BRIDGE METHODS OF MEASURING IMPEDANCES 



461 



For this reason, any references to, or comparison with existing special 

 types of bridge are omitted. 



TABLE II 

 Balance Equations 



2 These forms are not practical. 



R, L and C = series components of complex arms. 



G, L' and C = parallel components of complex arms. 



K has the value indicated on the individual circuits of Fig. 2. 



6 = Bab — Obc for Ratio Arm Type 

 e = Bad -\- Obc for Product Arm Type 



Table II gives the balance equations for each type of bridge for the 

 measurement of any component of the unknown impedance in terms 

 of resistance, capacitance, and inductance. These equations are 

 simply derived from the general equations (8) to (18) by substitution 

 of circuit constants for impedances and by the introduction of the 

 constant K. This constant must be evaluated from the relation 

 between the ratio arms or product arms shown in the individual bridge 

 forms of Fig. 2. At the bottom of Table II are given the corresponding 

 bridge figures for reference. This table shows no bridges having a 

 phase relation of 180° between the fixed arms. A little consideration 

 will show that since the phase relation between the unknown and the 

 standard for such bridges must also be 180°, they cannot be used to 

 measure any but pure reactances or negative resistances. Accordingly, 

 they are not considered herein. In the case of the 90° relation, both 

 signs must be considered and result in bridges which are complimentary 

 with respect to one another, that is while one measures only inductive 

 impedances, the other measures only capacitive impedances. Thus 



