Tolerance analysis for lumped element filters

I recently designed a high pass filter for our customer’s prototype. During simulation, I realized that S-parameter model was showing unexpected behavior in tolerance analysis on high frequencies. That finding was the inspiration for this study.

I compared three ways to do a tolerance analysis in RF circuit simulator:

1. Ideal component values

2. S-parameter models

3. Spice (hereinafter equivalent circuit) models

With 5G mid-band spectrum in mind, I designed the 5th order elliptic 3.5 GHz high pass filter with lumped element components (see following figure of schematics).

As a short summary – based on the following study, I recommend using equivalent circuit models for the most critical tolerance analysis.

Then a longer story…

Initial data and assumptions

All used S-parameters are valid between 100 MHz and 8.5 GHz. I didn’t model PCB traces in this simulation study. I used Murata 0201 components with tight tolerances, even though for some components even tighter tolerances are available. In simulation, all component tolerances have a uniform distribution. For equivalent circuit models, I applied tolerances only for the dominant equivalent component.

Schematics with ideal component values:

S-parameter model schematics remediated with ideal nominal “zero value” components to enable tolerance analysis:

As an example, here is an equivalent circuit for one component, 4.3 nH inductor. In tolerance analysis only dominant L2 has tolerances:

Simulations

To match filter nominal value responses better with each other, for the second capacitor, I used 2.8 pF value in S-parameter and equivalent circuit simulation instead of 2.7 pF which is used in an ideal model simulation. Responses are quite well inline frequency wise – actually, S-parameter and equivalent circuit responses are exactly on top of each other:

I set yield goal to greater than -1 for frequency range from 3.6 to 8.5 GHz (only for pass band) and run 1 000 iterations for all three cases:

And closer look to pass band:

Here are yield results in numbers:

Conclusion

As you can see, there is more variation on pass band with equivalent circuit schematic than with S-parameter one. The reason  is that tolerance behavior is different as a function of frequency.

I made tolerance analysis for 2.8 pF capacitor, GJM0335C1E2R8BB01, in common shunt circuit. Here is impedance as a function of frequency:

As you can see, the nominal behavior of S-parameter model and equivalent circuits model is exactly the same – as it should be. Also, on low frequencies the behavior of these two approaches is very similar. But near and beyond self-resonant frequency, results of tolerance analysis differ a lot e.g. on self-resonant frequency nothing happens with S-parameter model compared to equivalent circuit, that varies about 200 MHz.

If this filter will be implemented some day for the aforementioned 5G mid-band spectrum, corner frequency should be adjusted a little bit lower or even more tighter tolerance values should be used, and also layout traces should be taken into account.

As a conclusion, I recommend using equivalent circuit models for the most critical tolerance analysis, especially if self-resonant frequencies are near the frequency of interest.  Omitting proper tolerance analysis in designs with small margins may lead to poor production yield and product quality problems on the field.