To: file

From: Jon Hagen

Date: June 12, 2002

Subject: Operation of the 430 transmitter's EH waveguide tuner

Various mismatches in the platform-mounted waveguide circuitry produce a reflected wave which makes its way down the 1500-ft waveguide to the transmitter room. To protect the transmitter from this reflected wave, an antenna tuner is installed at the output of the transmitter. This "EH" tuner is a magic T hybrid, a 4-port microwave junction, as shown below in Figure 1. Motor-driven shorts are installed in Ports 3 and 4. The position of these shorts can be adjusted by operating joy stick switches at the transmitter console.

Figure 1 EH Tuner

It is interesting to see that this device is capable of presenting the transmitter with a perfectly matched load for any reflection coefficient appearing at the end of the waveguide. Figure 2 is a circuit diagram of the tuner, showing the four ports and the voltage transmission coefficients on the paths between these ports. is the reflection coefficient at the end of the waveguide and is the reflection coefficient seen by the transmitter.

Figure 2 Circuit Diagram

The figure contains the essentials of the analysis. At each port, arrows show the direction of the incoming and outgoing waves. The amplitudes shown for these waves are derived as follows.

We can begin be assuming, arbitrarily, that the wave exiting Port 3 has an amplitude of 1 + j0. This choice will determine all the amplitudes, including y, the amplitude of the incident wave from the transmitter. The short on this port causes a total reflection, so the amplitude of the wave reflected back into Port 3 can be written as ejb , where b is determined by the position of the short.

The wave leaving Port 4 is still unknown. We denote its amplitude as x. Likewise, we will denote the amplitude of the incident wave from the transmitter as y. The amplitude of the wave reflected back into Port 4 is therefore xeja , where a is determined by the position of the short on Port 4.

From the figure, we see that wave leaving Port 2 is just 2-1/2 times the sum of the waves entering Ports 3 and 4. This figure is indicated on the figure, together with Gamma times this sum, which is the wave reflected back into Port 2.

The waves incident on Ports 3 and 4 determine the wave leaving Port 2, as shown on the figure. The wave incident on Port 2 is just the outgoing wave, multiplied by . By inspection, we can now write expressions for the wave leaving Ports 4 and 3.

Adding Equations 1 and 2, y is eliminated, leaving

Solving Equation 3) for x, we find

From the figure, we see that, in terms x, the wave leaving Port 1, i.e. the wave reflected back to the transmitter is given by

Substituting Equation 4 to eliminate x, we find

If the tuner is to make = 0, the numerator of Equation 6 must vanish. This gives us

The phasors on the left-hand side of Equation 7 have magnitude 1/2. The maximum magnitude of is unity. It is easy to see that any can be flanked by the pair of phasors in a way that satisfies Equation 7. See Figure 3, below.

Figure 3 Canceling

Note that Equation 7 allows us to measure by simply measuring a and b, the round-trip phase paths in the two shorting arms of the tuner. By fitting scales to the shorting arms, we could read a and b. To set the scales, we could disconnect the waveguide and substitute a shorting plate. Then a network analyzer (or the transmitter) would be placed at the transmitter side and the shorts adjusted to eliminate any reflection. At these positions, a and b must be . The rate of change, in radians per inch, would be 4 / g , where g, the guide wavelength at 430 MHz, is 36.265". (The factor of 4 rather than 2 is because the round trip distance to the short changes by two inches when the short moves one inch). Remote readouts at the transmitter console would make the calibrated tuner even more useful. After noting the values of a and b, the magnitude of would be calculated from