Here we will be modeling the amplitude ultrasound scan or A-scan used in ophthalmology. It is the simplest type of scanning, relying on a one-dimensional pulse-echo technique similar to that used in the echo location (sonar) of fish.
While this analogy with ultrasound A-scanning is good, you will need to emphasise that the two coaxial cables of differing electrical impedance are representing two different materials in the eye of differing acoustic impedance. By knowing the speed of the pulses and where reflections occur, they can then calculate the lengths of the cables in a similar way to which distances to parts of the eye would be determined. With ultrasound there are far fewer multiple reflections of note, although false echoes can occur between tissue and bone, tissue and air, and tissue and the transducer. In most cases there would also be appreciable scattering and so the amplitude of any multiple reflections would prove tiny. With the electrical pulses the students should be able to see the multiple reflections as there is less scattering and attenuation.
If students are shown the original output pulse they will then note that, on reflection at the cable junctions, there is a phase change with the pulse being inverted. This is of no consequence with the ultrasound scan as it is just the amplitude of the reflected pulse that is important.
As students will have met propagation of light by internal reflection down optical fibers, it may be wise to comment that the electrical pulses effectively travel in a straight line down the cables as if they were laid out straight, there is no ‘bouncing’ off of the walls of the cables. They may well be surprised at the speeds of pulses in such cables being a substantial fraction of the speed of light.
The activity, whilst modeling the ultrasound A-scan, is a useful one for seeing how to obtain times from an oscilloscope screen and, in general, how to set up and use an oscilloscope. Whilst the activity could be conducted on a traditional oscilloscope (ideally of the storage type) it is certainly easy to do with aPicoScope 2202. If you have the older ADC-200 version then the same activity can be conducted with it too, as indeed it could with aPicoScope 3000 Series device. Obviously it does need an oscilloscope with a fast timebase.
The speeds of the pulses down coaxial cables tends to be around 2 x 108m/s. The two I used gave speeds of 1.95 x 108m/s and 1.99 x 108m/s which are rather close to each other. As the real speeds are not important I have suggested stating a speed of 1.90 x 108m/s for one cable and 2.10 x 108m/s for the other. The lengths they calculate will then not actually be the real ones, but there again I suspect no one is going to wish to unwind them and wind them back on the reels again, so that does not matter.
Output pulse: 708 ns.
First main reflection: 1681 ns.
Second main reflection: 3736 ns.
Time for pulse to travel to end of cable A and back: (1681 - 708) ns = 973 ns.
Speed of pulse down cable A is 2.10 x 108ms-1.
So length of cable A is given by:
Speed of pulse x ½ x time for pulse to travel = (2.10 x 108) x 0.5 x (973 x 10-9) = 102 m
Time for pulse to travel through cable A to the end of cable B and back: (3736 - 708) ns = 3028 ns. However, 973 ns is the time that this pulse was traveling through cable A, so the time in cable B must be (3028 - 973) ns = 2055 ns. Speed of pulse down cable B is 1.90 x 108m·s–1. So length of cable B is given by:
Speed of pulse x ½ x time for pulse to travel = (1.90 x 108) x 0.5 x (2055 x 10–9) = 195 m
Answers to questions
Q1Using the expression Ir/Ii= (Z2- Z1)2/(Z2+ Z1)2and substituting forZ1= 1.38 x 106kg m-2s-1andZ2= 6.5 x 106 kg m-2s-1we then have:
Ir/Ii= (6.5 x 106– 1.38 x 106)2/(6.5 x 106+ 1.38 x 106)2 = 0.42 (42%)
Q2Answers will depend on the results the students got but, assuming the cables are very similar to those I recommended cable A should be near 100 m in length and cable B near 200 m in length.
Figure 1: set up of PicoScope 2202, pulse generator, coaxial cables and computer
- PicoScope 2202 PC Oscilloscope#1
- USB cable (supplied with the PicoScope 2202)
- PicoScope software (supplied with the PicoScope 2202)
- Computer, monitor, keyboard, mouse, etc
- 2 x cable BNC plug to BNC plug 16-0330 (Rapid)#2
- 100 m 50Ω impedance RG58C/U coaxial cable 02-0220 (Rapid)
- 200 m 75Ω impedance RG59B/U coaxial cable CAB59 20 (Connectorco)
- 5 x standard coaxial plugs 16-0400 (Rapid)
- 2 x coaxial coupler 16-0417 (Rapid)
- Pulse generator (see construction details)
#1 Alternatively a Pico ADC-200 and parallel port cable can be used.
#2 Change one of these cables to BNC plug to coaxial plug.
Components required for pulse generator
- Stripboard 0.1" matrix with copper one side only 34-0505 (Rapid)
- 2 x 1.2 kΩ 0.6 W resistor 62-7734 (Rapid)
- 4.7 kΩ 0.6 W resistor 62-7764 (Rapid)
- 47 kΩ 0.6 W resistor 62-7812 (Rapid)
- 2 x 220 pF capacitor 08-0525 (Rapid)
- 2 x 2N3904 transistor 81-0484 (Rapid)
- 2 x 1N4001 diode 47-3130 (Rapid)
- 2 x BNC bulkhead mount socket 16-0110 (Rapid)
- Switch SPST subminiature toggle 75-0100 (Rapid)
- Battery clip for PP3 battery 18-0093 (Rapid)
- Diecast aluminium box 30-1532 (Rapid)
- Reel orange connecting wire 01-0325 (Rapid)
- Reel black connecting wire 01-0305 (Rapid)
- Reel red connecting wire 01-0335 (Rapid)
- Alkaline PP3 battery 18-4230 (Rapid)
- Access to soldering iron, drills, pliers, saw and file
Terminate each end of the coaxial cables with coaxial plugs. Label the 100 m cable A with a speed of 2.10 x 108m·s-1and the 200 m cable B with a speed of1.90 x 108m·s-1.
Remove one of the BNC plugs from the end of just one of the BNC plug to BNC plug cables and replace it with a standard coaxial plug.
Figure 2: matrix board layout and associated circuit diagram
Saw a piece of stripboard 12 strips x 17 holes as shown on the matrix board layout in Figure 2. Make the cuts in the board as indicated and then mount the components as shown together with the various connecting wires and the black lead of the 9 V battery connector. Note carefully which way round the diodes and transistors need to be mounted. Most faults in circuits occur when tiny solder links cross between the rows of copper, so check with a magnifying glass that such links have not been produced.
Stick a few strips of pvc insulating tape to the base of the diecast box where the stripboard is to be placed. This will prevent any shorting of the stripboard components by the aluminium of the box. Mount the BNC sockets and switch on the diecast box as shown in Figure 3, place the matrix board inside the box and link the orange connecting wires to the BNC sockets, the red connecting wire to the switch, and the red lead of the 9 V battery connector also to the switch. Label the top of the diecast box as shown in Figure 4.
Testing the pulse generator
Connect the pulse generator’s BNC socket labelledPicoto Channel A of the PicoScope 2202 or ADC-200. Connect a USB lead from PicoScope 2202 to a USB socket on the computer. (If you are uisng an ADC-200: connect the parallel port lead from the ADC-200 socket to the parallel port socket on the computer. Plug in the ADC200’s power supply.)
SwitchONthe computer and load the PicoScope software. Enlarge, if necessary, to provide a full screen display as shown in Figure 5 below with the program already running.
Figure 5: PicoScope initial screen display
Click the redSTOPbutton in the bottom left-hand corner of the screen. Adjust theTimebasesetting to 5 µs/div; theX-gainto x1;Channel Ato ±1 V, AC andY-gainof x1. LeaveChannel Boff. Now set theTriggerto Single, (channel) A, Rising and 5 mV, and thePre-triggerscreen display to -5%. The last of these lets you set when the trace is started from, in this case the first 5% of the display is prior to the pulse triggering.
SwitchONthe pulse generator and click the greenGObutton in the bottom left-hand corner of the screen. Figure 6 shows a typical output trace.
Figure 6: typical output trace from pulse generator
Now close down the Oscilloscope screen. Click on theFrequency metericon and select ch A, Frequency, Auto and AC in the Toolbar, and reset the Trigger to Auto but leave all the other settings as they were. Click on the greenGObutton You should get the screen displayed as in Figure 7 with the frequency of the pulses showing near 140 kHz. My pulse generator showed 137.4 kHz which is good enough.
Figure 7: frequency meter display
To finish with the program click onFilein the Menu bar and thenExitin its drop-down menu. Do not forget to switchOFFthe pulse generator if it is finished with at this stage and disconnect the cables.
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