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Home Impedancematching Networks Type IV Problem  
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Type IV ProblemAuthor: Edmund A. Laport
Procedure. Set up the known conditions in the form of a vector diagram of potentials and currents, as in Fig. 5.35. The problem does not specify an input impedance to either network A or network B.
In the vector form of the problem we lack only the potentials for V_{1} for each network. We know I_{0}. We do not know I_{1} but know its direction with respect to V_{0}. We do not know I_{2} but know its direction with respect to V_{1}. We can draw V_{1} directly since V_{0} and V_{g} are specified.
Thus we have enough information to complete the vector diagram of Fig. 5.37. This diagram reveals the nature and magnitude of each reactive element, and we obtain
The input impedance to the two networks in parallel is Vg/Ig, where Ig is the vector sum of I_{2A} and I_{2B}. The two series components of the input impedance are where
The entire circuit required to satisfy the problem is shown in Fig. 5.38. In a similar manner problems having a multiplicity of loads fed in any specified amplitudes and phases of potentials can be solved readily. Some examples of what can be done in this same simple procedure are given herewith. The following problem represents a special case of potential transformation with two equal loads for changing from a singleend generator to a balanced (pushpull) load.
Problem. It is desired to feed two 250ohm loads in pushpull with 500 volts across each resistance from a singleend generator having a terminal potential of 300 volts. What network is required, and what impedance is presented to the generator?
Procedure. Set up vectors representing the desired potentials at 180 degrees for the load, and draw the vector for the generator potential at 90 degrees to each of the load potentials. Thus we have stated the problem vectorially, as shown at the left of Fig. 5.39. The choice of the direction of Vg at 90 degrees to the load potentials is arbitrary. It could be any angle between the two. The 90degree choice, however, has symmetry which is usually desirable.
On the basis of L networks, we complete the vector diagram to obtain the desired information, as in the previous problem. The usual elementary considerations provide the basis for this procedure, from which we get Fig. 5.40 and Fig. 5.41. Tabulating vector lengths,
These values yield the circuit shown in Fig. 5.42.


Home Impedancematching Networks Type IV Problem 