circuit conditions, which will produce the 

 greatest percentage change in the impedance of 

 Iq_ for a given change in fluid conductivity, are 

 the conditions for greatest accuracy. 



The impedance of L]_ is essentially equal to 

 the reactance of the inductor paralleled by the 

 induced loss resistance due to the conductive 

 medium. The circuit conditions which will make 

 the value of this parallel resistance smallest 

 and the value of the parallel inductance rela- 

 tively greatest will produce the greatest accuracy 

 until the resistance is small compared to the 

 inductive reactance. When this condition is 

 reached the effect of the parallel inductance 

 will be small and the bridge will essentially 

 consist of k resistive elements. Under these 

 conditions the percentage change in the impedance 

 of the L]_ arm of the bridge will be determined 

 directly by the percentage change in the conduc- 

 tivity of the surrounding medium. Until this 

 condition is reached, the accuracy of the meter 

 is determined by the following considerations. 



The value of the induced loss resistance con- 

 sidered in parallel with the inductive reactance 

 of L]_ is numerically equal to the resistance of 

 the fluid path through and around the toroidal 

 inductor multiplied by the square of the number 

 of turns on the inductance. The value of the 

 induced resistance can then be decreased by 

 decreasing the resistance of the fluid path and 

 by decreasing the number of turns on the inductor. 

 Decreasing the number of turns of the inductor 

 decreases the parallel inductance by the same 

 ratio that the induced resistance is decreased 

 so that the sensitivity is independent of the 

 number of turns comprising the inductor. The 

 resistance of the fluid path is determined by 

 the physical geometry of the inductance. 

 Increasing the area of the hole through the 

 toroid and decreasing the length of the hole as 

 well as decreasing the cross-section of the core, 

 windings and covering material will decrease the 

 resistance of the fluid path and hence increase 

 the sensitivity of the device. 



The sensitivity of the device can likewise be 

 increased by increasing the relative value of 

 the parallel inductive reactance of L^ and L 2 . 

 The inductance of Lj_ and L 2 can be increased 

 without increasing the value of the induced 

 resistance by increasing the permeability of 

 the magnetic core material used. The inductance 

 can also be increased by increasing the fre- 

 quency of operation. Thus it is seen that the 

 accuracy of the device is proportional to the 

 permeability of the core material and the fre- 

 quency of operation and is dependent on the 

 physical geometry of the cores. 



PRACTICAL CIRCUIT CONSIDERATIONS 



In practice the two inductors, Lj_ and L 2 , 

 cannot be made exactly identical. They will be 

 found to differ both in inductance and loss. As 

 a result, some means must be provided to 



compensate for differences of inductance and loss 

 so that an initial balance of the bridge can be 

 obtained. Assuming that the loss component of the 

 impedance of the inductors is small compared to 

 the reactive component, the effect of an induc- 

 tance unbalance can be compensated by changing 

 the values of R^ and R 2 . The effect of a loss 

 component unbalance can be compensated by shunt 

 resistors across the appropriate inductor or 

 across both inductors. In practice R-^ and R 2 

 have been made variable in different degrees to 

 provide coarse and fine inductance balance con- 

 trols. Likewise, variable resistors shunted 

 across L^ and L 2 have been provided to obtain 

 coarse and fine loss balance controls. 



As was mentioned earlier it is desirable to 

 wind the inductors on toroidal cores having as 

 high a magnetic permeability as is possible. As 

 it is also desirable to operate at as high a fre- 

 quency as is practical, many high permeability 

 core materials cannot be used because of the great 

 amount of loss at high frequency. As a result 

 a compromise must be reached between these con- 

 flicting factors. At present, toroidal cores 

 made of a ferrite material having a permeability 

 in the region of 800 to 1,000 are used at a fre- 

 quency of approximately 500 Kcps . 



The impedance of the elements of the bridge 

 circuit is determined by the inductive reactance 

 of L]_ and L 2 . If the impedance is made too high, 

 stray capacity will alter the desired circuit 

 conditions and will make the circuit balance fre- 

 quency sensitive. If this impedance is made too 

 low, stray lead inductance will have the same 

 effect. This latter consideration has been a 

 problem particularly in designing the balance 

 resistance connected to the secondary winding on 

 L 2 . If stray inductance is present here, it 

 introduces a reactive component into the null 

 voltage, thereby reducing the accuracy with which 

 the null can be detected. In general the imped- 

 ance level of bridge components has been kept in 

 the region of 100 to 1,000 ohms. 



As it has been found possible to balance the 

 bridge circuit so that the amplitude of the output 

 to the null detector is of the order of 120 db 

 less than the input signal level, it is necessary 

 to design the apparatus physically so as to pre- 

 vent disturbances from outside influences . The 

 electrical circuitry is all enclosed in shielded 

 containers and the toroidal windings isolated 

 with Faraday shields. The mechanical supports 

 for the inductors are made quite rigid so as to 

 isolate the toroidal cores from mechanical stress. 

 This is necessary since the permeability of the 

 ferrite core is a function of the mechanical 

 stresses in the material. Care must be taken to 

 prevent variation of the circuit characteristics 

 by the use of good quality components and rugged 

 physical construction. 



An alternate method of balancing the loss com- 

 ponent induced in L^ by the conducting medium is 

 by the use of a variable shunt capacitor across 

 R]_. In this case, the secondary winding and 



26 



