Broadband Matching Between Cascaded Filters

[Darol Klawetter]

I'm cascading two bandpass SAW RF filters. Each filter has a center frequency of 1.35 GHz and bandwidth of 20 MHz. The filters have input/output impedances of ~50 ohms in the passpand. The impedances can vary widely outside the passband. Generally, out-of-band impedance variances require using a broadband impedance network (e.g., resistive pi) between the cascaded RF filters to obtain a true cascaded response. If a broadband match is not used, out-of-band reflections can result in degraded stop band performance.

The highest frequency presented to the filters is 4.5 GHz and there is a 0.1 inch long microstrip (Zo=50 ohms) that connects the output of the first filter to input of the second filter.

My question: Is there any reason to add a broadband match since the length of my microstrip is much shorter than the wavelength of my highest frequency, which means that I don't really need to treat the connection as a transmission line?

Thanks,

Darol Klawetter

[Tim Wescott]

Huh? What in heaven's name does the microstrip have to do with the
mismatch?

If the microstrip is lossless, then the SWR at the input side will be the
SWR of the load hanging of the output side. It won't affect the severity
of the mismatch, just its relative phase.

The shortness of the microstrip won't do anything to get you out of a
broadband match. Sorry.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

[o pere o]

If you want an accurate answer, you could find out what happens in the
cascaded connection of the three two-ports thay you have: #1 and #3 the
bandpass filters and #2 a short length of line, with S parameters

S2= [exp(-j*theta) 0
0 exp(-j*theta)]

Then, see what happens with a resistive pad with

S3= [0 alfa
alfa 0 ] with your choice of alfa<1

and draw your conclusions. Assuming you have the S parameters of your
SAW filter, you can translate from S to T, multiply T1*T2*T3 and bring
the result back to S.

I guess that the short line will have a negligible effect (compared to
no line) and that the resistive pad might well deliver the a cascaded
response for a sufficient high attenuation. You can tweak the value
until you are satisfied with the results.

Pere

[Chris Jones]

....though changing the length of the microstrip between the filters
might allow the response to be screwed up differently. (Maybe there is
one value of length that is less bad than others.)

A resistive attenuator between the filters sounds like a good idea if
the attenuation can be tolerated, otherwise an isolator, though it will
have to isolate out of band too since that is where the filters will
have the worst matching. Also a better SAW filter might avoid the whole
mess.

Chris

[Darol Klawetter]

Obviously, the impedance mismatch exists regardless of the length of interconnect, but the length of interconnect does relate to the effects of reflections due to the mismatch. Generally, if the length is small compared to the wavelength of the highest frequency of interest, then transmission line effects become less of a concern.

The constructive and destructive effects of the out-of-band reflections change with the interconnect length. The interconnect length can influence the out-of-band response of the cascaded filters and can produce a stop-band response that is less desirable than using only one of the filters.

[Darol Klawetter]

Yes, I've been running some simulations that indicate a broadband match is not required for an interconnect propagation delay that is 5% of the shortest out-of-band wavelength of interest. But it's so common to add a broadband match between filters I'm wondering if there is something I'm missing.

[Simon S Aysdie]

On Wednesday, July 24, 2013 9:43:21 AM UTC-7, Darol Klawetter wrote:
> I'm cascading two bandpass SAW RF filters. Each filter has a center frequency of 1.35 GHz and bandwidth of 20 MHz. The filters have input/output impedances of ~50 ohms in the passpand. The impedances can vary widely outside the passband. Generally, out-of-band impedance variances require using a broadband impedance network (e.g., resistive pi) between the cascaded RF filters to obtain a true cascaded response. If a broadband match is not used, out-of-band reflections can result in degraded stop band performance. The highest frequency presented to the filters is 4.5 GHz and there is a 0.1 inch long microstrip (Zo=50 ohms) that connects the output of the first filter to input of the second filter. My question: Is there any reason to add a broadband match since the length of my microstrip is much shorter than the wavelength of my highest frequency, which means that I don't really need to treat the connection as a transmission line? Thanks, Darol Klawetter

-------------------------
To the extent you can tolerate the loss of the high frequency resistive attenuator, yes, you should add it. The reason to use a pad is somewhat unrelated to the line length. "Shorter lines" may be better, in any case, for pure isolation concerns.

The rejection of passive filters works on the basis of reflectivity in the stop bands. However, their transmission function (H(s), Out(s)/In(s) if you like) is based upon broadband terminations at both ports. The return loss of the resistive attenuator is double (dB) the attenuation; they can indeed improve the rejection performance for this sort of cascade situation. Strictly speaking, you're doing something you are not supposed to do: directly cascade two SAWs, or *any* "reflective" filter, and the loss of "theoretical rejection" is expected. A "pad" would recover some of the supposed rejection performance, since you are violating the test conditions by cascading SAWs directly, or through some near lossless TX line of a given length.

In principle, a 50 ohm line will simply rotate the "reflection impedance" around the smith chart. Theoretically, I'll guess it would not matter. To the extent the situation is non-ideal, and you happened to end up transforming to a less reflective impedance, then some rejection could be lost. However, this is highly speculative. Put the s-params in AWR and mess with the line length. The "broadband match" is not so relevant to the line length in an obvious way. But I would be tempted to test it, and don't be surprised at hazards. Network analyzers are most accurate near 50 ohms. Precision at very high or low immitances will be less, and could hold some hazards if you make idealistic presumptions regarding vendor supplied s-parameters.

Also, you may run into simple isolation problems when it comes to the cascaded rejection (for *any* high rejection filter). Anytime the requested rejection is up into the 60-70-80 dB range, basic isolation becomes a problem aside from the performance of the filter under somewhat ideal conditions. Since the filters reflect, there will be standing waves on the lines at the out-of-band frequencies. Some will be radiated. An antenna works on the basis of standing waves. For testing a filter on an "open pcb," you'll never see the tiny amount radiated. Enclose these standing waves lines in a low loss enclosure (a shield) and you may see rejection plumment, as coupling between them will increase, since it no longer radiated into your office/lab. Keep those lines short, and possibly bury them, or keep the in and out "antennas" in separate "chambers." This *may* have implications regarding line length between the filters too.

[whit3rd]

On Wednesday, July 24, 2013 9:43:21 AM UTC-7, Darol Klawetter wrote:

> I'm cascading two bandpass SAW RF filters... If a broadband match is not used, out-of-band reflections can result in degraded stop band performance.

As others have said, an attenuator is a pretty good impedance match device (at
least, you control the output impedance well); I'd consider using an amplifier, too, unless
there's some reason to think the SAW devices' losses aren't going to imperil your
signal/noise headroom. It's pretty easy to bias a common-base transistor
for 50 ohms input impedance.