Edit Thu Oct 25 14:57:57 2018 (awade): Note that the LISO models here have wrong units. They are supposed to be in units of power but were not converted from V/V. Things listed as dB are correct but multiply the exponent of magnitude plots by two. This will be corrected in future posts.
I came across two interesting papers by Matt Morgan et al. on the subject of reflectionless RF filters.
It seems like there wasn't a lot of thought put into optimal RF filter designs before this point that properly terminated the stop band elements. The Morgan filters are essentially diplexing filters arraignments, that has been done before. However, in the case of these reflectionless filters, there are additional symmetries that lower the inductor and capacitor values, reduce the requirements on component Q and widen the component tolerance requirements in general. The matched component design means that all circuit parts can be drawn from the same batch, improving the manufacture variation errors and also reducing the sensitivity to temperature. Together this means that we can more readly make custum filters with off-the-shelf discreet components with more confidence they will preform as designed and be relativity imune to thermal variations.
Comparisons to the equivalent Butterworth and Chebyshev designs suggest that it performs just slightly worst than Chebyshev but with a better complex gain slope, this means flatter phase in the passband and better stability of the filter for mismatch with component variation. It seems like these reflectionless filter structures are more directly comparable to the inverse Chebyshev filters or the elliptic (Cauer filter) topologies. These have minimal or no pass band ripple at the expense of slower roll off in the stop band some stronger stop band dips. The bonus is that they are properly terminated at all frequencies and absorb all stopband by design.
The shape of the pass band response is much closer to the current elliptical filter installed in that there is a strong dip designed to coincide with the PDH modulation frequency. The dip corresponds to the first pole of the filter. As documented previously in PSL: 2238 the stop band attenuation of the TTFSS elliptical filters is not much better than 14 dB. However, the attentuation at the critical modulation frequency is 58 dB and that is what really matters. The problem with the current TTFSS RF demodulation design is that it does not have proper dumping the the stop band, much of the rejected ω and 2ω frequency components are reflected strait back into the mixer.
The naive wisdom is that we add a terminating resistor at the input of the RF LP filter to quell backreflections to the mixer. This is probably good enough for many configurations where we just don't care that much. However, 50 Ω to ground isn't strictly impedance matched accross the whole frequency band and messes up the impedance in the passband. What we want is something that optimally dumps the higher order RF terms and presents the mixer with a well defined impedance at its output* accross the whole band: that way the mixer is loaded properly to its design specs.
Below is an schematic of a first order reflectionless filter with component values selected to achieve the pole dip at 36 MHz.
Here the optimal choice for passive component values is:
where Z_0 is the input terminating impedance of the filter. It is also implicitly assumed that the output terminating impedance is matched to this Z_0 value.
I modeled the worst case filter design variations by performing a Monty Carlo simulation of the ideal circuit with LISO. I Assumed a standard deviation of compoent values of 5.0% (this is what the spec sheets claim and set each component to normal random sample for each component about its ideal design value. Below is a plot of 500 samples (thin low alfa lines) along with computed median and 1σ band. In reality the component variation will be much less as they are drawn from the same batch and the manufactures probably leave a margin of error in the absolute value of components that they can deliver to.
What the model shows is that the tolerance to component variation is probably ok. It doesn't show the impact of component Q on filter performace (especially about the deep notch around the pole is what we are really interested in). I'm working on getting PySpice to simulate this with the coilcraft spice models.
Here also is the input impedance of the filter as a function of frequency:
This seems less good, as can be seen from the actuall mismatch for individual samples. The real variation of inductors and caps drawn from the same batch probably isn't this bad.
*Its not clear to me what the output impedance of a naked mixer is supposed to be. In the TTFSS design a 22 Ω resistor is in series with a MAX333A switching chip before the RF filter (these 333A's have ~ 30 Ω series resistance): so it seems like that design assume that you need to add resistance in serieis to get to 50 Ω termination.
Also attached is the notebook used to compute the plots in this post using pyliso.
Edit Thu Feb 21 19:30:48 2019 (awade): fixing unrendered laxex