DE1424785C - Electrical analog circuit for the implementation of a non-similar electrical resistance - Google Patents

Description

The object of the invention is to provide an electrical analog circuit for realizing a non-linear electrical resistance, in which between the variable voltages V _A and V ₈ applied to its ends and the current flowing between its ends there is a dependency which is given by the following equation expresses:

Va - V _R =

2 V _n ■ K ■ I ^a

Kl ^a ; (1)

10

where V _{n is} the arithmetic mean of the variable voltages; V _n , K and α are constants.

This object is achieved according to the invention by a circuit which is characterized by the series connection of a constant linear resistor R with a voltage source E, which is formed by an operational amplifier A _{2 with a} high gain with a downstream cathode follower T ₄ , T ₅ , the input of this operational amplifier A ₂ via an inverting operational amplifier A ₁ the voltage V _A , via a further cathode follower T ₃ the voltage V _A - V dropping across the linear resistor R and via an input side with the two voltages V _A and V _B and according to the formula The analog circuit according to FIG. 1 consists of a linear resistor R, the resistance value of which is ψ and which is connected in series with a voltage source E, represented by the terminals D and F. The one variable voltage V _{A is applied} to the input terminal A of this series connection and V A is applied to the other terminal B. the other variable voltage V _{8 is} applied. This series connection is intended to satisfy equation (1) given above. The voltage source E , which is not connected to ground, must supply a voltage according to the following equation to achieve the above relationship according to equation (1):

E (K ₄₁ V ₈ ) = V (K ₄ , V ₈ ) - (V _A - V _B ) , (2)

where V (V _A , V _B ) is the voltage drop across resistor R.
So it results:

V '(V _A , Vs) = ^ -;

inserting the expression / from equation (1) gives:

_Vl _- ■

+ V _b )

30th + Vb) ■ (Va -

(2

(2KV _n) ^m

■ · (4)

working function generator G this output voltage K ₁ 'is supplied so that the voltage drop across the linear resistor R is always equal to the output voltage of this function generator G. Advantageous refinements for the design of the function generator emerge from the subclaims.

With a circuit according to the invention, for example, the movement of compressible Fluids, such as gases, can be simulated by pipeline networks. One possible application of the circuit therefore consists in investigating the mode of operation of gas pipeline networks in which the movement of the Gas in the individual lines is expressed by the relationship:

Pa - Pb ⁼ 2 p _N K · Q ",

which can also be written in the following form:

Pa - Pb =

2p _N KQ '

(Pa + Pb)

55

where p _{A is} the pressure at the inlet of the line, p _B that at the outlet, p _{N is} the atmospheric pressure, Q is the delivery volume and K and α are suitable constants.

The invention is illustrated schematically below with the aid of hand Drawings of exemplary embodiments in more detail • rlMutert.

Fig. 1 shows the basic circuit diagram of an inventive Analog circuit;

F i g. 2 and 3 show two possible embodiments for the construction of the function generator of the analog circuit according to the invention.

Therefore, if the circuit is to satisfy equation (1), the voltage drop corresponding to the resistance R of the circuit must satisfy equation (4).

The desired voltage E according to equation (4) is generated by the following circuit. The variable voltage V _B is fed via a cathode follower T ₁ to one input of a function generator J? and the second variable voltage V _{A is} fed through a cathode follower T _{2 to} the other input of this function generator jj. The voltage V _A is also fed from the output of the cathode follower T _{2 to} the input of an operational amplifier A ₁ , which supplies a voltage - K ₄ at its output and thus at the input of the subsequent operational amplifier A _2. The function generator fed with the voltages V _A and V _8? supplies an output voltage K ₁ ', which is also fed to the input of the operational amplifier A _2.

The voltage at terminal D, which corresponds to the voltage at terminal A minus the voltage drop at resistor R , ie K ₄ - V , since V denotes the voltage drop, is fed to _{the input of cathode follower T 3.} The output voltage K ₄ - V of this cathode follower is fed to the input of the operational amplifier A _1. The voltages - V _M V { and (K ₁ - V)) are thus present at the input of the operational amplifier A ₂ . Since this operational amplifier A _{2 has} a high gain so that its input signal must be zero, K ₁ '= V. The voltage drop across the resistor R is therefore always equal to the output voltage of the function generator_G. The function generator is selected so that it supplies a voltage on the output side that is dependent on V ₄ and V ₈ according to equation (4), so that the relationship applies:

+ Vb) - (Va-Vb) V " (2KV _n ) ¹¹ '

The output voltage of the operational amplifier A ₂ is via the cathode follower T ₄ . and T _s , which are fed from the rectifier circuit Q , are coupled to the terminals D and F.

The constant K can be changed by the switch S, ie

by changing the value - ^ - of the resistance K to be changed.

Fig. 2 shows a possible circuit for the function generator ^?, Specifically for those cases in which the constant K of equation (1) is variable within wide limits, while the exponent α is constant. The function generator G according to FIG. 2 comprises an operational amplifier A ₃ , by means of which the voltage V _{x is} invented. The output signal - V _x has the voltage V _B in the operational amplifier A ₄ . summed up, which comprises a negative feedback circuit with variable resistors K1 to Kn or Rl ' to Kn' and diodes Dl to Dn. The diodes become increasingly conductive with increasing voltage V { and therefore increasingly reduce the gain. The proportional to the mean V 4 V

Voltage - variable polarization voltage of the diodes is taken from the operational amplifier A ₅ , which adds the signals V _A and V ₈ . In this way, the operational amplifier A ₄ . applied signal (V _B - V _A ) from this amplifier reversed in sign and multiplied by the polarization voltage of the negative feedback circuit proportional to the mean voltage. The whole thing is also raised to -, where α is dependent on the value of the resistances of the negative feedback circuit. For this purpose, a corresponding switch is provided for these resistors. The output voltage F ₁ 'of the function generator corresponds to equation (4) in this arrangement. The constant K can be adjusted by changing the resistance value of the resistor K.

F i g. 3 shows an exemplary embodiment for the function generator Jj, in which both the constant K and the exponent α can be changed within wide limits. This generator takes advantage of the logarithmic relationship that exists between the grid current and the grid voltage of a tube. The voltages (V _B + V _A ) and (V _A - V _B ) are applied to the inputs of the two logarithmic amplifiers T ₆ and T _B. The operational amplifier A ₆ supplies the voltage - V _B. The logarithmic amplifiers T ₆ and T ₈ generate voltages that are proportional to log (V _B + V _x ) or log (Va - V _B ) and are summed in the operational amplifier A _1. The latter also takes care of dividing by the constant α. The output voltage F / of the operational amplifier A ₇ , which is the size

is proportional, is fed to the input of the exponential amplifier consisting of the amplifier A ₈ and the logarithmic element T _{7. The signal F 1} ', which corresponds to equation (4), is thus obtained at the output of this amplifier. The exponent α is set using the potentiometer ?.

Claims (3)

Patent claims: 1. Electrical analog circuit for realizing a non-linear electrical resistance, at. which between the voltages V _x and V _B applied at its ends and the current flowing between its ends / the following relationship exists: τ, " 2V _n -KI" - • Dog (K ₁ + FW + log (K, - V _B ) (V _x -V ₁₁ )] 60 where V _n , K and α are constants, characterized by the series connection of a constant linear resistance (K) with a voltage source (E), which is formed by an operational amplifier (A ₂ ) with a high gain with a downstream cathode follower (7 ^, T ^ ), the input of this operational amplifier (A ₂ ) via an inverting operational amplifier (Ai) the voltage - V _A , via a further cathode follower (T ^) the voltage V _x reduced by the voltage drop V across the linear resistor (K) and via a applied to the input side with the two voltages V _x and V _B and according to the formula ¹ G (2 KV _n ) ¹ " working function generator (G) this output voltage V ₁ 'is supplied so that the voltage drop V across the linear resistor (K) is always equal to the output voltage F ₁ ' of this function generator (G). 2. Analog circuit according to claim 1, characterized in that the function generator (GJ from an operational amplifier (A ₄ ) with a non-linear negative feedback circuit of diodes (Dl to Dn) and resistors (Kl to Rn, RV to Rn ') and the diodes through the before) a summing circuit (A ₃ ) supplied, the mean value of the two voltages V _x and V _n proportional voltage (Fig. 2). 3. Analogue circuit according to claim 1, characterized dadurcr that the function generator (G of two logarithmic amplifiers (7 ^, T is _8, of which the one (T ₆₎ the sum V _B + V _x and the other (7J) over a Amplifier (A ₆ ) the difference V _x - V _{B is} supplied and the output voltages of which are summed in an operational amplifier (A ₇ ) , the output of this operational amplifier (A ₁ ) being an expontential amplifier (A ₉ , T ₁ ) is connected downstream (Fig. 3). are polarized j 1 sheet of drawings