Wilkinson Power Divider
Objective:
A. To Design a 3-dB Wilkinson power divider on 0.031” thick Duroid using a surface-mount 100Ω chip resistor between the two arms of the power divider.
Design Specifications:
1. Structure must fit in the board size of 38 x 50 mm.
2. Center frequency = 2.4 GHz
3. Return Loss at all ports > 15dB over a 20% bandwidth.
4. Substrate = Rogers 5880 Duroid
5. εr = 2.2
6. Duroid thickness = 0.031” (0.787 mm)
7. Conductor = Copper
8. Conductor thickness = 8 μm
9. Dielectric loss tangent = 0.0009
10. Assume Zo = 50 Ω system
11. Minimum line widths and spacing = 0.012”
Wilkinson Power Divider:
The Wilkinson power divider splits an input signal into two equal phase output signals. It may also work as a combiner in which case it is used to combine two equal-phase signals into a single signal in the opposite direction. This divider was invented around 1960 by an engineer named Ernest Wilkinson. Wilkinson power divider is a solution of the loss less T-junction problems, which are not matched and non-isolated output ports. It is especially useful because the output ports are simultaneously isolated and matched.
Wilkinson power divider is a lossy three port network and it has a property of being lossless when the output ports are matched. Wilkinson relied on quarter-wave transformers to match the split ports to the common port. Since a lossless 3 port reciprocal network cannot have all three ports matched, Wilkinson added one resistor. The resistor fully isolates port 2 from port 3 at the center frequency without adding resistive loss to the power split, so an ideal Wilkinson splitter is 100% efficient.
A typical Wilkinson power divider looks like the one shown in figure:
Depending upon the power split Wilkinson Power splitters can be categorized into:
1. Wilkinson Equal Divider.
2. Wilkinson Unequal Divider.
The equal power division concept is dividing input power to equal or more than two ways equally. The most commonly used is the one we need to make in this lab assignment which is a three port network equal to two way divider. It is also called a 3dB power divider.
In this type of divider, there are four different sections- 1) Input port 2) Quarter wave transformer 3) Isolation resistors 4) Output port.
The input and output ports are identical and there impedance values are Zo. Quarter-wave transformer parts are called as quarter-wave transformer because of the length of these parts. The length of these parts is equal to the one fourth of the wavelength of the electromagnetic wave, which is propagating in this three port network. This results in matching of the output ports which leads us to have better power transfer results. Isolation resistor helps us to isolate the output ports. If there is coupling effect between output ports the perfect division of power cannot be possible. This isolation resistor avoids the coupling effects of the output ports.
Working:
When a signal enters port 1, it splits into equal-amplitude, equal-phase output signals at ports 2 and 3. Since each end of the isolation resistor between ports 2 and 3 is at the same potential, no current flows through it and therefore the resistor is decoupled from the input. The two output port terminations will add in parallel at the input, so they must be transformed to 2xZo each at the input port to combine to Zo. The quarter-wave transformers in each leg accomplish this; without the quarter-wave transformers, the combined impedance of the two outputs at port 1 would be Zo/2. The characteristic impedance of the quarter-wave lines must be equal to 1.414 x Zo so that the input is matched when ports 2 and 3 are terminated in Zo.
Final Design of the Wilkinson Power Divider:
I have used Microwave Office for designing the circuit. Based on the discussion above the components were laid out and appropriate interfacing microstrip lines were added to the circuit. And finally 50Ω ports were added to complete the design. The schematic of the design is shown below.
Layout of the power divider is as shown below:
Predicted performance of the Wilkinson Power Divider:
S11 being at the center of the Smith Chart means that there are no return losses or even if there are, since the point of S11 is not exactly at the center, we still expect negligibly low return loss. Also S32 being at the center would mean that the resistance of 100ohms which we are using to isolate the two ports is not working ideally and there is some coupling between the two ports. This has resulted the point to slightly drift from the center of the Smith Chart.
As we can see the S31 and S21 is 2.955dB which is very close to being 3dB down. Thus there is an equal power split between the ports 2 and 3. The reason of a difference of 0.045dB is due to the presence of a real resistance which would still couple a small amount of power. The S11 curve is 37.5 dB down which indicates minimum return loss. The S32 is 30.91dB down which means very negligible power being coupled between the two output ports. Thus the circuit is working exactly as expected.
In this graph we see a perfect phase match between the outputs at the two ports. There is absolutely no phase difference, which is in accordance to what we should be expecting in our results.
Performance of the circuit in Sonnet:
I exported the circuit and ran it in sonnet. Sonnet is an EM software which takes into account the parasitic inductances and capacitances of the circuit thus providing outputs. The circuit layout in Sonnet, the current density, the phase graphs and the S-parameter curves are shown below.
Circuit Layout in Sonnet
Current Density Distribution
Phase difference between S12 and S13
S11 Magnitude in dB Curve
S12 and S13 Magnitude in dB Curves
As we see Sonnet gives us some variation in the amount of power that is being coupled to port 2 and port 3. Though the power divided between the two ports revolves around 3dB but in Sonnet it doesn’t give us exactly 3dB power division. The reason behind this variation is the different lengths I am using between port 1 and the two ports.
LAB TESTING OF THE CIRCUIT:
Component Assembly:
- The layouts were sent to Raul in gerber format which he used to etch our circuit.
- To start with we figured out that there was a slight etching error on our board. The board was etched too sharp at the edges of the conductor resulting in reduced dielectric width around that areas as such we anticipated some deflection in our results from what was expected.
- Then the SMA connectors were soldered carefully.
- A 100Ω chip resistor was also soldered between the two lines.
- After the circuit was ready to be tested, the VNA was calibrated to 2 port testing.
- The unused port was terminated in 50Ω. We do this to make it as close to perfect matching as possible.
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