The progress in week 2

Second Lab Day

Details for 2nd weeks's activities:

1. For the second week our group are most focus on the knowledge learning of four way power divider, which constructed by cascading two basic two way power divider. According to previous relative research, it shows that the length of interconnection transmission lines can affect the properties of 4-way divider. We decided to build and simulate a 4-way Wilkinson power divider by using AWR, obtaining its input reflection, transmission, output reflection and isolation curves corresponding to different value of transmission lines' length. 
2. We have a group meeting with our supervisor Dr.Zhou on 7th Feb, 2014. Because of the knowledge absence for RF circuit field, Dr. Zhou have introduced the basic concept referred input and output reflection for a divider, as well as transmission, isolation and 'ABCD' matrix . Hence we are more concentrating on the calculation and results of input reflection, in order to knowing how to boarder or narrower the usable bandwidth by changing the length of transmission lines. The calculation of input reflection for a four way power divider with normalized frequency f'=f/fo (0<f'<2) is shown below,
   
   hence Φx represent the length of transmission lines and we only choose nπ/2 to ensuring the symmetry of response.
3. After meeting, we began to construct a basic four way Wilkinson power divider by using Microwave office software. Based on the outcome at week 1, the four way power divider is constructed by cascading two 2-way divider to another one. The designed circuit is shown below:
   
    The component that represent the length of transmission lines are shown in the circuit graph above, the length is presented in degree and hence the value is 90 degree.
4. Our group began to simulating the four way power divider and tried to obtaining its input reflection. It is complex and difficult to obtaining a series of ideal input reflection graphs for different value of transmission lines' length (Φx). It costed a long time to finding a suitable range of actual frequency, in order to getting a perfect input reflection graphs corresponding to varies Φx.Followed by setting the input reflection in S11 with unit dB and simulated the input reflection curves under five value of Φx in turns (0, π/2, π, 3π/2, 5π/2). The results is shown below respectively:

   

   Transmission lines' length is 0 in degree

   

   Transmission lines' length is 90 in degree

   

   Transmission lines' length is 180 in degree

   

   Transmission lines' length is 270 in degree

   

   Transmission lines' length is 450 in degree
5. Then we tried to combining these input reflection curves by superposition and analysis the effect of transmission lines on four way power divider. The graph is shown below:
   
   
   In normally, the usable bandwidth of the standard Wilkinson power divider means the frequency range that corresponding value of input reflections are better that -20 dB. It can be found that the usable bandwidth is boarder as the increase of Φx in order. Our simulation results have shown that the bandwidth of a 4-way power divider can be significantly boarder by choosing suitable length of transmission lines. 
6. At last, we tried to getting the graph of transmission, output reflection and isolation of the 4-way power divider with Φx equal to 5π/2. The results is shown below:
   
   
   While there are existing some error when compared with the ideally graph, the curve of S22 and S23 are wrong and the reason may due to this results are simulated under a theoretical situation. Our group will obtained a measured graph in later few days and then compare it to the ideally one again.

Summary of 2nd week's activities:

• Learning the effect of interconnection transmission lines on four-way Wilkinson power divider
• Using Microwave Office software to built a four-way power divider
• According to the simulation of the four-way power divider, obtained the input reflection graphs corresponding to different value of transmission lines' length.