US3775600A - Lethal rate analogue function generator - Google Patents

Lethal rate analogue function generator Download PDF

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US3775600A
US3775600A US00191402A US3775600DA US3775600A US 3775600 A US3775600 A US 3775600A US 00191402 A US00191402 A US 00191402A US 3775600D A US3775600D A US 3775600DA US 3775600 A US3775600 A US 3775600A
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temperature
generator
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06GANALOGUE COMPUTERS
    • G06G7/00Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/48Analogue computers for specific processes, systems or devices, e.g. simulators
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06GANALOGUE COMPUTERS
    • G06G7/00Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/24Arrangements for performing computing operations, e.g. operational amplifiers for evaluating logarithmic or exponential functions, e.g. hyperbolic functions
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06GANALOGUE COMPUTERS
    • G06G7/00Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/26Arbitrary function generators

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  • the present invention concerns an analogue function generator for use in calculations involving a heat sterilising or pasteurising process for substances such as foodstuffs. Two main methods for calculating the effectiveness of a heat sterilising process have been used heretofore.
  • the effectiveness of a sterilising process is normally specified by a quantity called the process lethality F.
  • F This may be defined asthe length in minutes of an idealised process having the same lethal effect for which the temperature is constant at a suitable reference level T
  • F is obtained by evaluating the integral with respect to time of the lethal rate, L, when L w T uz
  • T is the temperature at the critical (slowest heating) point of the substance being sterilised
  • Z is a constant for a given micro-organism and represents the temperature increment which produces a tenfold increase in the rate of destruction of the micro-organism.
  • the value of Z normally lies in the range of 10 to 22.
  • the value 18 (Clostridium Botulimum) is most frequently used.
  • T is almost invariably taken 250 F.
  • the general method consists of measuring the temperature history at the slowest heating point of a pack undergoing the given process, normally using a finewire thermocouple. From the temperature curve a corresponding L time curve is constructed using a table of L against T for the values of T and Z in question. F is then obtained by evaluation of the area under this lethal-rate curve.
  • the considerable labour of this procedure may be somewhat reduced by plotting temperature on lethal-rate paper which has an appropriately non-linear scale for the temperature co-ordinate. Measurement of the area under the curve with a planimeter will then permit calculation of F; Lethal-rate paper is normally only available for Z 18 and its use sacrifices flexibility in the choice of scale.
  • analogue function generator for use in calculations involving a heat sterilising or pasteurising process which is characterised in that it comprises an analogue function generator for use in calculations involving a heat sterilising or pasteurising process for substances such as foodstuffs, the generator comprising means for generating with respect to a predetermined constant determined by the microorganism involved and in accordance with an electrical signal representing the temperature of the process the lethal rate function of the process.
  • FIG. 1 is a block diagram of analogue function computer constructed in accordance with the present invention
  • FIGS. 2a 2c show a series of voltage waveforms illustrating the operation of the analogue function computer
  • FIG. 3 is a circuit diagram of the computer of FIG. 1.
  • the analogue function generator is arranged to generate the lethal rate function L 00 zsouz 10(260 7'b)/Z This re-arrangement is justified by the practical consideration that in-can processing temperatures never exceed 260 F so that the variable exponent (T 260)/Z will always be negative.
  • the temperature analogue representing T
  • T is supplied to one input of a comparator 2, the other input of the comparator 2 being generated by a multivibrator 1.
  • the temperature T assuming that the analogue function generator is being used in a real-time process, is derived from a thermistor or a thermocouple and is amplified. Neither the amplifier nor the thermistor nor the thermocouple is shown as these are both entirely conventional.
  • the amplified thermocouple output is scaled to give +6V. at 260 F and 0V. at 200 F at which temperature, assuming T to be 250 F, L will be negligibly small and may be taken as zero. Naturally, alternative scales may be used as will be discussed later.
  • the input from the multivibrator 1 appears as a periodic waveform comprising a step from 0 to +6V followed by a linear decay to zero.
  • the two waveforms are shown in graph a of FIG. 2.
  • the output of the comparator 2 is a square waveform, the width of the negative going pulses being equal to the time during which the input waveform from the multivibrator 1 is more positive than the temperature signal.
  • the duration of these pulses is thus proportional to 260 Tand the pulses are applied to a pulse amplifying stage 3 which converts them to positive going pulses between lOV. and 0V.
  • the output of the pulse amplifier is shown at b in FIG. 2.
  • FIG. 2 (C) shows the output from the detector and from the RC circuit 4.
  • the output of the multivibrator 1 is taken via a coupling capacitor C and an emitter follower T to the comparator 2.
  • the diode D sets the DC level.
  • the output of the comparator 2 is taken via an emitter follower T to the pulse amplifier 3.
  • the constant Z is introduced by the potentiometer RV and can thus be rapidly varied.
  • the output of the pulse amplifier is taken via emitter follower T to the detector 5.
  • the choice of the pulse repetition frequency is influenced by two considerations. Firstly, use of the genera tor for high speed analogue computing will necessitate a short response time. certainly not greater than 0.05 see. This factor will be determined by the response time of the detector circuit 5 which must thus have a suitably short time constant and this requirement can only be met in conjunction with accurate detection ifa suitably high pulse frequency is used. On the other hand the precision of the exponential rise generated by the integrating network depends on the sharpness of the leading edge of the applied pulses compared to their length, a factor which will deteriorate with increasing pulse frequency.
  • the generator is intended initially for use with existing analogue computing equipment and accordingly the design utilises the available voltages. namely i 10v and i v although, of course, alternative voltages would be possible.
  • the multivibrator waveform is at the wrong level for direct application to the comparator and so it is A.C. coupled to the base of T with its lower extremity clamped to earth by the diode D It is also necessary to adjust the amplitude of this waveform to precisely 6v.
  • variable resistor RV as part of the collector load of T
  • the exponentially rising pulse is produced by the resistor RV and the capacitor C the diode D being included to cause the rapid discharge of capacitor C; at the end of the input pulse thus ensuring the recovery of l0v datum level before the arrival of the next input pulse.
  • the derivation of the accumulated lethality requires integration of the lethal rate with respect to time in minutes rather than seconds as is the case with the conventional analogue integrator. This raises no problem in the case of a high speed simulation which would have its time scale speeded up by at least 60:l. For a real time computation, however, it becomes necessary either to divide the L voltage by 60 before integration or to choose components with a time constant of 60 sec. both of which procedures could prove unsatisfactory due to drift.
  • An alternative would be to integrate with a normal time constant and apply the output to a comparator which at a convenient level would automatically reset the integrator and generate a counting pulse. It could be arranged for these pulses to occur at lethal ity intervals of 0.1 min. and they could then be applied to a three-stage decade counter to give a ditital display.
  • the scaling procedure so far considered is based on the selection of 260 F as being the highest temperature likely to be used in any canning process and 200 F as being a convenient temperature at which I. is sufficiently small to be taken as zero.
  • corresponding temperatures T and T could have been selected, the former being any convenient temperature not less than that of the retort in a particular process under investigation.
  • the length of the comparator pulses must then be expressed as 7 (1),, T)/(T,, T,,)'r the ratio 1,11' must be made equal to 2.303 (T,,, Tnl/Z and the setting of the output potentiometer must be l0 1'10.
  • thermocouple e.m.f.
  • thermocouple connected to data logging device which is capable of providing a high level analogue output.
  • thermocouple connected to data logging device which is capable of providing a high level analogue output.
  • An example of this arrangement would be the use of a single channel potentiometric recorder having linked to the balancing mechanism a spare slave potentiometer from which a suitable voltage may be derived. This is a standard feature of some recorders but could in any case be provided without too much difficulty.
  • An analogue function greater for use in calculations involving a heat sterilizing or pasteurizing process for substance such as foodstuffs comprising:
  • comparison means responsive to an electrical signal representing the temperature of the process; means coupled to an input of said comparison means for periodically imposing a standard signal thereon, said comparison means generating an output signal of at least a selected magnitude and a duration proportional to a time in which the temperature signal is less than the periodic standard signal and means responsive to the output signal of the comparator for imposing upon said output signal a selected integration factor for producing an integrated output representative of the lethal rate function.
  • said comparator has two inputs, one
  • providing the periodic standard signal comprising: a multivibrator connected to the other input so that the output of the comparator is a square waveform dependent on the level of the temperature signal.
  • An analogue function generator as claimed in claim 1 wherein said means responsive to the composition for providing the selected integration factor includes: a pulse amplifier circuit connected to the output of the comparator and an RC network connected to the output of the pulse amplifier circuit.
  • An analogue function generator for use in calculations involving a heat sterilising or pasteurising process for substances such as foodstuffs, a generator comprising a comparator having two inputs, means for applying an electrical signal to one input of the comparator which represents the temperature of the sterilising process, a multivibrator connected to the other input of the comparator so that the output of the comparator is a square waveform, the pulse width of which depends on the level of the temperature signal, a pulse amplifying circuit for amplifying the output waveform of the comparator and introducing a constant value representing the temperature increment which produces a predetermined increase in the rate of destruction of the micro-organism to be destroyed by the pasteurising process, an RC network for integrating the output of the pulse amplifying circuit and a detector circuit for peak rectifying the output of the RC network to give a signal representing the lethal rate function of the sterilising or pasteurising processes.

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • General Physics & Mathematics (AREA)
  • Software Systems (AREA)
  • Apparatus For Disinfection Or Sterilisation (AREA)
  • Food Preservation Except Freezing, Refrigeration, And Drying (AREA)
  • Investigating Or Analyzing Materials By The Use Of Fluid Adsorption Or Reactions (AREA)

Abstract

The invention concerns the sterilisation or pasteurising of substances such as foodstuffs. The effectiveness of a sterilising process is normally specified by a quantity called ''''the process lethality F.'''' The invention provides an analogue function generator which calculates the lethality of a sterilising process from the temperature to which the substance being processed is subjected.

Description

United States Patent 1191 Skinner 1 Nov. 27, 1973 LETHAL RATE ANALOGUE FUNCTION 3,281,584 10/1966 Martinez 235/183 x GENERATOR 3,358,200 12/1967 Clifford 235/183 UX 3,536,904 10/1970 Jordan, Jr. et a1. 235/183 X [75] Inventor: Rodney Harold Skinner, Godalming,
England [73] Assignee: National Research Development m y xa iner-Felix D. Gruber Corporation, London, England Assistant ExaminerEdward J. Wise Att0rney-Cushman, Darby and Cushman [22] Filed: Oct. 21, 1971 [21] Appl. No.: 191,402
[30] Foreign Application Priority Data [57] ABSTRACT Oct. 21, 1970 Great Britain 50,072/70 The invention concerns the sterilisation or pasteuris- [52] U.S. C] 235/1515, 235/183, 235/134 ing of substances such as foodstuffs. The effectiveness 23 5/197 of a sterilising process is normallyspecified by a quan' [51] Int. Cl. G06g 7/18, G06g 7/26 y Called h pr l h lity The invention [58] Field of Search 235/1513, 197, 150.53, provides an analogue function generator hi h l 235/134 135 183; 32 /133 134 lates the lethality ofa sterilising process from the temperature to which the substance being processed is References Cited Subjected.
UNITED STATES PATENTS 2972,44? 2/1961 White 238/184 4 Claims, 5 Drawing Figures CUM/3 1K470? LETHAL RATE ANALOGUE FUNCTION GENERATOR The present invention concerns an analogue function generator for use in calculations involving a heat sterilising or pasteurising process for substances such as foodstuffs. Two main methods for calculating the effectiveness of a heat sterilising process have been used heretofore.
The two known methods for calculating F have become known as The General Method and the Formula Method." There are variations possible within these two basic methods.
The effectiveness of a sterilising process is normally specified by a quantity called the process lethality F. This may be defined asthe length in minutes of an idealised process having the same lethal effect for which the temperature is constant at a suitable reference level T In both these methods F is obtained by evaluating the integral with respect to time of the lethal rate, L, when L w T uz In this equation T is the temperature at the critical (slowest heating) point of the substance being sterilised, and Z is a constant for a given micro-organism and represents the temperature increment which produces a tenfold increase in the rate of destruction of the micro-organism. The value of Z normally lies in the range of 10 to 22. The value 18 (Clostridium Botulimum) is most frequently used. For canning processes T is almost invariably taken 250 F.
The general method consists of measuring the temperature history at the slowest heating point of a pack undergoing the given process, normally using a finewire thermocouple. From the temperature curve a corresponding L time curve is constructed using a table of L against T for the values of T and Z in question. F is then obtained by evaluation of the area under this lethal-rate curve. The considerable labour of this procedure may be somewhat reduced by plotting temperature on lethal-rate paper which has an appropriately non-linear scale for the temperature co-ordinate. Measurement of the area under the curve with a planimeter will then permit calculation of F; Lethal-rate paper is normally only available for Z 18 and its use sacrifices flexibility in the choice of scale.
In the formula method data determined for the given foodstuff by a heat penetration test are used in conjunction with tables and formulae either to determine the lethality of a proposed process or more usefully to predict the process time at a specified temperature required for a desired lethality. Because of approximations and generalisations in the theory of the formula method it must be considered less precise than the general method and it is common practice to use the latter to check a process predicted by the former.
It can be seen that both these methods have considerable disadvantages which are overcome by the present invention. The general method is extremely laborious and is also inflexible. Alternatively the formulae method is imprecise.
These disadvantages are overcome by the present invention which provides an analogue function generator for use in calculations involving a heat sterilising or pasteurising process which is characterised in that it comprises an analogue function generator for use in calculations involving a heat sterilising or pasteurising process for substances such as foodstuffs, the generator comprising means for generating with respect to a predetermined constant determined by the microorganism involved and in accordance with an electrical signal representing the temperature of the process the lethal rate function of the process.
An embodiment of the present invention will now be described by way of example and with reference to the accompanying drawings in which:
FIG. 1 is a block diagram of analogue function computer constructed in accordance with the present invention,
FIGS. 2a 2c show a series of voltage waveforms illustrating the operation of the analogue function computer, and
FIG. 3 is a circuit diagram of the computer of FIG. 1.
In the embodiment being described with reference to the accompanying drawings, the analogue function generator is arranged to generate the lethal rate function L 00 zsouz 10(260 7'b)/Z This re-arrangement is justified by the practical consideration that in-can processing temperatures never exceed 260 F so that the variable exponent (T 260)/Z will always be negative.
In the block diagram of FIG. 1 the temperature analogue, representing T, is supplied to one input of a comparator 2, the other input of the comparator 2 being generated by a multivibrator 1. The temperature T assuming that the analogue function generator is being used in a real-time process, is derived from a thermistor or a thermocouple and is amplified. Neither the amplifier nor the thermistor nor the thermocouple is shown as these are both entirely conventional. The amplified thermocouple output is scaled to give +6V. at 260 F and 0V. at 200 F at which temperature, assuming T to be 250 F, L will be negligibly small and may be taken as zero. Naturally, alternative scales may be used as will be discussed later.
The input from the multivibrator 1 appears as a periodic waveform comprising a step from 0 to +6V followed by a linear decay to zero. The two waveforms are shown in graph a of FIG. 2. The output of the comparator 2 is a square waveform, the width of the negative going pulses being equal to the time during which the input waveform from the multivibrator 1 is more positive than the temperature signal. The duration of these pulses is thus proportional to 260 Tand the pulses are applied to a pulse amplifying stage 3 which converts them to positive going pulses between lOV. and 0V. The output of the pulse amplifier is shown at b in FIG. 2. The pulses are then applied to a simple RC circuit and if their length is denoted by (260 Thu the capacitor will charge periodically to a voltage -10 exp (260 m where 1 pulse length when T= 200 F and 1- is the time constant of the RC circuit. If 1 /1 is made equal to 2.303 X /Z peak rectification will yield a direct voltage of-lO. 10(T- 260)/Z. A potentiometer is then used to multiply this by the factor l{(260 TIJ/ZL which is invariably less than unity to obtain a voltage numerically equal to L. The peak rectification is obtained in a detector circuit 5. FIG. 2 (C) shows the output from the detector and from the RC circuit 4.
In the more detailed circuit diagram shown in FIG. 3 those parts of the circuit corresponding to the block diagram of FIG. 1 are indicated by the same reference numerals. Thus the periodic input to the comparator 2 is obtained from the bare voltage of transistor T of the multivibrator 1. Adequate linearity is obtained by returning the base resistors R R of the two transistors T, and T of the multivibrator to a voltage well beyond the collector supply so that not more than about a quarter of a complete exponential charging curve is utilised. The potentiometer R can be set to control the point at which the multivibrator swings to set the level of the ramp.
The output of the multivibrator 1 is taken via a coupling capacitor C and an emitter follower T to the comparator 2. The diode D sets the DC level. The output of the comparator 2 is taken via an emitter follower T to the pulse amplifier 3. In the pulse amplifier 3 the constant Z is introduced by the potentiometer RV and can thus be rapidly varied. The output of the pulse amplifier is taken via emitter follower T to the detector 5.
The choice of the pulse repetition frequency is influenced by two considerations. Firstly, use of the genera tor for high speed analogue computing will necessitate a short response time. certainly not greater than 0.05 see. This factor will be determined by the response time of the detector circuit 5 which must thus have a suitably short time constant and this requirement can only be met in conjunction with accurate detection ifa suitably high pulse frequency is used. On the other hand the precision of the exponential rise generated by the integrating network depends on the sharpness of the leading edge of the applied pulses compared to their length, a factor which will deteriorate with increasing pulse frequency.
.The generator is intended initially for use with existing analogue computing equipment and accordingly the design utilises the available voltages. namely i 10v and i v although, of course, alternative voltages would be possible.
The multivibrator waveform is at the wrong level for direct application to the comparator and so it is A.C. coupled to the base of T with its lower extremity clamped to earth by the diode D It is also necessary to adjust the amplitude of this waveform to precisely 6v. and of the possible methods of achieving this the most stable was found to be the inclusion of the variable resistor RV as part of the collector load of T This provides a variable limitation to the collector voltage swing by virtue of the time constant (R, RV,) C being long compared with the conduction period of T The exponentially rising pulse is produced by the resistor RV and the capacitor C the diode D being included to cause the rapid discharge of capacitor C; at the end of the input pulse thus ensuring the recovery of l0v datum level before the arrival of the next input pulse.
The derivation of the accumulated lethality requires integration of the lethal rate with respect to time in minutes rather than seconds as is the case with the conventional analogue integrator. This raises no problem in the case of a high speed simulation which would have its time scale speeded up by at least 60:l. For a real time computation, however, it becomes necessary either to divide the L voltage by 60 before integration or to choose components with a time constant of 60 sec. both of which procedures could prove unsatisfactory due to drift. An alternative would be to integrate with a normal time constant and apply the output to a comparator which at a convenient level would automatically reset the integrator and generate a counting pulse. It could be arranged for these pulses to occur at lethal ity intervals of 0.1 min. and they could then be applied to a three-stage decade counter to give a ditital display.
The scaling procedure so far considered is based on the selection of 260 F as being the highest temperature likely to be used in any canning process and 200 F as being a convenient temperature at which I. is sufficiently small to be taken as zero. Alternatively, corresponding temperatures T and T could have been selected, the former being any convenient temperature not less than that of the retort in a particular process under investigation. The length of the comparator pulses must then be expressed as 7 (1),, T)/(T,, T,,)'r the ratio 1,11' must be made equal to 2.303 (T,,, Tnl/Z and the setting of the output potentiometer must be l0 1'10.
Such a rescaling will often be desirable in the interests of accuracy whilst for thermal processes other than canning (e.g., pasteurisation, U.H.T. sterilisation) the scale factors can be altered.
It is anticipated that the complete system for computing lethality could take one of the following three forms:
a. A completely integrated unit including power supplies and an amplifier for the thermocouple e.m.f.
b. The lethal rate generator as previously described used in conjunction with a standard small analogue computer which will provide power supplies and the necessary amplification and which would be available for other uses.
c. Basically the alternatives mentioned in paragraphs (a) or (b) with the thermocouple connected to data logging device which is capable of providing a high level analogue output. An example of this arrangement would be the use of a single channel potentiometric recorder having linked to the balancing mechanism a spare slave potentiometer from which a suitable voltage may be derived. This is a standard feature of some recorders but could in any case be provided without too much difficulty.
Naturally, any convenient linear sweep generator could be used in place of the multivibrator described hereinbefore.
Layout of formulae could be improved. It was done with some care in the original, but possibly where formulae appear cramped they could be given a line to themselves.
I claim:
1. An analogue function greater for use in calculations involving a heat sterilizing or pasteurizing process for substance such as foodstuffs, the generator for calculating a lethal rate function of the process comprising:
comparison means responsive to an electrical signal representing the temperature of the process; means coupled to an input of said comparison means for periodically imposing a standard signal thereon, said comparison means generating an output signal of at least a selected magnitude and a duration proportional to a time in which the temperature signal is less than the periodic standard signal and means responsive to the output signal of the comparator for imposing upon said output signal a selected integration factor for producing an integrated output representative of the lethal rate function. 2. An analogue function generator as claimed in claim 1, wherein said comparator has two inputs, one
responsive to the temperature signal and the means for.
providing the periodic standard signal comprising: a multivibrator connected to the other input so that the output of the comparator is a square waveform dependent on the level of the temperature signal.
3. An analogue function generator as claimed in claim 1 wherein said means responsive to the composition for providing the selected integration factor includes: a pulse amplifier circuit connected to the output of the comparator and an RC network connected to the output of the pulse amplifier circuit.
4. An analogue function generator for use in calculations involving a heat sterilising or pasteurising process for substances such as foodstuffs, a generator comprising a comparator having two inputs, means for applying an electrical signal to one input of the comparator which represents the temperature of the sterilising process, a multivibrator connected to the other input of the comparator so that the output of the comparator is a square waveform, the pulse width of which depends on the level of the temperature signal, a pulse amplifying circuit for amplifying the output waveform of the comparator and introducing a constant value representing the temperature increment which produces a predetermined increase in the rate of destruction of the micro-organism to be destroyed by the pasteurising process, an RC network for integrating the output of the pulse amplifying circuit and a detector circuit for peak rectifying the output of the RC network to give a signal representing the lethal rate function of the sterilising or pasteurising processes.

Claims (4)

1. An analogue function greater for use in calculations involving a heat sterilizing or pasteurizing process for substance such as foodstuffs, the generator for calculating a lethal rate function of the process comprising: comparison means responsive to an electrical signal representing the temperature of the process; means coupled to an input of said comparison means for periodically imposing a standard signal thereon, said comparison means generating an output signal of at least a selected magnitude and a duration proportional to a time in which the temperature signal is less than the periodic standard signal and means responsive to the output signal of the comparator for imposing upon said output signal a selected integration factor for producing an integrated output representative of the lethal rate function.
2. An analogue function generator as claimed in claim 1, wherein said comparator has two inputs, one responsive to the temperature signal and the means for providing the periodic standard signal comprising: a multivibrator connected to the other input so that the output of the comparator is a square waveform dependent on the level of the temperature signal.
3. An analogue function generator as claimed in claim 1 wherein said means responsive to the composition for providing the sElected integration factor includes: a pulse amplifier circuit connected to the output of the comparator and an RC network connected to the output of the pulse amplifier circuit.
4. An analogue function generator for use in calculations involving a heat sterilising or pasteurising process for substances such as foodstuffs, a generator comprising a comparator having two inputs, means for applying an electrical signal to one input of the comparator which represents the temperature of the sterilising process, a multivibrator connected to the other input of the comparator so that the output of the comparator is a square waveform, the pulse width of which depends on the level of the temperature signal, a pulse amplifying circuit for amplifying the output waveform of the comparator and introducing a constant value representing the temperature increment which produces a predetermined increase in the rate of destruction of the micro-organism to be destroyed by the pasteurising process, an RC network for integrating the output of the pulse amplifying circuit and a detector circuit for peak rectifying the output of the RC network to give a signal representing the lethal rate function of the sterilising or pasteurising processes.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2972447A (en) * 1956-06-14 1961-02-21 White Roby Byron Optimal controller
US3281584A (en) * 1959-05-11 1966-10-25 Yuba Cons Ind Inc Multiplier apparatus using function generators
US3358200A (en) * 1964-04-01 1967-12-12 Computing Devices Canada Electro-mechanical integrator
US3536904A (en) * 1968-09-23 1970-10-27 Gen Electric Four-quadrant pulse width multiplier

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2972447A (en) * 1956-06-14 1961-02-21 White Roby Byron Optimal controller
US3281584A (en) * 1959-05-11 1966-10-25 Yuba Cons Ind Inc Multiplier apparatus using function generators
US3358200A (en) * 1964-04-01 1967-12-12 Computing Devices Canada Electro-mechanical integrator
US3536904A (en) * 1968-09-23 1970-10-27 Gen Electric Four-quadrant pulse width multiplier

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