A bidirectional clipper using superconductors

A bidirectional clipper using superconductors M.V.S.

Lakshmi and M. S a t y a m

Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore-560012, India

Received 3 July 1991; revised 26 September 1991 This note describes a bidirectional clipper based on the properties of the critical current associated with a superconductor. The new device has been tested using high Tc superconductors.

Keywords: bidirectional clippers; high Tc superconductors; critical currents

With the discovery of high Tc superconductors there has been considerable interest in fabricating conventional superconducting devices like Josephson junctions, cryotrons, superconducting fault current limiters etc. as well as developing new devices like varistors 2, superconducting current controlled switches 3, level sensors 4, etc. based on the properties of the critical current associated with superconductors. A bidirectional clipper has been designed based on the current threshold property of superconductors and is described in this note. A clipper is a device which allows the input signal to pass through up to a certain amplitude and blocks (or clips) it above this amplitude. Figure 1 shows a schematic diagram of a clipper. It should allow the flow of current up to the needed voltage level V and above this level it should be clipped. An ideal clipper should be able to conduct without any voltage drop across it up to a certain applied voltage (I1) or current (I) and should drop the entire voltage above this level. This implies that the clipper should have a zero resistance up to a certain voltage/current level across it and should offer infinite resistance (dynamic) for voltages/currents above this level. The V - I characteristics, therefore, of an ideal clipper should be as shown in Figure 2.

Clipping device

R/

V

0

0

Figure

1

S c h e m a t i c diagram of a clipper

>

1 Current,

Figure 2

V-I

!

characteristics o f an ideal clipper

Superconductor as a clipper It is well known that a superconductor becomes a normal conductor when the current density (J) exceeds the critical current density (Jc). This property satisfies the

requirement that the drop across it is zero up to a certain clipping level (current), but beyond this level the dynamic resistance (Rs) is finite. This results in a clipper which allows a small portion of the input signal to appear across the load above the clipping level. Thus the output waveform of this will be slightly different from that of an ideal clipper. Further, the clipping takes place for both positive and negative input signals; in other words, this is essentially a bidirectional clipper. 0011 - 2275/92/030300 - 03 © 1 9 9 2 B u t t e r w o r t h - Heinemann Ltd

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The output waveform of a bidirectional clipper using a superconductor of uniform cross-section with I - V characteristics shown in Figure 3, is given in Figure 4. This waveform differs from that of an ideal bidirectional clipper shown by the dotted lines. The deviation AVo from the clipping level is an index of the quality of the clipper (as shown in Figure 4). AVo depends on the peak input voltage, normal resistance of the superconductor, load resistance and the critical current. Since all these parameters except AV~ and RL are constants of the clipper, one may define the quality factor (Q) of a clip-

A bidirectional clipper: M. V.S. Lakshmi and M. Satyam

/

AVo = V~

+

- lcRt.

(3)

The quality factor Q may be then written as

VT

Q-

O3

AVi

Vi -- IcR L

-

(4)

>O

\R~ + RLJ

! C

Current, I

Figure :3 V - I characteristics of a superconductor w i t h uniform cross-section (VT = threshold voltage)

+V

It may be seen that a superconductor having a high normal resistance compared to the load resistance gives a better performance from the point of clipping. However high resistance can be obtained only by having a small cross-section of a superconductor of considerable length. A small cross-section implies the current at which clipping takes place is low. By increasing the cross-sectional area the clipping level can be raised, but the length of the superconductor has to be increased. The performance of clippers with superconductors of different cross-section and length has been calculated through the output waveforms. The method of calculating the output waveform and the quality factor is described below.

I~ t

Calculation of output waveform of a superconductor clipper -V

Figure 4 O u t p u t w a v e f o r m of a bidirectional clipper using a superconductor w i t h uniform cross-section

Consider the clipping circuit shown in Figure 1 with a superconductor of uniform cross-section. The input voltage

v~ = vs~+ Vo per for a given R L as Q -

~E AVo

-

E-vc V o - V~

(1)

where Vi is the maximum input voltage, Vc is the voltage level at which clipping takes place and Vo is the maximum output voltage. For V~ < I~RL the entire input voltage appears across the load resistance, since there is no drop across the clipper. For I~RL <- V~ < I~(RL + R~) the output voltage remains almost at a value =IcRL. The deviation of the output from this value depends upon the variation of the resistance of the superconductor with current, in the transition region. This transition being generally sharp, the characteristics of the clipper are similar to those of an ideal one in this input voltage range. For V~ > Ic(RL + R~) the output voltage increases with the input voltage given by

and AVo is given by

AVo=Vo--Vc

(5)

where V~cis the voltage across the superconductor clipper and Vo is the voltage across the load. As the input varies from zero to V¢, where Vc = IeRL, the voltage drop V~ = 0 and therefore, Vi = Vo. When Vi is increased beyond Vc the output waveform is constructed in the following way. When the current in the clipper, I1 > I¢, the voltage across the clipper Vs~ is given by Vcs = 11Rs(I1)

(6)

where R~(ll) is the resistance of the clipper at 11. The output voltage Vo is then given by Vo = I1RL

(7)

and the corresponding Vi by V~=I~(R~(~) +RE)

(8)

Thus for a current I there is a particular value of Vi and 1t'o. A graph between Vo and Vi is drawn. From this graph the output voltages corresponding to different input voltages are read and the corresponding output waveform is drawn. A typical output waveform is shown in Figure 5. The quality factor is then calculated from this waveform using Equation (4). The quality factors for a few clippers as a function of RL and input voltage are given in Table 1.

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A bidirectional clipper: M.V.S. Lakshmi and M. Satyam Table 2 Quality factors of B i - S r - C a - C u - 0 superconducting thick-film clipper (dimensions: length = 12 mm and width = 12 mm, Rs = 30 fL and Ic = 0.4 mA) with varying input voltage and load resistance

Vi=10 Vo =6.5 Vc =5.5 E

I= t (ms)

0

Vi (mY) I

RE (f~)

O (calc)

O (obs)

10.0 13.5 17.0

50 68 50

6.0 3.18 2.24

4.52 2.64 2.0

Figure 8 Typical output waveform of the superconductor clipper

a

b

t (ms)

c

t (ms)

t (ms)

Figure 6

Output waveforms of a bidirectional clipper using a B i - S r - C a - C u - O thick-film superconductor with dimensions 1 2 m m x 1 2 m m : (a) V i = 1 0 m V a n d R L = 5 0 f l ; (b) V i = 1 3 . 5 m V a n d R L = 68f~; (c) V i = 1 7 m V a n d R L = 5 0 f l

Table 1 Quality factors of superconductor clippers with varying input voltage and load resistance

Vi (mV)

RE (fl)

(Rs = 30 fl)

(Rs = 50 fl)

10 10 20 20

25 50 25 50

4.05 6.0 2.72 2.46

3.86 2.7 3.35 2.25

Q* quality factor of clipper with dimensions: length = 12 mm and width = 12 mm O * * quality factor of clipper with dimensions: length = 10 mm and width = 10 mm

Experimental verification The device proposed here is essentially a superconducting film with uniform cross-section. In our case the superconducting film is made of bismuth strontium calcium copper oxide. A mixture of BiO2, SrCO3, CaCO3 and CuO in appropriate proportions (466, 295, 200, 239 mg respectively) is made into a paste using triethanolamine and printed using a screen printing technique on alumina (96% A1203) substrates with silver buffer layers (which prevent the poisoning of the superconducting filmS). The silver films were obtained by printing and firing silver paste (Ag and frit glass) on alumina substrates (firing schedule: 150°C for 15 min and 850°C for 30 min). The printed BiO2, SrCO3, CaCO3, CuO film is dried at 250°C for 20 min and fired at 850°C for 240 min. After firing, the film is cooled at a rate of 2°C min -j down to 500°C and then

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furnace cooled. The typical thickness of the film is about 30 #m. Silver contacts are evaporated on to the samples for measurements. This clipper is connected in series with RE as shown in Figure 1. The output waveform is traced on an oscilloscope (Tektronix Type 549 storage oscilloscope) for different values of input voltage ranging from 5 mV to 20 mV. The procedure is repeated with different values of RE ranging from 50 to 100 •. Output waveforms for typical input voltages and load resistances are given in Figure 6. The quality factors are given in Table 2. From these observations it is clear that a superconducting film with uniform cross-section can function as a bidirectional clipper.

Conclusions This note proposes the use of a superconducting film with uniform cross-section as a bidirectional clipper. It is pointed out that this clipper is almost like an ideal clipper in a specific voltage range for a given load resistance. It is also indicated how a superconductor clipper can be designed to meet specifications such as clipping level, quality factor etc.

References 1 Gray, K.E. and Fowler, D.E. J Appl Phys (1978) 49 2546 2 Laksluni, M.V.S., Ramkumar, K. and Satyam, M. Rev Sci lnstrum (1989) 60 1340 3 Ma, Q.Y. and Yang, E.S. Cryogenics (1990) 30 1146 4 Siegmann, St., Frey, T., Ramseyer, J.P. and Guntherodt, H.J. Rev Sci lnstrum (1990) 61 1946 5 Hashimoto, T., Kosaka, T., Yoshida, Y. Fueki, K. and Koinuma, H. Jap J Appl Phys (1988) 27 L384