Microprocessor-based device for measurements on a superconducting transmission line

Microprocessor-based device for measurements on a superconducting transmission line A two-part microprocessor-based circuit can m e a s u r e the torque - velocity c h a r a c t e r i s t i c of the m e c h a n i c a l a n a l o g u e of a s u p e r c o n d u c t i n g transmission line. F S J a m z a d e h gives the details L A microprocessor-based circuit is described which is capable o f measuring the torque-velocity characteristic o f the mechanical analogue o f a superconducting transmission line. This model consists o f 30 pendulums connected to each other with flexible couplings. The model is driven by compressed air. The circuit is composed o f two parts. The first part measures the air velocity; this is equivalent to measurement o f the applied torque. The second circuit measures the average velocity o f a kink on the analogue line. Both measurements are converted to analogue signals and recorded on an x - y plotter as a point on the t o r q u e velocity characteristic. This characteristic corresponds directly to the current-voltage characteristic o f the actual transmission line. microprocessors

Josephson junctions

o

/

.r0 sin

II II m

Figure 1. Equivalent-circuit approximation o f a Josephson junction

model

There has been a large amount of interest in understanding the propagation of electromagnetic waves on superconducting transmission lines ~'2. The transmission line is composed of Josephson junction elements 3 coupled together by linear inductors. A Josephson junction is basically a nonlinear inductor governed by the following equations: d~

-

2n

V

dt ~o / = / o sin~

(1)

where/o and ~o are constants and/, V and ~ are the current, the voltage and the magnetic flux of the inductor. Given the loss and the capacitance associated with the junction, an electrical model of it has the form shown in Figure 1. Combining equation (1) with this figure results in a second-order differential equation for the junction current l=losin~+

~o

~

I

d~ + C d2~ )

( ~ cl~

dt ~

(2)

Newton's law of motion for the simple pendulum shown in Figure 2 is given by T = T o s i n ~ + D d~ -dt

+M

d2~ dt 2

13)

where To is the pendulum moment arm, M is its moment of inertia, D is the damping coefficient and T is the applied

mg

Figure 2. A simple pendulum

Computer-Aided Engineering Centre, College of Engineering, University of Wisconsin--Madison, 1500 Johnson Drive, Madison,

Wl 53706, USA 0141 --9331/83/070324-06 $3.00 © 1983 Butterworth & Co (Publishers) Lid 324

microprocessors and microsystems

B

iP

L

/_

L

J2~JL--

G

-ro sin

cT

Figure 4. Equivalent-circuit approximation of the transmission line

03

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Figure 3. Photographs o f the mechanical model torque. A comparison of equations 12) and [3) indicates the analogy between the pendulum and the Josephson junction. In particular, the pendulum torque and velocity are analogous to the junction current and voltage respectively. If many simple pendulums/in this case 30) are coupled together by springs, equivalent to linear inductors, the analogue of the superconducting transmission line is constructed {Figure 3). The model is similar to one described elsewhere4's . Each section has two pendulums and a disc attached to a rod supported by two ball bearings. An applied torque is coupled to each section via air at high pressure. Each disc has a corrugated polystyrene ring attached to it for coupling to the air jets. The applied torque can be varied by regulating the compressed air lines. The electrical diagram for this nonlinear active transmission line is shown in Figure 4. The governing equation for the electrical device, and similarly for the mechanical one, is given in normalized form by 2 ~Jtt = ~ X X

+

I + sin~ + KdPt

I

I

-2

-I

0

I I

I 2

I 3

X

Figure 5. Voltage waveform along the transmission line

One kink

P One ontikink

{4)

where / is the bias current and K is the loss factor due to the junction resistance. The subscripts x and t denote differentiation in space and time respectively. The solution to this equation for the voltage is a quantized bell-shaped pulse. Figure 5 shows the variation {bt in the voltage along the transmission line for a particular time. Each quantum of the electromagnetic wave corresponds to a 27r kink in the mechanical model. {A kink is basically a rotation of 2zr in the model, i e when a kink exists in the model the angle between the first and the last pendulum is 360 ° {Figure 6).) Kinks and antikinks {rotations in the opposite direction) can be steered along the mechanical model by applying

vol 7 no 7 sept 1983

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-3

Figure 6. A kink and an ant/kink along a mechanical mode/ torque to each pendulum with high-velocity air. Interest in the wave propagation along a ]osephson transmission line has led several authors 4-~ to build the mechanical analogue of the device. Kink propagation was then studied on the model as an alternative to the investigation of wave propagation on an actual device. In this paper we report on circuitry which is capable of measuring the torque-velocity characteristic of an analogue with a one-to-one relationship to the current-voltage characteristic of the transmission line.

325

Pencontrol

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converter

Reset ~

Free running ( ~ ~ [ ' disc

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recorder

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D/A converter

Counter

Reset

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Start Figure 7. Block diagram o f the entire system

Manualpushbutton switch

t

74121monostable multivibrotor 5

I d 74'2'mon°st I °b'e !

Enobfloerc6ounters

Pulsesfrom free-running pendulum indicating air flew

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!

74191 ,#-bit counter Ripple clock

Clock

741914-bit counter Clock

A3

t AO-

AO-A7 i DAC-03 D/A converter

I

AI analogueoutput to vertical section of the plotter

Figure 8. Circuitry that operates the vertical axis o f the plotter

326

microprocessors and microsystems

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l ..... 8212 input port I

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'LPen clown J_..~ Plotter relay

I

l

~

L l

o,,

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converter t-O'axis of ,/ plotter

Jl DiP switches Figure 9. Circuitry for the horizontal section of the plotter

Interrupt ,i

switches J

I~,,o.1 numl:x~rof pulses ,

i ~ait,or I

J-I ReadADoi J

40 ms

J

~ Countthe J time in 30sJ incrementsJ

reached Yes

u~nd~~pPrlO .oc

.

overflr -

Yes JLift thepenI -k~,,ghtLE~ I

the pen

ut the numberof I ulses and J ut pen downJ

~pOUtp Figure 10. FIowchort o f the software

vol 7 no 7 sept 1983

327

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7.5

/

,?

/2 ?

x E z

2.5

t

o.I

I

0.2

I

0.3

velocity/ms -I

Figure 11. Torque-velocity characteristic o f the superconductor transmission line mode/ The details of a microprocessor-based circuit are provided below. This circuit is capable of measuring the torque velocity characteristic of the mechanical model without interfering with the performance of the model. The block diagram of the entire system is shown in Figure 7.

MEASUREMENT OF TORQUE The torque on the mechanical model is proportional to the velocity of the air impinging on the pendulums. To measure the air velocity we exploit the fact that a simple disc with negligible moment of inertia simulates a resistor. When air impinges on the disc, the disc rotates at a constant velocity. As it rotates, a counter counts the number of revolutions per specified unit of time (Figure 8). A 74121 monostable multivibrator shapes and filters the signals ~rom the freerunning disc. The result is sent to a 74191 4-bit counter. Since the ripple clock carry of the counter is fed into another 4-bit counter, we have an 8-bit counter altogether. This counter operates for only 6 s after a manual push button switch has been depressed through another monostable multivibrator. In this way we eliminate the possibility of overflow in the counter. A digital-to-analogue co'nverter is driven by the counter. The analogue signal, which is proportional to the torque on the mechanical model, actuates the vertical section of the x - y recorder directly.

coils as a complete revolution of the pendulum. Using the software to block further inputs to the microprocessor for a short period of time after every pendulum revolution, we were able to reject these false readings. In a typical experiment there can be many different combinations of kinks and antikinks on the transmission line at one time. This will require the duration of the experiment to vary greatly. In order to set the duration, the microprocessor reads a few DIP switches. To achieve a certain accuracy in every measurement, there is a minimum number of revolutions that the microprocessor must count before it timesout. This minimum number is also communicated to the microprocessor through DIP switches. After the set time, the microprocessor sends out the number of revolutions counted if no underflow or underflow occurs. A digital-to-analogue converter receives this information and activates the horizontal section of the x - y recorder. At the same time the microprocessor signals a relay to put the recorder pen up and down twice. After this point has been recorded the air velocity is increased manually and the entire process is repeated. This is done until enough data points have been obtained.

SOFTWARE The software developed for the microprocessor to perform the communication and computational functions in the experimental measurements is written in standard Intel 8085 assembly language and has been crossassembled on an HP1000. The object code generated by the assembler is programmed into ultraviolet-erasable 2716 PROM. A flowchart for the software is shown in Figure 10. On execution of the velocity measurement software, an initialization routine is entered which sets up the operating parameters and the initial value of the countdown timer. When this routine is finished the main section of the software begins. This section performs the following functions • •

it keeps counting the time if interrupt 7.5 of the 8085 is triggered, it jumps to the service interrupt routine • in the service interrupt routine it adds one to the number of revolutions counted and then waits for 40 ms so that oscillatory motions of the magnet following a kink do not trigger the processor again When the main section is completed and the time runs out, the final result is checked against the minimum number of counts set at the start of measurement. The possible occurrence of an overflow is also checked. If neither case arises, the number of revolutions is sent out and the recorder pen is pushed up and down twice.

VELOCITY MEASUREMENT

CONCLUSIONS

The support of an Intel 8085 microprocessor is required to measure the average velocity of one of the 30 discs in the mechanical model. It simply counts the number of revolutions over a specific period of time. Besides its computational support, the microprocessor is used to set up the parameters of each experiment and to verify the final result. Figure 9 shows the microprocessor-based circuit. A piece of permanent magnet is used as a weight on one of the pendulums. Then a pickup coil can detect the revolution of pendulum. The signal, after it has been shaped by a monostable multivibrator, interrupts the microprocessor to add one to the number of revolutions counted so far. After every revolution the pendulum oscillates several times before it stops. These oscillations may be sensed by the pickup

The microprocessor-based measurement of the t o r q u e velocity characteristic of a superconducting transmission line enabled us to start an investigation of the wave propagation on Josephson junction transmission lines more easily and efficiently. A few preliminary charts are given in Figure 11. The flexibility of the microprocessor-based system allows the effects of many variables on the mechanical model to be studied.

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REFERENCES 1 Parmentier, R D 5olutions in Action Lonngren, K E and Scott, A C (eds) Academic Press (1981)

2 Scott, A CAm. J. Phys. Vol 37 (1969) p 52

microprocessors and microsystems

3 Josephson, B D Phys. Lett. Vol 1 (1962) p 251 4 Cirillo, M, Parmentier, R D and Save, B Physica D Vol 3 /1981) p 565

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5 Radparvar, M and Nordman, J E IEEE Trans. Magn. Vol 19/1983) p 1017 6 Nakajima, K, Yamashita, T and Onodera, YJ. AppL Phys. Vol 45 (1974) p 3141

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