Circuit Arrangement for Converting a Bridge Unbalance Into a Frequency Variation

The invention relates to a circuit arrangement for converting an unbalance of a resistor bridge having four resistors, which bridge is supplied from a voltage source, into a frequency variation of an RC-oscillator which is proportional thereto. The output terminals of the bridge are connected to the input terminals of a compensation amplifier, whose output voltage directly or indirectly controls a controllable resistor. One of the output terminals of the bridge is moreover connected via a resistor to the output of a negative feedback operational amplifier, whose input is connected to the voltage source via the controllable resistor. The controllable resistor, as well as the operational amplifier, form part of the frequency-determining network of the RC-oscillator. A further amplifier is connected to the output of the operational amplifier via an all-pass network which includes three ohmic resistors and a capacitor, in which network the one resistor which is connected to ground is controllable. The output of the further amplifier is connected to the input of an integrator and an amplitude detector is connected to the output of the integrator. The detector in turn controls the controllable resistor of the all-pass network in such a way that the voltage at the output of the integrator is constant, said voltage being the supply voltage to the resistor bridge.

By means of this circuit arrangement, described in U.S. Pat. No. 3,845,385, a bridge unbalance is converted exactly linearly into a frequency variation. In the case of a series of measuring transducers employed in such bridge circuits, the relationship between the output quantity and the measuring quantity, however, is only approximately linear. For accurate measurements, said non-linearity of the transducer characteristic should therefore be taken into account. As the frequency which represents the measuring quantity is generally electronically processed, it is therefore also necessary to provide an electronic compensation of the aforesaid non-linearity. This may for, example, be effected by means of known diode function generators or by means of digital function generators. A drawback of diode function generators is the thermal instability and in the case of digital function generators the extensive circuitry.

It is an object of the invention to provide a simple and inexpensive, yet extremely stable circuit arrangement, by means of which non-linearities of measuring transducers can be compensated for to a greater extent. According to the invention this problem is solved in that the output voltages of one or more differentiation circuits and/or integration circuits of at least partly different order, which are connected to the oscillator, are applied to the input of the compensation amplifier and are superimposed on the compensation voltage. These output voltages are effectively applied to the input of the compensation amplifier via weighting resistors, for example by means of a summing amplifier. In the oscillator the output of the further amplifier, the output of the integrator and the output of the operational amplifier may be used as connection points for the differentiation circuits and integration circuits respectively, which outputs either exhibit a different mutual phase relationship or a frequency dependence. The connection points for the individual differentiation circuits and integration circuits respectively are selected so that their output voltages have the correct phase, as the case may be, by means of an additional inverter.

Embodiments of the invention will be described with reference to the drawing. In the drawing:

FIG. 1 shows a block diagram of a complete circuit arrangement according to the invention,

FIG. 2 shows a network for the formation of non-linear frequency-dependent voltages, and

FIG. 3 is a simplified version of a network in accordance with FIG. 2.

In FIG. 1 the oscillator OS includes a negative feed-back operational amplifier V.sub.3, which supplies the compensation voltage U.sub.k as well as the supply voltage for the all-pass network consisting of the resistors R.sub.1, R.sub.2, R.sub.3 and the capacitor C.sub.1. The outputs of the all-pass network, which is connected as a bridge, are connected to the inputs of the amplifier V.sub.1, which takes the form of a differential amplifier. The output of amplifier V.sub.1 supplies an integrator consisting of the high-gain inverting amplifier V.sub.2, an integration capacitor C.sub.i which shunts said amplifier, and a preceding ohmic resistor R.sub.i. The output of the integrator is connected to an amplitude detector AR, which in turn varies the grounded variable resistance R.sub.1 in the all-pass network in such a way that the amplitude of the voltage at the output of the integrator is always constant. The output voltage of the integrator also constitutes the supply voltage U.sub.s of the bridge B', which for simplicity is represented as a block. The integrator further supplies the potentiometer P, whose output is connected to the non-inverting input of the operational amplifier V.sub.3 and whose dividing ratio is controlled by the compensation amplifier KR. The frequency of the voltage supplied by the oscillator OS is linearly dependent on the dividing ratio adjusted with the potentiometer P and thus linearly on the bridge unbalance.

The output voltage of the bridge B' is first applied to a differential amplifier V.sub.B whose output is connected to a summing amplifier V.sub.S. The output of said summing amplifier is connected to the input of the compensation amplifier KR, whose output signal controls the potentiometer P. The compensation voltage at the output of the operational amplifier V.sub.3 is applied, via a further input to the summing amplifier V.sub.S, in such a way that the voltage produced by the unbalance bridge B' is compensated for.

In order to compensste for non-linearities of the bridge B' and of the measuring transducer included therein, the summing amplifier V.sub.S comprises another input, which is connected to the output E of a network N. From voltages at the connection points of the oscillator OS, said network derives different voltages which have the same phase as the constant-amplitude supply voltage U.sub.s of the bridge B' and the compensation voltage U.sub.k, but which depend on the frequency in a non-linear manner. The voltages produced in the network N are proportionally added to or subtracted from the compensation voltage in the summing amplifier V.sub.S, which is only possible in the case of phase equality or phase opposition respectively. The bridge unbalance caused by the variation of the bridge resistor or resistors to be measured, is then no longer exclusively compensated by the frequency-proportional compensation voltage U.sub.k, but also proportionally by the said correction voltages produced in the network N so that a corresponding non-linear relationship between the bridge unbalance and the oscillator frequency is obtained.

FIG. 2 shows an example of a network N which in FIG. 1 is represented as a block. The network N comprises a number of similar differentiation circuits D.sub.1, D.sub.2 and D.sub.3 which each consist of a high-gain inverting differential amplifier V.sub.D, a differentiation resistor R.sub.D which shunts said amplifier, and a differentiation capacitor C.sub.D which precedes the amplifier input. Furthermore, four similar integration circuits I.sub.1, I.sub.2, I.sub.3 and I.sub.4 are provided which each comprise a high-gain integration amplifier V.sub.I, an integration capacitor C.sub.I which shunts said amplifier and an integration resistor R.sub.I which precedes the amplifier input. The operation of these circuits will be explained hereinafter.

By differentiation of the compensation voltage U.sub.k, which is proportional to the frequency, a voltage is obtained which is a quadratic function of the frequency. This voltage, however, is 90.degree. phase-shifted, so that it is not suitable for compensation of a bridge unbalance. However, at the output of the all-pass differential amplifier V.sub.1 a voltagre is available which, relative to the compensation voltage U.sub.k, has a constant frequency-independent amplitude ratio but which is at least 90.degree. phase-shifted. When said voltage is differentiated, the desired voltage of the correct phase is obtained with a quadratically frequency-dependent amplitude. This is effected with the aid of the differentiation circuit D.sub.3 whose input B is connected to the output of the all-pass differential amplifier V.sub.1. By double differentiation of the compensation voltage U.sub.k, it is also possible to obtain a voltage of the correct phase, but whose amplitude is proportional to the third power of the frequency. This is effected by means of the cascaded differentiation circuits D.sub.1 and D.sub.2. By integration of the constant-amplitude bridge-supply voltage U.sub.s, however, a voltage can be obtained whose amplitude is inversely proportional to the frequency. However, said voltage is not suited for compensation because, relative to the compensation voltage, it is at least minus 90.degree. phase shifted. However, a voltage of the correct phase, which is inversely proportional to the frequency, can also be obtained by double integration of the frequency-proportional compensation voltage U.sub.k. This is effected by means of the integration circuits I.sub.1 and I.sub.2. By twice integrating the bridge supply voltage U.sub.s by means of the cascaded integration circuits I.sub.3 and I.sub.4, whose first input C is connected to the bridge supply voltage U.sub.s, a voltage of the correct phase is obtained which is inversely proportional to the square of the frequency.

When the characteristic of the measuring transducer to be linearized, .DELTA. R/R = g (X) in which X = measuring quantity, is represented by a series expansion ##EQU1## so that to a satisfactory approximation f .about.X, the voltages produced by the differentiation circuits D.sub.1, D.sub.2, D.sub.3 and by the integration circuits I.sub.1, I.sub.2, I.sub.3 and I.sub.4 may be added with the correct weight via the summing resistors R.sub.10 to R.sub.13 of the amplifier V.sub.E, which includes negative feedback via a resistor R.sub.E, and applied to the compensation amplifier KR via the summing amplifier V.sub.S. The correct weight is obtained by making the summing resistors correspond to the associated coefficients of the series expansion. Via the resistor R.sub.14 a component of constant amplitude corresponding to the coefficient a.sub.O is added to the aforesaid voltages. If required, inverting amplifiers, not shown, may be connected in series for correction of the sign, or a summing amplifier with positive and negative inputs may be used. The integration circuits, which produce voltages proportional to the negative powers of the frequency, in particular influence the low frequency end of the conversion characteristic, while the voltage components produced by the differentiation circuits, which are proportional to the positive powers of the frequency, substantially influence the high-frequency end thereof. When in the case of extreme curvatures of the transducer characteristic correction elements of a higher order are required, these may be realized with the correct phase by double differentiation or integration respectively of correction voltages which are proportional to a power of the frequency which is each time two less. For example, a voltage proportional to the fourth power of the frequency can be obtained by double differentiation of the output voltage of the differentiation circuit D.sub.3 by means of two further identical differentiation circuits.

A modification of the network of FIG. 2 having the same effect is shown in FIG. 3, in which some circuit components may be dispensed with. The amplifiers in the differentiation circuits D.sub.2 and D.sub.3 may be replaced by the amplifier V.sub.E, so that the differentiation capacitors C.sub.2 and C.sub.3 are directly connected to the input of this amplifier. Weighting can then be achieved by a voltage divider (not shown) which precedes the differentiation circuit or the differentiation capacitors respectively. Furthermore, the voltages at the inputs A and C of the network may be integrated together via the same chain of integration circuits, so that the two integration circuits I.sub.3 and I.sub.4 with associated amplifiers are dispensed with. The weighted summation is then effected at the input of the integration circuit which corresponds to the integration circuit I.sub.1 in FIG. 2. This circuit consists of the amplifier V.sub.4 and the capacitor C.sub.4. The weighted summing resistors R.sub.4 and R.sub.6 together serve the integration resistance for the integration circuit. Furthermore, the amplifier V.sub.E may be dispensed with or be combined with the summing amplifier V.sub.S in FIG. 1, if said summing amplifier can be provided with suitable additional summing inputs.

Depending on the number of differentiation circuits and integration circuits used, the circuit arrangement described hereinbefore is capable of compensating for substantially arbitrary non-linearities of measuring transducers. Moreover, it provides the very interesting possibility of exactly linearizing the quadratic relationship between, for example, the flow rate and the differential pressure in the case of a flow transducer in accordance with the differential pressure principle. In this respect it is also possible to introduce a zero offset of the frequency (life zero), i.e. that a finite frequency is obtained already for the measuring value zero. This is very advantageous for transmission and for calibration purposes.