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Hybrid Coils
Hybrid coils are used to isolate an unwanted signal from certain parts of a circuit, and allow the signal to be used in other parts of the circuit.
In the hybrid coil shown in Fig. 156 (a) the lower windings or primary sections are balanced with respect to each other, and the two resistors R_{2} and R_{3} are equal. Voltage E_{0} applied between the primary center tap and ground causes equal currents to flow in opposite directions through the two halves of the primary winding, and therefore produces zero voltage in the secondary winding. By this means, signal E_{0} arrives at resistors R_{2} and R_{3} undiminished, but there is no voltage in R_{4} connected across the secondary coil. Figure 156(b) shows what happens in this circuit if the voltage is applied across R_{3} instead of across R_{1}. In this case, the voltage E_{3} appears across resistors R_{1}, R_{2}, and R_{4}, that is, in all parts of the circuit.
It has been assumed that R_{2} and R_{3} are equal and that the two primary halfwindings are of equal number of turns. This is not necessarily true, for, if the resistance of R_{2} is twice that of R_{3}, the number of turns connected to R_{2} should be twice those connected to R_{3}. However, it is important that, through the range of frequency in which the hybrid coil is desired to function, the balance between the two halves be maintained closely. The most exact balance is achieved for R_{2} = R_{3} by winding the two halves simultaneously with two different wires. This method gives good isolation of the undesired signal. Other methods introduce some ratio error which reduces the isolation. For the same reason, it is necessary to balance the circuit with regard to capacitance and leakage inductance. That is, if a capacitance exists across R_{3}, such as line capacitance for example, an additional equivalent amount should be added across R_{2} in order to achieve the balance desired. Likewise, any inductive apparatus, adding either series or parallel inductance in one circuit, should be compensated for by inductance of like character in the other circuit. Adding series inductance, for example, in series with R_{3} will not compensate for shunt inductance across R_{2}, or vice versa, as the two have opposite effects with regard to frequency and therefore balance is attained only at one frequency. Assume a perfect transformer having no exciting current and no leakage inductance between the two halves, and a transformer with equal turns in the two halves of the primary winding. Assume currents in the directions shown in Fig. 156 (d). Then
On the assumption of equal turns in the two halfwindings, E_{1} = E_{2}. If the magnetizing current is assumed to be zero, the ampereturns and hence the voltamperes in the two primary halves are equal. The secondary load can be considered as reflected into the primary winding as resistor R_{4}.
If equations 88 to 92 are combined, an expression for Z_{3} can be found:
If the secondary circuit is open, R_{4} = ∞, and equation 93 becomes


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