parallel coupled line resonator

Dear all;

As we know, parallel coupled-line (PCL) BPF could be electrically equivalent with BPF with series stubs. However, I find a discrepancy between them.

At first, if we plot the equivalent circuit of each coupled stage of a PCL filter, we can obtain one series open stub at both ends of a quarter wavelength transmission line. Next, by cascading n+1 coupled stage to compose of one n-order BPF, we finally would achieve a filter with n+2 series open stubs. For n-order BPF; nevertheless, it only has n series open stubs.

How to interpret this discrepancy? Could everyone explain this? Thanks a lot!

Yes, a parallel coupled line in TEM structure (Stripline, slabline) can be modelled that way.

But you do realize that one of these quarterwave coupled line sections only forms 1/2 of a half wavelength resonator. In other words, EACH resonator contains two of these model structures.

Dear biff44;

Thanks for your kindly reply.

But I still have no idea what you mean "EACH resonator contains two of these model structures". In the classical filter book written by Matthaei/Young/Jones, it seems that the first and end coupled-line sections are not included the circuit model. Why? If the PCL lacks of these two coupled-line stages, it implies that it dosen't form passband response. But if we consider them in the circuit model, the order will increase, I think it is wrong. Could you kindly give me more explicit answer.

Thank you very much!

Check out table 8.09-1 and figure 8.09-2 in Matthaei, Yound, & Jones.

This is a 6 pole filter because there are 6 half-wavelength long resonators. But you could also look at this as being composed of 7 quarterwavelength long sections. The one section at the front, and the one section at the end, are just impedance matching sections for the 50 ohm to first or last resonator.

Each of these 7 quarterwave sections would be modeled by its own structure, such as shown in figure 5.09-2 b.

Once agian, figure 5.09-2 b. is only valid for stripline or other TEM structure. It will not work well for simulating microstrip.

Dear biff44;

Thanks for you kindly reply.

You answer is clear and I can understand your meaning.

I appreciate it. :D