# Using audio LC filter circuits instead of RC.

#### ColinT

Joined Aug 5, 2020
11
I'm designing a small mixer and stopped at the equalizer section when I recalled the number of small inductors (axial and SMD) in my parts kit.

If you search 'filter circuits' or similar you'll ALWAYS get the standard RC topologies, and I'm thinking more of IC feedback types than the usual passive 'pass-throughs'. However, given that a wide range of inductors are now readily available, wouldn't it be better to develop LC filter topo's instead of the traditional RC ones?

#### Delta prime

Joined Nov 15, 2019
580
I think it has to do with something called The IDEAL (I am not yelling)
Component , resistor, capacitor , inductors, .When we design real world electronic circuits we reference the IDEAL .These ideal mathematical abstractions of voltage sources, current source, transistors , op-amp
Inductors are not ideal. They present resistive loss, core saturation, skin effect and many more complicated characteristics
Capacitors are very close to the “ideal” model in normal condition. It rarely matter that a 60 hz filter could become non linear at 50 ghz.
RC filters are much smaller than RL filters
transient response improvement, dc decoupling and for filter frequency control, bass/treble controls. loudness control and rejecting RF components from inputs. Zobel networks on the output to balance the inductive component of the loudspeaker.
Inductors are more expensive, take more board space and are heavier

#### LvW

Joined Jun 13, 2013
1,127
Today it is common practice to replace the inductors (coils) with "active inductors" - realized with operational amplifiers.
This is a very versatile method in case you want to build higher-order filters (derived from classical R-L-C- ladder structures) instead of series connections of several 2-nd-order blocks.

#### AlbertHall

Joined Jun 4, 2014
10,572
Inductors are commonly used in loudpseaker crossover filters.
Inductors for audio frequencies have to be bigger and heavier than their RF counterparts but this is less of a concern in a crossover filter. A resistor with the same impedance as the inductor would dissipate a lot more of the amplifier's output than an inductor. The impedances needed in a crossover are pretty low (think 8Ω speaker).

In an active filter on a PCB, the size and weight of an inductor becomes a problem but the loss in a resistor is easily compensated by the gain of the active circuit. The impedances needed in such a filter will be orders of magnitude bigger than the crossover increasing size weight and cost.

#### ColinT

Joined Aug 5, 2020
11
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.

#### LvW

Joined Jun 13, 2013
1,127
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?
You are comparing an "RLC circuit" with a "multipole RC circuit"....
What does this mean ? How many poles do you assume for the RLC filter?
In general, all of the known filter realizations - passive or active, indpendent on the order - have the same response (transfer functions), provided the used parts (active and passive) are IDEAL.
However, we live in a real world - and, therefore, we have to live with non-idealities and with deviations from the ideal response.
But each filter topology reacts differently on non-idealities (tolerances, unwanted phase deviations) and, therefore, we have defined active and passive sensitivity figures which help to select a suitable structure for a specific application.
This choice is always a trade-off between conflicting requirements.

In your case: Of course, opamps introduce additional phase shift (depending on the opamp type and the operating frequency); on the other hand, real inductors are lossy and have some other unwanted properties......as mentioned: The selection process is a trade-off....

#### ColinT

Joined Aug 5, 2020
11
> What does this mean ? How many poles do you assume for the RLC filter?

As I said, I'm a filter novice. I'd compare a filter circuit consisting of sequential RL and RC with two sequential RCs. My question is whether, given appropriate values, they might have similar or identical frequency pass characteristics but different phase characteristics, the former perhaps being superior.

I'm well aware of the difference between "ideal" and the real world. I'm also aware that all design begins with ideal mathematical models, and gradually introduces modifications to accommodate these differences. And, of course, that all real-world artefacts are approaches to various conceptual ideals.

#### LvW

Joined Jun 13, 2013
1,127
As I said, I'm a filter novice. I'd compare a filter circuit consisting of sequential RL and RC with two sequential RCs. My question is whether, given appropriate values, they might have similar or identical frequency pass characteristics but different phase characteristics, the former perhaps being superior.
OK - perhaps a misunderstanding...because: When you are speaking of RC filters (in comparison to RLC topologies) I have, of course, assumed that you were referring to ACTIVE RC structures. Otherwise, we cannot make a comparison because passive RC structures do not allow complex poles (higher Q-values). That is the only reason we have developped active RC filters: Complex pole distribution (like passive RLC filters).

Again: Under idealizes conditions ALL known filter realizations (active or passive) can be equipped with identical transfer functions (provided that the topology allows/enables the required pole/zero location)

#### Delta prime

Joined Nov 15, 2019
580
I have no favorite component I think of every component as ammunition when I bring out the big guns.
I like to think of it or this is what I do when I design badass amps I think of them as networks that are composed of, or can be reduced to, one reactive
component (L or C) and one resistance (R). The time
constant τ is either L/R or CR
Amplifiers are classified according to the shape of their
frequency response, |T(jω)|.
The transfer function T(s) ≡ Vo(s)/Vi(s) of a voltage
amplifier can be determined from circuit analysis.
Substituting s = jω gives T(jω), whose magnitude
|T(jω)| is the magnitude response, and whose phase
φ(ω) is the phase response, of the amplifier.

#### Papabravo

Joined Feb 24, 2006
14,700
> What does this mean ? How many poles do you assume for the RLC filter?

As I said, I'm a filter novice. I'd compare a filter circuit consisting of sequential RL and RC with two sequential RCs. My question is whether, given appropriate values, they might have similar or identical frequency pass characteristics but different phase characteristics, the former perhaps being superior.

I'm well aware of the difference between "ideal" and the real world. I'm also aware that all design begins with ideal mathematical models, and gradually introduces modifications to accommodate these differences. And, of course, that all real-world artefacts are approaches to various conceptual ideals.
Each reactive component in a filter contributes a pole to the transfer function which relates the output to the input. Transfer functions are normally expressed as rational fractions consisting of polynomials for the numerator and denominator. A pole represents a frequency where the denominator goes to zero and the transfer function becomes infinite. The use of non-ideal components prevents the creation of an infinite voltage of course, but it does get larger than you might expect. Filters and other circuits are often designed by specifying the pole locations in the complex plane. For stable systems those poles will be in the left half-plane.

#### Ian0

Joined Aug 7, 2020
759
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.
You should try an RCRC filter - the Q is low but the roll-off is 12dB per octave, and there are no inductors with parasitic capacitance, or op-amps with phase-changes to spoil it.
Calculate R and C as you would for a single order filter, then repeat - that gives a Q of 0.333
Or, for the second RC use 10R and C/10 - that gives a Q of approaching 0.5 - works very well.
Nice RCRC filter design tool: http://sim.okawa-denshi.jp/en/CRCRkeisan.htm

There are two main problems with inductors :
1. Non linearity (as mentioned by Delta Prime) - mainly due to core saturation. You'll struggle to get better than 0.05% thd.
2. Parasitic capacitance - which I'm surprised no one has mentioned. An inductor of a few Henries will look more like a capacitor than an inductor at frequencies as low as 10kHz, and it will no longer be a low-pass filter.
Look for the value of Self Resonant Frequency in the datasheet. Above that frequency, it's a capacitor.

#### LvW

Joined Jun 13, 2013
1,127
My question is whether, given appropriate values, they might have similar or identical frequency pass characteristics but different phase characteristics, the former perhaps being superior.
Colin - this is impossible!! The magnitude characteristics (..."pass characteristics") are closely related to the phase response.
Again: All alternatives for filter realisations (circuits) have identical transfer functions (if properly designed) - provided all components are ideal (no tolerances, no parasitics).

#### LvW

Joined Jun 13, 2013
1,127
You should try an RCRC filter - the Q is low but the roll-off is 12dB per octave, and there are no inductors with parasitic capacitance, or op-amps with phase-changes to spoil it.
...but one should know that this realisation has no low-resistive voltage output. Hence, each load will influence the filter response.

#### Ian0

Joined Aug 7, 2020
759
Neither does an RLC filter. A low impedance output may not be required, and if it is, it could be buffered with an op-amp, and doing so requires a much lower gain-bandwidth-product than an op-amp in an active filter circuit.

#### jeffl_2

Joined Sep 17, 2013
30

#### AA+

Joined Jan 4, 2014
3
Inductors are poor because of DC resistance and turn capacitance. Capacitors work out better as pure capacitance. That's why one would make inductors out of op-amps, resistors, and capacitors. Such fake inductors can much better work out as pure inductors.
Best wishes --- Allen

#### ColinT

Joined Aug 5, 2020
11
> The magnitude characteristics ... are closely related to the phase response.

My mind works conceptually by creating moving images depicting my understanding of events and phenomena. I do not have the easy, immediate, intuitive grasp of physical processes that gifted mathematicians demonstrate. For me, maths is largely just a process that gives a numerical result, although I do have some experience of its abstract and intuitive aspects.

This is the reason I've never "gotten into" filters: I've never taken the time to create the dynamic images I need for what, to me, is "understanding" (rather than just getting the right answers to test questions).

The quote above triggered an old memory, and further pondering produced insight. Eureka!

Passive RZ (Z = L or C) filters work by changing the phase of voltage and current. The output is the current-induced voltage of the circuit rather than the input voltage itself.

An active filter could be said to "work" by creating a phase-shifted analogue of the input voltage, and combining it with the input voltage. The gain of the opamp permits phase-shifted components that would be too small to have much effect in a passive circuit to exert considerable influence in an opamp circuit, hence its power.

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.

And I'm most grateful for the other replies: the variety of information and perspective has given me much to think over as I now develop my conceptual imagery of the topic well beyond what it's been to date.

#### jeffl_2

Joined Sep 17, 2013
30
I also could have mentioned that in regard particularly to analog (many of them DO also happen to have their equivalent in digital but it's "different") there are "standard" filter classes that really derive from the nature of the circuit's transfer function (output over input in Laplace variables). In that "space" you may encounter at least the following: Bessel, Butterworth, Chebyshev, Elliptical, and there are many more, and there's also the "order" (number of poles) of the filter (generally at a maximum stopband slope of about 6db/pole). These are most frequently determined by the shape of the pole plot of that transfer function, and each type has other characteristics such as the phase response, these are well-documented in the literature, but those concepts are a bit abstract, that's why you may want to defer to letting the tools do the work. Now there's no "absolute" reason you have to follow these designs precisely, but they have the advantage that they've been well-analyzed and are fairly simple to replicate. There's one other point about phase versus magnitude, they're not completely independent BUT if you are willing to take the time you CAN rather easily modify the phase of a filter without modifying the magnitude (it's called all-pass), but doing it the other way is very difficult at best. That's as much as I want to say for now, in order to learn I would say just plunge ahead and see where your tools can take you, or get inspired to "do your own thing"!

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#### jeffl_2

Joined Sep 17, 2013
30
And I guess the other important thing, the ideal transfer functions of any formal filter function is EXACTLY the same for active RC as it would be for passive RLC, EXCEPT you aren't constrained by limited "Q" of the inductors, or other incidental losses in the implementation (active RC is very close to theoretically "ideal" response, except for maybe noise and dynamic range and other issues which always need to be looked after).