A CAPACITANCE-WIRE RECORDER FOR SMALL WAVES

For some years there has been an increasingly urgent requirement for a satisfactory device for the measurement of small waves such as those in harbour models and wave tanks. Many earlier instruments developed for this purpose used floats, but these suffer from certain practical disadvantages. In particular a large arm is necessary to transmit the motion of the float to the measuring device, which must be well clear of the water surface, and this arm introduces inertia and hence lag into the system. To reduce this lag the float has to be fairly large, and it cannot be regarded as measuring the wave height at a point on the surface. The device described below, in which the capacitance between an insulated copper wire and the surrounding water is measured (figure l), does effectively measure the height at a point on the surface and has given satisfactory results in several applications.

For some years there has been an increasingly urgent requirement for a satisfactory device for the measurement of small waves such as those in harbour models and wave tanks.
Many earlier instruments developed for this purpose used floats, but these suffer from certain practical disadvantages.
In particular a large arm is necessary to transmit the motion of the float to the measuring device, which must be well clear of the water surface, and this arm introduces inertia and hence lag into the system.To reduce this lag the float has to be fairly large, and it cannot be regarded as measuring the wave height at a point on the surface.The device described below, in which the capacitance between an insulated copper wire and the surrounding water is measured (figure l), does effectively measure the height at a point on the surface and has given satisfactory results in several applications.
Instruments working on this principle are used in many hydraulics laboratories, and a description of those used at the Laboratoire Dauphinois d'Hydraulique has been given by Boudan in "La Houille Blanche", Vol. 8, p. 526 (Aug.-Sept. 1953).
The National Institute of Oceanography demonstrated one of these wave recorders at the Conversazione of the Institution of Civil Engineers in June 1952, and it was briefly reported in the July 1952 issue of "The Dock and Harbour Authority".
The instrument described below appears to be simpler than others at present in use, and the authors feel that a description of it will be of general interest.

THE MEASURING HEAD
The measuring head consists of an insulated wire stretched vertically through the water surface between two supports.
In practice it is convenient, where it is permissible, to loop the wire round the bottom support and bring it back up to the top support, since this avoids the necessity of insulating the lower end (figure 2).
The wire we have mostly used up to the present time is 24 s.w.g.copper wire insulated with medium thickness 'Lewmex' enamel giving a capacitance of about 15 ppSS? per cm.
So far none of our measured curves of the capacitance of the measuring head against water height for a head made with this wire has deviated from the best straight line by more than 1$> of the maximum capacitance (a rapid calibration of a previously dry wire must be madesee below).
Some of the other types of wire we have tested have not been satisfactory in this respect.
If the wire is handled carefully during construction of the head, it is unusual for a test at 250V D.C. to reveal faulty insulation.
A major disadvantage of this type of insulation is

S -H
•H its property of slowly absorbing water and increasing its dielectric constant, causing an increase in the capacitance of the wire (figure 3)-The effect is serious for accurate work, but for many purposes can be overcome by keeping the wire out of the water except during the actual periods of measurement.
It is also advisable to calibrate the wire at regular intervals.
If the wire is left permanently in position, the sensitivity of the underwater part of the wire increases and a non-linear characteristic results.
Water absorption can be avoided by using wire insulated with polythene, whose water absorption is negligible, but the only suitable wire of this type which the authors have been able to obtain (20 s.w.g.copper with 0.024 in.radial thickness of polythene) has comparatively thick insulation and gives a capacitance of approximately 2/UuF per cm.
This, unfortunately, is too low for the authors' most important application, which is measuring waves on a reservoir where the measuring head has to be at the end of up to about 100 metres of coaxial cable with a total capacitance of about 0.01yuF.
However,' it is satisfactory for use with up to 10 metres of coaxial cable, which is adequate for most model work.
Surface tension produces a meniscus which rises about 0.5 mm up the Lewmex wire and about 1 mm up the polythene wire, but the static value of this height will be more or less constant when the wire is in use and the static errors introduced will not be large.
If the water level drops rapidly a thin film of water may be left round the wire, acting as a conducting sheath giving a spurious increase in capacitance.
This problem is not so serious as might at first appear, since we have found experimentally that it is not possible to wet the thin wires used for measuring small waves.
However, viscosity will prevent the water leaving the wire instantaneously as the level falls,, and the thicker wires which have to be used to measure large waves may be permanently wetted.Now most methods of measuring a capacitance use a sinusoidal oscillating voltage, and the effect of the water film round the wire can be minimised by choosing the correct frequency for this voltage.
If we consider the capacitor formed by an upper part of the film of water, the current through this capacitor has to pass through the lower part of the film before reaching the main body of the water.
The equivalent circuit is of the type shown in figure k-If the resistance is sufficiently high compared with the impedance (the A..C. equivalent of resistance) of the capacitor, this will be effectively isolated and will not be measured.The impedance of a capacitor decreases as the frequency increases, so that the resistances become comparatively larger and the effect of the film decreases.
The upper limit of frequency is reached when the effective resistance R of the main body of water which is in series with the capacitance C of the underwater part of the wire becomes appreciable.It can be shown that for the part of the wire below the surface 3/Z = 10" 12 pKf [log e (2S/D 2 )]/l.8log^D,/^) where Z = 1/aC is the impedance of the capacitance of the wire p is the restivity of the water K is the dielectric constant of the wire insulation f is the frequency D is the diameter of the conductor D is the overall diameter of the wire S is a distance which may be termed the effective distance, of the wire from the earth conductor.
If the wire continued to the bottom of the tank, assumed to be an insulator, and the earth electrode was a cylinder also extending from the surface to the bottom, S would be the radius of this cylinder.
Substituting values of K, D, and D_ corresponding to 24 s.w.g.The maximum permissible value of B/i depends to some extent on the type of measuring circuit used, but is probably of the order of 0.1, which would give a maximum frequency of about 1 Mc/s for the Lewmexcoated wire and about 20 Mc/s for the polythene-coated wire.
However, the value of p varies greatly and might in certain cases reach 10 times the value used above, so that a large factor of safety has to be allowed.
A further limitation to the maximum frequency is the length of the cable connecting the measuring head to the electronic circuit.
The electromagnetic wavelength in the cable corresponding to the frequency used must he long compared with the length of cable if resonance effects are to be avoided.
Even with the maximum length of cable specified below, which is only about 2/30 of a wavelength, an appreciable increase in sensitivity occurs and the head must be calibrated with its cable connected in circuit.
It is also desirable that the frequency used should not correspond with that of a widely used radio programme, though the amount of power radiated will be extremely small.
Taking these factors into account, a frequency of 60 kc/s was chosen for use with the Lewmex-insulated wires (maximum cable length 100 metres) and 600 kc/s for use with the polythene-insulated wires (maximum cable length 10 metres).

THE ELECTRONIC CIRCUITS
The two commonly used methods of detecting a small change in capacitance are to cause it to unbalance a bridge, or to cause it to change the frequency of an oscillator and then to detect this change in frequency.
Though at first sight the bridge method appears to be the more straightforward approach, in practice it involves considerable complication since it requires an oscillator, amplifier, phase-sensitive detector and output stage.
The second, or frequency-modulation method is simpler, requiring an oscillator, frequency-deviation detector and output stage.It is interesting to note that a bridge-type circuit developed by the David Taylor Model Basin (unpublished report) uses seven active valve elements, i.e., triodes or pentodes, up to the point corresponding to the grid of our output stage, whereas we have only one active valve up to this point.
Figure 5 shows a battery-operated circuit suitable for use with a Lewmex-insulated wire measuring head at the end of up to 100 metres of cable, and figure 6 shows a mains-operated circuit suitable for use with a polythene-insulated wire measuring head at the end of up to 10 metres off cable.
Both circuits are similar in principle.
The changes in capacitance of ibhe measuring head alter the resonant frequency of a valve-maintained inductance-capacitance tuned circuit.
A voltage from this circuit is fed to a frequency discriminator similar in principle to that used in most F.M. radio receivers, and this is followed by a simple D.C. amplifier output stage.
It is desirable to have an oscillator whose amplitude is as stable as possible against changes in the damping of the tuned circuit, since the frequency discriminator imposes a considerable load which varies with the frequency deviation, and the insulation resistance of the measuring head is not always very high.
A bridge-stabilized oscillator would be best in this respect, but has the disadvantage of being comparatively complicated and of consuming more H.T. and L.T. power than simple oscillators -an important point in the battery-operated circuit.
The best simple oscillator uses a triode maintaining valve with grid bias obtained by rectifying the oscillator voltage, and this also has the minor advantage that the amplitude of oscillation may be monitored simply by connecting a D.C. meter in series with the grid-leak resistor.The bias is obtained by grid rectification in the mains-operated circuit, but in the battery circuit a germanium diode is used since the grid of a 1S5> even when connected to the diode unit, will not rectify efficiently with the low-value grid-leak resistor made necessary by the meter.
The frequency discriminator works by first converting the frequency deviation into a phase shift.This is achieved by means of a series tuned circuit driven from a low impedance: the voltage across the inductance is 90° out of phase with the driving voltage at resonance, and this phase shift increases at lower frequencies and decreases at higher frequencies.
In figure 6 this circuit is formed by C8 and C9 and the primary of T3.
Owing to the effect of stray capacitances and inductances, the phase on the secondary of T3 at resonance is not quite the theoretical value, and has to be corrected empirically using RV2.
(in practice this resistance is adjusted till the overall calibration curve is symmetrical about zero output.) The voltages appearing on the secondary of T3 are shown' in figure 7« The voltage at G-1 is rectified positively, that at &3 is rectified negatively, and half the sum of the rectified voltages appears on the grid of the output stage.
It will be seen that a D.C. voltage is produced which is proportional over a limited range to the deviation of the oscillator frequency from the resonant frequency of the discriminator.
An interesting phenomenon occurs owing to the coupling of the two resonant circuits.
The impedance of a series resonant circuit is purely resistive at the resonant frequency, but above resonance it has an inductive component and below resonance a capacitative component.
Thus, if an increase in the capacitance of the measuring head lowers the oscillator frequency, the discriminator resonant circuit will effectively connect a further capacitor across the oscillator circuit, and will further lower the frequency.
If the coupling and Q of the discriminator circuit are high enough, this process can become unstable and the oscillator frequency will give a sudden large jump for a minute change in the capacitance of the measuring head.
Jbr this reason the coupling must be kept low.
In the battery circuit it is necessary to compensate for slow changes in the battery voltages, which would otherwise alter the sensitivity.
It is particularly important to keep the amplitude of oscillation constant, and this is achieved by varying the H.T. voltage using HV3 (figure 5).This adjustment will also greatly reduce variations in the gain of the output stage.
HT-^2.The full lines show the voltages at re-sonance} the broken lines show the voltages when there is a frequency deviation.
Pig. 8. Typical overall calibration curve using the circuit of Fig. 5 and a measuring head of 24 s.w.g."Lewmex H.F." insulated wire.The curve was obtained by keeping the wire immersed for some days and then reducing the water level in stages.The output was measured with a 500-ohm meter connected directly between the output anodes.
An attempt was made to replace the thermionic diodes in the battery circuit by germanium-crystal diodes, but these were found to be extremely noisy.
Very small selenium rectifiers were then tried, which reduced the noise by a factor of about 10 but introduced a large amount of drift.
Copper oxide rectifiers have too large a capacitance to be used at these frequencies, and silicon diodes have a ratio of backwards to forwards resistance which is too low to give efficient and stable rectification.
In an instrument built to the circuit of figure 5> the drift in output zero corresponded to a change in the capacitance of the measuring head of about 15/UuF during the first 10 minutes after switching on, and subsequent drift over a period of two hours was equivalent to less than

METHODS OF KEC0EDIN&
The frequency of the waves which these instruments will be used to measure is usually too high for the ordinary graphic pen recorders.We normally use fast mirror galvanometers recording on photographic paper, and our circuits are designed to drive such a system.Some users may prefer a fast pen recorder, of which there are several types now on the market, and these are usually provided with a special driving amplifier which may be coupled directly to the output of the frequency discriminator.

ACCURACY.
The main limitation to the accuracy of the instrument is probably the lag caused by viscosity.
If the water level is raised and lowered rapidly the shape of the meniscus can be seen to change, but the authors have been able to think of no satisfactory way of measuring the effect on the capacitance of the measuring head.
In practice, it will probably result mainly in a time lag and is unlikely to produce an error in amplitude of more than about 2 mm.The rapid fluctuations in the output produced by the circuit itself have an r.m.s.amplitude corresponding to a change in capacitance of about 0.5/uuF in the circuit shown in figure 5> and corresponding to a change in capacitance of about 0.01 AW.F in the circuit of figure 6 (recorded with a 7-c/s galvanometer critically damped).
The slow drift may be a nuisance, but will not produce errors in the measurement of wave height.
The non-linearity of the calibration curve (figure 8) may be allowed for, if necessary, when measuring the records.II convient pour la mesure d'ondes dans les modeles de ports et dans les reservoirs a. houle et a ete utilise pour mesurer des ondes depuis quelques mm a 50 cm de crete a creux.

Fig. 1 .
Fig. 1.The principle of operation of the instrument.