Another Equal Valued Active LPF

[mawyatt]

Awhile back we discussed a 3rd Order Butterworth Active LPF based upon using equal valued Rs and Cs:
https://www.eevblog.com/forum/beginners/calculation-of-the-3rd-order-rc-filter/msg5343509/#msg5343509

And a State Variable Version:
https://www.eevblog.com/forum/projects/state-variable-active-filter/msg5959645/#msg5959645

In another thread macaba discusses a DC Accurate 3rd Order LPF:
https://www.eevblog.com/forum/metrology/dc-accurate-low-pass-filter/msg5570041/#msg5570041

And a Bandpass rendition:
https://www.eevblog.com/forum/projects/edn-published-active-bpf-in-error/msg5563865/#msg5563865

We've include a quick analysis of the DC Accurate 3rd Order LPF, note that if the Rs and Cs are equal valued then the filter becomes a classic 3rd Order Butterworth. Having equal valued Rs and Cs makes creating a filter much easier as we have shown below.

Also note that if the shunt capacitance C1 (C3 in schematic) is removed the result becomes a 2nd Order Butterworth LPF with a corner frequency 1/rt(2) below the 3rd Order for the same valued components. This maybe is surprising as removing capacitance lowers the corner frequency!!

These DC accurate LPF have the advantage that the active op-amp offset and bias currents are removed from the result by the 2 coupling capacitors, thus the term DC accurate. However, they do have a high output impedance (R at DC) and may require a buffer in actual use (we didn't use a buffer). Another issue we mentioned in the thread above is the output stop band attenuation is limited by the op-amp output impedance. Faster op-amps tend to have lower output impedances at a given frequency and one can buffer the output or add a "bleed" resistor if desired for improvement. Another option also mentioned earlier was to split the input resistor and add a shunt capacitor to ground to attenuate the higher frequencies before "seeing" the op-amp.

Anyway, just having some fun with active filters and thought others may want to play around

Best

[LaserSteve]

Thank You!

[Circlotron]

I was going to get on and complain that I got way different results in that the LPF response fell off something terrible below the cutoff frequency. The response looked more like a lame bandpass.

Then I realised that I was taking the output from the opamp output, not from the junction of the two capacitors above the opamp. After that, voila, it worked great.  I drew up a unity gain Sallen key version to compare the response and it was identical except for the input offset voltage of the SK version.  I especially like the 3rd order version. Thanks for posting.

[mawyatt]

You are quite welcome, glad to see some interest in this

With the SK version, did you use the Equal Valued Component 3rd Order Butterworth LPF we posted here awhile back?

Best

[Circlotron]

No, I didn’t do the third order one, I did a second order unity gain SK one for comparison.
I did have a look at the links, but it got a bit confusing with so many twists and turns.
If you could post a link to that specific filter, I’ll give it a try.

[mawyatt]

See attachment below. We've posted on here numerous times, the concept dates back almost 1/2 century ago and we posted an EDN article on such way back.

The interesting thing about this topology, outside the equal valued components, it has the least sensitivity to component variations attributed to the buffer amp impedance isolations, and swapping the R and C transforms from a LPF to a HPF with the same corner frequency

BTW the LTspice simulation schematic in our first post above contains this topology to yield the ideal Butterworth 3rd Order Transfer function and show response. It's the top circuit with the Unity Gain VCVSources. Here we've added the 3rd Order Sallen-Key to the LTspice schematic with sim results.

Anyway, we've utilized this topology many times over the decades since Quad-Amp Packages were and still are very cheap 

Best

[David Hess]

Some old multimeters use this filter configuration for the obvious reasons.  There is less cause now because we now have precision operational amplifiers with low offset and low input bias current, and automatic calibration.  The example below is from 1975.

There is a similar method to make a precision rectifier and remove the offset and bias current errors using AC coupling.

[Circlotron]

I had a long winded reply typed out and while editing a screenshot, Wine made Irfanview fall over and that took out almost everything and I was back to a login screen, 

Anyhoo, short story, have a look at this graph. To get your cct to function exactly as a unity gain Sallen Key the feedback resistor needs to be doubled, according to my sim at least. The two plots are then almost identical

1 is your cct
2 is with 20k feedback resistor
3 is unity gain Sallen key.

[mawyatt]

The 2nd order Sallen-Key doesn't use equal valued components for Butterworth response, only the unique 3rd order we posted above.

The 2nd Order Sallen-Key details are shown below.

Best

[mawyatt]

Some old multimeters use this filter configuration for the obvious reasons.  There is less cause now because we now have precision operational amplifiers with low offset and low input bias current, and automatic calibration.  The example below is from 1975.

There is a similar method to make a precision rectifier and remove the offset and bias current errors using AC coupling.

Yes the 2nd order DC accurate LPF dates back to that time frame when we 1st saw it. The 3rd order DC accurate LPF came later and not sure who created this, we certainly didn't!!

However we did create the 3rd Equal Valued Butterworth LPF (Sallen-Key type) way back, at least Walt Jung at ADI thought so. When he found out about it (well before we published in EDN) and called and asked if he could use such in one of his publications (app note and/or book, can't remember).

Anyway, these are very old and almost forgotten analog designs from yesteryear, but still fun to play with

Best

[David Hess]

Anyway, these are very old and almost forgotten analog designs from yesteryear, but still fun to play with

I do not remember if Maxim did, but Linear Technology had DC accurate switched capacitor filters with much higher orders.

[Circlotron]

The 2nd order Sallen-Key doesn't use equal valued components for Butterworth response, only the unique 3rd order we posted above.

The 2nd Order Sallen-Key details are shown below.

Best

Oh yeah. Remove the cap and two 10ks become a single 20K.
So I was right but for the wrong reason. Something like that.

[macaba]

It's good to see some discussion of this topology, it remains a favourite of mine.

My prior research gave the earliest instance I could find in the year 1973:
https://www.eevblog.com/forum/projects/unkown-low-pass-filter-design/msg5028064/#msg5028064
I suspect it to occur even earlier, as that source is a compendium of known techniques.

I make a point of this because I think there is unrealised potential to dig out these old analog techniques and put a modern spin on them (mainly thanks to OPAs with fantastic specifications released in the last 20 years).

My experiments show it's not possible to go above 3rd order with equal values due to instability, instead requiring unequal values. An example of this is shown in Datron DMM calibrator service manuals as a 7th order Bessel. I built a similar 7th order circuit, tested successfully, with different component values.

[Circlotron]

Okay, so i tried out that 3 opamp LPF and it's pretty good. The single opamp version seems to run out of puff after a while but the 3 opamp version keeps on chugging. Probable because most of the capacitors go directly to ground rather than being feed from an opamp that has finite output impedance or suchlike.

[RoGeorge]

If the requirement is to make a 3rd order LP filter with equal RC values, and if it is allowed to use 3 opamps, then why not just make an RC followed by an opamp, and repeat that 3 times, or n times, to get an n^th order RC filter?

[David Hess]

If the requirement is to make a 3rd order LP filter with equal RC values, and if it is allowed to use 3 opamps, then why not just make an RC followed by an opamp, and repeat that 3 times, or n times, to get an n^th order RC filter?

That works, and is done sometimes, but cascading 3 stages yields a poor filter shape with a more gradual transition band that is not even as good as a Bessel filter.

[mawyatt]

If the requirement is to make a 3rd order LP filter with equal RC values, and if it is allowed to use 3 opamps, then why not just make an RC followed by an opamp, and repeat that 3 times, or n times, to get an n^th order RC filter?

Basically you can't achieve a Butterworth response which is maximally flat magnitude response at the origin, the only filter type that can achieve this. Bessels are max flat phase at origin, not amplitude.

Best

[mawyatt]

It's good to see some discussion of this topology, it remains a favourite of mine.

My prior research gave the earliest instance I could find in the year 1973:
https://www.eevblog.com/forum/projects/unkown-low-pass-filter-design/msg5028064/#msg5028064
I suspect it to occur even earlier, as that source is a compendium of known techniques.

I make a point of this because I think there is unrealised potential to dig out these old analog techniques and put a modern spin on them (mainly thanks to OPAs with fantastic specifications released in the last 20 years).

My experiments show it's not possible to go above 3rd order with equal values due to instability, instead requiring unequal values. An example of this is shown in Datron DMM calibrator service manuals as a 7th order Bessel. I built a similar 7th order circuit, tested successfully, with different component values.

The PhD dissertation by Dr Odorcic is a must study for anyone seriously interested in this topic. Somehow we missed that thread, thanks for posting

BTW it seems that Dr Odorcic didn't discover the DC Accurate 3rd Order Equal Value Butterworth which is surprising, considering all the other variations on such!!

Agree the op-amps are so good today and cheap, there's even versions of the LM358/324 types that have pretty low offsets, and CMOS version that have really low bias currents and rail to rail outputs. You can even get a couple OP-07s for less that a quarter

This brings back memories of when the CD4000 CMOS logic was introduced by RCA way back, we would use a CMOS inverter as a "buffer" for a bipolar op-amp (741) to achieve overall rail to rail output capability!!

Best

[mawyatt]

Okay, so i tried out that 3 opamp LPF and it's pretty good. The single opamp version seems to run out of puff after a while but the 3 opamp version keeps on chugging. Probable because most of the capacitors go directly to ground rather than being feed from an opamp that has finite output impedance or suchlike.

Nice work!! Yep without the shunt C between the resistors in "T" network, the effective R now becomes twice the value and the 3rd Order morphs into a 2nd order Butterworth but at a corner frequency that's 1/(rt(2)) the 3rd Order corner. What we find intriguing is that removing a shunt cap causes the corner frequency to decrease rather than increase which intuition would suggest, we understand why but intuitively this seems surprising!!

Also it's the op-amp output impedance that limits the stop band rejection. We've discussed this a few times in various threads. 

Op-amps output Z looks inductive at higher frequencies with a rising impedance with frequency, the can create havoc with stop band rejection with active filters. Higher speed op-amps usually have a lower output Z at moderate to high frequencies than GP types. With GP op-amps like the LM358/324 types you can improve the stop band rejection by biasing the output with a resistor to the VEE rail, this causes a bias current to flow thru the LM358 output Darlington pair and reduces the output Z.

Anyway, glad to see you are having fun with this. Be sure to visit Dr Odorcic PhD dissertation mentioned above if you want a deep dive into this DC Accurate Filter topology, it's fascinating

BTW recall you have a Siglent DSO and AWG? If so, run some Bode plots of these filters, even more fun ahead!!

Best

[mawyatt]

I make a point of this because I think there is unrealised potential to dig out these old analog techniques and put a modern spin on them (mainly thanks to OPAs with fantastic specifications released in the last 20 years).

Agree!!

Long ago we acquired access to some really fast IC processes like Bell Labs Complementary Bipolar process (Si) which later became CBIC-V2, then SiGe (IBM BiCMOS) and much later InP. The device Ft migrated from 10GHz, to 400GHz to 700GHz respectively and along those lines we applied old analog techniques at Microwave, even MMW frequencies. Much later DARPA started developing analog things at higher frequencies like a 100GHz Op-Amp in InP.

So old analog didn't totally die, it migrated into the RF, MW and MMW domains

Best

[RoGeorge]

Wanna see a funny one?

From this:


to this:


The diodes are there to rectify the fixed cutting-frequency inconvenient. 
No longer DC accurate, but now it's a 3rd order voltage-controlled filter! 

Notice how at DC all diodes are in series.  All 3 diodes are parsed by exactly the same DC current.  This same bias current will dictate the dynamic resistance of each diode.  So, for a small AC signal, the 3 diodes will appear as 3 equal resistors of value Rd, which dynamic resistance, together with the 3 capacitors, will give the cutting frequency of the filter.

Rd is adjustable by changing VFctrl, because a closed loop opamp will always keep both of its inputs at the same potential.

At DC, the opamp will adjust its output voltage such that, no matter the voltage drop on D2 and D3, the in- will be kept at the same potential with VFctrl.  This voltage at the negative input of the opamp, together with the the Rbias, will set the DC bias current through D1, and because all 3 diodes are in series, the same current will pass through D2 and D3, too, therefore the VFctrl will adjust the dynamic resistance of all 3 diodes at once.

In the end, the cutting frequency of this filter can be controlled by a DC voltage. 

[mawyatt]

Wanna see a funny one?

From this:


to this:


The diodes are there to rectify the fixed cutting frequency inconvenient. 
No longer DC accurate, but now it's a 3rd order voltage-controlled filter! 

Notice how at DC all diodes are in series.  All 3 diodes are parsed by exactly the same DC current.  This same bias current will dictate the dynamic resistance of each diode.  So, for a small AC signal, the 3 diodes will appear as 3 equal resistors of value Rd, which dynamic resistance, together with the 3 capacitors, will give the cutting frequency of the filter.

Rd is adjustable by changing VFctrl, because a closed loop opamp will always keep both of its inputs at the same potential.

At DC, the opamp will adjust its output voltage such that, no matter the voltage drop on D2 and D3, the in- will be kept at the same potential with VFctrl.  This voltage at the negative input of the opamp, together with the the Rbias, will set the DC bias current through D1, and because all 3 diodes are in series, the same current will pass through D2 and D3, too, therefore the VFctrl will adjust the dynamic resistance of all 3 diodes at once.

In the end, the cutting frequency of this filter can be controlled by a DC voltage. 

Interesting what happens when the input is large signal, say 2VPP?

Best

[RoGeorge]

It's "for a small AC signal", as mentioned in the description.  Luckily, except for D1, the AC voltage on the diodes is always smaller than the input signal.  For the AC on D1, there is a max +3...4dBc peak, during the cutting corner.

(The goal of trying to turn that filter into a VCF was for using it in an electronic synth, though I didn't say.  In such analog musical instruments everything must be voltage controlled:  oscillators, filters, modulators, etc., while other things like distortions, or DC accuracy/opamp offset removal, are not important.)

[sergey_g]

Maybe someone will find the simulation results in Fig. useful.
The calculation is carried out taking into account the actual parameters (GBP and Avd) for the operational amplifier TL081C
The red rectangle shows the Low-pass filter circuit based on a single-capacitor selective filter.
Cutoff frequency depends on the square root of the frequency Unity-gain bandwidth. Unity-gain bandwidth depends on the technology and the temperature of the microcircuit chip.
The exact formula for cutoff frequency is still unknown.
Large Signal Voltage Gain has little effect on Cutoff frequency over a wide range.

[MariuszD]

This circuit reminded me of the active ripple filter for a high-voltage power supply that I once designed. This circuit, similarly, connects thru two capacitors to the amplifier. Thanks to this, the low-voltage amplifier can suppress ripple at high voltage. I was wondering if the 3rd order filter presented in the topic can be used for power supply filtration, but it seems that it is not possible because the low series resistance R causes an increase in quality factor.