I'm getting to grips with designing coupled line filters and wanted to implement the band-pass filter described in Example 8.7, p. 435 in David Pozar's excellent "Microwave Engineering" just as a first toe-dip into the discipline. However, the outcome for the insertion loss is very much unlike the one stated in the example. I am missing something very basic, probably.

The filter itself is N=3 (four coupled lines) with a 0.5 dB equal ripple response and a center frequency of 2 GHz. \$ Z_0=50\Omega \$ and the bandwidth is 10%.

The stated odd and even mode impedances are:

| n | Z_0e (ohm) | Z_0o (ohm) |
| 1 | 70.61      | 39.24      |
| 2 | 56.64      | 44.77      |
| 3 | 56.64      | 44.77      |
| 4 | 70.61      | 39.24      |

Using Qucs 0.0.18 and its line calculation tool I make the following schematic, assuming I have a 254 um thick ceramic substrate of sorts and that the couplers are \$\lambda/4\$ long at 2 GHz:

Qucs 0.0.18 schematic

I now get the following results:

S11, S21 in dB

Close-up of S11, S21

which is significantly worse than I expected. There is no ripple in the passband, as seen in Pozar's results, and I only ever achieve a -3 to -4 dB insertion loss.

If I add some transmission lines for impedance matching, I might gain 1 dB in S21 at the expense of bandwidth.

Obviously it is possible to design a much better functioning filter, like this one in the qucs example folder for 10 GHz: http://sourceforge.net/p/qucs/git/ci/master/tree/examples/bpf_10Ghz.sch

Could this be the microstrip models in qucs adding too much reality to the results? ;-) Any comments are greatly appreciated.

  • 1
    \$\begingroup\$ Did you try taking tand and rho to near zero? \$\endgroup\$
    – The Photon
    Commented Oct 26, 2015 at 23:41
  • \$\begingroup\$ Incidentally, your h and t parameters look typical for printed circuit scenarios, but your er is awfully high. What substrate are you trying to model? \$\endgroup\$
    – The Photon
    Commented Oct 26, 2015 at 23:44
  • \$\begingroup\$ @ThePhoton, looks like substrate is Alumina (\$\epsilon _r\$=9.8). \$\endgroup\$
    – gsills
    Commented Oct 27, 2015 at 2:06
  • \$\begingroup\$ @ThePhoton Loss tangent and conductivity: Yes, I had the same thought, however, the improvement was marginal. \$\endgroup\$ Commented Oct 27, 2015 at 5:15
  • \$\begingroup\$ @ThePhoton Substrate material and thicknesses: Yes, this combination is not the most realistic one. I redid the simulation with qucs' built-in RO4350 substrate parameters and recalculated dimensions. I didn't change the outcome very much. \$\endgroup\$ Commented Oct 27, 2015 at 5:18

1 Answer 1


So, I double checked one of ThePhoton's suggestions, and of course he's right. It was all about the conductivity. Look what happens when I reduce the specific resistance with 4 orders of magnitude:

enter image description here

enter image description here

So, going lossless is the way to reconcile it with Pozar's results. Case closed and thanks for helping out! Ready for next step.

  • 1
    \$\begingroup\$ Good that you got if figured out. If you want a real-world (partial) solution it probably means using a thicker substrate (larger h) so that all your Ws will end up larger. \$\endgroup\$
    – The Photon
    Commented Oct 29, 2015 at 0:58
  • \$\begingroup\$ Thanks, enlarging the W to reduce conductor loss is probably the way to go. \$\endgroup\$ Commented Oct 29, 2015 at 9:25

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