Tolerance analysis for lumped element filters

They say “a dear child has many names” – (statistical) tolerance analysis, yield analysis and Monte Carlo (yield) analysis. But in this instance, we talk about tolerance analysis, which aims towards predicting the quality of certain product blocks, in other words how the products ultimately meet the customer expectations. For high volume or critical products it’s important to understand how component tolerances affect production yield and product quality.

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:

Etteplan tolerence analysis graph 1

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

Etteplan tolerence analysis graph 2

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



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:

Etteplan tolerence analysis graph 4

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:

Etteplan tolerence analysis graph 5

And closer look to pass band:


Here are yield results in numbers:



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:

Etteplan tolerence analysis graph 7

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.

Jani Vauto

Jani Vauto

Director, Wireless Solutions
+358 46 851 5965
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