US2986704A

US2986704A - Function generator

Info

Publication number: US2986704A
Application number: US594839A
Authority: US
Inventors: Roland M Lichtenstein
Original assignee: General Electric Co
Current assignee: General Electric Co
Priority date: 1956-06-29
Filing date: 1956-06-29
Publication date: 1961-05-30
Anticipated expiration: 1978-05-30
Also published as: GB844872A; NL218516A; FR1187745A; DE1252800B

Description

y 30, 1.961 R. M. LICHTENSTEIN 2,986,704

FUNCTION GENERATOR Filed June 29, 1956 3 Sheets-Sheet l Inventor: fife/and ML/chtensteirv,

by M 2% His Attorrveg.

May 30, 1961 R. M. LICHTENSTEIN FUNCTION GENERATOR 3 Sheets-Sheet 3 Filed June 29, 1956 PUL SE S OURC E PULSE SOURCE 75 Inventor" fPo/c-znd M. Lichtenstein,

log/26m 9 M H/s Attorney- United States Patent FUNCTION GENERATOR Roland M. Lichtenstein, Schenectady, N.Y., assignor to General Electric Company, a corporation of New York Filed June 29, 1956, Ser. No. 594,839

22 Claims. (Cl. 323-142) This invention relates to a pulse rate measuring apparatus which produces a signal which is a desired function of input pulse rate. In addition, this invention relates to a class of function generators utilizing this principle that converts an input current into an output current which is some prescribed function of the input current.

In many engineering, scientific, and industrial areas, it becomes necessary to measure the characteristic parameters of a time series of events. In practice, many different types of time series may occur. However, the simplest and most important of these are the periodic series and the stationary random series. In the periodic series, the time interval between any two consecutive events has the same fixed duration T. The quantity is called the rate. A random series, on the other hand, is characterized by the following property: The probability that an event occurs in the short time interval t-t+dt is rdt, Where r is a characteristic parameter of the series similarly called the rate. If the rate for a random series is a constant, the random series is called stationary. In such a stationary random series, there occur, on the average, rt events during a time interval of duration t, or r events per unit time. However, the rate r may depend on time, in which case the random series is, technically, no longer stationary. However, the random series may be regarded as stationary for all practical purposes, as long as the rate does not vary too rapidly with time, i.e., as long as r a! is small as compared to r.

In detecting and measuring nuclear radiation, for example, random time series appear and are quite significant. That is, the radiation is detected by means of counters, such as pulse chambers, proportional counters, or scintillation counters, which produce individual output pulses in response to the radiation intensity representing the events in the time series. When the radiation intensity does not vary with time, the random series is stationary. However, as pointed out before, even if the radiation intensity does vary with time, the random series may be regarded as stationary for all practical purposes if the rate does not vary too rapidly. In practice, this condition is often fulfilled and, as a consequence, the stationary random series is of practical importance in nuclear instrumentation.

Thus, industrial control systems for nuclear reactors require a device that measures the rate r of a time series. Such a device is normally denominated as a counting rate meter. In a nuclear reactor during thestart-up period, this rate r may vary over ma y many decades. Consequently, such control systems then require a counting rate device whose output current is proportional to thelogarithm of the rate, so that the device is able to follow the radiation intensity without scale switching. Furthermore, the time derivative of the logarithm of the radiation intensity, the reciprocal of this quantity being called the period of the reactor, is of fundamental importance in reactor control. Thus, a combination of a counting rate meter with a logarithmic output and a differentiating means constitutes a period meter. In View of these characteristics-ability to handle large ranges and convertibility into a period meter-a counting rate meter with a logarithmic output is a highly important and desirable device in the field of industrial control systems. v v p All hitherto available devices having a logarithmic response have utilized a thermionic diode as one of the elements. Such devices, however, are very hard to keep stable since they are quite susceptible to errors due to diode drift. That is, voltage shifts of the operating char-'- acteristics of the diode occur due to changes in the tube parameters, such as changes in the emission characteristics of the cathode. Consequently, devices of thistype are extremely unsatisfactory due to the inherently unstable characteristics of the thermionic diodes.

In the field of computers, especially analog computers, it is extremely desirable to provide function generator; which convert input current into an output current which is some prescribed function of the input current. Count ing rate devices whose output current is proportional to a desired function of the repetition rate'of pulsesj may be cascaded to provide such function generators. Funetion generators which utilize the principles of counting rate devices are especially desirable in the computer'field if the counting rate devices do not utilize unstable elements such as thermionic diodes, and if they may be constructed of simple components that are relatively in expensive. 1

It is an object of this invention to provide a highly accurate counting rate apparatus of simple design constructed with simple components and relatively inexpen' sive to manufacture.

A further object of this invention is to provide a count ing rate device with a logarithmic output which does not contain any unstable elements. 7

Yet another object of this invention is to provides network having a transfer admittance which is a specified function of a complex frequency which represents aura put pulse rate. l 5 Still another object of this invention is to provide a general class of function generators which produce an output current which is a desired function of current.

Yet another object of this invention is to provide ail apparatus which provides a pulse output, the repetition rate of which is a desired function of an input current.

In practicing the invention, a net-work is provid which is constructed of simple components such asjgresistors, capacitances, and induotances.' The network is so constructed, according to network synthesis, principles, that a current is caused to flow when randominput pulses are applied thereto which is a desired function of the rate of occurrence of the pulses. That is, the transferee; mittance of the network is made a desired function of it complex frequency, in this case representing twice t e pulse rate, so that a current flows which depends on the pulse rate in the same manner as the admittance of the network depends on the complex frequency, rinspecifig, function depends on the design of the network. By as plying successively positive and negative voltagestoi tlii network in response to the occurrence of successive events in the time series", an output current is produced which a desiredfunction of the'inputpulse rate.

' It is also possible by utilizing such a counting rate device in conjunction with other elements" to reverse the operation and produce a pulse output whose repetition frequency is a desired function of an input current. That is, the output from a pulse source having a variable and adjustable repetition rate is applied to'a counting rate apparatus including a network of the type described above, to produce an output current which is a desired function of the pulse repetition rate. The output of the counting rate device is compared to the input current and the repetition rate of the pulses produced by the .pulser is varied until the output current from the counting rate device equals .the input current. When this i equality is achieved, the repetition rate of the output pulses is a specified function of the input current. Adevice of this type may be denominated asan anti-counting rate apparatus since it produces a controllable pulse repetition rate in response to an input current.

By cascading an anti-counting rate device and a counting rate apparatus, it is possible to produce a function generator which converts an input current into an output current which is a given desired function of the input current. That is, the repetition rate of the pulses from an anti-counting rate apparatus may be made a desired function of an input current by controlling the nature of the network within this apparatus. These pulses are then applied to the input of a counting rate apparatus which supplies an output current which is a desired function of this input repetition rate by controlling the type of network within this apparatus. Thus, the output current can be made a desired function of the input current. Since the function generator contains two networks, one in the anti-counting rate apparatus, and the other in the counting rate apparatus, it can be seen that a very large number of function generators may be synthesized by varying the individual characteristics of these networks. V The novel features which are believed to be characteristic of this invention are set forth with particularity in the appended claims. The invention itself, however, both as to its organization and method of operation, together with further objects and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying drawings in which:

Fig. '1 is a schematic diagram of a network embodying the principles of this invention and constructed in accordance therewith;

'Fig. 2 is a schematic circuit diagram of a counting rate apparatus constructed in accordance with the invention and which embodies a network such as is shown in Fig. 1;

Figs. 3a and 3b are block diagrams of the showing of Fig. 2 and is utilized to show the underlying theoretica considerations of the circuit of Fig. 2;

Figs. 4a, 4b and 4c are a series of graphs of the voltage and current wave forms appearing in different portions of the circuit shown in Fig. 3;

Fig. 5 is a showing, partially in block diagram form, of anti-counting rate apparatus constructed in accordance with this invention;

Fig. 6 is a showing, also partially in block diagram form, of a function generator constructed in accordance with this invention and utilizing constructions such as shown in Figs. 1 and 2 as portions thereof.

Referring now to Fig. 1, a network is provided which is characterized by the fact that it will transform input pulses into an output current which is a function of the rate of occurrence of the input pulses. The relative magnitudes of the network forming components are such that the transfer admittance of the network is a function of the complex frequency which, in the instant case, is the pulse rate of the input pulses.

; The transfer admittance of a network may be defined m the'following manner: if a two-terminal-pair network has an input voltage applied to one pair of terminals,

4 which will be denoted as the input terminals, and the output terminals are shorted together, the current flowing in the output terminals will be determined by the transfer admittance of the network. That is, assume that a voltage v(t) which is a function of time is applied to the input terminal and is given by: v(t) =V e where V and s are constant complex numbers. The parameter s is called the complex frequency. In steady-state A.C. analysis s is normally restricted to purely imaginary values is), where w is the radian frequency. However, it is more useful to permit s to be a general complex number rather than to restrict it to purely imaginary values. When the voltage v(t)=V e is applied to the input, then in the short-circuited output there flows a current i(t) which as a function of time t will be given by i(t)=l e The ratio of i(t) to v(t) is an admittance and is given by the equation I Y(s) T707) and is the transfer admittance of the network. It can be seen that this transfer admittance is a function of the complex frequency s.

Fig. 1 shows a network 1 having a pair of input terminals 2 and a pair of output terminals 3. The network consists of n parallel branches, which for the sake of simplicity and for illustrative purposes, have been shown as

branches

4, 5, 6, 7, and 8. Each branch consists of a series connected resistance-capacitance combination such as R4C4, R5C5, etc.

The network is characterized by a transfer admittance which is a desired function of the complex frequency where the complex frequency represents the rate of occurrence of the input pulses applied between the terminals 2, so that a current flows in the output terminals 3 and through a load circuit which is related to the rate of occurrence of the pulses in the same manner as the transfer admittance. Thus, the network 1 may be described by the fact that the time average T of the output current depends on the rate of occurrence of the input pulses. That is,

The precise functional relationship of the time average of the output current T and the rate of occurrence r of the pulses may be controlled by controlling the relative magnitude of the resistive and capacitive components of the network. Thus if an output current is desired which, for example, is a logarithmic function of the input pulse rate, a network is synthesized in which the resistive and capacitive elements of the various branches are related according to the equation:

where R, T, are design parameters, and a is a dimensionless number assumed to be greater than unity. Dimensions of R and T are those of a resistance and time respec tively. The exact manner in which these formulae for the resistance and capacitance elements are derived will be shown in detail later when a rigorous mathematical analysis will be disclosed. However, it must be pointed out that the synthesizing of networks having desired admittance characteristics are techniques well known to those skilled in the art, and reference is made to Symposium on Modern Network Synthesis, Polytechnic Institute of Brooklyn, New York (1952), which provides an excellent review of the techniques and principles of network synthesis.

In a similar fashion, it is possible to synthesize a network which has an admittance that is a fractional power of the complex frequency s where the complex frequency represents twice the rate of occurrence 2r of S111 1m log a Tsin 1ra10ga MP1 where A, a, T and a are design parameters and a is a dimensionless number larger than unity and a .is larger than and smaller than unity. Then Y (s) and, in this particular case Y (2r), is approximately By properly choosing values of at in the range between 0 and unity, a network may be synthesized which produces an output current which is any desired fractional power of the input pulse rate.

It is possible, of course, by utilizing network synthesis techniques to synthesize many other types of networks having other functional relationships to the complex frequency and, in turn, to a pulse repetition rate than the specific ones disclosed above. Consequently, these examples are not to be considered as limiting, but merely illustrate specific examples of the broader inventive concept.

Referring now to Fig. 2, there is disclosed a counting rate apparatus which includes, among other elements, a network of the type disclosed in Fig. 1. The counting rate apparatus of Fig. 2 comprises a network which is characterized by a transferadmittance which is a desired function of the complex frequency where this complex frequency represents apulse rate, an electronic switch means which is adapted to be switched successively to positive and negative states by successive input pulses representing the events in a random time series, and unidirectional conducting means coupled to the output of the network whereby a current flows which is a desired function of the rate of occurrence of the input pulses.

The switch means consists of a bi-stable multivibrator 20 which, as is well known, possesses two conditions of stable equilibrium. The bi-stable device 20 consists of two cross-coupled

electron discharge devices

21 and 22. The electron discharge device 21 is a vacuum triode which has its anode connected to a source of energizing voltage with respect to ground B-+ through an anode resistance 23. The cathode is connected to a source of reference potential such as ground through a cathode resistance 25 which is by-passed for AC. by means of a capacitance 26. In a similar manner, the electron discharge device 22 has its anode connected to a source of voltage 8+ through an anode resistance 24 while its cathode is connected to a source of reference potential such as ground by means of the same cathode resistance 25. Thus, the cathodes of the two electron discharge devices are connected through the common cathode resistance 25 and the bypass capacitance 26 to provide a suitable cathode bias for the grids of the electron discharge devices.

The anode of the discharge device 21 is coupled to the control grid of discharge device 22 through a parallel resistance capacitance circuit 29 and to ground through the grid leak resistance 30. Similarly, the anode of discharge device 22 is coupled to the control grid of the electron discharge device 21 through a parallel resistance capacitance circuit 27 and then to ground through the grid leak resistance 28. Circuits of this type are char- .acterized :by the :fact that they possess two conditions of stable equilibrium. One of these conditions is when the discharge device 21 is conducting and the discharge device 22 is non-conducting; and the other when discharge device 22 is conducting and discharge device 21 is cut off. The circuit remains in one or the other of these two conditions with no change until some action occurs which causes the non-conducting tube to conduct. The tubes then reverse their functions and remain in the new condition until another action occurs. .It is because of this characteristic of remaining in one state of equilibrium until an event occurs which reverses the situation and brings about another state of equilibrium, that this circuit is known as a bi-stable circuit.

In order to change the equilibrium states of the device, it is necessary, as has been pointed out, that the conducting tube be caused to become non-conducting while the cut-off tube becomes conductive. To this end, it is necessary to inject negative triggering pulses into the circuit in order to achieve the reversal of states. A double diode 31 mounted in a single envelope provides the means for injecting triggering pulses into the circuit. The diode 31 contains a common cathode member 32 connected to an input terminal 35 to which are applied a series of negative pulses representing the random events in the time series whose rate of counting is to be measured. A pair of diode anode members 33 and 34 are connected respectively to the anodes of the

discharge devices

21 and 22.

Consequently, negative pulses appearing at the input terminals 35 are applied through the diodes 31 to the anode of the non-conducting tube, since the anode of the non-conducting tube and that of the diode connected to it is at a high positive potential relative to a cathode 32 of the diode 31, thus permitting conduction of the diode. The negative pulse applied to the anode of the non-conducting tube is applied to the grid of the conducting tube through the capacitance element of one of the parallel resistance-

capacitance circuits

27 and 29. The conducting tube is thus cut off, by virtue of the negative pulse applied to its control grid, causing its anode voltage to rise thereby raising the grid voltage of the formerly non-conducting tube, causing to to become conductive. This condition then continues until the next negative-input pulse comes in at which time the equilibrium condition will again be reversed in'a similar fashion. Thus, the

electron discharge devices

21 and 22 will be switched successively to conducting and non-conducting conditions by successive input pulses. As a result the anode voltage of the electron discharge device 22 will successively be switched to a positive condition when the discharge is not conducting and to a negative state when it is conducting.

Connected to the anode of the discharge device 22 is a network 10 of the type shown in Fig. 1 which consists of a number of parallel branches, 11, 12, -16- n, each of which consists of a series connected resistance capacitance combination. Coupled to the output of the network 10 are a pair of oppositely poled

rectifiers

36 and 37 and a meter 38 to provide a measure of the current iiowing through the network 10 and the rectifiers. The network 10, as was pointed out previously, may be constructed to have a transfer admittance which is a 1 I 7 function of the complex frequency which in this instance i represents a pulse rate. Thus, there flows in the output .of the network a current which is a desired .function of the input pulse rate.

In operation, successive input pulses between terminal 35 and ground causes the plate voltage of 'the electron discharge device 22 to become successively positive and. negative, since it is successively caused to be conducting and non-conducting, and apply to the network 10 consecutive step voltages of positive and negative signs which have the same rate of occurrence as do the input pulses to terminal 35 which represent events in a time serie'i,-

T7 ,Thus, if network 10 is constructed according to the formula:

2 log a a T log a a" that the output current may be utilized for other purposes, such as controls, than actuating a meter.

The foregoing description and explanation of the measuring apparatus illustrated in Figs. 1 and 2 will be more easily understood and the full scope of the inventive concepts established if the following theoretical basis is established.

In order to do so, a generalized form of the apparatus of Fig. 2 is shown as Figs. 3a and 3b and will be utilized in establishing the theoretical basis. The circuit of Fig. 3 consists of:

(1) Two

voltage generators

42 and 43 functioning equipment and operating voltages, which, as functions of the time t, are written as v(t) and -v(t) respectively;

(2) A stable linear network 40, active or passive, including two terminal pairs of suitable transfer admittance e (3) Two synchronized single-pole, double-throw switches 41 and 44, both thrown either to the upper or lower position simultaneously. These switches are actuated in such a fashion that they change position whenever an event in time series occurs.

The network shall have a transfer admittance Y(s), where s is a complex frequency. The implication of this statement may be seen most clearly with reference to Fig. 3b. When a voltage W(t) that vanishes for t and is quite arbitrarily for t 0, is applied to the left hand or input terminal of the previously quiescent network 40, the

current i(t) in the upper lead of the right hand or output terminal is given by the equation Here L- denotes the operation Take the inverse Laplace transform of, and L denotes the operation Take the Lalace transform of. In detail,

Equations

1 and 2 are i(t) f Ye W(s) e"ds 3 Where here i= and the integral in Equation 3 is taken along a suitable contour in the complex s plane, according to the teachings of the calculus of Laplace transforms, a

common tool in the analysis of transients. Combining

Equations

3 and 4 gives the resultant equation "8 4b which show respectively the configuration of w(t) and i(t). As a consequence of this restriction, the Equation 5 takes the form f Ye :w(r)e'"drds=0 a if the function W(r) fulfills the condition The operation of the device shown in Fig. 3a is as follows: Assume that the voltage generators are turned on at the time t=0 (there is no loss of generality in this assumption), simultaneously the synchronized switches are thrown alternately to the plus position into the minus position whenever an event of the time series occurs. The position of the switches may be described by a switching function (t), which assumes the value plus one when the switches are in the plus position, and the value minus one when the switches are in the minus position. An example of such switching function is illustrated in Fig. 4c. The steps in the switching function, of course. coincide with the events of the time series.

The voltage that is presented to the input of the network 40 of Fig. 3a is then no longer v(t) but v(t)f(t). According to Equation 5 the current i,,(t) in lead a" is given by the equation Furthermore, the current i(t) in lead b" is defined by These two equations may be combined into one equation by rewriting them as combining (8) and (10) results in the form Considering a large number or ensemble of identical devices of the type shown in Fig. 3a, and assuming each member of the ensemble is excited by identical voltage generators furnishing the voltages v(t) and -v(t), a final generalization of the circuit may be achieved. The switches of each member of the ensemble are thrown according to a time series which differs from member to member. However, all of the time series shall be stationary random series the same rate r for all members of the ensemble. Consequently, the ensemble average denoted by angular brackets-of the current i(t) is formed. Accordingly, Equation 11 assumes the form since at any instant 1- there are, on the average, as many members of the ensemble with the switches in the plus position (f(-r) =+1) as there are members with the switches in the minus position (f(-r) =-l).

Furthermore, f(t)f('r) =+1 if an even number of switching occurred between the instance I and 'r and j(t)f(-r)=l if an odd number of switching occurred between the instance 1 and '1'. These two be combined into one by writing equations may Inserting Equation 13 and Equation 16 into Equation 12 changes its form into e r] 1 u t(t) 2 Y(s)e form-)4; e d-rds (17 The integral over '1' that occurs in Equation 17 may be transformed as follows:

f v()2 sin M21 (1' t) e "1dr -r=0 Inserting Equation 18 into Equation 17 provides form i(l) =A-B (19) Where It will now be shown that the expression B vanishes. Making the substitution for one of the integration variables in Equation 21 gives an expression for B which states 10 Changing the name of the integration variable a inton the following form for the equation is achieved Furthermore, because of the factor sin h(2r1-) which vanishes for 1'=O,

Comparing Equation 22 with Equation 6, and Equation 24 with Equation 7 it can be seen that B=0 ('25-) Combining

Equations

19, 20, and 25 transforms the equation for the ensemble average of i i) into the form Now, according to the definition of the Laplace transform,-

V(8) =Lm run Hence,

f (T) -(n-Zr) rd VG-27) Combining Equation 26 and Equation 27 results in the following form of the equation Substituting a=s2r for the integration variable, theequation takes the form Changing the name of the integration variable into .9, transforms the equation into Equation 30 is the key formula on which many practical devices may be based. This equation states that the ensemble average of the current in lead B of the deviceshown in. Fig. 3a is the same as the output current for an unswitched network excited by the same voltage, re duced by the factor A, if the unswitched network is chosen in such a manner that its transfer admittance is related to the transfer admittance Y(s) of the switched network by Y+ (s)=Y(s -|-2r).

In particular, when the voltage generators furnish di rect current voltages +V and -V, then Equation 30 then assumes the form For large values of the time t, it can be shown that lim L Y s+2T ]=1im [8'1-Y(8+2T)]=Y(2T) H 8 8%0 s so that 1-H 2 The meaning of the term large values of the time t is that transients that are caused by the switching on of the generators (not transients that are caused by the switching, since these are essentially to the operation) have had time to die out. Consequently, from now on the assumption is made that those transients have died out, so that Equation 33 may be rewritten as i(t) =i Combining this with Equation 34, it can be seen that mgr 21 as) From Equation 35, it can be seen that a measuring apparatus can be constructed, the output current of which depends on the rate of occurrence of input pulse to the network. A condition for constructing a measuring apparatus having these characteristics is that the input pulses to the network are alternately positive and negative. Thus, by connecting an electronic switch which is sequentially switched to positive and negative states by successive pulses representing a time series the above requirement is satisfied. It is also apparent from Equation 35 that the transfer admittance of the network is a function of a complex frequency which, in the instant case, represents a pulse rate. Consequently, if the network is constructed to have a transfer admittance which is a desired and specific function of the complex frequency, it will produce an output current which in a similar fashion is functionally related to the input pulse rate.

It has also been shown that in the generalized apparatus of Fig. 3 that the output current is positive when the last throw of the right hand switch 44 was positive, and is negative when the last throw of the switch 44 was to the minus position. Consequently, the right hand switch 44 of Fig. 3 may be replaced by a pair of oppositely poled diodes such as are shown in the specific embodiment of Fig. 2. Similarly, the left hand switch of Fig. 3 may be replaced by an electronic switch, such as a bi-stable multivibrator, which is actuated by pulses coincident with the events in the time series and function to switch the equilibrium condition alternately to a positive and negative state. Thus, it can be seen that the generalized apparatus of Fig. 3 may be replaced by simple electronic equipment to produce a counting rate apparatus, such as shown in Fig. 2, embodying the instant invention.

As was pointed outwith reference to Figs. 1 and 2, it is desirable for many purposes, such as nuclear instrumentation, to provide a counting rate measuring apparatus which has a logarithmic relationsip between an output electrical signal, such as a current, of the apparatus and the input pulse rate. That is, it is desired that the output depend on the rate r according to the equation =%1 1+m (so where R and T are designed parameters. This may be achieved by constructing a two-terminal pair network of the type shown in Fig. 1, characterized by a transfer admittance such that the current flowing in its output is ap' proximately that defined by Equation 36. Thus, according to Equation 35 a network must be synthesized which has a transfer admittance Y(s) as a function of the complex frequency s as given by the equation Y(s log (1+%') 37 This equation is of the form Y(s) g(z) with Z=8T (38) In the instant case this can be rewritten as z (1+5) (so It will now be shown how it is possible to synthesize very simple networks for a wide class of functions g(z). This class of functions has the property that g(z) may be expressed in the form where sc 0 and. h(:c) 0 for 2:22; (40) Obviously g(z) must fulfill certain conditions so as to be expressed in the form disclosed in Equation 40. However, it is not necessary to spell out these conditions in advance. They become clear as one attempts to solve for the function h(x). After the function h(x) has been found, it is possible to select the proper circuit elements, resistors, capacitors and inductors, in order to achieve the desired result.

The necessary first step is to find the function h(x). This may be done by means of well-known procedures utilized in the theory of analytical functions (the transfer admittances are analytical functions of the complex frequency). Starting with the Cauchy integral form where the integration contour enclosures, in a counterclockwise direction, the point z but no singularity of an I If the functions g(z) are restricted to a type whose only singularity lies on the negative real axis to the left of some point Z 0, the following integration contour may be used advantageously.

13 contour'consists. ofa circular portion and a hairpin portion. If; furthermore, g('z) fulfills the condition then, as the radius of the circular portion is made larger and larger, the contribution to the integral of Equation 41 from thecircular. portionoithe contour tends to be 0. Thus, Equation 41 assumes the form 1 z 1 3? lbelow Where ()-]above:

is the value of the multivalued function g() on the upper leg of the shrunken hairpin and Where [8) ]below is the value of the multivalued function g() on the lower leg of the shrunken hairpin.

Making: the substitution. =x for the integration variable, and denoting -2 by x ('x 0),vthe;equation takes the: following form In the particular example shownin Equation 39,.itcan beseen that-'z =2, hence 76 :2, and

consequently h(x)'=% V 1-4 and' Thus; Mac); has turnedoutto. be positive for'x x as-is clearly shown by Equation 47. At this point itis-neces. sary. to check Equation 48.. It can be seen that; Equation 48, upon substitution of the proper functions therein, takes the form A (2+ 2) z i l? 1+2 It" is obvious, once the. substitution is made, that Equation 48 devolves into the desirable form exhibiting logarithmic characteristics.

In order to facilitate the'synthesis of the network, it is desirable to make the following substitution x=2+2a dx=2(log a)a dn in the integral of Equation 49. From this substitution Equation 49 takes the form The integral of' Equation 50 maybe approximated" by a sum, which thus permits the obtaining of an approximate value Y s) for the transfer admittance. Thus the equation. for; the. approximate: value Y fi) is 2 log a 2 8 T 2a R s T+2+2a 2+2a or, rewriting the above equation, it takes the form This equation. may then be rewritten. in. the following. form then with the terms R andC being defined by the following equations Equation 53 shows that the transfer admittance is the admittance of a circuit with an infinite number of parallel branches, n being the order number of the branches,

with. branch n consisting of a resistor with resistance R,

and a capacitor with capacitance. C connectedin, series.

In the limit a- 1, the approximation for the transfer admittance becomes exact, as is shown by the following equation There arepractical advantages, relatingto the. number of. parallel branchesrequired, in choosing. the number, a;

which is a design parameter, to be quite a bit larger than '15 unity. The advantage to be gained is that the larger a the fewer branches are necessary if a specified range of rates is to be covered. Consequently, it is necessary to determine how well Y (s) approximates Y(s).

For the purpose of a counting rate meter it is necessary to examine Y ,(s) and Y(s) for s=2r, where r is the rate of events. Thus, comparing the transfer admittance Y(s) and the approximation thereof, the following relationship may be seen r T a It is now necessary to compare Y -(2r) for two rates r and r related by l+r T=a(l-{rT) The equation for the approximate value of the transfer admittance is defined as follows:

Y (w,. s a 1+rT 1 1 H R 5,, a(l+rT)+a= 1+a 2loga g l-l-rT 1 :l

R 1+1'T+a 1+0.

or, on changing the summation index from n to n+1 2 log a 1+T 1 rmnr( '1) R gm 1+ T+ n 1+an+1] Combining

Equations

57 and 56 provides the following transformation In the last sum all terms cancel except the terms However, since a l, the following relationship between the transfer admittances for the two rates may be established uma) pnr( R g a Furthermore, it can be seen from Equation 55 that the following relationship also exists Combining Equation 5 8 and 59 provides the following equation appr( 1)' 1)= appr( This equation shows, that if Y flr) tracks Y(2r) rather 16 well over the range 1+rT=l to 1+rT==a, it will track also over the range 1+rT=a to 1+rT=a and over the range 1+rT=a to 1+rT=a etc. Hence, the approximation need only be examined over the range 1+rT=l to l+rT=a. For the choice 11:10 the tabulation exhibits the following characteristics:

14mm -Y(2r) It can be seen that, even with a value of a as large as 10 the tracking is excellent. The largest deviation between is only .002. Of course, when the design parameter a is chosen closer to unity, the tracking will be even better. However, as was pointed out previously, in that case larger numbers of the parallel branches will have to be utilized.

In order to illustrate a practical example of such a logarithmic counting rate apparatus, it may be assumed, for the purpose of illustration, that it is desired to measure an rT which covers the range from 0 to 10 Ideally, the output current would be defined by the equation V l ldenll 2 g However, let it be assumed that an accuracy defined by the formula is satisfactory, Consequently, it will suffice to let n, the number of parallel branches in the network, run from X -2 to +6. Thus, nine resistance capacitance combinations will be required for this desired accuracy. Furthermore, assuming that the following choices for the other parameters are satisfactory:

V=23.0 volts T=1 sec. R=1.152 meg.

the output current is approximately i=20 microamps log(1+rT) For the range rT=0 to 10 the counting rate covers the range r=0 to 10 sec- The current for r=l0* see is then i=20 microamps log (10,001)=184 microamps. The values of the resistances and capacitances for our choices of the design parameters R, T, and :1 become i=20 microamps log(1+r sec) to within 0.2 microamps.

It is obvious, of course, that there is a wide range of choice in the three design parameters R, T, and a, so

that counting rate meters with logarithmic outputs may be designed according to a wide range of specification.

In the mathematical analysis made above, it has been shown by Equation 35 that counting rate devices may be designed having output currents which are a specified function of an input pulse rate. Furthermore, a network was synthesized for use in such a device which provides an output current which is a logarithmic function of the input pulse rate. It must be realized, however, that many other networks having functional relationships other than logarithmic may be synthesized for use in devices of this type.

For example, it is possible to synthesize a network, and a counting rate meter, which is characterized by the fact that the transfer admittance and the output current is related to the rate r by the equation t- (2rT) (61) where R, T, a are design parameters, and a is restricted to the values O zx 1. In this instance the current is proportional to a fractional power of the rate r. According to Equation 35 there must be synthesized a network having a transfer admittance defined by the equation This network will also be constituted of a number of parallel branches, each of which comprises series connected resistance-capacitance combination. In this particular case the function g(z), as defined in relation to Equation 38 takes the form The branch point 2 is now Equation 46 may now be utilized to find the functions g above and below, thus Thus, utilizing Equation 40 the term Zu may be :determined,

It is again necessary to check the above equation in order to determine whether it takes "the proper form. It can be seen, on substituting the proper functions therein that Making the following substitution in the above equation,

L Y d dY z 1Y z (1-Y) it is transformed into the following form The latter integral is well-known, and there may be substituted therefore the following equation 1 f Y (1-- Y) dY=1(a)I(1-a) Y=0 where 1 denotes the gamma function. Furthermore, it is well-known that On making the following substitution,

x=a dx= (loga) a dn Equation 67 takes the form sT sT+a Y(s) R T a dn (68) Again it is possible to approximate the above integral by the following sum Equation 70 shows that the transfer admittance is the admittance of a circuit with an infinite number ofparallel branches, n being the order number of the branches, with branch n consisting of a resistor with ,a resistance R and a capacitor with a capacitance q connected ,in

19 series. Equation 71, which defined the magnitude of the resistance and capacitance components is utilized in designing the various components of the network. The parameter a therein is a dimensionless number which is greater than and less than 1, while R is a design parameter.

In a manner similar to the two examples disclosed here, many other types of networks may be synthesized in order to produce a counting rate device which produces an output signal which is a desired function of the input pulse repetition rate. The mathematical analysis principle of this invention has been based on a repetition rate of the input pulse that is random. However, it can be shown mathematically that the apparatus designed by operation with random series may be utilized as well for other time series, such as the periodic. It can be shown that the current produced by the application of a periodic series will exceed that produced by the application of a random series. However, for high counting rates, the excess becomes constant and may, therefore, be cornpensated for by means of calibration techniques. Consequently, for higher counting rates, the apparatus here disclosed may be utilized with periodic time series, as well as with stationary random series.

It will be appreciated from the foregoing discussion that it is possible with the teaching of this invention to construct counting rate measuring devices having many different types of response, where the term response refers to the functional relationship between the output current and the input pulse rate. However, it should also be understood that it is possible with the teaching of this invention that any counting rate apparatus may be converted into an anti-counting rate apparatus. That is, a device that converts a current into a pulse rate having a desired functional relationship to the current. Broadly speaking, such an anti-counting rate device may be constructed by combining a source of variable pulses and a counting rate device.

Referring now to Fig. 5, there is shown an anti-counting rate apparatus embodying the principle of the instant invention. There is provided a pulse source 53 having a variable pulse rate. The pulse source 53 may be any one of the many well known types which have a variable pulse repetition rate. One type of pulse source which may be advantageously utilized in this circuit is the random pulse generator of the radiation detector type. That is, a radiation detector of the proportional counter or scintillation type is positioned in a constant magnitude radiation field. The output of the detector is coupled to a discriminating tube, which functions to control the number of pulses per unit time passed to its output circuit.

The discriminating circuit includes a grid biased triode, with the magnitude of the grid bias determining the number of pulses per unit time which are passed. By controlling the magnitude of this grid bias in response to a control signal, it is possible, therefore, to vary the number of pulses per unit time produced by this pulse producing circuit. Reference is made to Patent No. 2,662,188, issued to K. C. Crumrine et al. for a typical showing of a circuit of this type.

The output from the pulse source 53 is connected to an output terminal 52 and to the input of a pulse rate measuring apparatus 54 of the type illustrated in Fig. 2. The counting rate apparatus 54 includes a network 60 having a transfer admittance which is a desired function of a complex frequency, where this complex frequency represents the input pulse rate. Coupled to the input of the network 60 is an electronic switch means 57, of the bi-stable multi-vibrator type, which provides alternately positive and negative pulses in response to the input pulses from the pulse source 53. Coupled to the output of the network 60 are a pair of oppositely poled

diodes

63 and 64.

, The bi-stable multivibrator 57 consists of two alternately conducting

space discharge devices

58 and 59 of the vacuum triode type, which have their anodes and control grids cross-coupled by means of the parallel resistance,

capacitance networks

61 and 62. Circuits of this type are characaterized by the fact that they possess two condi tions of stable equilibrium. The multivibrator remains in one of the other of these two conditions until some action occurs which causes the non-conducting tubes to conduct. The tubes then reverse their function and remain in the new condition until another action occurs.

In order to change the equilibrium state of the multivibrator 57, the pulses from the pulse source 53 are injected into the circuit by means of the double diode 56. The pulses are applied through the diode 56 to the control grid of the

discharge devices

58 and 59. The negative pulses will, as was explained with reference to Fig. 2, cause the conducting tube to be cut off while the nonconducting tube becomes conducting. This condition then continues until the next negative pulse, at which time the equilibrium condition will again be reversed. Thus, the

electron discharge devices

58 and 59 are successively and alternatively actuated to conducting and non-conducting states by successive input pulses. As a result, the anode voltage of the electron discharge divice 59 is successively at a maximum level when the discharge device is non-conducting and at a minimum level when it is conducting, thus effectively applying alternately positive and negative voltages of the type shown in Fig. 46, to the network 60.

Coupled to the output of the counting rate measuring apparatus 54 is a comparison means, comprising a capacitance C wherein the output current from the measuring apparatus 54 is compared with the input current supplied through terminal 51 to provide a control voltage on capacitance C for varying the repetition rate of the pulse source 53 until the two currents are equal. If the output current from the counting rate apparatus 54 does not equal the input current applied to the terminal 51, there will be produced a voltage on capacitor C which is applied by means of leads 65 to the input of a direct current amplifier 55. Although in the embodiment of Fig. 5, a capacitance C has been shown for the sake of simplicity, it will be obvious that many other suitable comparison means may be utilized. For example, a differential amplifier system of the type disclosed in Waveforms, Chance, Hughes, MacNichol, Sayre, and Williams, McGraw-Hill Book Co., New York, 1949, vol. 19, Radiation Laboratory Series, page 642, Fig. 18.13, may be utilized in place of the capacitance C.

The output of the direct current amplifier 55 is in turn connected to the pulse source 53 in order to vary its repetition rate until the output current from the counting rate apparatus 54 equals the input current at the terminal 51. When this equality between the two currents is achieved, the repetition rate of the pulse source appearing at the output terminal 52 is functionally related to the input current in a manner depending on the specific character of the network 60 in the counting rate apparatus 54. For example, if the network 60 is of the type which produces an output current which is a logarithm of the input pulses, the repetition rate of the output pulses at the terminal 52 will be exponential function of the current applied at the input terminal 51. By examining the equation:

it can be seen that the rate r is an exponential function of the input current I, that is,

In a similar fashion, by utilizing networks having characteristics other than logarithmic, it is possible to produce at the output terminal 52 pulses having repetition rates which are different functions of the input current.

Demonstrating the broad scope of the inventive concept, is the fact that it is possible by utilizing the various pieces of apparatus disclosed above, i.e. the anti-.counting rate apparatus, to produce a general class of function generators which will convert an input current into an output current having a desired functional relationship to the input current. Since the anti-counting rate device contains a network of the type illustrated in Fig. 1, while the counting rate apparatus also contains a network of this type, and since it is possible to produce network having many varied types of functional relationships, it can be seen that many varieties of function generators may be constructed in carrying out the teachings of the instant invention.

Fig. 6 illustrates a function generator embodying the principles of the instant invention. 'Ihisfunction generator consists, broadly speaking, of an anti-counting rate apparatus 70 having an output terminal 72 connected to the input of a counting rate apparatus '86 having an output terminal 96. The primary components of the function generator are operationally related in that the anti-counting rate apparatus produces an output pulse rate at its output terminal 72, which is a desired function of a current applied to its input terminal 71. These are ap-. plied to the counting rate apparatus 86 and are converted into an output current appearing at the output terminal 96 which is a specified function of the input pulse rate. Consequently, the output current at the terminal 96 is a function of the input current at 71, the specific function depending on the type of network utilized both in the anti-counting rate apparatus and the counting rate apparatus.

The counting rate apparatus 70 includes a pulse source 73 having a variable repetition rate which may be adjusted in response to a control signal. The pulse source 73 may be of any well known type and, specifically, may be a scintillation detector or proportional counter type discussed in detail with reference to Fig. 5.

Coupled to the output of the pulse source 73 is a counting rate device 74, comprising bi-stable multivibrator 7-7 and network 100, which, for the sake of clarity in distinguishing it from the counting rate apparatus 86, will be referred to as an internal counting rate apparatus.

The internal counting rate apparatus 74 functions to produce an output current which is a desired function of the repetition rate of the pulses from the source 73. This output current is applied to a comparis n means con-,

sisting, in this instance, of a capacitance C where it is compared with a current applied to the input terminal 71. If the current applied to the input. terminal 71 and the current from the internal counting rate apparatus 74 are not equal, a control signal is applied by means of the lead 85 to the input of the direct current amplifier 75. The output of the amplifier 75 is connected to the pulse source 73 and operates to adjust the repetition rate of the pulse source 73 until an equality between the two currents is achieved. When such equality is achieved, the pulse repetition rate of the pulse source 73 appearing at terminal 72, is functionally related to the input current in a manner depending on the type of network utilized in the internal counting rate meter. That is, iffor example, a network having a logarithmic characteristic is utilized, the repetition rate of the output. pulses, as will .be shown later by a rigorous mathematical analysis, Will be an exponential function of the input current. i

The internal counting rate meter 74 comprises a bistable multivibrator 77 which functions to apply alternately positive and negative pulse voltages to a network in response to successiveinput pulses from the pulse source 73. The bi-stable multivibrator consists of two

space discharge devices

78 and 79 of the vacuum triode type having their anodes and control grids cross coupled by means of the

parallel resistancercapacitance network

80 and 81. The input pulses from the source 73 are applied to the bi-stable multivibrator 77 by means of a double diode 76 having a common cathode and two anodes that are connected respectively to anodesof the

triodes

78 and 79. The multivibrator 77 is characterized by two conditions of stable equilibrium. The circuit remains in one or the other until an input pulse arrives from the pulse source 73. Upon the occurrence of such a pulse, the circuit reverses its condition until the occurrence of the next pulse. As a consequence, the anode of the triode 79 is alternately at a maximum level and a minimum 'level depending on whether the tube is nonconducting or conducting.

Connected to the anode of the tn'ode 79 is a network of the type disclosed in Fig. 1 which consists of a multiplicity of parallel branches, each of which consists of a series resistance-capacitance combination. Connected to the output of the network 82 are a of oppositely poled

diodes

83 and 84. The network 82, as has been pointed out previously, may be constructed to have a transfer admittance which is a desired function of the complex frequency and which, this instance, represents a pulse rate. Thus, there flows in the output of the network a current which is a desired function of the input pulse rate. Consequently, the output terminal 72 provides output pulses which have a repetition frequency which is a specified function of the input current applied to the terminal 71 of the counting rate apparatus 70.

Connected to the terminal 72 is a counting rate apparatus 86 which, as explained previously, functions to transform these pulses into an output current which is a specified function of the repetition rate of the pulses. The counting rate apparatus 86 similarly includes a bi-stable multivibrator 88 having coupled to its output a network 87 whose transfer admittance is a desired function of the input pulse rate. The bi-stable multivibrator 88 comprises two

space discharge devices

89 and 90 of the vacuum triode type, having their anodes and control grids cross-coupled by means of the parallel resistance-capacitance networks 91 and 92. The input pulses from the terminal 72 are applied to the bi-stable multivibrator 88 by means of a double diode 93 having its anode members connected respectively to the anodes of the

triodes

89 and 90. The input pulses function to reverse the equilibrium conditions of the circuit upon the occurrence of each input pulse. Consequently, the vacuum triode 89 is successively placed in a conducting and non-conducting condition by these pulses, and its anode voltage is alternately at maximum and minimum level depending on its conducting or non-conducting conditions. These effectively alternate positive and negative pulse voltages are applied to the network 87 and will cause a current to flow which is a specified function of the pulse rate.

Coupled t0 the output of the counting rate apparatus 86 is an adjustableconstant current source 97. This constant current source functions either to add a constant DC. current of a given magnitude or to subtract a constant DC current of a given magnitude. The function of this constant current source will be explained in greater detail when a more rigorous mathematical analysis of the operation of the function generator is given. The constant current source may be any of many well known types. For example, it could constitute a battery, or a constant current pentode, or even a regulated current source. The specific construction of the constant current source is not critical as long as the magnitude of the current produced thereby is both constant and adjustable.

As has been stated previously, the pulse rate r appearing at the output terminal 72' is a function of the input current I applied at the terminal 71. The precise function depends on the design of the network 82 in the internal counting rate apparatus 74, Forexample, if. a network is synthesized which provides a logarithmic res sponse, then the relationship between the current and rate of pulses is defined by the equation:

23 Thus, it can be seen that the repetition rate of the output pulses is an exponential function of the input current 1. Suppose that for the counting rate apparatus 86 a network is utilized that has a linear scale, so that its output current I follows the equation:

where A is a design parameter. Consequently, the output current may be defined in terms of the input current I by the equation:

A RI li'e p 7 If a constant DC. current of magnitude is added to the output current I, then the current appearing at the output terminal 96 may be defined by the equation:

Thus, there has been constructed a function generator which produces a current K that is an exponential function of an input current I.

In order to demonstrate the extreme flexibility of the instant invention in constructing function generators having many sorts of functional relationships between the input current and the output current, assume that the network 82 in the internal counting rate apparatus 74 has a linear scale and the network 87 of counting rate apparatus 86, has a -logarithmic scale. Thus, the relationship between the input current I to the anti-counting rate device 70 and the pulse rate is defined by the equation:

I=Ar or 1-:

Since the output current I may be defined by the equation:

1 J log (1+TT) this equation in its final form states,

Suppose that from some given current H there is subtracted a constant current of a magnitude If the difference of these two currents is then applied to the combination of anti-counting rate apparatus and counting rate apparatus, the input current I to the terminal 71 takes the form:

As a consequence, the output current I may now be defined by the equation:

In this manner, it has been possible to construct a func- 24 tion generator that produces an output current I which is a logarithmic function of an input current.

From these examples, it should be obvious that a very large class of function generators may be constructed embodying the principles of the instant invention. The precise functional relationship of the input to the output current which may be created will depend on the character of the networks 82 and 87 which are utilized. Although the networks which have so far been illustrated and discussed, have contained resistance and capacitance elements, it is obvious, of course, that reactive elements other than capacitances may be utilized. That is, thenetwork may be constructed of resistive and inductive elements, for example, and still fall within the scope of this invention. It is also possible to use series inductive-capacitive combinations as along as the circuits are such that the current pulse illustrated in Fig. 4b eventually reaches a steady state condition.

Furthermore, although the components of these networks have been shown as passive elements, so that the network as a whole is passive, the inventive concept is not limited to passive networks but may incorporate therein active elements such as amplifiers. It should also be pointed out that although the previous discussion has been carried out in terms of transfer admittances which describe relationships between input voltages and output currents, it is quite obvious that the instant invention is not limited thereto. That is, the voltage sources v(t) and -v(t), illustrated in Fig. 3a, may be replaced by constant current sources i(t) and i(t) and a network synthesized having the desired transfer impedance.

While I have shown a particular embodiment of this invention it will, of course, be understood that the invention is not limited thereto since many modifications both in the circuit arrangement and in the instrumentalities employed may be made. It is contemplated by the appended claims to cover any such modifications as fall within the true spirit and scope of this invention.

What I claim as new and desire to secure by Letters Patent of the United States is:

l. A pulse rate measuring apparatus, comprising means actuated in response to input pulses having a variable rate of occurrence for furnishing successive positive and negative pulses, network means coupled to said last named means, said network means characterized by an admittance which is a function of a complex frequency representing a pulse rate so that an output signal is produced whichis dependent on the rate of occurrence of said pulses, and unidirectional conducting means coupled to the output of said network.

2. A pulse rate measuring apparatus, comprising switch means actuated in response to pulses having a variable rate of occurrence, said switch means adapted to furnish successive positive and negative pulses in response to successive input pulses, network means coupled to said switch means characterized by an admittance which is a function of a complex frequency representing a pulse rate so that an output signal is produced which is dependent on the rate of occurrence of said pulses, and unidirectional conducting means coupled to the output of said network.

3. A pulse rate measuring apparatus, comprising switch means actuated in response to random pulses having a variable rate of occurrence, said switch means adapted to furnish successive positive and negative pulses in response to successive input pulses, network means coupled to said switch means for receiving said successive positive and negative pulses, said network being characterized by a transfer admittance which is a logarithmic function of a complex frequency representing a pulse rate so that a current flows which is a logarithmic function of the rate of occurrence of said input pulses, and unidirectional conducting means coupled to the output of said network.

4. A pulse rate measuring apparatus, comprising switch means actuated in response to random pulses having a variable rate of occurrence, said switch means adapted to, furnish successive positi e; and negative pulses in, re; sponse to successive input pulses, network meanscoupled, tosaid switch means for receiving said successive positive and; negative pulses, said network being characterized by a transfer-- admittance which is. a fractional power {1111C} tionof a; complex frequency representing a pulse rate sothata; current flows which is a fractional power function, of the rate of-occurrence of said input pulses, and uni directional conducting means coupled to the output of; said; network. 7

5,. A pulse ratemeasuring-apparatus comprising switch means actuated in response, to pulses having a; variable rate of occurrence, said switch means adapted to furnish successive positive, and negative pulses in response to successive input pulses, network means, coupled to, said switch means for receiving said successive positive and negative. pulses, said network being characterized by a transfer admittance which is a logarithmic function of a complex frequency representing a pulse rate whereby a current flows which is a logarithmic function of the. rate of occurrence of said pulses, said network comprising a multiplicity ofparallel connected series resistance capacitance branches, and undirectional conducting means coupled to the output of said network.

6. A pulse rate measuring apparatus, comprising switch means actuated in response to random pulses having a variable rate of occurrence, said switch means adapted tofurnish successive positive and negative pulses in: response to successive input pulses, network means. coupled to said switch means for receiving said successive positive and negative pulses, said network being characterized by a transfer admittance which is alogarithmic function of a complex frequency representing a pulse rate so that a current flows which is a logarithmicfunction of the rate of occurrence of said pulses, said network comprising n parallel connected series; resistance-capacitance branches, the magnitudes of; the resistive and capacitive elements-being defined by where r is the ratev of occurrence of the input pulses, T is time, and a and R are designed parameters, and unidi rectional conducting means coupled to the output of said network;

7. A pulse. rate measuring apparatus, comprising electronic switch means actuated in response to random pulses, having a variable rate of occurrence, said switch meansadapted to furnish successive positive and nega-v tive pulses in response to successive input pulses, network means coupled to said switch means for receiving said positive and negative pulses, said network beingcharacterized by a transfer admittance which is a function of a complex frequency repr enting a pulse rate so that a current flows; which is dependent upon the rate of occurrence of said input pulses, aunidirectional conducting means coupled to the output of said network.

8. A pulse rate measuring apparatus, comprising electronic switch means actuated in response to random pulses having a variable rate of occurrence, said switch means adapted to furnish successive positive and negative pulses in response to successive input pulses, network means coupled to said switch means for receiving said PQSitive and negative pulses, said network being characterized by a transfer admittance which is a loga rithmic function of a complex frequency representing a pulse rate. so that a current flows which is a logarithmic 26 nd paral e a con e ed un di a cond c n coupled to the output of said network.

9; A pulse rate measuring apparatus, comprising a bias-table multivibrator actuated in response to -succes-; sive input pulses to transfer its conductive states and furnish successive; positive and negative pulses, saidine put pulses having a variable and random rate-ofioccur rence, network means coupled to said multivibrator-for receiving said positive and negative pulses, said network; being characterized by a transfer of admittance which is a logarithmic function of a complex frequency rep-.- resenting a pulse rate so that a current flows which is a logarithmic t'unction of the rate of occurrence of said input pulses, said network comprising a multiplicity of series resistance-capacitance combinations connected in parallel, oppositely poled rectifying means connected to said network.

10. A pulse rate measuring apparatus, comprising; a bi-stable multivibratoractuated successively to transfer its conductive states to furnish successive positive and negative pulses in response to successive input pulses, said input pulses having a random and variable rate of occurrence, rectifying means connected to the input of said multiyibrator to'apply said pulses thereto, network means coupled to the output of said multivibrator to receive said positive and negative pulses, said network being characterized by a transfer admittance whichis a logarithmic function of a complex frequency representing a pulse rate so that a current flows which is a logarithmic function of; the rate of occurrence of said input pulses, said network comprising a multiplicity of series resist} antic-capacitancecombinations connected in parallel, and oppositely poled, diodes connected to said network.

' 11. Inan apparatus for generating pulses whose repetition rate is a function of an input current, the combina tion comprisingpulse generating means having a variable repetition rate, counting rate means coupled to said pulse generating means for producing a current which a f c o i h r pe i io r t of a Pu in l ins a swi ch ns a t n po e to pu se r m said generating means to furnish successive positive, and negative. pulses, a network coupled to said switch, means for; receiving said positive and negative pulses, said net: work having an admittance that is, dependent on the pulse repetition rate for producing an output current which is a functionv 0f the. pulse repetition rate, comparison means having applied thereto current from saidcountng ate. means, and said input current, and means to vary the repetition rate of said pulse generating means until said currents. are equal whereby the repetition rate, of saidpulse generating means is a function said input current.

'12,. In an apparatus for generating pulses Whose rcpefi; tion rate is a function of an input current, the combina: tion comprising pulse generating means having a variable repetition rate, counting rate means coupled to said pulse generating means for producing a current which is a function of the repetition rate of said pulses including a switch means, actuated in response. to pulses from, said generating means to furnish successive positive and negative: pulses, a network coupled to said switch means for receiving said positive and negative pulses,.said network being characterized .by a transfer admittance that is dependent on the pulse repetition rate for producing an output current which is a function of the pulse repetition rate, comparison means including a storage means having applied thereto the current from said counting rate means and the input current, means to vary the repetition rate of said pulse generating means until said cur-rents are equal whereby the repetition rate of said pulse generating means is a function of said input current.

13. In an apparatus for generating pulses whoserepcti; tion rate is a function of an input current, the combination,

function of the rate of. occurrence of said inpu rulsea 76 comp is ng Pul e nera g me n having a afiablerqpg;

27 tition rate, counting rate means coupled to said pulse generating means for producing a current which is a logarithmic function of the repetition rate of said pulses including a switch means actuated in response to pulses from said generating means to furnish successive positive and negative pulses, a network coupled to said switch means for receiving said positive and negative pulses, said network being characterized by a transfer admittance which is a logarithmic function of a complex frequency representing said pulse rate for producing an output current which is a logarithmic function of the pulse repetition rate, comparison means including a capacitance having applied thereto the current from said counting rate means and said input current, means responsive to the output from said comparison means to vary the repetition rate of said pulse generating means until said currents are equal whereby the repetition rate of said pulse generating means is an exponential function of said input current.

14. In an apparatus for generating pulses whose repetition rate is a function of an input current, the combination comprising pulse generating means having a variable repetition rate, counting rate means coupled to said pulse generating means for producing a current which is a logarithmic function of the repetition rate of said pulses, said counting rate means including electronic switch means adapted to furnish successive positive and negative pulses in response to successive input pulses from said generating means, and a network coupled to said switch means having transfer admittance which is a logarithmic function of a complex frequency representing said pulse rate for producing an output current which is a logarithmic function of the pulse repetition rate, comparison means having applied thereto the current from said counting rate means responsive to the output from said comparison means and the input current, means to vary the repetition rate of said pulse generating means until said currents are equal whereby the repetition rate of said pulse generating means is an exponential function of said input current.

15. In an apparatus for generating pulses whose repetition rate is a function of an input current, the cambination comprising pulse generating means having a variable repetition rate, counting rate means coupled to said pulse generating means for producing a current which is a logarithmic function of the repetition rate of said pulses, said counting rate means including electronic switch means adapted to furnish successive positive and negative pulses in response to successive input pulses from said generating means, and a network coupled to said switch means for receiving said positive and negative pulses, said network comprising a multiplicity of parallel connected series resistance-capacitance combinations having a transfer admittance which is a logarithmic function of a complex frequency representing said pulse rate for producing an output current which is a logarithmic function of the pulse repetition rate, comparison means responsive to'the output from said comparison means having applied thereto the current from said counting rate means and said input current, means to vary the repetition rate of said pulse generating means until said currents are equal whereby the repetition rate of said pulse generating means is an exponential function of said input current.

16. The apparatus of claim wherein said comparison means includes a capacitance. j

17. In a function generator, the combination comprising means to generate pulses havinga repetition rate which is a given function of an input current, means coupled to said pulse generating means to produce an output current which is a function of the repetition rate of said pulses including a switch means actuated in response to pulses from said generating means to furnish successive positive and negative pulses, a network coupled to said switch means for receiving said positive and negative pulses, said network being characterized by a transfer admittance which is a function of a complex frequency representing said pulse'rate so that a current flows which is dependent 28 on the repetition rate of said pulses whereby the output current is a desired function of the input current.

18. In a function generator, the combination comprising means to generate pulses having a repetition rate which is a given function of an input current including a variable rate pulse source, a counting rate means to produce a current which is a function of the pulse rate, means to vary the repetition rate of said pulses until the current from said counting rate means equals said input current whereby the repetition rate is a function of the input current, means coupled to said pulse generating means to produce an output current which is a function of the repetition rate of said pulses including a switch means actuated in response to pulses from said generating means to furnish successive positive and negative pulses, a network coupled to said switch means for receiving said postive and negative pulses, said network being characterized by a transfer admittance which is a function of a complex frequency representing said pulse rate so that a current flows which is dependent on the rate of occurrence of said pulses whereby the output current is a desired function of the input current.

19. In a frmction generator, the combination comprising means to generate pulses having a repetition rate which is an exponential function of an input current, including a pulse source having a variable repetition rate, a switch means actuated in response to said generating means to furnish successive positive and negative pulses, a network coupled to said switch means for receiving said positive and negative pulses, said network being characterized by a transfer admittance which is a logarithmic function of a complex frequency representing the pulse rate and causes a current flow which is a logarithmic function of the pulse repetition rate, means coupled to said pulse generating means to produce an output current which is a linear function of the repetition rate of said pulses whereby the output current is an exponential function of the input current.

20. In a function generator, the combination comprising means to generate pulses having a repetition rate which is a linear function of an input current including a pulse source having a variable repetition rate, a switch means actuated in response to pulses from said pulse source to furnish successive positive and negative pulses, a network coupled to said switch means for receiving said positive and negative pulses, said network being characterized by a transfer admittance which is a linear function of a complex frequency representing said pulse rate whereby a current flows which is a linear function of the pulse repetition rate, means coupled to said pulse generating means to produce an output current which is a logarithmic function of the repetition rate of said pulses whereby the output current is a logarithmic function of the input current. v

21. In a function generator, the combination comprising means to generate pulses having a repetition rate which is the given function of an input current including a pulse source having a variable repetition rate, and counting rate means to produce a current which is a function of the repetition rate including a switch means actuated in response to pulses from said generating means to furnish successive positive and negative pulses, a network coupled to said switch means for receiving said positive and negative pulses, said network being characterized by a transfer admittance which is a predetermined function of a complex frequency representing the pulse rate whereby a current flows which is a predetermined function of the input pulse repetition rate, means to compare the current from said counting rate means and the input current, means responsive to the output from said comparison means to vary the repetition rate of said pulses until the current from said counting rate means equals the input current whereby the repetition rate is a function of the input current, means coupled to said pulse generatingmeans to produce an output current which is 29 a function of the repetition rate of said pulses including a network characterized by :a transfer admittance which is a function of a complex frequency representing said pulse rate so that an output current dependent on the repetition rate of said pulses flows whereby the output current is a desired function of the input current.

22. The apparatus of claim 21 wherein said counting rate means includes a network characterized by a transfer admittance which is a function of the repetition rate of the pulses produced by said pulse source.

References Cited in the file of this patent UNITED STATES PATENTS Dietzold Apr. 17, 1951 Leste June 12, 1951 Lovell Nov. 3, 1953 Philbric'k Jan. 10, 1956 Lilienstein July 8, 1958