# Active Filter butterworth 8 order

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#### TXRX

##### Full Member level 2
From simulation you receive a noise of 240V - See graph - Why ?

#### FvM

##### Super Moderator
Staff member
Look sharp. Input voltage is 1V. In AC analysis, it's just a factor. Noise gain is 240V/1V. q.e.d.

#### TXRX

##### Full Member level 2

See attached - i inject 1VAC and receive 1.06VAC so the Gain is 1.06V/1V - i do not understand how you receive Gain of 240 ?

LvW

### LvW

Points: 2

#### LvW

TXRX,

as explained by FvM (posting #12 and #20), dont mix signal gain with noise gain (see the equivalent circuit diagram in posting #20).

Signal gain G=Hf/Hr (Forward gain/Feedback factor).
Noise gain NG=1/Hr.
First stage: Hf=150/(62k||68k + 150)=0.0046.

Thus, with G=1.1 you will get approx. for the 1st stage:
NG=1.1/0.0046=240.

FvM

### FvM

Points: 2

#### TXRX

##### Full Member level 2
Why you put resistors 62k||68k instead of 240k||100k which are the feedback resistors ?

#### LvW

Why you put resistors 62k||68k instead of 240k||100k which are the feedback resistors ?

As you can see, I have circumvented to calculate Hr (feedback factor). Of course, Hr would contain the feedback resistors.
More than that, by calculating Hf (see above) I have neglected all elements which are in parallel to 150 ohms (because they are large if compared with 150 ohms).
This makes the calculation easy (nevertheless, exact enough).

FvM

### FvM

Points: 2

#### TXRX

##### Full Member level 2
Hi FvM,
In order to receive G=240 in simulation - can you send the details of the Sources & OPA ?

Is it AC simulation and not Transient ?

#### FvM

##### Super Moderator
Staff member
All relevant information is directly visible from the simulation schematic, as you can see from the netlist. It's an AC anlysis, as already mentioned in a previous post.

Although I thought the schematic to be self-explanatory, it apparently isn't.

Please notice that the input source V1 is disabled "AC 0" while the noise source V2 is active "AC 1". That's the whole secret of getting either noise gain or signal gain in the simulation. The only difference to a real design is using a controlled source as ideal OP model.

Code:
* MFB-BP.asc
R1 N002 N001 32.43k
R2 N001 0 150
V1 N002 0 AC 0
C1 N001 N003 1n
C2 N001 Out 1n
R3 Out N003 70.58k
E1 Out 0 N004 N003 1e5
V2 N004 0 AC 1
.ac dec 2000 35e3 75e3
.end

#### FvM

##### Super Moderator
Staff member
To illustrate a previous comment about the role of filter topologies, I see that a Sallen Key biquad with similar Q (≈10) and also equal cap dimensioning has a noise gain around 60, 1/4 of the MFB variant. Besides better noise performance, the OP GBW requirements are reduced by the same factor.

I understand, that the topology doesn't fit your virtual ground design that well.

LvW

### LvW

Points: 2

#### TXRX

##### Full Member level 2
Hi,

I divide the values of the resistor by 10 and multiply the value of the capacitor by 10 and receive the same noise output.
As you said the resistors noise are not dominant.

---------- Post added at 16:08 ---------- Previous post was at 16:06 ----------

To illustrate a previous comment about the role of filter topologies, I see that a Sallen Key biquad with similar Q (≈10) and also equal cap dimensioning has a noise gain around 60, 1/4 of the MFB variant. Besides better noise performance, the OP GBW requirements are reduced by the same factor.

I understand, that the topology doesn't fit your virtual ground design that well.

I will check how to operate Sallen Key with single voltage

I simulate with filter-pro (TI Software) and receive that the last stage (#4) need Min of GBW of 136.97MHz, this value is the same for MFB and SK !

The parameters of the filter: Fc=50KHz, BW=5KHz, Ripple=1dB

---------- Post added at 17:05 ---------- Previous post was at 16:08 ----------

Hi FvM,

I simulate according your data and receive G of 234, If V1 is disable or enble with voltage of 1V there is no effect on G=234, the calculation of the gain done with V2.

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#### FvM

##### Super Moderator
Staff member
I simulate with filter-pro (TI Software) and receive that the last stage (#4) need Min of GBW of 136.97MHz, this value is the same for MFB and SK !
The parameters of the filter: Fc=50KHz, BW=5KHz, Ripple=1dB
Two comments on the FilterPro design:
- The 1 dB ripple parameter is meaningless for a butterworth prototype. It has only the parameters center frequency and bandwidth.
- The implementation is partly different from my design, stage Q and individual center frequencies are however fixed by the butterworth prototype.

The FilterPro design also has about factor 4 noise gain difference between MFB and SK. But they don't consider it in the specified "GBW requirement", apparently because they use a simplified criterion.

I simulate according your data and receive G of 234, If V1 is disable or enble with voltage of 1V there is no effect on G=234, the calculation of the gain done with V2.
Activating both sources doesn't serve a purpose. With V2 of 1V, you are determining noise gain.

About which circuit are you talking?

#### LvW

Hi TXRX,

just one reminder: In case noise is a critical issue, you also could consider some filter topologies other than the cascade approach (active realization of a passive ladder structure or PRB approach)

#### TXRX

##### Full Member level 2
Activating both sources doesn't serve a purpose. With V2 of 1V, you are determining noise gain.

About which circuit are you talking?

Hi FvM - I refer to the first circuit with the MFB topology.

---------- Post added at 09:49 ---------- Previous post was at 09:46 ----------

The FilterPro design also has about factor 4 noise gain difference between MFB and SK. But they don't consider it in the specified "GBW requirement", apparently because they use a simplified criterion.

Do you have any idea how to calculate the minimum GBW or other software that you are familiar.

---------- Post added at 09:51 ---------- Previous post was at 09:49 ----------

Hi TXRX,

just one reminder: In case noise is a critical issue, you also could consider some filter topologies other than the cascade approach (active realization of a passive ladder structure or PRB approach)

Hi LvW - Do you familiar with software for design the topologies that you mentioned ?

#### FvM

##### Super Moderator
Staff member
Do you have any idea how to calculate the minimum GBW or other software that you are familiar.
There's no exact minimum. The Q enhancement due to finite GBW can be determined analytically, you can also adjust the filter parameters according to real OP properties. Some commercial filter tools like Nuhertz Filter Solutions have the option.

You can always refer to a SPICE simulator to calculate the actual frequency response. With advanced tools like the PSpice optimizer, you can also perform an automatic adjustment to meet a given filter prototype. If you have an analytical expression for the frequency characteristic, you can do the same with the MS Excel solver.

#### TXRX

##### Full Member level 2
Hi FvM,
Yes you right, I simulate the SK vs. MFB and see that with the SK i can reach to much lower GBW than the MFB, the only issue in the SK is that for a lower GBW the Fc move a little (so it is need to compensate in the simulation).

But it is look that the SK very sensitive to components tolerance value.

#### LvW

Hi LvW - Do you familiar with software for design the topologies that you mentioned ?

Hi TXRX,

I dont know any software that supports the PRB design (Primary Resonator Block). Thus, you must consult some specific filter literature.
However, the design package "Filter solutions" (NUHERTZ.com) contains two design options (leapfrog, GIC-ladder) that are NOT based on cascading 2nd order stages.
There is a free version (Filter-free) that, unfortunately, supports bandpass design up to 6th order only.
For your information I attach a pdf file showing the result for a 6th order bandpass in GIC ladder topology.
However, please consider that this package uses a somewhat uncommon nomenclature as far as the filter order is concerned.
That means: A 6th order bandpass (with 3 pole pairs and a 6th order denominator) is called "3rd order". Thus, don`t be confused by this.
Regards
LvW

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#### TXRX

##### Full Member level 2
Hi LvM,
Thanks, I simulate and check your design of GIC.

What is the name of the Filter-free software ?

Do you have any idea about the noise-gain of the GIC and leapfrog?

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#### LvW

Hi LvM,
Thanks, I simulate and check your design of GIC.
What is the name of the Filter-free software ?

It's the free version of "filter solutions" and can be downloaded from the Nuhertz.com side.

#### TXRX

##### Full Member level 2
Is the Noise Gain depend on GBW parameter ?

#### FvM

##### Super Moderator
Staff member
Is the Noise Gain depend on GBW parameter ?
If we define noise gain = |1/β| (inverse feedback factor) it doesn't depend on GBW respectively available loop gain. The actual noise gain will be sligthly reduced (as well as signal gain) if the available loop gain at the frequency of interest is low.

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