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user129412 Asks: Improving a lumped element low pass LC filter design
For our research we've been looking at lumped-element on-chip LC filters, like the one discussed in the paper Circuit Quantum Electrodynamics Architecture for Gate-Defined Quantum Dots in Silicon by Mi et al. from 2017 (published version here). We work on similar experiments such as these, and with this question I was hoping to leverage the knowledge of the community to improve on this design. I've started looking into the large body of literature myself, but I think most of it assumes you have access to standardized surface mount components of all sorts of values, which for us is a bit hard to achieve with on-chip lithography.
The details are not all that relevant, but to summarize the work I am referencing, they have DC bias lines that come into close proximity with GHz-scale resonators (parallel LC circuits) and they want to avoid that resonator losing its energy through their parasitic coupling to these bias lines. So they construct a low-pass filter that makes the DC line a poor path to decay into for the resonator.
They construct the following filter, shown in panel a:
It consists of a square-type planar spiral inductor, and an interdigital capacitor. Noteworthy also is that the material is thin film superconductor and thus essentially lossless.
Given how much work exists on low pass filters, I was wondering if someone would have a recommendation for an improved filtering design. As you can see, at 6 GHz they only reach about -20dB with the first order filter, which I'd prefer to be at least -40.
I suppose what is important is to summarize the design constraints
Although I think here I am mainly using the pragmatic requirements that I am used to thinking of. I suppose the language one think sof instead is filter order, flatness and sharpness of the cutoff, in determining optimal filter topology. From what I have found, one typically uses either Butterworth, Chebyshev, or Elliptic filters, depending on needs for flatness and/or sharpness. That is a fair question, but to that I would say I would first prefer to identify the type(s) of filters that are achievable with the given design constraints. I could imagine, for example, that certain topologies require better targeting of Ls and Cs than others?
Also, I understand that I am leaving this question here without showing a lot of work from my side. Based on what I could find, perhaps something like a 5th order Chebyshev makes sense? I have mainly just been playing around at RF Tools | LC Filter Design Tool to come to that conclusion, but putting in a cutoff of 2 GHz gives reasonable values, except that the capacitance is a bit on the higher end of what I can achieve.
For our research we've been looking at lumped-element on-chip LC filters, like the one discussed in the paper Circuit Quantum Electrodynamics Architecture for Gate-Defined Quantum Dots in Silicon by Mi et al. from 2017 (published version here). We work on similar experiments such as these, and with this question I was hoping to leverage the knowledge of the community to improve on this design. I've started looking into the large body of literature myself, but I think most of it assumes you have access to standardized surface mount components of all sorts of values, which for us is a bit hard to achieve with on-chip lithography.
The details are not all that relevant, but to summarize the work I am referencing, they have DC bias lines that come into close proximity with GHz-scale resonators (parallel LC circuits) and they want to avoid that resonator losing its energy through their parasitic coupling to these bias lines. So they construct a low-pass filter that makes the DC line a poor path to decay into for the resonator.
They construct the following filter, shown in panel a:
It consists of a square-type planar spiral inductor, and an interdigital capacitor. Noteworthy also is that the material is thin film superconductor and thus essentially lossless.
Given how much work exists on low pass filters, I was wondering if someone would have a recommendation for an improved filtering design. As you can see, at 6 GHz they only reach about -20dB with the first order filter, which I'd prefer to be at least -40.
I suppose what is important is to summarize the design constraints
- Size constraints limit capacitive elements to around pF per section, and inductive elements of at most a few nH. We could probably cascade a few of these though, but I doubt we can go much higher than 5th order.
- Nanofabrication accuracy limits value-accuracy of Cs and Ls to about ~10-20%
- The line is to be used for DC bias; it has to be low pass down to DC
- We would like to filter at least -40 at 6 GHz
- Would like to keep self resonances below 3 GHz. Or better said, keep everything above 3 GHz to at least -20dB.
Although I think here I am mainly using the pragmatic requirements that I am used to thinking of. I suppose the language one think sof instead is filter order, flatness and sharpness of the cutoff, in determining optimal filter topology. From what I have found, one typically uses either Butterworth, Chebyshev, or Elliptic filters, depending on needs for flatness and/or sharpness. That is a fair question, but to that I would say I would first prefer to identify the type(s) of filters that are achievable with the given design constraints. I could imagine, for example, that certain topologies require better targeting of Ls and Cs than others?
Also, I understand that I am leaving this question here without showing a lot of work from my side. Based on what I could find, perhaps something like a 5th order Chebyshev makes sense? I have mainly just been playing around at RF Tools | LC Filter Design Tool to come to that conclusion, but putting in a cutoff of 2 GHz gives reasonable values, except that the capacitance is a bit on the higher end of what I can achieve.
