Analysis of the instrument for measuring impedance. Encyclopedia of radio electronics and electrical engineering

Encyclopedia of radio electronics and electrical engineering / Antennas. Measurements, adjustment, coordination

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The device is a voltage divider, one arm of which contains a resistor and a capacitor with known parameters, and the parameters of the elements of the other load arm, for example, antennas, are unknown. The divider is powered by a sinusoidal signal source with a frequency f. With the help of diode rectifiers with capacitive filters connected to the divider elements, the voltages falling on them are measured. Assuming that the rectifiers are linear over a sufficiently wide voltage range, it is possible to construct a vector voltage diagram from the measured direct voltages.

The equivalent circuit of the divider is shown in fig. 1, where RoCo are elements with known parameters; RnSn - load elements, the parameters of which are to be determined. The voltages on the divider elements are also shown there.

Vector voltage diagrams, complete and partial, are shown in fig. 2.

These diagrams can be described by the equations:

From equations (2) and (3) we obtain

Thus, the last two equations are necessary and sufficient for calculating the required quantities, and the first of them and the element Ro are redundant. For an unambiguous solution of the problem, it is only necessary that the known element has reactance, which will allow us to determine the sign of the reactivity of the unknown.

The equivalent circuit of the device after its simplification and the vector diagram for working with a load containing a capacitive component are shown in fig. 3 and 4, respectively.

The method of working with a simplified device is similar to working with its prototype, it is only necessary to add that the values ​​Urn and Ukn found from the diagram must be converted into resistances. Recalculation is carried out through a scale factor

The desired values ​​are found by the formulas

The disadvantage of the graphical solution of the problem is its high complexity, the impossibility of mechanizing the solution process.

Much more convenient is the analytical method of solving, without running to the construction of a vector diagram.

For this we use the equations

describing the diagram of fig. four.

These equations can be solved on a computer or on a calculator. At the same time, it must be borne in mind that if, as a result of the solution, the value Uхн is obtained with a + sign, then this means that the load has a capacitive component, and if with a - sign, then it is inductive. The practical scheme of the device is shown in fig. 5. In it, unlike the prototype, resistors R1 and R2 are introduced, which ensure the normal operation of the rectifiers when the output of the power source and load is "closed", that is, open to DC.

The value of C1 should be chosen such that its capacitance at the operating frequency is close to the expected value of the load resistance. Under this condition, the measurement accuracy will be higher. For the same purpose, the input voltage must be at least 5 V (effective value) with a minimum harmonic content.

During trial operation of the prototype sample, the measurement accuracy was obtained on average no worse than ±10%.

Author: V. Korobeinikov, Izhevsk

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