Patent Description:
Ozone may be generated in many ways, one of which is by the ionization of oxygen using electrical discharge to create a plasma. Ozone when generated by electrical discharge has a concentration that depends on many factors, including but not exclusively, the composition of the feed gas, the flow rate of feed gas, the temperature of ozone generation cell, the dimensions and materials of the cell, and the electrical power used to generate the plasma. The plurality of factors affecting ozone production makes it very difficult to predict ozone production with any precision. If control or knowledge of ozone production is desired, it is necessary or desirable to monitor ozone production. An analyzer on site is required for this purpose.

There are several different techniques available to an analyzer for measuring the concentration of ozone in a gas. These include using the absorption of UV light in the gas, such as found in the products from Oxidation Technologies, LLC of Inwood, Iowa and Teledyne API of San Diego, California. This technique is effective but production costs are high. Furthermore, no information on the composition of the feed gas to the ozone-generating cell is obtained. Knowledge of the feed gas composition, which may consist of dry air with an increased concentration of oxygen, is desirable. Electrical discharge ozone generators operate more efficiently with a high proportion of oxygen. Therefore, oxygen concentrators are sometimes used to increase oxygen from <NUM>% (ambient air) to values above <NUM>%. For an electrical discharge ozone generator, the presence of small amounts of nitrogen in the feed gas appears to enhance efficiency significantly. But it is possible to remove too much nitrogen from the feed gas such that efficiency of the cell is reduced. In such oxygen-concentrated air, the principal components are nitrogen, oxygen, and a small amount of argon. By complementation, the concentration of nitrogen can be estimated from the concentration of oxygen.

Use of the speed of sound to estimate the concentration of ozone in a gas is described in <CIT>). With the temperature of the feed gas, the speed of sound of the feed gas, the temperature of the gas as it emerges from an ozone generator, and the speed of sound of the gas as it emerges from the ozone generator measured or known, the speed of a sound pulse in the gas is determined by measuring delay over a known path length. The four measured or known variables are used to estimate the concentration of ozone. However, with a resonant transducer a pulse necessarily consists of multiple cycles which make the precise determination of the arrival of a pulse of sound difficult; it is difficult to ascertain when a pulse begins and when it ends. A further disadvantage is that the described system is complex. The sound pulses require relatively long measurement paths and hence conduits with relatively high volume which increases the required sample gas volumes. A scavenging pump, which is costly, is used to move either the feed gas to the ozone generation cell or the output gas from the cell. This complicates the measurement system. The pump must be made of materials that do not deteriorate over time in the presence of high concentrations of corrosive ozone.

The speed of sound in a continuous sonic wave is used to help determine the concentrations of two gases, neither of them ozone. <CIT> and <CIT> by the present inventor describe a system in which that technique is combined with another. Two distinct and unrelated physical parameters, paramagnetism and the speed of sound, are measured to determine the concentration of both oxygen and carbon dioxide in respiratory gas. In this case, the use of sound alone cannot determine the concentration of either gas.

Hence there is a need for a low cost analyzer with the capability to measure both the concentration of oxygen in feed gas to an ozone generating cell and the concentration of ozone in the cell output. Such an instrument may be used for the assessment of generated ozone and for process control. For example, oxygen concentration may be adjusted, based upon instrument output, so as to maintain a desired concentration of ozone, and cell power may be controlled, based instrument output to maintain a desired concentration of ozone. A single low-cost analyzer to handle both of these functions would be both convenient and economical. It is an object of the present invention to perform both functions in a single, reliable, low-cost instrument. <CIT>, <CIT>, <CIT>, <CIT>, <CIT> are useful for understanding the invention.

The present invention provides for an analyzer for one or more gases derived from a first gas of known composition and speed of sound, each derived gas having a concentration of a component changed. The analyzer has: a first transducer which drives continuous sound waves responsive to a fixed frequency signal source; a conduit acoustically connected to the first transducer and selectively receiving and holding samples of the first gas and one or more derived gases; a second transducer acoustically connected to the conduit opposite the first transducer unit, the second transducer which receives sound waves from the first transducer through the conduit and generates second transducer signals responsive to the received sound waves; a processing unit which receives the fixed frequency signal source signals and the second transducer signals, and which determines a relative phase shift between the frequency source signals and second transducer signals for a gas sample in the conduit, the relative phase shift corresponding to a difference of speed of sound in one gas sample relative to another gas sample, the processing unit including circuitry lowering the frequency of the received fixed frequency source signals and second transducer signals to expand the range of measurement of the relative phase shift; and a calculating unit which determines from the first gas of known composition the speed of sound of the one or more gases derived from the first gas, and which calculates the composition of a sample of one or more derived gases from the first gas as a reference.

There is also provided a method (not part of the present invention) of operating an analyzer for one or more gases derived from a first gas of known composition and speed of sound, each derived gas having a concentration of a component changed. The method has the steps of: driving continuous sound waves with a first transducer in response to fixed frequency electrical signals through a conduit holding a sample of the first gas or one or more derived gases at a time; receiving the sound waves driven through the conduit by a second transducer and generating electrical signals in response to the received sound waves, a relative phase shift between the received sound wave signals and the driven sound wave signals corresponding to a relative speed of sound in the gas samples; processing the fixed frequency electrical signals and the electrical signals generated signals in response to the received sound waves at a lowered frequency to expand the range of measurement of the relative phase shift; determining the speed of sound of the first gas of known composition and one or more gases derived from the first gas in the expanded range from the relative phase shift of gas samples of the first gas ofknown composition and one or more gases derived from the first gas in the conduit; and calculating a composition of a sample of one or more gases derived from the first gas as a reference.

There is provided a method (not part of the present invention) of determining the composition of one or more gases derived from a first gas of known composition and speed of sound. The method has the steps of: driving continuous sonic waves through a conduit at a fixed frequency, a phase difference between sonic waves entering the conduit and leaving the conduit corresponding to a speed of sound of a gas in the conduit; processing electronic signals corresponding to the continuous sonic waves entering the conduit and leaving the conduit at a lowered frequency to expand the range of measurement of the phase shift; changing the gas in the conduit among the first gas and the one or more derived gases; determining the speed of sound of the first gas of known composition and the one or more gases derived from the first gas in the expanded range from a relative phase shift of gases of the first gas ofknown composition and the one or more derived gases, the relative phase shift corresponding to a difference of speed of sound in one gas sample relative to another gas sample; and calculating a composition of the one or more derived gases from the first gas as a reference.

Other objects, features, and advantages of the present invention will become apparent upon consideration of the following detailed description and the accompanying drawings, in which like reference designations represent like features throughout the figures.

As described below, the present invention provides for the measurement of ozone concentration with high resolution and precision. The ozone concentration is measured relatively independently of the oxygen concentration in the feed gas and independently of temperature. The construction of the analyzer is also simple and low-cost.

<FIG> shows a generalized view of a portion of an ozone generation system with a continuous sonic wave analyzer unit according to one embodiment of the present invention. It should be noted that drawing is representational and the elements of the drawing are not drawn to scale. The system has an ozone generation block <NUM> and a continuous sonic wave analyzer unit <NUM> which is formed by a transducer/valve block <NUM> and controller/analysis block <NUM>. The ozone generation block <NUM> receives compressed air from a source (not shown) and delivers generated gas including ozone to a process, i.e., the particular application of the ozone. The compressed air (gas flow is shown by the broadened arrows in the drawing) is received by a concentrator <NUM> which increases the percentage of oxygen in the resulting gas. The gas from the concentrator <NUM>, which may be a swing pressure absorption device, is passed to an ozone generator <NUM>, typically an electrical discharge cell. The gas output from the ozone generator <NUM> is sent to an inlet pressure regulator <NUM> which controls the pressure of the gas and ozone sent to the process, the application using the generated ozone.

The analyzer unit <NUM> determines the relative speeds of sound of gas at different locations of the ozone generation block <NUM> and comprises a transducer/valve block <NUM> and a controller/analysis block <NUM>. The transducer/valve block <NUM> processes samples of gas from the different locations and the controller/analysis block <NUM> controls the operations of the transducer/valve block <NUM> and analyzes the output from the transducer/valve block <NUM>. The transducer/valve block <NUM> has a first input valve <NUM> which receives the compressed air from the source to the concentrator <NUM>; a second input valve <NUM> which receives the output gas from the concentrator <NUM> to the ozone generator <NUM>; and a third input valve <NUM> which receives the output gas from the ozone generator <NUM> to the inlet pressure regulator <NUM>. The outputs of the valves <NUM>-<NUM> are connected to a first transducer unit <NUM> which has its output connected to a gas conduit <NUM> which in turn is connected to a second transducer unit <NUM>. The transducer unit <NUM> transmits sound in a continuous wave through the conduit <NUM> to the receiving transducer unit <NUM> to determine the relative speed of sound through the gas in the conduit <NUM> (and transmitting transducer units <NUM> and receiving transducer unit <NUM>). The gas output of the receiving transducer unit <NUM> is connected to a destruct unit <NUM> which eliminates the ozone in the sampled gas before releasing the gas into the ambient air.

In general, a reference phase reading is taken for a first gas of known composition (usually ambient air) and then unknown second and third gases are introduced, producing corresponding changes of phase shift, and from these changes of phase shift and the known speed of sound of the first gas, the speed of sound of the second and third gases are computed.

Ozone is highly corrosive and care is taken in the selection of the components in contact with ozone. The transducer units <NUM> and <NUM> are formed from aluminum which forms a tough coating of aluminum oxide and the conduit <NUM> is formed from polytetrafluoroethylene (PTFE) tubing which resists ozone. The conduit <NUM> is also temperature-controlled to maintain the temperature of the gas in the conduit at a desired temperature and has a relatively large thermal mass to stabilize the conduit temperature. The length L of conduit <NUM> is preferably long enough to give good sensitivity to the device and to prevent artifacts due to standing waves, yet short enough to be low in volume, convenient to fabricate, and unambiguous with respect to measuring phase shift. From the point of view of sensitivity and standing waves, a preferable pathlength L may be about <NUM> wavelengths, although other pathlengths may be used. But a pathlength of <NUM> wavelengths may result in ambiguous readings due to excessive change of phase shift as speed of sound varies with changing gas composition. For example, phase shift due to replacing air with oxygen would be about <NUM> wavelengths. Phase shift due to replacing air with a mixture of ozone and oxygen may be as much as two wavelengths. A method to mitigate this problem using frequency division is a feature of the invention and is described below. The method allows choice of pathlength based on a desired compromise of the mentioned factors without concern for ambiguous results from a phase detector.

The controller block <NUM> of the analyzer unit <NUM> has an oscillator unit <NUM> which drives the first transducer unit <NUM> in the transducer/valve block <NUM>. A first counter <NUM> receives a control signal from the control unit <NUM> and a driving signal from the oscillator <NUM>. An amplifier <NUM> in the controller block <NUM> receives the electrical output of the second transducer unit <NUM>. The output of the amplifier <NUM> is received by a comparator <NUM> which shapes the amplified signals to square waves. The comparator output is sent to a second counter <NUM> which counter <NUM> also receives a control signal from the control unit <NUM>. The outputs of both counters <NUM> and <NUM> are sent to a phase detector <NUM> and the phase detector output is passed through a low-pass filter <NUM> to the control unit <NUM>.

The present invention uses the speed of sound in a gas to determine the concentration of ozone in the gas. Sound in ozone is considerably slower than sound in oxygen due to higher molecular weight of ozone relative to oxygen. Likewise, sound in oxygen is slower than sound in air, due to higher average molecular weight of oxygen relative to air. For a gas which has only two components and if the speed of sound of each component is distinct from the other, the measured speed of sound though the gas is characterized by the proportions of the two components. This is true even if the components themselves comprise mixtures of more than one gas. Discussion of this may be found in the previously cited <CIT>and <CIT>.

The speed of sound in a gas is found by the known characteristics of the first gas introduced, and the corresponding change in phase shift which the continuous sonic wave originating from the source transducer undergoes as the wave travels to the receiving transducer with subsequent gases. <FIG> shows the sonic wave train from the transmitting transducer <NUM> as a series of square waves indicating the digital nature of the signals and the circuitry processing the signals. Analog signals and circuitry may also be used. The rising edges of the waves shown as solid vertical bars to serve as reference points to aid the reader's understanding. Likewise, another series of square waves received by the second transducer <NUM> is illustrated with solid bar rising edge of each sonic waves received by the second transducer <NUM>. An arrow indicates the phase shift reflecting the time interval for a particular wave front to travel from the source transducer <NUM> to the receiving transducer <NUM>. It should be evident that the longer the time interval, or the slower the speed of the sonic waves through the gas medium, the greater the phase shift.

The phase shift should be kept within a restricted range due to the nature of the continuous wave to determine the amount of shift with certainty. For example, it is difficult to determine whether a phase shift is x or x + i*<NUM>°, where i is an integer. So in this example only phase shifts of less than <NUM>° should be undertaken. But this severely limits the range of speeds which can be determined. It should be noted that limited phase range is also dependent upon the circuits used to determine the phase shift which may limit the phase shift even more, such as from <NUM>° to <NUM>°. In any case, the present invention expands the range of speeds which can be determined as explained below.

While the source transducer is driven at a fixed frequency, the frequency of the source signals is lowered for processing. <FIG> represents an exemplary lowering of frequency of <NUM>% or stated differently, dividing the frequency by <NUM>, by the elimination of <NUM> out of <NUM> vertical bars. Elimination is indicated by the replacement of a solid bar (representing a rising edge) with a barred bar. With the lowering of the frequency, the phase shift range (and hence the sound speed range) which can be determined is accordingly expanded. That is, assuming a phase limitation of <NUM>-<NUM>°, the frequency lowering by <NUM> allows the phase shift range to be expanded by <NUM> so that the range is expanded to <NUM>-<NUM>°. Frequency reduction proportionately increases the range of phase shift measurement and allows high precision measurement without the shortcomings of a short path length conduit. A short path length may typically introduce signal artifact due to standing waves or residues of standing waves in the conduit. Frequency reduction avoids these problems.

A simple representation of the electronic circuitry in <FIG> demonstrates the measurement of phase shifts as previously described. Two square wave data streams, A representing the signals for the transmitting transducer (<NUM> in <FIG>) and B representing the signals for the receiving transducer (<NUM> in <FIG>), are input to an Exclusive-OR logic gate (part of the circuitry of phase detector <NUM>). The output C of the gate is input to a low-pass filter (<NUM> in <FIG>) which has an output D. <FIG> shows the relationship of the A and B signals, and the output C signal of the Exclusive-OR gate. Besides an Exclusive-OR gate, an Exclusive-NOR gate may also used for the phase detector <NUM>.

<FIG> also shows the output D signal of the low-pass filter <NUM> by which the mostly varying signal of the Exclusive-OR gate is filtered to reflect the "average" value of the output signal. For example, if the A and B signals are completely out of phase with each other (i.e., a phase difference of <NUM>°), then the filtered phase difference, or phase shift, signal, the output D, is a maximum; if the A and B signals are completely in phase with each other (i.e., a phase difference of <NUM>°), then the output D is a minimum, i.e., zero. If the A and B signals are "half" out of phase, or half in phase, i.e., the phase difference is <NUM> °, and the output D is halfway between the maximum and the minimum, i.e., one-half the maximum. <FIG> illustrates how this phase detector value, the output D, varies with the phase difference between signals A and B. Here the phase differences are shown as values less than -<NUM>° to greater than <NUM>°. The minus and positive values indicate whether the A, or the B, signals leads the B, or the A, signals. As described above, the A signals lag the B signals. <FIG> further graphically shows why the phase shift should be within a restricted range. In this illustration the phase shift should be restricted to a range of <NUM>° to avoid ambiguity in determining the phase shift from an output D value.

When the frequency of A and B signals is lowered, the output D of the low-pass filter <NUM> is changed. In the example of <FIG> counters (<NUM> and <NUM> in <FIG>) are inserted into the data streams of the A and B digital signals to lower the frequency by a divisor of <NUM> (N=<NUM> for the counters). The divisor N is arbitrary and chosen to suit the convenience of the designer. The output D is correspondingly spread. Instead of a cycle of <NUM>° (as shown in <FIG>), the output D cycle is <NUM> times larger, <NUM>°, i.e., the output D signal repeats every <NUM>°. In this example, the phase shift is expanded to a range of <NUM>°, one-half of <NUM>°. This is a far larger range than <NUM>° restriction without the frequency-lowered signals.

Thus an expanded range for the filtered phase shift signal, the output D, is easily implemented by digital counters, e.g., counters <NUM> and <NUM> in <FIG>. Using the example above where N = <NUM>, the counter for the A signal data stream is set to zero and then started. When the A counter reaches a particular value, say <NUM>, then the counter for the B signal data stream is set to zero and started. This assures a non-negative starting value for the phase detector where N = <NUM>. The output D is thus between zero and <NUM> (assuming the maximum output D is <NUM>). The amount <NUM> is <NUM>/<NUM>. If the phase difference between the A and B signals, due to a different gas sample in the conduit <NUM> (see <FIG>), now increases, the output D also increases linearly over a range of <NUM>° (<NUM>° * (<NUM>- (<NUM>/<NUM>)) up to the maximum value. Again it should be noted that the counter divisor N and corresponding expansion of the phase shift measurement is arbitrary.

The two frequency-lowering counters <NUM> and <NUM> introduce phase uncertainty. In the above case of divide-by-<NUM>, there are <NUM> possible phase relationships depending on the counting relationship of the two counters. If the first counter <NUM> has count N, then the second counter <NUM> may have any of (N + n) mod <NUM> values, where n equal any integer in the range <NUM> to <NUM>. If every waveform is properly counted, that relationship is maintained indefinitely. Control of the number n provides the opportunity to adjust the baseline with a resolution of <NUM>/<NUM> of full scale. In example immediately above, the receiving transducer signal initially starts in the "<NUM>nd" relationship with the transmitting transducer signal, (N + n) mod <NUM> = <NUM>. By controlling n so that (N + n) mod <NUM> = <NUM>, the baseline is adjusted so the phase measurement range is expanded to its maximum extent and the determination of gas composition is maximized, and is a feature of the present invention.

For the phase shift detection described above, the electronic circuitry of the controller block <NUM> of the analyzer unit <NUM> is implemented by digital circuits, according to an embodiment of the present invention. The oscillator block <NUM> generates signals at a fixed frequency. In this embodiment the frequency is <NUM>. The oscillator block signal drives the transmitting transducer <NUM> and is divided in frequency by <NUM>, or stated differently, the counter <NUM> steps down, or lowers, the signal frequency by a factor of <NUM>. The output of the counter <NUM> is received by the phase detector block <NUM>.

The output of the receiving transducer <NUM> is processed into square waves by comparative logic (block <NUM>) after being amplified by the amplifier <NUM>. The counter <NUM> divides the signal frequency by <NUM>. The output of the counter <NUM> is also received by the phase detector block <NUM>. Through the operation of an Exclusive-OR or an Exclusive-NOR gate, the phase detector <NUM> output varies between the two power levels of the logic gate, say, <NUM> and <NUM> volts, for example. The low-pass filter <NUM> eliminates the AC component of the output signal.

Control of the continuous sonic wave analyzer unit <NUM> is performed by the control unit <NUM> in the controller/analysis block <NUM>. In this embodiment the control unit <NUM> is basically a programmed microprocessor or microcontroller with memory. Among other contents, the memory stores values from the filtered phase detector <NUM>. Control lines from the unit <NUM> extend to each of the valves <NUM>-<NUM> and the counters <NUM> and <NUM>. The unit <NUM> also receives phase shift values from the output of the low-pass filter <NUM>. A display <NUM> is connected to the control unit <NUM> provides a visual interface for the operations of the analyzer unit <NUM>.

Under the control unit <NUM>, the analyzer unit <NUM> with an expanded phase shift range determines the speed of sound in multiple gases and the composition of gases. The following description refers to the production of ozone and to the <FIG> system, but the analyzer unit should not be considered so limited. Briefly stated, ambient air, is introduced into the conduit and the valves closed. The output of the filtered phase detector is read and recorded for ambient air. Then feed gas, oxygen-enriched air, is introduced into the conduit and the valves closed. The output of the filtered phase detector is read and recorded for the feed gas. Finally ozone-bearing gas is introduced into the conduit and the valves closed. The output of the filtered phase detector is read and recorded for ozone-bearing gas.

<FIG> shows a process flow of the operation described immediately above. The steps of the process flow are generalized in that the gases are labeled A, B and to indicate that more gases derived from the initial gas may be included in this process flow. After the system is initialized as represented by the dotted arrow <NUM>, step <NUM> initializes an index Valve # to zero. Then the valve indicated by Valve # is opened and the gas selected by the opened valve is fed into the conduit by step <NUM>. (In the <FIG> ozone generation system, index Valve # = <NUM> corresponds to value <NUM>, index Valve # = <NUM> corresponds to value <NUM>, and index Valve # = <NUM> corresponds to value <NUM>). Step <NUM> closes the valve. Step <NUM> tests whether the index Valve # is zero or not. If the index is <NUM>, the counters are reset and the output value of the filtered phase detector is read and recorded by step <NUM>. If the index is not <NUM>, the test of step <NUM> moves to step <NUM>. After step <NUM> the index Valve # is tested whether it is equal to <NUM> by step <NUM>. If not, then step <NUM> increments the index Valve # by <NUM> and the process returns to step <NUM>. The steps are repeated until index Valve # is equal to <NUM> and the process ends by step <NUM>.

From the recorded phase shift values, the control unit <NUM> analyzes the data to determine the speed of sound and composition of the gases. A comparative technique is used. With the speed of sound and composition of the first gas already known, dehumidified ambient air is used as a reference to determine the speed of sound and composition of gases derived from the first gas, the ambient air. In particular, the speed of sound of the dehumidified ambient air at the set temperature of the temperature-controlled conduit is known and used as a reference to calculate the speed of sound of the second gas, oxygen-enriched feed gas, and of the third gas, the enriched air bearing ozone, from the measured phase shifts.

The gases are processed in the order of decreasing speed of sound, i.e., ambient air, ambient air enriched with oxygen, and oxygen-enriched air bearing converted ozone. The enriched air is derived from the ambient air and the ozone-being air is derived from the enriched air. Each gas is more dense than the gas preceding it, and the speed of sound decreases relative to the speed in previous gas(es). The first gas (dry ambient air) is treated as a reference gas because its composition is known. Its speed of sound at a given temperature is also known. While it is possible to allow the temperature to vary in the manner described in the previously described <CIT>), it is preferable that the temperature of the gases be maintained at a set temperature. The temperature-controlled gas conduits, such as illustrated in <FIG>, have been found effective at maintaining gases at a set temperature. Thus in calculating the speed of sound in the oxygen-enriched air and ozone-bearing air, it is assumed that all gases have the same temperature. The addition of thermal mass or control of the environmental temperature is desirable in order to minimize error. With the speed of sound being the greatest in the reference first gas, the baseline may be adjusted as described earlier so that the phase shift ranges of the oxygen-enriched air and ozone-bearing air are expanded to accommodate the compositions of those gases.

The sound propagated in oxygen-enriched air arrives at the second transducer a little later than for ambient air. The additional delay is measured by the phase shift in combination with the known conduit length L between the first and second transducers. This allows determination of the speed of sound of the oxygen-enriched air as a function of speed of sound of ambient air and the additional phase shift. As described above, there is a direct relationship between the phase shift and delay. In particular, with L = length of sound path, S0 = known speed of sound in ambient air, then delay D0 of the ambient air is D0 = (L/S0), a known quantity. The delay D <NUM> of oxygen-enriched air is D0 + Dx, where Dx is the additional delay due to slower speed of sound in the oxygen-enriched air and is known from the additional phase shift for the oxygen-enriched air. Hence S1 = L/D1 = L/(D0+Dx). With L, D0 and Dx known, S1 is determined.

The speed of sound of the ozone-bearing air is measured in the same fashion. With S0 = known speed of sound in the ambient air, S1 = speed of sound in the oxygen-enriched air, and S2 = speed of sound in the ozone-bearing air. The delay D2 of ozone-bearing air is D0 + Dz, where Dz is the additional delay due to slower speed of sound in the ozone-bearing air and is known from the additional phase shift for the ozone-bearing air. Hence S2 = L/D2 = L/(D0+Dz). With L, D0 and Dz known, S2 is determined.

The speed of sound S0 of ambient air, which has an oxygen composition of <NUM>%, is known and the speed of sound of <NUM>% oxygen is also known. The measured speed of sound SI of the oxygen-enriched gas should fall between the two known speed of sound values as a proportion of oxygen representing a mixture of the two gases, ambient air and <NUM>% oxygen. This proportion may be calculated: proportion O<NUM> = (S1 - S0) / (Sox - S0) where Sox, is the speed of sound in <NUM>% oxygen gas. This discussion avoids many complex factors. The theoretical speed of sound in a gas can calculated from many models, which in turn have many factors, including Boltzmann's constant, temperature, mass of a molecule, and adiabatic constant (which is not the same for all gases under discussion), discourage theoretical certainty. Fortunately, certain assumptions of linearity yield reasonable approximations in the regions of interest. Empirical scaling yields good results.

Hence it has been found that: percentage O<NUM> = <NUM> x (proportion O<NUM> x O<NUM>scale) + <NUM> is a very good approximation. Because this model is approximate and small variations will occur in the real world, the scaling factor O<NUM>scale, near unity, is used to proportion O<NUM>.

Similarly, for the ozone-bearing air: proportion O<NUM> = O<NUM>scale x <NUM> x (S1 - S2)/ (calculated speed of sound in pure ozone). The speed of sound in pure ozone is calculated because there is likely no way of empirically determining that speed of sound at ordinary temperatures due to the explosively unstable nature of such a gas. The number used is by calculation based upon molecular weight, temperature, and adiabatic constant. O<NUM>scale is an empirical scale adjustment having a value of near unity.

To determine the concentration of ozone in terms of amount of ozone per cubic centimeter the following equation may be used: grams of ozone per cm<NUM> = proportion O<NUM> x <NUM>.

Correction factors arise from complexities in the measurement of gas composition. The production of ozone may not depend on dilution of one gas by another. For example, if <NUM> mole of oxygen passes through an electrical discharge ozone cell and <NUM>% of the O<NUM> is converted to O<NUM>, the emerging ozone from the cell is <NUM>. mole due to the reduction in the number of molecules from the conversion from O<NUM> to O<NUM>. The total oxygen emerging is <NUM> mole. Hence the total emerging gas is <NUM>. mole and the molar percentage O<NUM> is <NUM>%. But the speed of sound still has a <NUM>-to-<NUM> relationship to the ozone concentration.

If the gas entering the discharge cell consists of more than one component, the situation is similar. For example, if the gas entering the cell is <NUM>% O<NUM> and <NUM>% N<NUM> by molar measure, <NUM> mole of gas consists of <NUM> mole O<NUM> and <NUM> mole N<NUM>. With <NUM>% of the oxygen converted to O<NUM>, the emerging gas consists of <NUM> mole O<NUM>, <NUM> mole O<NUM>,and <NUM> mole N<NUM> for a total of <NUM> mole. The molar percentage O<NUM> is <NUM>%. The speed of sound still has a <NUM>-to-<NUM> relationship because each gas has a concentration that is a unique function of the ozone concentration, and hence has a unique speed of sound corresponding to that concentration.

The change in the speed of sound depends upon the change in ozone concentration in a gas. In ozone generation systems, the oxygen content in air is typically increased before the resulting gas is sent to the ozone generation cell. Hence it is good to know the composition of the gas entering the generation cell, as well as after the cells. Air, for example, can be assumed to be <NUM>% N<NUM>, <NUM>% O<NUM> and <NUM>% argon. The published speed of sound at <NUM>° C is respectively <NUM>/s, <NUM>/s, and <NUM>/s through these respective component gasses. By averaging these speeds in proportion to their proportion in air, an overall speed of sound in air is found to be <NUM>/s. This compares well to a published speed of <NUM>/s. A reasonable estimate for the speed of sound in ozone at <NUM>° C is <NUM>/s, though this is an unlikely direct measurement since high concentrations of ozone are unstable.

The following are illustrative examples with different concentrations of oxygen entering the discharge cell. The first illustration assumes that a sample of gas consisting of <NUM> mole N<NUM> and <NUM> mole O<NUM>, an approximation of air. Following the calculations above, the speed of sound in this mixture is <NUM>/s. If this sample is then passed through an ozone generating cell, some of the O<NUM> is converted to O<NUM> which reduces the total molar quantity of gas. Assuming that <NUM> mole of the O<NUM> is converted to O<NUM>, the total output is <NUM> mole N<NUM>, <NUM> mole O<NUM>, and <NUM> mole O<NUM>, for a total of <NUM> mole. The molar percentage of O<NUM> is <NUM>%. The speed of sound in the mixture of gases is <NUM>/s and the change in speed of sound is -<NUM>/s with the proportional change - <NUM>.

In comparison, with the assumption that the sample of gas consists of <NUM> mole O<NUM>, i.e., the sample is all oxygen, the speed of sound in this mixture is <NUM>/s following the calculations above. If the sample is passed through an ozone generating cell, some of the O<NUM> is converted to O<NUM> to reduce the total molar quantity of gas. Assume, as in the last case, that <NUM> mole of the O<NUM> is converted to O<NUM>. The total output is <NUM> mole O<NUM>, and <NUM> mole O<NUM>, for a total of <NUM> mole. The molar percentage of O<NUM> is <NUM>% as before. The speed of sound in the mixture of gases is <NUM>/s. The change in speed of sound is -<NUM>/s and the proportional change is - <NUM>.

It should be noted that the proportional change of the speed of sound relative to proportion of oxygen in the feed gas entering the cell is greater for pure oxygen than for air. This may be viewed in heuristic fashion. The proportion of nitrogen in the ozone-bearing gas increases, as oxygen is converted to ozone, if there is a lot of nitrogen to begin with. The increased nitrogen, having a relatively high speed of sound, tends to counteract the reduction in the speed of sound due to increasing proportion of ozone.

In returning to the conduit path length L, there should be considered some practical constraints to the length of the conduit as mentioned earlier. These constraints depend on the speed of sound of the gases being measured, the frequency of operation, and the method of measuring or detecting phase shift. For each gas, there is a corresponding speed of sound and a corresponding wavelength. Among the gases there is a gas with a maximum wavelength tax and a gas with a minimum wavelength λmin. If phase shift is to be limited to <NUM> degrees, then L/ λmin - L/λmax. must be less than <NUM>, i.e.:
<MAT>.

This corresponds to the difference in number of wavelengths contained in the conduit is less than <NUM>. By manipulating the terms to determine the conduit length, one obtains:
<MAT>.

Similarly, if phase shift is to be limited to <NUM> degrees, then L/λmin - L/λmax must be less than ½, i.e.,
<MAT>
<MAT> in this case.

Some exemplary numbers may illustrate these points. With the frequency of the analyzer fixed at <NUM>, and assuming that the speed of sound of the reference gas (air) Sref is <NUM>/s or λref = <NUM>, and the range of speed of sound of other gases (oxygen-enhanced air and ozone) in the analyzer, ΔS, is <NUM>/s, the maximum wavelength λmax (λref) is <NUM> and the minimum wavelength λmin is <NUM>. If phase shift is to be limited to <NUM> degrees, then L((<NUM>/. <NUM>) - (<NUM>/<NUM>)) < ½, Of L < <NUM>. Similarly, if phase shift is to be limited to <NUM> degrees, then L < <NUM>. These numbers correspond to <NUM> wavelengths of the reference gas (λref) and <NUM> wavelengths of the reference gas (λref) respectively.

But very short conduits cause artifacts due to standing waves, artifacts due to the acoustic contribution of holes for ingress and egress of test gases, artifacts due to the uncertain phase relationship of electrical signals to acoustic signals, and artifacts due to electrical and/or acoustical noise. For these reasons, it is desirable to have a conduit that includes at least <NUM> wavelengths of sound in the reference gas in order to minimize these artifacts. As described in the previous paragraph, a conventional phase detector places a severe constraint on conduit length. In the case of a <NUM>° phase shift detector, path length L of the conduit in terms of number of wavelengths of the reference gas can be no greater than <NUM>, and in the cases of a <NUM> degree phase shift detector, the path length can be no more <NUM> wavelengths of the reference gas.

However, by the application of the previously described frequency division technique upon the particular phase shift detection method, the constraint on the conduit path length L can be removed and L lengthened. If the frequency is divided by n, n = <NUM> for example, the maximum number of wavelengths and the maximum length L are each multiplied by a factor of n = <NUM>. That is, the upper bound for the conduit path length becomes:
<MAT> depending upon whether the phase shift detector is <NUM> degrees or <NUM> degrees respectively.

On the other hand, even with the frequency division technique the upper bounds of the conduit path length are not limitless. Long conduits also cause problems which include signal attenuation, high sample volume, and bulky design. It is desirable to limit the conduit length L to about <NUM> wavelengths, at which point the disadvantages of long path length begin to become severe.

In a preferred embodiment, a length of conduit corresponding to about <NUM> wavelengths of sound in reference gas (λref) was selected, i.e., L approximately = <NUM> * <NUM>. This creates a situation in which phase shift exceeds the limit of the <NUM>° phase detector selected, but the use of the frequency division technique described maintains the advantages of a relatively long signal path.

The described relatively simple and low-cost gas analyzer measures the concentration of ozone in an ozone generation system with high resolution and precision, and relatively independently of the oxygen concentration in the feed gas and independently of temperature. Additionally, the concentration of oxygen in the gas fed to the ozone generation is precisely measured. This provides an inexpensive and productive way of generating ozone on site and at the time of use.

Claim 1:
An analyzer (<NUM>) for one or more gases derived from a first gas of known composition and speed of sound, each derived gas having a concentration of a component changed, the analyzer (<NUM>) comprising:
a fixed frequency signal source (<NUM>);
a first transducer (<NUM>), the first transducer (<NUM>) driving continuous sound waves responsive to the fixed frequency signal source (<NUM>);
a conduit (<NUM>) acoustically connected to the first transducer (<NUM>), the conduit (<NUM>) selectively receiving and holding samples of the first gas and one or more derived gases;
a second transducer (<NUM>) acoustically connected to the conduit (<NUM>) opposite the first transducer (<NUM>), the second transducer (<NUM>) receiving sound waves from the first transducer (<NUM>) through the conduit (<NUM>) and generating second transducer signals responsive to the received sound waves;
a processing unit (<NUM>) receiving fixed frequency signal source signals and the second transducer signals, the processing unit (<NUM>) determining a relative phase shift between the frequency source signals and second transducer signals for a gas sample in the conduit (<NUM>), the relative phase shift corresponding to a difference of speed of sound in one gas sample relative to another gas sample, and
a calculating unit (<NUM>) determining from the first gas of known composition the speed of sound of the one or more gases derived from the first gas, and calculating the composition of a sample of one or more derived gases from the first gas as a reference; and
characterised in that the processing unit includes circuitry (<NUM>, <NUM>) lowering the frequency of the received fixed frequency source signals and second transducer signals to expand the range of measurement of the relative phase shift.