quality of these disks has been degraded during mechanical handling. Detailed investigations of the superconducting and structural properties of the disks will be reported elsewhere. To investigate the transmission properties of the YBCO cylindrical waveguide we have build a setup consisting of a 50 mW Gunn diode oscillator which excites the TE10 mode at 15.3 GHz in a rectangular waveguide. A commercial rectangularto-circular transition was then used to launch the TE11 mode into the YBCO test section immersed in a liquid nitrogen cryostat. This mode was then fed to a home made conical corrugated horn of 15° semiflare angle to excite the HE11 hybrid mode.
oHz =or ¼ 0 ) Jn0 ðkc aÞ ¼ 0
ð1Þ
where r and z are respectively the radial and axial coordinate, a is the radius of the waveguide and kc is the cutoff wave number [3]. In deriving the above equation, the perfect conductor boundary conditions where assumed, namely, that the component of the electric field tangent to the surface vanishes and that the magnetic field is normal to the surface of the conductor. When the waveguide material becomes lossy however, the perfect conductor boundary conditions are perturbed by the penetration of magnetic field, skin depth in the case of normal metal or the London penetration depth in the case of a superconductor. It can be shown that for TE modes and to first order, the change in the propagation constant due to electromagnetic field penetration can be written as [4]: b2 b2o 1 1 Zs ¼ 2i pffiffiffiffiffiffiffiffiffiffiffiffiffi ½x2 þ u ðbo aÞ 2 Zo bo 1 x2
ð2Þ
where xðrÞ ¼ x=xc , u is a number which depends on the nature and order of the propagating mode, b and bo are respectively the propagation constants for the superconducting and ideal conductor, Zo is the impedance of free space and Zs is the surface impedance of the waveguide material. For a waveguide in the superconducting state with T Tc , Zs =Zo 1, hence the cutoff frequencies of the waveguide remain close to those of a perfect conductor waveguide [4,5]. Near the transition temperature however, the surface impedance of the material increases sharply, causing a small, yet a detectable change in the complex propagation constant, which can be written as: b ¼ bo þ b1 þ ib2
ð3Þ
The real part b1 causes a shift in the cutoff frequency while the imaginary part b2 gives the attenuation. Clearly, a change in the waveguide surface impedance will influence both quantities.
G. Yassin et al. / Physica C 372–376 (2002) 523–525
The power radiated by the horn antenna was received by a detector located approximately 80 cm away from the horn. In this way we could both identify the waveguide mode (by taking a polar radiation pattern of the horn) and measure the change in the transmitted power through the waveguide as a function of the circular waveguide temperature. The transition between the superconducting and normal state was monitored by measuring the inductance of test copper coils wound around each disc. An example of a typical result obtained during a thermal cycle consisting of an initial temperature decrease from above the critical temperature of the YBCO waveguide down to 81 K, followed by a subsequent temperature increase well above Tc is shown in Fig. 1. Here we have plotted the transmitted power and inductance as a function of the channel number of data acquisition arrangement. One can see two pronounced dips in the transmission curve. The minima occur in the close vicinity to the critical point when the YBCO undergoes transitions between normal and superconducting state and vice versa. Sharp increase of the attenuation in the vicinity of Tc can be attributed to a sharp increase of the waveguide surface impedance when the temperature approaches the critical one. From Eq. (2) we see that the change in the surface impedance influences the transmission through the waveguide in two ways. The real part (surface resistance) influences the attenuation co-
525
efficient directly and the reactive part influences the attenuation indirectly by increasing the cutoff frequency which also influences attenuation, in particular near cutoff. The overall performance of the discussed setup can substantially improved by making straightforward modifications to the experimental arrangement. First, the waveguide itself can be fabricated from a single homogeneous tube to guarantee better uniformity in the S–N phase transition. Secondly, the sensitivity of the measurements can be increased many times by choosing the waveguide dimensions, or the frequency of operation such that the S–N transition would occur very close to the cutoff. 4. Conclusions We have investigated the behavior of superconducting circular waveguides, well below and very close to the transition temperature. In the former case the waveguide behaved very similar to a normal waveguide with perfectly conducting walls. It can therefore be safely used in RF systems where low losses are crucial, e.g. in high performance horn antenna receivers for the cosmic microwave background investigations. During the S–N phase transitions we obtained dips in the transmitted power which can be enhanced by tuning the operating frequency near cutoff. This phenomenon may be employed to study the behavior of the surface resistance of the superconducting material of the waveguide by measuring the attenuation near cutoff. References
Fig. 1. Power transmitted through the YBCO waveguide and the inductance of one of the rings during a thermal cycle of cooling across the N–S transition down to 81 K (data channels 1– 22) followed by a heating up to 160 K (channels 22–45). The N–S and S–N transitions are marked by the dashed lines in the figure.
[1] A.P. Jenkins, K.S. Kale, D. Dew-Hugh, in: Studies of High Temperature Superconductors, vol. 7, Nova Science Publishers, New York, 1996, p. 179. [2] J. Gallop, Supercond. Sci. Technol. 10 (1996) A120. [3] S. Ramo, J.R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics, John Wiley and Sons, New York, 1965. [4] G. Yassin et al., IEEE Microw. Wireless Comp. Lett. 11 (2001) 413. [5] V. Meerovich et al., IEEE Trans. Appl. Supercond. 9 (1999) 4666. [6] G.J. Chaloupka, IEEE Microw. Wireless Comp. Lett. 10 (2000) 114.
Microwave transmission through high-temperature superconducting waveguides a,*,1
G. Yassin
, I. Barboy b,1, V. Dikovsky b, M. Kambara c, D.A. Cardwell c, S. Withington a, G. Jung b,2
a
b
Cavendish Astrophysics, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK Department of Physics, Ben Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel c IRC in Superconductivity, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK
Abstract Microwave transmission through HTSC circular waveguides close to the cutoff conditions has been investigated. Applicative consequences of a sharp decrease in the transmitted power observed in the vicinity of the superconducting transition are discussed. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction A common way of investigating electromagnetic properties of superconducting materials at microwave frequencies consists of inserting samples into bulk resonant cavities and measuring the Q factor of the loaded resonators at temperatures well below the critical temperature of the sample [1]. Frequently, thin film technology has also been employed to fabricate resonators in which the superconducting element constitutes an integral part of a microstrip or a coplanar thin film resonant structure [2]. The advantage and high sensitivity of all cavity methods is based on the fact that the mi*
Corresponding author. G.Y. visits to BGU and I.B. participation in EUCAS conference were supported by the president of Ben Gurion University, Prof. A. Braverman. 2 Also with Instytut Fizyki PAN, 02-668 Warszawa, Poland. 1
crowave signal bounces back and forth many times before it decays as a result of the losses in the cavity associated with the presence of the superconducting sample. In this paper we report our investigations of the influence of the superconducting transition in the waveguide walls on the propagation properties of a bulk superconducting circular waveguide. The experiments were performed at 15 GHz, and the waveguide dimensions were chosen such that in the normal state it only propagated the lowest order TE11 mode with a cutoff frequency close to 10.5 GHz. We have observed a sharp decrease in the transmitted power whenever the waveguide walls undergo the transition from the superconducting to normal state, or vice versa. Accurate measurement of attenuation change near cutoff may allow determination of the surface resistance of the superconducting material. In what follows we shall present preliminary results that illustrate the feasibility of this method.
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 0 7 8 4 - 0
524
G. Yassin et al. / Physica C 372–376 (2002) 523–525
2. Superconducting waveguides
3. Experimental investigation
The characteristic equation of a TE mode propagating along an ideal cylindrical waveguide is given by
Experiments were carried out using 50 mm long YBa2 Cu3 O7d (YBCO) cylindrical waveguide which was assembled from six disks, each of 16.3 mm inner diameter and 32 mm outer diameter, fabricated by top seeded melt growth technique. This involved placing a small single crystal NdBCO seed on the top surface of a sintered YBCO pellet and heating the arrangement above the peritectic decomposition temperature of YBCO. The partially decomposed sample was then cooled below its solidification temperature and processed isothermally for 48 h. The samples were additionally oxygenated in a separate process to enhance their superconducting properties. The disks were then machined flat and a cylindrical tube of internal diameter 16.3 mm was drilled ultrasonically at the center of each. The disks were finally re-oxygenated and the cylindrical waveguide was constructed by gluing the disks together with a conducting silver epoxy. The first measurements were dedicated to evaluating the superconducting properties of the discs. The critical temperature of each disc was determined by an inductive technique previously employed for evaluation of properties of active elements of superconducting fault current limiter [6]. The transition temperature of our discs was fairly homogenous and contained in the range 86– 90 K. However, only few discs demonstrated sharp superconducting transitions narrower than 2 K while the transition width of the majority of our elements extended over several degrees. We suspect that the quality of these disks has been degraded during mechanical handling. Detailed investigations of the superconducting and structural properties of the disks will be reported elsewhere. To investigate the transmission properties of the YBCO cylindrical waveguide we have build a setup consisting of a 50 mW Gunn diode oscillator which excites the TE10 mode at 15.3 GHz in a rectangular waveguide. A commercial rectangularto-circular transition was then used to launch the TE11 mode into the YBCO test section immersed in a liquid nitrogen cryostat. This mode was then fed to a home made conical corrugated horn of 15° semiflare angle to excite the HE11 hybrid mode.
oHz =or ¼ 0 ) Jn0 ðkc aÞ ¼ 0
ð1Þ
where r and z are respectively the radial and axial coordinate, a is the radius of the waveguide and kc is the cutoff wave number [3]. In deriving the above equation, the perfect conductor boundary conditions where assumed, namely, that the component of the electric field tangent to the surface vanishes and that the magnetic field is normal to the surface of the conductor. When the waveguide material becomes lossy however, the perfect conductor boundary conditions are perturbed by the penetration of magnetic field, skin depth in the case of normal metal or the London penetration depth in the case of a superconductor. It can be shown that for TE modes and to first order, the change in the propagation constant due to electromagnetic field penetration can be written as [4]: b2 b2o 1 1 Zs ¼ 2i pffiffiffiffiffiffiffiffiffiffiffiffiffi ½x2 þ u ðbo aÞ 2 Zo bo 1 x2
ð2Þ
where xðrÞ ¼ x=xc , u is a number which depends on the nature and order of the propagating mode, b and bo are respectively the propagation constants for the superconducting and ideal conductor, Zo is the impedance of free space and Zs is the surface impedance of the waveguide material. For a waveguide in the superconducting state with T Tc , Zs =Zo 1, hence the cutoff frequencies of the waveguide remain close to those of a perfect conductor waveguide [4,5]. Near the transition temperature however, the surface impedance of the material increases sharply, causing a small, yet a detectable change in the complex propagation constant, which can be written as: b ¼ bo þ b1 þ ib2
ð3Þ
The real part b1 causes a shift in the cutoff frequency while the imaginary part b2 gives the attenuation. Clearly, a change in the waveguide surface impedance will influence both quantities.
G. Yassin et al. / Physica C 372–376 (2002) 523–525
The power radiated by the horn antenna was received by a detector located approximately 80 cm away from the horn. In this way we could both identify the waveguide mode (by taking a polar radiation pattern of the horn) and measure the change in the transmitted power through the waveguide as a function of the circular waveguide temperature. The transition between the superconducting and normal state was monitored by measuring the inductance of test copper coils wound around each disc. An example of a typical result obtained during a thermal cycle consisting of an initial temperature decrease from above the critical temperature of the YBCO waveguide down to 81 K, followed by a subsequent temperature increase well above Tc is shown in Fig. 1. Here we have plotted the transmitted power and inductance as a function of the channel number of data acquisition arrangement. One can see two pronounced dips in the transmission curve. The minima occur in the close vicinity to the critical point when the YBCO undergoes transitions between normal and superconducting state and vice versa. Sharp increase of the attenuation in the vicinity of Tc can be attributed to a sharp increase of the waveguide surface impedance when the temperature approaches the critical one. From Eq. (2) we see that the change in the surface impedance influences the transmission through the waveguide in two ways. The real part (surface resistance) influences the attenuation co-
525
efficient directly and the reactive part influences the attenuation indirectly by increasing the cutoff frequency which also influences attenuation, in particular near cutoff. The overall performance of the discussed setup can substantially improved by making straightforward modifications to the experimental arrangement. First, the waveguide itself can be fabricated from a single homogeneous tube to guarantee better uniformity in the S–N phase transition. Secondly, the sensitivity of the measurements can be increased many times by choosing the waveguide dimensions, or the frequency of operation such that the S–N transition would occur very close to the cutoff. 4. Conclusions We have investigated the behavior of superconducting circular waveguides, well below and very close to the transition temperature. In the former case the waveguide behaved very similar to a normal waveguide with perfectly conducting walls. It can therefore be safely used in RF systems where low losses are crucial, e.g. in high performance horn antenna receivers for the cosmic microwave background investigations. During the S–N phase transitions we obtained dips in the transmitted power which can be enhanced by tuning the operating frequency near cutoff. This phenomenon may be employed to study the behavior of the surface resistance of the superconducting material of the waveguide by measuring the attenuation near cutoff. References
Fig. 1. Power transmitted through the YBCO waveguide and the inductance of one of the rings during a thermal cycle of cooling across the N–S transition down to 81 K (data channels 1– 22) followed by a heating up to 160 K (channels 22–45). The N–S and S–N transitions are marked by the dashed lines in the figure.
[1] A.P. Jenkins, K.S. Kale, D. Dew-Hugh, in: Studies of High Temperature Superconductors, vol. 7, Nova Science Publishers, New York, 1996, p. 179. [2] J. Gallop, Supercond. Sci. Technol. 10 (1996) A120. [3] S. Ramo, J.R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics, John Wiley and Sons, New York, 1965. [4] G. Yassin et al., IEEE Microw. Wireless Comp. Lett. 11 (2001) 413. [5] V. Meerovich et al., IEEE Trans. Appl. Supercond. 9 (1999) 4666. [6] G.J. Chaloupka, IEEE Microw. Wireless Comp. Lett. 10 (2000) 114.