# Using audio LC filter circuits instead of RC.

#### LvW

Joined Jun 13, 2013
1,126
Thanks to LvW for his patience and persistence. Our minds obviously work differently and it took a few exchanges for each to understand the other.
Hi Colin. Thank you for your nice words....however, I do not completely agree with you.
I do not think that our "minds work differently".....I am with you regarding the aim to conceptually understand the working principles of parts and circuits. I really think that this is always the necessary background for designing circuits - that means: Not blindly follow any formulas or design rules but to know what happens within the circuit - and why !
(Remark: For example, that is the reason I must know how a transistor really works - voltage or current controlled - although in many cases, this is not really relevant for designing amplifying stages..)

#### ColinT

Joined Aug 5, 2020
11
> "... to conceptually understand ... how a transistor really works"

Nobody knows how a transistor "really works" because, in the most fundamental sense, nobody knows what reality "really is". We each develop our own concepts of this and other fundamental ontologies beginning in childhood. By the time we are adults our "minds" are structured with precepts and prejudices founded in abstractions that are largely cultural, in "ideas" that can only be expressed in the words of whatever languages we speak, these being inevitably cultural, and in the thought processes we have used to come to terms with the demands of our existence, which are cultural, social and experiential. We are inescapably the products of our environment and experience.

I spent many happy years in the Orient, and it was my experience teaching hitech to, and working with Oriental post-grads that taught me, not only just how differently the Oriental and Occidental minds work, but that the vast majority of people not only do not recognize the extent and depth of these differences, but aren't interested in them. Few people understand what their "minds" really are, much less how they work. Such insights are the first goal of true meditation; deep meditation eventually arrives at simple communication with the "soul", which is where contemplation begins.

All of which is completely irrelevant to the subject-matter of this hitech forum, and so is "off-topic", even though such areas have fascinated and occupied me much more than hitech as a profession and pursuit. And all of which you are free and likely to disagree with. No point in discussing it here since it's a vast area of study that cannot be summarized in a few words. What I will say is that I've always believed that, as a planetary race, we're on the boundary of discoveries that go far beyond today's hitech into completely different types of technologies, but that we'll never make that transition without a far better understanding of reality, and hence of physical theory, than we presently possess.

#### LvW

Joined Jun 13, 2013
1,126
Nobody knows how a transistor "really works" because, in the most fundamental sense, nobody knows what reality "really is". We each develop our own concepts of this and other fundamental ontologies beginning in childhood.
Well - I can certainly agree with these philosophical thoughts.
What I only wanted to express is the following:
With formulas and functions we have created a tool with which we can analyse and describe, calculate and design electronic circuits. But in addition it is also very important to try to understand and explain logically the observed processes and effects.
This is what I mean by "how ....really works".
And there can be contradictions between "handy" formulas and physical facts.
Of course this does not need to be a problem, if you know both points of view.
And with regard to my example (bipolar transistor), I think it is important to consider that physical explanation as "correct", which fits best to the numerous effects whch can be observed.
A simple example: In calculation and electronic circuits, we very often pretend that the current flowing through a resistor would generate a voltage across this resistor.
And this works very well in analysis - but it is physically wrong.
It is always the voltage that allows the physical effect we call "current".

#### ColinT

Joined Aug 5, 2020
11
Well said. Something that has fascinated me since childhood is "What IS an electric field?" Or a magnetic one for that matter. It's only when you deeply ponder such "obvious" things that you realize how little we really understand the world around us.

As an engineer or technician, you can't afford to question the scientific "facts" you "know" and have been taught, otherwise you'd never move through to practical results. In fact, many large companies are now refusing to hire techs they suspect may be too interested in the "why and wherefore" of a task rather than just getting the job done and moving on to the next one.

As an applied scientist you don't question the scientific bases of your work if you want results. As a experimental scientist you CAN question your own field within acceptable limits, but will be harassed if you move beyond it.

It's only as a practising (NOT academic) philosopher that you can take on the whole world - the entire Universe if you want - and question whatever you like (philos = lover, seeker and sophia = truth, wisdom). But once you do that, it may take most of a lifetime to answer even the most basic questions you set out to investigate in the confidence and certainty of youth. And I speak from sad experience.

#### jeffl_2

Joined Sep 17, 2013
28
Oh yes and there's one more way of looking at equalizer design if you want to truly innovate. It turns out that your opamps can be connected with a few resistors to make circuits known as gyrators, and the topology you would probably be interested in would be the Antoniou gyrator. You can then connect that to a capacitor, and with a circuit analysis trick known as a Bruton transformation you can create a circuit component called a "frequency-dependent negative resistor" (FDNR), which in itself is interesting because a "negative resistor" is really a resistor with gain (!). And it turns out that an FDNR is a useful component to create a quasi-parametric equalizer! There probably isn't a lot of what I've just described that you've ever heard of, so it sort of depends how you look at how interested you are in learning about technologies (I can't really say they're "new" because right after this stuff came out digital filters became the "shiny new object" so they didn't get real popular), but these tricks DO solve circuit synthesis issues that are hard to fix any other way, besides it's kind of fun to design circuits that hardly anyone else can figure out how it really works!

#### ColinT

Joined Aug 5, 2020
11
Hey, thanks. Always interested in new circuit possibilities. Back in the day (late 70s I think) I had a sales job for a fellow with a really unique product range due to his unusual defence connections. I've always been a lousy salesman, but this stuff was so fascinating that my enthusiasm just bubbled over.

Amongst it was a shiny new Digital Filter. What the heck is THAT? Turns out it was put on the market by a company contracted to help fix problems with the Space Shuttle engines, specifically the turbine pumps and their worn out bearings (VERY quickly). The best way to detect worn bearings is to listen to their acoustic/ultrasonic noise, when wear becomes readily apparent. Problem was, with a Shuttle engine going full blast a few yards away, listening was somewhat problematic. Solution? A VERY good filter. In fact, you had to filter out what was essentially VERY LOUD white noise and try to find a squeaking bearing amongst it. Hence the digital filter.

So who on Earth am I going to sell this to? After doing the rounds, I decided that my premise was too limited. It was obvious that few people on Earth would have the slightest idea what the thing WAS, let alone what use to make of it. Perhaps I should be looking farther afield. Perhaps someone on Arcturus would be interested, or maybe Betelgeuse ...

Never sold even a one, but a few years after I left I heard that they'd eventually sold a couple to the local police lab for filtering out the sounds of a shower running behind bugged conversations etc. Not my field.

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#### LvW

Joined Jun 13, 2013
1,126
..........................
You can then connect that to a capacitor, and with a circuit analysis trick known as a Bruton transformation you can create a circuit component called a "frequency-dependent negative resistor" (FDNR), which in itself is interesting because a "negative resistor" is really a resistor with gain (!). And it turns out that an FDNR is a useful component to create a quasi-parametric equalizer!
..............
....resistor with gain...? I rather would describe it as a voltage-controlled current source having a current that goes through the controlling source.
And if you are asking what will happen putting an FDNR in parallel to an ohmic R, the formula says:
* There is one frequency where the resulting R is infinite.
* What does this mean in reality? Is the known formula for parallel connections still applicable?
* Is there any similarity to a classical ideal LC tank circuit (infinite Z at one frequency)?
* Yes - the parallel connection (FDNR)||R forms a resonator and can oscillate. More than that - it forms one of the most versatile two-opamp oscillator circuits (tunable by a single grounded resistor).

#### Ian0

Joined Aug 7, 2020
743
I know about FDNR, but I didn't know that the technique was called a "Bruton transformation". Thanks for that piece of information.

#### LvW

Joined Jun 13, 2013
1,126
I know about FDNR, but I didn't know that the technique was called a "Bruton transformation". Thanks for that piece of information.
It is a "trick" but quite simple.
Example: Let us assume that you have a simple passive RLC lowpass.
When you divide the numerator as well as denominator of the corresponding transfer function by the expression (s*T) you will get a new function. Because the expression (s*T) is dimensionless the new function still contains impedances - however with a new meaning.
It is not difficult to see that R is transferred to a capacitive expression, L is now a resistor and C is a new element called FDNR. This new element is negative and frequency-dependent - but has no frequency-dependent phase shift.
The time constant T can always be chosen so that suitable values for the new components are possible.

#### MrAl

Joined Jun 17, 2014
7,849
Thanks for the replies - informative. I confess that I posted the thread without running the numbers - seldom a good idea - but there are two other aspects. Opamp design is a VERY occasional task for me, and filter theory one of many things I've never had time to go into: when need arises I adapt a published circuit. Synthesizing an inductor with an opamp (gyrator?) has always intrigued me, but again, time ...

So, first the numbers. If we assume a nominal impedance of 10k then we have:
Code:
f    20Hz    200Hz    2kHz    20kHz    200kHz
L    80H       8H    800mH     80mH      8mH
... which shows how out-of-order my original question is. A 100mH through-hole part is about 9mm diameter by 11mm high, and anything of higher value will be too big for today's PCBs.

BUT ...

Out of curiosity, given my knowledgeable audience, and assuming that we're looking at higher frequencies, would an RLC circuit offer better phase response than a multipole RC circuit? I know (or think I know) that phase-shift in multipole filters can be problematic, especially when used in an opamp feedback loop. Perhaps the opposite phase shifts of the L and C would cancel, giving better phase performance whilst retaining the other characteristics?

The other item on my "to-do" list is a PWM filter for a uC output, probably up around 100kHz. Found an excellent app note from Texas Instruments on the topic, and again it's all-RC. This might be more practical for an RLC solution.
Hello,

In the modern world the only time inductors are used is when they have to be used. That is because they are more expensive, often larger, have serious undesirable parasitic properties, and are not as linear as other components usually used in filters, and precise values may be much more expensive if obtainable at all. The time they are usually needed is when there is some relatively large power involved such as with power supply filters and raw speaker crossovers. Circuits like equalizers are almost always made out of RC components because they are cheaper and more predicable.