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4. Detailed Circuit Description | 6. Conclusion | |
5.1 Static Testing: longitudinal.
5.2 Static testing: Transverse.
5.3 Dynamic Testing.
5.4 AGC circuit response.
The testing of this device was carried out in two phases: static testing, to monitor the output of the position sensing detectors in order to check that the output is linearly dependent on position; and dynamic testing, to make sure that the circuit can respond fast enough and accurately enough to the changes at its inputs. Recall that in this application, the muscle sarcomere length will be changing on a time scale of 10 mS or less. In addition, the AGC circuit's response was determined.
A laser and diffraction grating were used to obtain two beams, which were directed onto the detectors, mounted perpendicularly to the optical axis as in figure 11. The detectors were placed on a piece of veroboard, and held in an adjustable clamp. The position of the detector board could be adjusted accurately using a knob on the clamp; 20 turns of the knob corresponded to about 40mm of linear movement. The voltage output of the device was monitored with a digital voltmeter, while the detector board was moved longitudinally along the optical axis, in half-turn steps (corresponding to approximately 1 mm movements) This caused the two diffracted beams to move apart on the detectors. In the real experiment, the varying separation of the beams would indicate the changing sarcomere length. Simulating the sarcomere movements in this way is a good test of the linearity of the circuit and
detectors. The voltage at each point was recorded, and the entire set of results repeated five times. Statistical calculations were performed on the five voltage readings at each point, to determine mean and standard deviation. The results are shown plotted against distance (turns of the clamp knob) in figure 13. The exact units of distance are unimportant here.
Notice that the graph tails off at either end: this is where the diffracted laser beams fall off the edge of the detectors.
The graph shows excellent linearity: it is almost an exact straight line. Note that in this testing, no special precautions were taken to shield the detector from ambient light, although fluorescent lighting in the laboratory was found to cause a large 100 Hz disturbance at the output, and so the measurements were conducted in daylight, with artificial lighting switched off. In a darkened laboratory, or with elaborate detector shielding, the already excellent output can only improve further.
Recall that as discussed previously, the output must be unaffected by both diffracted beams shifting simultaneously, that is, the light spots on the detectors move relative to the detectors, but
not relative to each other. This condition may be simulated by keeping the detector board at a fixed distance from the diffraction grating, but moving it transverse to the optical axis, see fig 11.
Once again five sets of results were recorded across the full area of the detectors, and subjected to statistical analysis to determine the standard deviation and mean. The graph in fig 14 is a plot of the output voltage against transverse distance moved, again in arbitrary distance units, 1 turn corresponding to a movement of about 2 mm.
For relative comparison with the longitudinal graph (fig 13) this graph is plotted using the same vertical scale. The output is nearly zero, indicating again excellent linearity of the
detectors, not only individually, but also comparative to each other. If the output of the detectors was slightly different at a given beam position on their surface, this difference would be noticeable on this transverse graph. The graph in fig 15 shows the same results, but on a larger scale for closer inspection.
Notice that at the ends, the output suddenly increases: this is due to non-linearity at the very edges of the detectors, and is of no concern.
Even in these uncontrolled lighting conditions, the magnitude of the output for transverse movements across the whole central portion of the detector is less than 0.5% of the magnitude of the voltage change for the longitudinal direction. This is excellent; with improved light shielding etc, this could even improve further.
In order to test the reaction times of the circuit, it is necessary to cause the beam positions to vary quickly across the detector surface. It would be difficult to rapidly change the spacing or position of the diffraction grating, or to insert some optical shifting mechanism in the light path to move the diffracted beams; therefore I decided to attempt to rapidly move the detectors. The easiest way of doing this is to mount the detector board onto the cone of a loudspeaker, then connect this to a signal generator in order to vibrate the cone back and forth.
The apparatus was set up as in figure 12; the loudspeaker was mounted perpendicular to the optical axis, so that the vibrations of its cone would cause the detectors to be moved rapidly in the longitudinal direction. This simulates rapid movements of the muscle sarcomere. The detector was taped securely onto the cone of a 10 inch loudspeaker, connected to a signal generator at maximum output setting. The connections to the detectors were made with very thin enamelled wire, so that they would impede the
movement as little as possible. The frequency was varied across a wide range, to test the response of the circuit.
Quantitative measurements of this kind of testing are difficult to make: there is no alternative way of measuring the displacement of the loudspeaker cone, hence nothing to compare the circuit's output against. However, good qualitative observations were made.
The movement of the loudspeaker cone was tiny: at the most, that is, at the loudspeaker's resonance frequency (~35-45 Hz), the movement of the cone was less than 2mm, and quickly became very small for frequencies over 100 Hz. Despite this the output from the circuit, viewed on an oscilloscope along with the signal generator output (sine wave), remained strong, easily distinguishable from background noise, for frequencies in excess of 2 KHz. This corresponds to a period of only 0.5 mS, far shorter than the response time required in order to be able to react quickly to the changes in sarcomere length.
In order to further check the response of the circuit, one of the inputs was connected to the signal generator instead of the detector, and the other inputs grounded. The output of the device accurately resembled the input at frequencies well above 5 KHz; at frequencies higher than this the signal began to be attenuated. This is due to the finite bandwidth of the 741 and LM13700 op-amps.
So that the reaction time of the AGC circuit could be checked, the sum input to one AGC circuit was temporarily disconnected and replaced by a connection to the signal generator, with its output
set for a fairly low amplitude. The preset was adjusted to give a constant voltage at the output (pin 5) of the LM13700a, as required. (Refer to main circuit, diagram 1). This indicated that the oscillations were being treated as intensity variations and compensated for; as further confirmation, the gain input (pin 1) and also the output of the second transconductance op-amp LM13700b showed sine wave oscillations 180 degrees out of phase to the simulated 'sum' input, as expected. The AGC circuits continued to compensate for the perceived variations in intensity, for frequencies exceeding 5 KHz; at these frequencies the gain of the op-amps has started to decrease anyway, due to their bandwidth (as found in section 4.3)
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4. Detailed Circuit Description | 6. Conclusion | |