Power dividers and directional couplers are passive microwave components used for dower division or power combining. In power division, an input signal is divided by the coupler into two (or more) signals of lesser power. The coupler may be a three-port component with or without loss, or may be a four-port component. Hybrid junctions have either a 90° (quadrature) or a 180° (magic-T) phase shift between the outport ports. Quadrature hybrids are 3 dB directional couplers with a 90° phase difference in the outputs of the through and coupled arms. This type of coupler is made in microstrip or stripline form and is known as branch-line hybrid.

This design is to introduce us as students in the understanding of the manufacture and problems with using different variables in developing the type of microwave devices. Couplers are generally specified by their coupling (C), directivity (D), and load impedance (Zo). There are several applications for these couplers. In passive devices they are tuners, delay lines, filters and matching networks. In active devices they are balanced amplifiers, mixers, attenuators, discriminators and phase shifters. In addition, there are several other factors that go into a design that we are not informed of but we tried our best to meet all the design factors of our design. Of course, with some trial and error or more time in doing our design, we could have met all of the design factors.

With reference to Figure 1, the basic operation of the branch-line coupler is as described below. With all ports matched, power entering port 1, or the input port, is evenly divided between ports 2 and 3, the output ports, with a 90° phase shift between these outputs. No power is coupled to port 4 (the isolated port). The branch-line hybrid has a high degree of symmetry, as any port can be used as the input port. The output will always be on the opposite side of the junction from the input port, and the isolated port will be the remaining port on the same side as the input port. This symmetry reflected in the scattering matrix, as each row can be obtained as a transposition of the first row.

The schematic circuit of the branch-line coupler in normalized form, as shown in Figure 2 above, each line represents a transmission line with indicated characteristic impedance normalized to ZO. Assume that a wave of unit amplitude A1 = 1 is incident at port 1. The circuit can be analyzed by superposition of an even-mode excitation and an odd-mode excitation, which this report will not go in depth.

In practice, due to the quarter-wave length requirement, the bandwidth of a branch-line hybrid is limited to 10-20%. But as with multisection matching transformers and multihole directional couplers, the bandwidth of a branch-line hybrid can be increased to a decade or more by using multiple sections in cascade. Of course, in our design we will not be using more than one section because we will be designing for one frequency (but this information is useful for later designs).

To start our design we need to know a few things to start. We need to know the real permittivity (e r) of the material that we are using. And we need to know the height (h). Other factors will include the frequency f0 that we will design for and we want to use 50 W impedance for the input and output load matching. For this design we were given the factors of our circuit board and if ideal (printed circuit boards have just as many variances in changing the calculations that are not factored in our final product). We will use values given to us at the start of our design:

e r = 4.2

h = 32 mils

We also need to know a few other things before we start:

K -10 Log 1, = [(K + 1)]

,

And (by symmetry)

, K =

P2 = P3 = 3 dB (by symmetry) so 3 dB = = 0.5 Pin

Inverting for Impedance:

W Z1 = Z4 = 50 W

Now we need to figure out our resistance using the dielectric and height factors of the printed circuit board in solving for our width and length of the runs.

With calculated Z0 = 50 W and Z2 = 35.4 W

and our height

h = 32 mils = 812.8 x 10m

our wavelength formula is

l = ,

this gives the length for L2 to be

L2 = = = 40.97 10m = 40.97 mm

From our microstrip matching circuits formulas

and A is solved with the formula

A = exp

With our solved values for L1 = 39.99 mm, L2 = 40.97 mm, W1 = 4.79 mm and W2 = 2.755 mm. We then made a puff analysis of our project using our values to make sure that we were near in our calculations (surprisingly we were right on the mark). Then we made some adjustments to our artwork that changes our values; we did not consider how we were going to connect our connectors to the quadrature. So we were pressed for time, so we just made some bump outs for easy access for our connectors. These bump outs caused several problems with the results of our calculations and if we spent more time, we would have calculated the correct impedance of the transmission lines for our design.

The results of after the circuit after coming back from going out to a company for the etching process and with our errors, we made several graphs of the coupler. We installed connectors and the isolation termination (which later cause some problems also). The insertion loss for the coupler from 1 to 2 and 1 to 3 were -2.9 and -3.1 dB at the design frequency. These looked all right but resistor that we used for the isolation port was a through hole and not surface mount, which put some stray impedance on the results.

The Voltage Standing Wave Ratio (VSWR) was not close; we never had any experience in installing connectors so some more errors were added onto the ideal circuit. The VSWR for the ports is plotted and the results at the design frequency is for port 1, -18.6 dB; port 2, -13.2 dB; and port 3, -9.8 dB. These values are extremely bad and especially for port 3 which 'sees' port 4 with the resistors connected to it. Generally, to cure these would be to be diligent with our soldering and to use SMT type resistors for port 4, the isolation port.

The phase for port 1 to port 2 measured -118.34° and for port 1 to port 3 measured 142.9° . These results give us a 98.76° phase shift between the two output ports, depending on close we wanted our results to be 90° (I never personally measured phase for the calibration laboratory, so I don't know how important the error is in value, the phase was measured every time but we ignored the result in the lab where I worked).

This design was very informative and gave me a lot of practical knowledge in understanding of how important everything is doing a microwave design. Which includes the connectors in being diligent in doing the soldering, making sure of the calculations are correct, ensuring the values of the printed circuit boards are proper and ensuring that our test setup for testing is correct. Hopefully with this new knowledge, I will be able to carry on and be able to understand new designs and be able to understand where problems may arise when they show up.