BRIDGE METHODS OF MEASURING IMPEDANCES 465 



of frequency, which is usually desirable. Capacitance ratio arms 

 have certain advantages for particular cases. They may be readily 

 chosen to give high impedance values, this being an advantage in 

 certain cases, for instance in the measurement of small capacitances 

 at low frequencies. This form is also desirable where high voltages 

 must be used, since the ratio arms may be designed to withstand high 

 voltages without the dissipation of appreciable energy. It also has 

 the advantage that where measurements are desired with a direct 

 current superimposed on the alternating current, the direct current 

 is automatically excluded from the ratio arms and thus all of the direct 

 current applied to the bridge passes through the unknown and there 

 is no dissipation due to the direct current in the ratio arms. The 

 impedance of the ratio arms decreases as the frequency increases, 

 which is usually a disadvantage but may have advantages in some 

 cases, such as the measurement of capacitance. There may be a 

 disadvantage, in some cases, due to the load on the generator being 

 capacitive, thus tending to increase the magnitude of the harmonics, 

 and again, in the case of the measurement of inductances, there may 

 be undesirable resonance effects. 



The inductance ratio arm type has advantages where heavy currents 

 must be passed through the bridge, since the ratio arms of this type 

 may be designed to carry large currents with low dissipation. A 

 modification of this type, where there is mutual inductance between 

 the ratio arms, gives the advantage of ratio arms of high impedance 

 with a corresponding low impedance input. A further modification 

 consists in making the ratio arms the secondary of the input trans- 

 former, thus combining in one coil the functions of ratio arms and 

 input transformer. This form, of course, departs from the simple 

 four-arm bridge, but is mentioned here due to its simplicity and actual 

 practical advantages. 



Substitution Methods 



In any of the bridges discussed and, in fact, in practically all bridges, 

 it is possible to evaluate the unknown by first obtaining a balance 

 with the unknown in the circuit and then substituting for it adjustable 

 standards which may be adjusted to rebalance the bridge. This is, in 

 general, a very accurate method, eliminating to a large degree the 

 necessity for the bridge to meet its phase angle requirement. How- 

 ever, in the case of complete substitution of standards to balance both 

 components of the unknown, the method has no advantage except 

 accuracy over the bridges of type 1, Fig. 2, since standards of the same 

 type as the unknown must be used and, in general, this method lacks 



