The Magic-Tee

Copyright 1999, Mike Ellis

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Of all the passive circuits employed by the RF engineer, there are probably very few so misunderstood as the "magic tee" hybrid power splitter/combiner. The "magic tee" is an alternative to the 6 dB power splitter shown in figure 1. The advantage of the "magic tee" is that the two output ports are isolated from each other and the theoretical loss is only 3 dB.

Source VT causes equal currents I1 and I2 to flow as shown in figure 2. By inductive action, E1 and E2 are equal magnitude, but opposite polarity, so that there is no voltage across the 150 ohm resistor. However, because the 150 ohms is stepped down to 37.5 ohms by the 4:1 transformer action of the center tapped inductor, the magnitude of E1 and E2 is equal to ERT and each 75 ohm load sees a 75 ohm source.

In figure 3, the voltage E2 induced into the right side of the inductor is equal to E1 with the same polarity. Because the 150 ohm resistor is stepped down to 37.5 ohms on both sides of the inductor, the voltage drop E1 is equal to 1/2 of the voltage drop across the 75 ohm source resistor. Since E2 = E1, the voltage is zero at the 75 ohm resistor, RB. By Kirchhoff's law, the voltage drop across the 37.5 ohm center tap resistor must also equal E1, therefore 1/2 the source voltage is dropped across RA, 1/4 across the left side of the inductor, and 1/4 across the 37.5 ohm resistor.

By adding a second voltage source as illustrated in figure 4, the "magic tee" becomes a two-way hybrid power combiner. In this case, isolation still exists between the two ports.

Figure 1. Resistive in-phase 6 dB power splitter/combiner

In figure 5, an autotransformer has been added to match a 75 Ω load to the inductor mid-point. The autotransformer has seven turns, tapped two turns down for a 37.5 ohm match. The matching is a function of the square of the turns ratio given by

(1)

So far, the discussion has dealt with zero degree (in-phase) hybrid power splitters and combiners. The same "magic tee" circuit can be used as a 180 degree two-way power splitter/combiner by simply replacing the 150 ohm resistor with a 1: turns ratio isolation transformer as shown in figure 6.

Figure 2. "Magic Tee" building block used as an in-phase power splitter

Figure 3. "Magic Tee" isolation

Figure 4. Basic "Magic Tee" hybrid used as an in-phase power combiner

Figure 5. "Magic Tee" in-phase power splitter using an autotransformer to match the 37.5 ohm mid-point to 75 ohms.

As a 180^{o} power splitter, a signal applied to primary of the 1: transformer divides into two equal amplitude (but out-of-phase) outputs at ports A and B (assuming both ports are terminated in 75 ohms. Under these conditions, no power is lost in the 37.5 ohm termination resistor and half the input power is delivered to each 75 ohm load. Thus, the only loss from the input to each output is that caused by the 3 dB split, just as in the case of the zero degree hybrid splitter. In figure 7, the isolation transformer has been combined with the "magic tee" inductor.

Figure 6. "Magic Tee" used as a 180^{o} power splitter/combiner

Figure 7. "Magic Tee" 180^{o} power splitter/combiner with 75 ohm impedance matching on all ports