Filter types, a few questions - Page 1
Forum section: electronics / beginners

author: Infraviolet
author_rank: Super Contributor
timestamp: November 06, 2023, 10:49:20 pm
content: I've been reading up about pasive and active filters, for use in a near future project I'm planning. The use case being one of "if a frequency in this range is present, give some indication, roughly, of how big its peak-to-peak voltage is", and doing that separately for several frequency ranges each quite close to each other.I've been particularly interested in things which are "brick wall" like, not too bothered about ripples within or outside the passband. Just something which will give a unity or positive gain within the band, and then give attenuation of 1/100 (or more suppressive) at frequencies only a few tens of percent greater than the pass band ends.I've seen about Bessel, Butterworth, Chebyshev and Elliptic filters. But I'm a little confused, when you put these in to real circuitry, is there a different topology of component layout for each filter type? Or are these different types of filters really just about different ways (in terms ofwhere you put the pass band limits of each stage) in which you combine an active or passive RC filter stage after one-another? Output of each filter becoming the input of a successive one? Each filter in the stage being a normal active or passive RC?Are there good resources about the practical implementation of Elliptic filters? Focused not on the math behind them, but simply on the topology needed in the circuit and sets of equations which let you select the pass band limits, the minimum gain in the pasband, the maximum gain outside the passband, and how quickly to have the gain drop off at the passband limit? Elliptics, for what I've read so far, look best for having a really sharp drop-off at the band ends, if you can tolerant them having really weird shapes to the gain-with-frequency curve,subject to not much more condition than "above a certain minimum level in passband, below a certain maximum outside the band" . But there's a lot less online about them than for Butterworth or Chebyshev.Also, is there such a thing as a "semi-active" filter? A passive one just uses R and C, an active one uses op-amps to process a voltage difference between the op amp's inputs. A semi-active one would be using single input amplifier stages, either as just buffers to read in the voltage of the previous stage with negligible current draw and then feed each subsequent stage from a low impedance source, or with some fixed amount of gain when doing so. These would be the sort of things easily produced with small counts of transistors, or with the "CMOS NOT gate as amplifier" trick.Thanks

author: Benta
author_rank: Super Contributor
timestamp: November 06, 2023, 11:28:22 pm
content: Sorry to be a spoilsport, but you can't escape the maths.Topology doesn't even come into it, until you enter the realm of elliptic, aka Cauer filters.Let's stick to low-pass filters.Bessel, Butterworth and Chebyschev filters all share the same type of transfer function, and between the three named types there are an infinite amount of others. All are realized using the same circuit.They all have all-pole transfer functions.Cauer/elliptic filters have resonant dips in the stop-band and are pole/zero filters. A different circuit is needed there.I don't think I've ever seen Cauer filters in low fequency applications, but they are used in MHz/GHz passive circuits, often as helical filter sections.

author: srb1954
author_rank: Super Contributor
timestamp: November 07, 2023, 12:05:03 am
content: Quote from: Infraviolet on November 06, 2023, 10:49:20 pmGetting a roll-off that fast is not likely to be feasible with a conventional active or passive filter. This would likely require a crystal filter or a digital filtering technique.QuoteBessel, Butterworth and Chebyshev are all-pole filters and can be implemented with a standard Sallen & Key or multiple feedback filter configuration. Elliptic function (and inverse Chebyshev) also require zeroes in their response and so require a different filter configuration, usually implemented around a twin-Tee notch filter.Normally, you break down the filter response into a series of 2-pole stages and implement each of those stages around a single op amp. The stages can be easily cascaded together as the low output impedance of the op amp isolates the interactions between stages. If you have a filter with an odd number of poles the single pole stage can be implemented with a simple RC filter.QuoteI haven't found any good resources for active elliptic function filter design although I haven't researched much on this topic lately.Back in the days before the internet provided all the answers I had to come up with my own design method for elliptic filters. I started out selecting a suitable response from design tables in Zverev's book "Handbook of Filter Synthesis", factored those responses into a series of 2-pole and zero functions and then used my design method to calculate out the Rs and Cs for each filter stage.It takes quite a bit of effort to design high performance active filters and requires selection of high quality precision passive components to achieve satisfactory results. I generally used 0.5% metal film resistors and 1% polystyrene capacitors. Unfortunately, polystyrene capacitors seemed to have disappeared from the market and it is hard to get equivalent performance out of modern replacements.QuoteYou could make a semi-active filter but there wouldn't be much point in doing so as you would only be able to synthesise filters having real poles. You need to have some feedback around the op amps to get the complex poles necessary for the higher performance filter types.

author: Infraviolet
author_rank: Super Contributor
timestamp: November 07, 2023, 04:32:53 pm
content: Thanks, looks like I will have to look further into the details of the maths. Can anyone point me to a good online resource about it? Hopefully one which treats the maths as a practical step to building filters, rather than (as so many do) one which sticks to an abstracted purely mathematical perspective.P.S. when I say "topology" I'm meaning the generalised layout of circuits, the "net list" or "schematic". I realise there can be much more mathematical meanings to this too.

author: TimFox
author_rank: Super Contributor
timestamp: November 07, 2023, 04:51:56 pm
content: For passive (L-C and crystal) filters (Butterworth, Chebyshev, linear-phase, and elliptic), a useful source of information, using graphical numerical results and discussions of topology, the "Filters: Modern-Network-Theory Design" chapter of the "Reference Data for Radio Engineers" (old title), now "Reference Data for Engineers" (9th ed, 2001).https://shop.elsevier.com/books/reference-data-for-engineers/van-valkenburg/978-0-7506-7291-7Older copies are available as pdf:https://www.worldradiohistory.com/BOOKSHELF-ARH/Technology/Technology-General/Reference-Data-for-Radio-Engineers-5th-ITT-1972.pdf

author: Infraviolet
author_rank: Super Contributor
timestamp: November 12, 2023, 06:03:16 pm
content: To check my understanding:1. Plain RC passive filters, however you cascade them, can never have particularly shrap fall-offs at the pass band edge?2. LC filters can quite easily achieve sharp fall-offs and huge Q values?3. Because real inductors are pretty non-ideal, it is favoured to use op amps to make virtual inductors ("gyrators") using combinations of op amps, resistors and caps? And with real inductors often having pretty wide tolerances, 10% or such, what is supposed to be say a narrow bandwidth filter with say a 2dB permissible passband ripple, ends up with a passband where there are 15dB ripples present if the L and C values aren't accurate to multiple significant figures (I found an online simulator page which showed this difference when you told it to give solutions with exact coponent values vs solutions rounded to the nearest commonly available value for components).4. Is there a way to make these "gyrators" with single transistor setups rather than two-input op amps? I understand gyrators need feedback paths, in some cases transistors can do this?5. Can R, C and transistors be used to make a fairly sharp fall-off bandpass then?Is there any other type of circuit than a true filter which can let one get an output (either the analog signal itself, or something heavily distorted but giving proportionate results for peak values when put through a rectifier...), roughly proportional to signal strength, if and only if a signal at some specific frequency (+/- a tolerance bandwith around it, incase the signal's frequency is a little bit off) is present?Thanks

author: MarkT
author_rank: Frequent Contributor
timestamp: November 12, 2023, 06:44:33 pm
content: Any passive RC filter or passive RL filter can only have real poles, meaning no resonance.Passive RLC or active RC or active RL have second-order differential equations, so the poles can be complex, not just real, meaning resonance is possible, allowing sharp frequency transitions.Well worth getting a basic understanding of pole-zero diagrams, its pretty intuitive. They encode all the linear differential equation stuff without needing to understand them.

author: srb1954
author_rank: Super Contributor
timestamp: November 12, 2023, 07:33:52 pm
content: Quote from: Infraviolet on November 12, 2023, 06:03:16 pmCorrect.QuoteModerately sharp filters and moderately high Q values. Building high-Q inductors is not a trivial exercise.QuoteThat is one approach but typically requires greater circuit complexity that other active filter configurations, especially where floating simulated inductors are required. Another approach is FDNR (frequency dependent negative resistor) filters. This is a fairly simple transformation applied to a passive RLC filter design to eliminate the inductors and replace with active components but it results in a fairly complex overall circuit.QuoteInductors can be made to better than 10% tolerance and can also be made in adjustable configurations to allow filter tuning. This was commonly used in the past where LC filters where implemented using "pot-cores" with adjustment for tuning the filter to spec.QuoteYes, but possibly with reduced performance. Op amps give better performance, take up less PCB space and are hardly any more expensive than discrete transistor designs.QuoteOnly moderately sharp band-pass filters but at the expense of circuit complexity.QuoteDepending on the number of different frequencies you are trying to detect a digital filtering solution may be the best. You can use an FFT algorithm or the simplified Goertzel algorithm. Other sampled data techniques like switched capacitor filters or commutating filters may be worth looking at.

author: tggzzz
author_rank: Super Contributor
timestamp: November 12, 2023, 07:50:13 pm
content: Ive just resurrected a.circuit I designed in 1979. It uses 8 10% capacitors, one 10% resistor, and 8 analogue switches.The key performance points are Q>1000, flat passband, and initial rolloff is >20000dB/decade. Stopband can be 20-40 dB down. And yes, despite typing this on a tablet, those are the right number of zerosWould that do?

author: Benta
author_rank: Super Contributor
timestamp: November 12, 2023, 09:10:01 pm
content: Yes, if you go away from the continuous time domain, a lot of things are possible.Whether it's applicable here, IDK.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: November 12, 2023, 09:54:30 pm
content: Quote from: Infraviolet on November 12, 2023, 06:03:16 pmFor example, for a 2nd order filter, the middle term of the transfer function denominator (the \$\omega^1\$ term) has a minimum coefficient of 2 in the limiting case when R2/R1 --> infty, i.e. the second RC loads the first RC minimally. And such a quadratic (of the form x^2 + 2x + 1, scaled to the given cutoff frequency) is a repeated root (in the denominator: repeated pole), always real.IIRC, the equal-value RCRC lowpass gives a middle coefficient of 7. So it's pretty de-Q-ed.You only get oscillating transient (impulse or step) response for complex poles, i.e.  response of the form \$t^n e^{\frac{-t}{\tau}} e^{j \omega t}\$; the cases directly correspond.Mind, with clever application of zeroes, an RC filter can still have (voltage) gain slightly over 1, but it's still very gradual with respect to frequency; you can't make a sharp peak. (You can make a sharp valley (notch), though.)QuoteI wouldn't say "huge", but commercially available parts fall in the 10-200 range, and you can make your own in the thousands. More than some thousands -- I mean, thousands you're looking at quite an expensive construction to begin with, but beyond that you pretty much have to look at mechanical or acoustical solutions.Anyway, with clever band planning, such high selectivity isn't usually a problem. It's more a matter of frequency stability, and the shortcut of having a single pre-made slam-dunk component, that makes crystal/ceramic filters so valuable.That's somewhat in historical context, for example VHF and low UHF radios were just fine with LC tuning and vacuum tube amplifiers throughout the 1930s to 60s. Maybe not great; even SW is a bit of a challenge without crystals (and a synthesizer for that matter) if you're working SSB. But they managed, and some manufacturers made some very finely tuned equipment, temperature compensated, mechanically compensated, the works. You'd see crystals mostly for precision work, for narrow-band or special purpose radios, and most of all of course, television colorburst.And, whatever telecom used at the time; I don't have a clue what the market was like -- and it might not be very obvious even for those in the know, just because everything went through Western Electric back then, Bell was very vertically integrated -- but I at least imagine they used a lot of crystals as well. The advantage there being, telecom bands were strictly defined (these are bands on the line, not in air!), so mixing a voice band with a selected sequence of crystal tones, and some nice sharp LC filters to clinch the band edges, was an effective way to multiplex (FDM) many voice calls on a single trunk line (and, ultimately where T1 lines came from, once those bands were reused for digital purposes).With microwave comms being pervasive today, the use of narrow sub-bands, digital; crystals are pretty much mandatory.Or, there are actually some "silicon oscillators", that I'm not clear on whether they're just very well tuned RC oscillators, or LC or wave something or other, but they offer specs comparable to crystals. I think crystals are still the cheaper option overall, so still dominant.QuoteYes, but not quite as stated. Yes, to the extent that inductors are non-idealwhere?: at low frequencies where the part size is massive, or at high impedances where inductance is hard to construct at all.Op-amps aren't good at high Q, as it doesn't take much phase shift or gain error to push that complex pole pair from the left half-plane (sharp resonance) to the right (unstable, an oscillator). Not to say it can't be done, but it is tricky, and a frequency-mixing scheme becomes desirable.Tolerance isn't much of an issue, in that, if the filter spec can't be met by off-the-shelf or mildly-custom parts, and the system can't be re-designed to, or to use other methods, then it needs to be tuned. Which goes even for precisely machined e.g. cavity filters for example, for multi-user antenna installations, cellular transceivers, etc., which regularly use high-order diplexing filters to separate rx/tx, or multiple customers (of the antenna/tower installation), tuned with a whole mess of screws perturbing the cavities.QuoteConsider the Bode plot of the element: at low frequency (down to DC), there is some "DCR" due to finite amp gain (i.e., 1/gm). At mid frequencies, Z ~ F and we have inductance. At high frequencies, the amp itself rolls off, or stray C takes over, and it drops off again, and there is some R at the peak. There may be a flat region at HF due to limited amp speed/gain, or circuit resistances, before C takes over; depends.Well, simply given an impedance function with one zero and one pole, Z = (1 + s/w_z) / (1 + s/w_p), for w_z < w_p, the slope of that midband transition region, where it's inductive, is slightly less than proportional, and by how much, depends on how close those corner bends in the curve are.You can think of the Bode plot as a perfect sharp bend, plus this curvature function, where the nonideality of what would otherwise be a sharp bend (from flat to +20 dB/dec) is superimposed on the ideal function.The closer the two corners are together, the more of their nonideality overlaps.And this is a simple rational function, so the nonideality is simply inverse with distance from the corner. We're all doing proportions here.So, if you want a Q of 10, you need the corner and shelf frequencies at least a factor of 10 below and above the range of interest. A total range of 100x is pretty reasonable; an emitter follower can even manage that.Or if you want a Q of 1000, you need a 10^6 range of pure slope, to begin approaching that number in the middle of it. That's pretty serious, but a good op-amp probably can manage.You can imagine, any little gain/phase error will tweak that response, and sure you could easily tweak in some negative resistance intentionally, but now you're artificially peaking a network and the response isn't just the component values (including synthesized inductors) and coupling factors, but it depends on gain factors too, and probably device properties, and the whole thing starts getting just as messy as you had (in part) meant to avoid by using active circuitry.(There are of course many reasons to use active filters, and many reasons not to. One of them is that, for the cascaded tuned amplifier topology, coupling (feedback) between stages is ideally zero, so the pole pair of each individual stage can be designed and tested independently. In an LC filter, couplings are perfectly symmetrical, and adjusting any one component value changes the whole response, necessitating changes almost everywhere else.)This may be food for thought: for my 20m radio project a while ago, I opted for an active filter to clean up the final AF output. I used a simple follower:6V6 at these bias conditions, is a close model to the 5702 submini pentode I used (in turn similar to 6AK5, etc.). SPICE models of little-used parts can be dubious, but the operating point checks out in this case, and the model matches measurements.This is just a plain old Sallen-Key unity-gain prototype, set up for a bandpass response. It's maximally bandpassed, in the sense that the slopes are ideally 40dB/dec; it's 2nd order and the amplifier is doing its job, peaking response slightly.The -47dB-ish shelf at HF matches the feed-forward path, R2+R3 into R9 || Rk, where Rk is about 1/gm, and gm is about 4mS or 1/250Ω here.QuoteWelcome to the wild world of hetrodyning, and mixing in general.I expect the reference here:Quote from: tggzzz on November 12, 2023, 07:50:13 pmis a synchronous type, omittinga fewcomponents (oscillator or clock input, amplifiers or buffers), and caveats or assumptions (aliasing filters?).Switched capacitor filters work on two principles:1. A capacitor toggled between an input and an output port, conveys a slug of charge per clock pulse, proportional to the voltage between ports; doing this at Fclk means a current flow of (V1 - V2) * Fclk * C, in other words Fclk * C is an equivalent resistance.2. Signals alias around Fclk. There will also be charge injection due to imperfectly balanced switches, so use exactly at Fclk (or harmonics) can be dubious, or challenging, or limited in noise floor; but in any case the effect is a synchronous modulator and detector all in one.We can implement what is apparently a very narrow bandpass filter, by using simply a very low cutoff lowpass filter, and synchronously modulating it up around a center frequency. Downsides include aliasing, poor skirts, etc. (Of course, using a higher-order filter, and a transfer function rather than a self-impedance -- using an input and an output mixer -- can afford a much squarer passband.)Spotting modulators in the wild is a handy trick. Consider the familiar ZVS oscillator circuit:The supply inductor (47-200uH) acts with the load (seemingly an LC resonant tank) with respect to its center frequency. That is, when lightly loaded, the amplitude (and proportionally, the cycle-averaged voltage at the center tap) can bounce and oscillate; and when a load is attached, AC current is drawn, which is reflected as DC current draw -- the AC current draw is synchronously detected by the alternating transistors, drawing supply current, as it of course and necessarily must.The conservation of energy isn't a surprise, but what's neat about this perspective is, if we modulate the input voltage, or load current, and if we have a bandpass filter circuit attached to the output, or lowpass to the input, the frequency response of that filter is visible on the other side, due to reciprocity across the modulator.Put still another way: the LC tank resonates at Fo with impedance Zo, but it manifests to the supply port as an equivalent RC circuit, where C is twice the 0.68uF (plus whatever other equivalent is attached). Thus we expect the amplitude/envelope to bounce at a rate determined by this equivalent C, and the series inductor; and dampened by reflected equivalent load resistance.It is a tricky matter of course, because as a self-oscillating modulator, center frequency is always the peak frequency it latched onto, and that frequency will be skewed by whatever impedance is attached to it. If we use an external oscillator, the equivalence is much more direct.The general lesson (and by "lesson", I hardly mean to teach the entirety of the subject; for my part, it took years to develop a full appreciation of all the implications, what it means, how it works, and a familiarity with network theory; at best, more just to hint at where to go, and get a flavor for what's going on here), is that reciprocity is a double-edged sword. At the same time it makes filters more complicated (every value influences every other), but it also makes clever mixing strategies possible.Tim

author: tggzzz
author_rank: Super Contributor
timestamp: November 12, 2023, 10:02:37 pm
content: Quote from: tggzzz on November 12, 2023, 07:50:13 pmHere is the transfer functions. Key points:100kHz centre frequency,140000dB/decade falloffQ of 15000, 3dB down at+-3Hz, 20dB down at +-30HzThose are higher that the figures I mentioned above, since I shifted it to a higher centre frequencyWhat's not to like

author: tggzzz
author_rank: Super Contributor
timestamp: November 12, 2023, 10:07:35 pm
content: Quote from: Benta on November 12, 2023, 09:10:01 pmCorrect and correct.It is pleasing to be able to jolt people out of the standard ruts that they have become used to living inToo many people have constrained thinking, e.g. sampled time domain => ADCs and DACs. Nasty things, although stunningly better than when I started.

author: tggzzz
author_rank: Super Contributor
timestamp: November 12, 2023, 10:18:25 pm
content: Quote from: T3sl4co1l on November 12, 2023, 09:54:30 pmMy bandpass example exceeds that performance by orders of magnitude.Cost: how much do 8 capacitors, one resistor and an IC cost (expensive new IC: £5, the one I originally c1980: £0.25 100 off).QuoteAliasing yes, but bog-standard ordinary filters can ameliorate that.I'm not sure what you mean by "poor skirts".

author: T3sl4co1l
author_rank: Super Contributor
timestamp: November 12, 2023, 11:00:07 pm
content: Quote from: tggzzz on November 12, 2023, 10:18:25 pmAh, so I can pick -120dB signals out of it? -160dB?QuoteThe inner filter element is only so-and-so many dB down by the time the aliasing products come in. The resulting filter (by itself, without AAF) therefore has maximum attenuation at midband.This can be low enough not to care, namely if Fc is below Fclk by a comparable ratio. Which is almost certainly the case in your example, give or take noise floor (switching noise? buffers? VNA? Oh, it better be a pretty damn good VNA at this resolution, not to forget; it might well be outperforming the VNA itself). But all the same, they're not perfectly general, you wouldn't use one for a wide filter -- perhaps obviously, but it's important to note that the reasoning behind selecting a filter design and type is also reciprocal, i.e. we choose such a filter where it's suitableandwe avoid it when it's unsuitable.Tim

author: tggzzz
author_rank: Super Contributor
timestamp: November 12, 2023, 11:20:11 pm
content: Quote from: T3sl4co1l on November 12, 2023, 11:00:07 pmThe receiver I designed in c1980 had a 180dB dynamic range. The system was limited by the transmitter's power output to 70dB.Yes, switched gain amplifiers preceded the filter, and there were no interfering signals other than random noiseQuoteThe last sentence is spot on; back in 1980 it wasn't easy to ensure this filter was suitable. Naturally the alternatives I discovered had less pleasing characteristics, albeit in different ways.The stopband attenuation is imperfect, and can be made greater or smaller with various tradeoffs. It is limited by the ratio of the switch resistance to the single resistor I mentioned.I haven't characterised the current filter's noise floor, due to lack of time. It was an issue with the old switch IC, and I'm curious as to whether I've found a way to mitigate it.I wasn't using a VNA per se. I used a Digilent Analog Discovery, which is a pleasingly capable beast for the money, e.g. 14bit ADCs and DACs (none of that 8bitstuff) I'm looking forward to discovering whether the filter or the tool becomes the limiting factor, and then pushing the design so the other becomes the limiting factor.

author: Benta
author_rank: Super Contributor
timestamp: November 12, 2023, 11:37:15 pm
content: Ah, the bad old days...

author: Infraviolet
author_rank: Super Contributor
timestamp: November 23, 2023, 03:21:28 pm
content: tggzzz: I'd definitely be interested to see a schematic of the 1979 circuit you described.Benta: What sort of things does escaping the continuous time domain involve, what does it enable, what limitations does it cause?Also, I've seen some diagrams of multiple feedback bandpass filters. These use 3 resistors and 2 caps and an op-amp per filter stage. The op amp seems to be in an inverting amplifier configuration with a virtual ground on the non-inverting input. Does this mean one could use a 74HCU04 as an amplifier here instead of an op amp? With the virtual ground being set at the half Vcc level about which the 74HCU04 would naturally amplify? I'm expecting the project I'm planning to end up needing to detect signals somewhere in the 5MHz to 20MHz range, I know there are op amps with GBWP this high, but my understanding is that in filtering applications the op amp typicaly needs to be MUCH faster than the frequency you're selecting for, so using an unbuffered inverter gate could be advantageous? And these MFB bandpasses can then be placed as a series of subsequent stages with the values of each stage selected to make an overall Chebyshev, Elliptic or other filter type?

author: mawyatt
author_rank: Super Contributor
timestamp: November 23, 2023, 04:39:38 pm
content: Here's reference to the Commutating Filter. Note one can move the resistor to the left of the switch and only require 1 resistor (we kept the individual resistors to help match the individual caps and compensate for switch variations with Rdson and charge injection in actual use way back then, as mentioned simple NMOS switches perform the best).https://www.eevblog.com/forum/index.php?action=dlattach;topic=263424.0;attach=1132282;imagehttps://www.eevblog.com/forum/rf-microwave/an-alternative-to-quartz-filters/msg3368862/#msg3368862Also note the reference to the PolyPhase Mixer which is a fascinating extension of this Discrete Time Continous Amplitude (DTCA) signal processing technique that evaded discovery for many decades!! Be careful here, this is a deep dive if one "really" wants to understand what's going on (be sure to thoroughly study mentioned IEEE papers). For example, how can a passive Bi-Phase mixer have a Noise Figure less than theoretical 3.92dB (can actually approach 0dB with more taps!!), create complex passive input impedance including +-j matching that tracks clock over decades without tunable elements or inductors, exhibit almost +30dBm TOI, push sampling artifacts (Nyquist/alaising if you will) well out of band, like for an 8 PolyPhase rendition with first at 7th and 9th harmonic responses, and so on!! We got started on this back in ~2005 and developed some interesting receiver concepts based upon such, as did Cornell. This reminds of a Ring Tone Receiver not mentioned before, will post in thread below for reference.https://www.eevblog.com/forum/rf-microwave/polyphase-or-n-path-mixer/msg3381802/#msg3381802Anyway, this DTCA signal processing can indeed open up many limitations of CTCA analog signal processing, fun topic for those interestedBest,

author: tggzzz
author_rank: Super Contributor
timestamp: November 23, 2023, 04:50:23 pm
content: Quote from: Infraviolet on November 23, 2023, 03:21:28 pmIt is a very complex circuit - notThe reference which inspired me ishttps://archive.org/details/sim_att-technical-journal_1960-09_39_5page 1321 onwardsEscaping the continuous time domain involves moving from s-plane to the z-plane. In other words, the Laplace transfrom is replaced by theZ-transform. FFI: consult a mathematician for the consequencesDo have a look at the refs provided by mawyatt: he took the idea and ran with it in far more detail that I was able to.

author: mawyatt
author_rank: Super Contributor
timestamp: November 23, 2023, 05:39:09 pm
content: Quote from: tggzzz on November 23, 2023, 04:50:23 pmRecall from way back in early days of DSP that one could visualize when moving to Discrete Time Domain by having the Imaginary Axis as a circle with radius of sample rate, thus for analog continuous time (sample rate infinite) Imaginary Axis is vertical straight line to +- infinity (infinite radius circle), and for Discrete Time the axis begins to bend. The System Poles and Zeros don't move with sample rate but the Imaginary Axis does and you can see when the system becomes unstable as the axis bends enough to intersect the System Poles, or stability decreases as the axis gets closer to the Poles.This was great visual aid for folks to get their arms around Discrete Time Systems and how the sample rate affects system stability.Best,

author: mawyatt
author_rank: Super Contributor
timestamp: November 23, 2023, 06:24:21 pm
content: Quote from: tggzzz on November 23, 2023, 04:50:23 pmOur rendition was based upon Fig 10 pg 1344 of the Journal. Zverev Handbook of Filter Synthesis also has a similar version. What a great resource the Bell Journals were, and we squandered the LabsBest

author: tggzzz
author_rank: Super Contributor
timestamp: November 23, 2023, 07:37:13 pm
content: Quote from: mawyatt on November 23, 2023, 06:24:21 pmI used to say that all interesting electronic research was done at Bell Labs, and all interesting computer research was done at Xerox Parc. Yes, I know that isn't true, but it contains more than a grain of truth.One squandered by a government, the other by a corporation. Conclusion: people are the problem, where ever they work.

author: Infraviolet
author_rank: Super Contributor
timestamp: November 25, 2023, 01:24:35 am
content: Perhaps before more detailed discussion I ought to check, what is the best filter type for my sort of use cases?I'm expecting to need:..Bandpass..A centre frequency placed somewhere (depending on things yet to be decided) in the 5MHz to 20MHz range..Passband width of perhaps 1MHz, or a bit less..To detect and show a response within less than 10 cycles of the frequency of frequency being present..Don't care much about bandpass flatness..Very fast drop offs outside the passband, getting to 1/200th or less of passband amplitude once at something like >Centre+1.5MHz and <centre-1.5MHz, and either futher dropping off at more extreme frequencies or simply staying somewhere below the 1/200th level, however rippled..Not really bothered about distortion of post-filter waveform, so long as I get a strong signal when a frequency in the passband is present and minimal output when it isn't..To have the passband not shift around by more than a few 100KHz due variations within typical tolerance specified on components, or due to temperature...Is this actually a task best suited to LC filters?Thanks

author: T3sl4co1l
author_rank: Super Contributor
timestamp: November 25, 2023, 01:41:05 am
content: Try a PLL.The bandwidth is fine for a coupled-resonator style LC filter, but the adjacency ratio or skirts are unrealistic, 46dB in +/- 7.5 %BW.You absolutely will not get the required transient response.Tim

author: Infraviolet
author_rank: Super Contributor
timestamp: November 28, 2023, 03:18:16 am
content: Attempting to search for terms related to using a PLL as a bandpass filter only gave results relating to using low pass filters within PLL circuits as a means of converting pulses from a phase comparator in to DC levels. Can you provide a link to a page specifically discussing using a PLL in the way in which you are talking about?Thanks

author: Infraviolet
author_rank: Super Contributor
timestamp: December 08, 2023, 03:52:52 pm
content: I'm still not sure what form a PLL acting as a bandpass filter would take, any suggestions? Thanks

author: SuzyC
author_rank: Frequent Contributor
timestamp: December 08, 2023, 06:35:36 pm
content: A PLL can act as a bandpass filter because the oscillator lock-in range is small and freq. outside the max or min lock of the PLL will be ignored.

author: Coyote2025
author_rank: Newbie
timestamp: May 02, 2025, 02:40:37 pm
content: Perhaps someone is interested in the formulas for the filter transmission coefficient of multi-stage RC filters with a resistive load of up to 5 caskades. I do not know of any other source for these formulas except the link provided.https://dzen.ru/a/aBPKumO5-WIBHhib

author: tggzzz
author_rank: Super Contributor
timestamp: May 02, 2025, 02:42:55 pm
content: Quote from: Coyote2025 on May 02, 2025, 02:40:37 pmCAUTION.First post is a necropost to an obscure russian server/document.

author: tooki
author_rank: Super Contributor
timestamp: May 02, 2025, 02:52:04 pm
content: This kind of filter design isfarafield of anything I have experience with, so I’m hoping one of the experts here can chime in: could this be something where a lock-in amplifier would be a good solution? (A colleague told me about how he used them in a project, and so I skimmed a bit of literature about them, so my knowledge ends there.)

author: tggzzz
author_rank: Super Contributor
timestamp: May 02, 2025, 03:29:36 pm
content: Quote from: tooki on May 02, 2025, 02:52:04 pmDepends on what you mean by "this kind".Key point about pick-up amplifiers is that they need the source clock/frequency as one input, the other being the response of interest.

author: tooki
author_rank: Super Contributor
timestamp: May 02, 2025, 11:44:18 pm
content: Quote from: tggzzz on May 02, 2025, 03:29:36 pm= to do what OP needed to do.