August 1932 RadioCraft
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published 1929  1953. All copyrights are hereby acknowledged.

This is the third and final installment of Hy Levy's series on attenuators, line filters, and matching transformers. Audio and low IF frequencies are used in the examples, but the formulas and principles can be extended to higher frequencies. Bifilar windings are covered as a method of minimizing selfinductance in wirewound resistors. Although inductance is not desired in resistors, bifilar windings can also be connected to have current in both wires flowing in the same direction, thereby increasing the magnetic field rather than canceling it. You will probably want to read the previous two parts to work up to this point. The Theory and Construction of Attenuators, Line Filters and Matching Transformers (Part I) The Theory and Construction of Attenuators, Line Filters and Matching Transformers (Part II) The Theory and Construction of Attenuators and Line Filters (Part III) The Theory and Construction of Attenuators and Line Filters (Part III)In the May and June issues of this publication there was described the theory and operation of impedance matching. In this discussion, final calculations for "H" and "T"type pads are submitted by the author. By Hy Levy We can now proceed with the design of an Htype pad to give us the desired 20 decibel loss as determined in our own problem under consideration. Assume we did not have Table 3 from which the values of Z_{1} and Z_{2} may be obtained, but that we wish to calculate our own values of Z_{1} and Z_{2} for the pad. To determine the constants of the pad, it is necessary to know the working formulas for an Htype network. The working formulas will not be derived in these papers, but it can be shown that the formulas for Htype networks are as follows: Examples of Design Fig. 10 (top)  Htype pad working between two 200ohm impedances. Fig. 11 (middle)  A completed Htype pad causing a 20 db. loss. Fig. 12 (bottom)  A typical Ttype network.
Table 4  Impedance values for decibels Fig. 13 (top)  Equivalent circuit of Fig. 12. Fig. 14 (bottom)  A Ttype network working between two 200ohm impedances. We may now proceed with the application of these formulas to the design of the Htype pad to give us the desired 20 decibel loss as previously determined in our own problem under discussion. Given: To design a 20 decibel pad to work between two 200ohm impedances. (See Fig. 10.) From Table 3, the value of "A," (see Fig. 9) the amplification constant, can be determined. The amplification constant V_{1}/V_{2} at 20 decibels is given as 10. Therefore "A" is equal to 10. Z_{0} is equal to 200 ohms (given). Then "Z_{1}" the series element from equation (1) is Z_{1} = 100 x 0.82 Z_{1}  82.0 ohms and "Z_{2}" the shunt element from equation (2). The completed network will look as shown in Fig. 11. As shown in this figure, the Htype pad having the series element equal to 82.0 ohms, and the shunt element equal to 40.4 ohms, will cause a 20 decibel loss to be introduced between V_{1} the input terminals, and V_{2} the output terminals, reducing the input voltage of 1.5 volts to the desired value of 0.15 volts across "Z_{0}" the load impedance, which was the problem under consideration. It will be noticed that the calculated values of "Z_{1}" and "Z_{2}" check with the values given in Table 3. It was previously stated, that the image impedance must equal the characteristic impedance, in order to realize perfect impedance matching characteristics. This equality is shown below: "Z_{0}" the image impedance  200 ohms (given). "Z_{0}" the characteristic impedance from equation (3). Therefore "Z_{0}" the image impedance of 200 ohms equals "Z_{0}" the characteristic impedance, which also equals 200 ohms. Design of "T" Pads Having designed an Htype pad to give us the desired loss, let us proceed to do the same with a "T"type pad. This attenuator is so called, because it is composed of three resistors taking the form of the letter "T." This pad is known as an unbalanced network in that series resistors are used in only the high side of the line. The other side of the network mayor may not be grounded depending on the type of circuit in which it is to be placed. This network is shown in Fig. 12. The equivalent circuit of Fig. 12, is given in Fig. 13, and everything that has been said about Htype pads, holds true for the Ttype pad, except that "Z_{1}" the series arm for a Ttype pad is exactly twice the value of "Z_{1}" for an Htype pad giving the same loss. This is easily seen, for if we take the series arms out of the low side of the line, and still wish to maintain the same characteristic impedance in the circuit, the series arms in the high side of the line, must be exactly twice their original values. Therefore, knowing the constants for an Htype pad, and wishing to design a Ttype pad to give the same loss, all that would have to be done, is to leave the two series arms out of the low side of the line entirely, and make the two series arms in the high side of the line just twice their original values. The shunt arm "Z_{2}" remains the same in both cases. The working formulas for Ttype networks are as follows: Example of Design As an example of design to illustrate the use of this type of network, we may proceed to apply the above formulas to the design of a Ttype pad to also give a 20 decibel loss. Given  To design a 20 decibel pad to work between two 200ohm impedances, (see Fig. 14). Then "Z_{0}" is equal to 200 ohms (given). From Table 4, the value of "A," the amplification constant for 20 decibels, is given as 10. Then "A" is equal to 10. Solving for "Z_{1}" the series element from equation (4). "Z_{2}" the shunt element is the same as for the Htype pad, as the formulas from which "Z_{2}" the shunt arm is determined, is the same for both H and Ttype pads. This is seen from inspection of the formulas for the two types of networks. The completed network shown in Fig. 15, having the constants as determined above, of "Z_{1}" the series element equal to 164 ohms, and "Z_{2}" the shunt element equal to 40.4 ohms, when interposed between the two 200ohm impedances, will give the desired 20 decibel loss. It will be noticed (see Fig. 15) that the series arm "Z_{1}" as determined for the Ttype pad, is exactly twice the value found for "Z_{1}" in the Htype pad, and checks with the values given in Table 4, from which the constants "Z_{1}" and "Z_{2}" for Ttype pads may be found, when working between 200 500 and 600ohm impedances. Design Information for Resistors Used in Attenuators Fig. 15 (top)  A completed Ttype network causing a 20 db. loss. Fig. 16 (bottom)  Illustrating a bifilar winding. A and B are the ends of the winding. The resistors used in attenuators must be nonreactive (have negligible inductance and capacitance) so that the attenuator will maintain a constant impedance throughout the audio band to the impedances between which it is working. By designing the attenuator to have a constant impedance, it will offer the same degree of attenuation to all audio frequencies, with the result that the frequency response characteristics of the circuit will be practically flat, which is the ideal strived for in all voice transmission circuits. The following constructional data on the resistors used in attenuators is given, so that the above mentioned characteristics may be obtained. All resistors lower than 300 ohms are wound in bifilar fashion. The bifilar method consists of paralleling the wire throughout the winding as shown in Fig. 16. For all resistors below 300 ohms, the following accuracy limits for resistance should be adhered to: Resistors whose values are greater than 300 ohms, are wound in the wellknown reversed layer method, in which the layers are wound upon each other in reversed directions. For all resistors above 300 ohms, the following accuracy limits tor resistance should be adhered to: The inductance of a resistor is expressed in microhenries, and the capacitance of a resistor is expressed in micromicrofarads. The maximum allowable inductance in microhenries for resistors below 1,000 ohms is given in the following table. The maximum allowable capacitance in micromicrofarads for resistors above 1,000 is given below: If the resistors are wound as specified, and the accuracy limits for resistance, inductance, and capacity, as given above are maintained, a practically constant impedance attenuator will be the result. Posted Marc h 15, 2017 