Efficient Impedance Bridge Analysis

Of concern are the detector voltage and current of an unbalanced impedance bridge for the general case when both the source and detector impedances are finite. A convenient expression for the exact Thevenin impedance seen by the detector is derived. Several examples are given to illustrate the observation that this Thevenin impedance is barely sensitive to the source impedance. Two approximate Thevenin impedances are easily obtained, either by element combination or as limiting forms of the exact Thevenin impedance. They are nearly equal and bracket the actual Thevenin impedance. A conservative error bound is given. Algorithms suitable for programming impedance bridge problems are discussed. Also, for use with hand-held calculators, an approximate method for calculating the detector voltage and current is given. The method is direct, rapid, and accurate; it employs just one approximation-the Thevenin impedance.