# Quality factor of capacitor and inductor in filter design

I designed my desired Chebyshev filter with these parameters (F0=100 MHz, BW=10 MHz, attenuation=40 dB at 20 MHz). The results are acceptable.

After changing the quality factors of inductors and capacitors to default values (which are available in markets) from Q=30 to Q=50, the results are something weird (s21 becomes less than -20dB at F0.) How can I solve this problem?

• I wondered why our filter designers always wound their own silver plated wire inductors on low loss polystyrene formers for their 50 M and 500 MHz narrowband bandpass filters, it was Q and loss. Apr 14, 2022 at 11:42
• Dear Neil, Thank you for your comment. Could you introduce me to two components an inductor (1nH) and a capacitor(470pF) with Q more than 250? Because I searched in Murata company for high Q but I didn't find something good. Apr 14, 2022 at 11:56
• Your L/C ratio is somewhat off at O(1 ohm), post the schematic for the filter Apr 14, 2022 at 16:41
• I appreciate your help, Here you can see the schematic: ufile.io/bxxlcspa Apr 14, 2022 at 18:12
• Very often you have to make impedance transformations before you can implement the basic design, to accommodate real components, especially with high order filters. What tool did you use to design the basic filter? Most good tools will also help you with impedance transformations. Apr 14, 2022 at 18:22

The ratio of component Q and filter alone is not adequate to choose a passive part. You must also consider the test and circuit frequency or the ratio self-resonant frequency (SRF) to circuit application frequency.

Considering the lower frequency effects.

The phase shift is critical for high order filters to work together as it is the complex impedance ratios that result in the overlapping peaks of separate resonances that create each filter characteristic. This is true for maximally flat amplitude, maximally flat phase response and equi-ripple Chebychev filters.

Consider the 1st order response of any passive part as R/L or RC where the -3dB transitions at 45 degrees at the break point and about 86% of the expected 90 deg transition spans +/- 1 decade.

Consider the 2nd order response with parasitic interwinding capacitance on L and conductor effective series inductance (ESL) on capacitors each create the SRF. Now the phase response is about 91% over +/- 1 decade.

When choosing Inductors with a real option of SRF's and Q @ f, compute the parasitic and include them in your model.

Choosing coils for RF filters is not easy as there may be requirements for tolerance, Q, SRF , shielding and current. Air coils offer the highest Q an SRF. So this demands special attention to selection.

Caps less than 100 pF ought to be low ESR such as NP0/C0G, 1%. Add 0.5 to 0.8nH/mm to each Cap and traces.

When this is not readily available, simulate the consequences and alternatives and your "must have design specs". Old TV tuners used air coils for RF filters for this reason in a much larger shielded partition.

Sometimes a bandstop response can be added to overcome weakness in the bandpass response with a Notch-BPF combination.

The result is you can verify if you like that your requirements for any active filter are $$\GBW >Av*f_0*Q^2\$$