On Separate and Independent Balancing of AC Bridges

M. S. ROITMAN

(Presented to the jubilee conference dedicated to the 40th anniversary of October)

Measurement of complex impedances with AC bridges produced by domestic industry is usually associated with a very lengthy and tedious process of balancing the bridge circuit by successive adjustment of parameters. Therefore, the problem of creating AC bridges with separate balancing, allowing measurements to be carried out in two or three strictly defined operations, is a very urgent one. This problem was first considered most fully in works [1, 2]. As shown in [1, 2], “separate balancing of a bridge reduces to two independent operations—the finding of the point of intersection of the principal balance lines and the bringing together of potential points into one.” Consequently, a necessary condition for separate balancing is the presence of a special indicator that makes it possible to determine the point of intersection of the principal balance lines. Various differential indicators are used as such indicators. However, the use of differential indicators leads to the appearance of a number of additional errors, substantially reducing measurement accuracy [3]. In addition, a drawback of AC bridges with differential indicators is also the presence of an auxiliary operation for finding the point of intersection of the principal circles of balance. It is obvious that, from the standpoint of speeding up measurements and increasing accuracy, the best solution would be the creation of AC bridges that make it possible to reduce balancing with the aid of a zero phase-sensitive indicator to two transitions: balancing of the active component and independent balancing of the reactive component of the complex impedance. Let us consider the possibility of creating such bridges, i.e., bridges “with independent balancing circuits” [4]. The unbalance voltage at the output of the bridge circuit, when the input resistance of the indicator is much greater than the output resistance of the bridge, is equal to

\[ \dot U_{cd} = \dot U_{ab}\, \frac{\overline z_{3}\,\Delta \overline z} {(\overline z_{1}+\Delta \overline z+\overline z_{2})(\overline z_{3}+\overline z_{4})} \simeq \dot U_{ab}\, \frac{\overline z_{3}(\Delta r \cdot j \Delta x)} {z_{1,2} e^{j\gamma}\, z_{3,4} e^{j\delta}}, \tag{1} \]

where \(\Delta \bar z=\Delta r+j\Delta x\) is the detuning impedance. It follows from equation (1) that, for large detunings, the quantity \(\Delta \bar z\) in the denominator cannot be neglected, and its variation changes the impedance of branch \(\bar z_{1,2}\) both in magnitude and in phase. In the general case, when the measured impedance \((\bar z_1)\) and the balancing impedance are in different arms of the bridge, in the process of balancing the impedance of the other branch also changes.

Fig. 1.

Fig. 2.

\(\bar z_{3,4}\). In the case, however, where the measured complex impedance and the balancing impedance are connected into one arm of the bridge, the impedance of the other branch will always remain unchanged,

\[ z_{3,4}e^{j\beta}=A=\mathrm{const} \]

and

\[ \dot U_{cd} = \dot U_{ab} \frac{\bar z_3(\Delta r+j\Delta x)}{z_{1,2}e^{j\alpha}\cdot A} = \dot U_{ab} \frac{(\Delta r+j\Delta x)B}{z_{1,2}e^{j\alpha}\cdot A}. \tag{2} \]

Two variants of bridge circuits satisfy this condition: bridges with adjacent connection of the main arms (when they are connected in one branch) and resonance bridges. By connecting at the bridge output a zero phase-sensitive indicator and rigidly linking the vector of the control voltage with the current vector through the main branch

\[ \left(I=\frac{\dot U_{ab}}{z_{1,2}e^{j\alpha}}\right), \]

we obtain a bridge with independent balancing circuits

\[ \dot U_{cd} = \frac{\dot U_{ab}(\Delta r+j\Delta x)B}{z_{1,2}\cdot A} = \Delta r\,\frac{\dot U_{ab}}{z_{1,2}\cdot A} + j\Delta x\,\frac{\dot U_{ab}B}{z_{1,2}\cdot A} = \dot U_{cdr}+\dot U_{cdx}. \tag{3} \]

Indeed, from the vector diagram of a bridge with adjacent connection of the main arms (Fig. 2) it is evident that the unbalance voltage \(\dot U_{cdx}\), caused by a change in the reactive component \((\Delta C_x)\), is perpendicular to the voltage vector \(U_R\), while the active component \(\dot U_{cdr}\) coincides in direction with it for any changes in the components \((r\) and \(x)\) of the measured impedance. By choosing the voltage \(\dot U_R\) as the control voltage of the phase-sensitive indicator and shifting it by \(90^\circ\), we balance the circuit with respect to the reactive component, i.e., bring point \(C\) to \(C_1\). Then we switch the phase of the control voltage by \(90^\circ\) and balance the circuit with respect to the active component.

The control voltage $\dot U_y = \kappa \dot U_R$ will vary with the change in the resistance being measured. Taking into account that the measured resistances may vary over a wide range of values, for stable operation of the phase-sensitive indicator it is necessary to introduce automatic gain control or output-voltage limiting. The block diagram of the bridge may take the form shown in Fig. 2, where KP is a cathode follower, PC is a phase-shifting circuit, LIM is a limiter, and PSD is a phase-sensitive detector.

Fig. 3.

It is evident that independence of the adjustments is possible only in the absence of phase distortions in the path and with stable operation of the vector device. It should be pointed out that even in the presence of some mutual coupling of the “balancing loops,” the balancing time is sharply reduced as a result of improved convergence of the bridge. V. Yu. Kneller [4] showed that “decoupling of the balancing loops” is especially desirable in the design of fast-acting automatic bridges.

On the basis of bridge circuits with “independent balancing loops,” a number of very valuable instruments can be created. Thus, for example, we have developed an indicator of short-circuited turns whose readings do not depend on the self-capacitance of the coils being tested (Fig. 3).

One short-circuited turn 1.5 cm in diameter, made of wire 0.05 mm in diameter, produces a deflection of the indicator pointer by three scale divisions, while connecting a capacitance of 15,000 pF in parallel with the core produces only half a division.

References

1. Karandeev K. B., Bridge Methods of Measurement, State Technical Publishing House of the Ukrainian SSR, Kiev, 1953.

2. Shvetskii B. I., Separate Balancing of AC Bridges, dissertation for the degree of Candidate of Technical Sciences, Lvov, 1951.

3. Silamaa Kh. V., Automatic AC Bridges, dissertation for the degree of Candidate of Technical Sciences, Lvov, 1955.

4. Kneller V. Yu., On one type of AC bridge with automatic balancing by two parameters, Automation and Telemechanics, vol. XIX, no. 12, 1958.

5. Roitman M. S., Device for separate measurement of the active and reactive components of complex impedances, Inventor’s Certificate No. 121862.