Hello all,
This is my first post on AAC, so I thought to start with asking about a very basic fact that I do not know about, and which often causes me a great deal of trouble in my designs.

So, can anyone please tell me that whether the roll-offs we all study and calculate for the stop-band in active filter implementations actually do meet the theoretical/calculated expectations? For example, let's say I designed a fourth-order basic Butterworth LPF. Its a well-known fact for the Butterworth transfer function to have a 20dB/decade (first order) roll-off in the stop-band. So, for a second-order implementation, the roll-off becomes 40dB/decade, and for a fourth order implementation, it becomes 80dB/decade. So, I do not yet know how strictly I should expect my fourth-order Butterworth implementation to comply with this well-accepted fact?


Thank you very much.

 

So, I do not yet know how strictly I should expect my fourth-order Butterworth implementation to comply with this well-accepted fact?

Usually, a filter implementation will depart from the ideal response in several ways:

First, resistor and capacitor tolerances will usually cause the filter response to be different from that calculated in the upper portion of the passband; for a Butterworth filter, in other words, the passband won't be perfectly flat and may have a db or more of droop, peaking or even ripple leading up to the rolloff frequency. The cure for this is to use precision, tight-tolerance resistors and capacitors as much as possible.

And second, the finite op amp gain-bandwidth product, as well as the non-zero op amp open-loop output impedance, will often cause the filter response to deviate from the ideal in the upper reaches of the stop band and at some point the -XX db/decade slope of the response curve may even reverse direction and become positive. Using op amps with very large GBW products and low open-loop output impedance will minimize this problem.

Generally, the higher the filter order, the more difficult it becomes to achieve a near-perfect "textbook" response. 2nd-order filters are fairly easy; 8th-order filters are the stuff of nightmares.

 

Thank you very much OBW0549 for your clear and appreciable response.

 

So, I do not yet know how strictly I should expect my fourth-order Butterworth implementation to comply with this well-accepted fact?

It isn't that I am not satisfied with your answer, OBW0549, but my question still holds its place. To make it clearer, I still do not have any quantifiable scale, like this to this is bad, this to this is fair, this to this is good, this to this is excellent, etc.

 

To make it clearer, I still do not have any quantifiable scale, like this to this is bad, this to this is fair, this to this is good, this to this is excellent, etc.

As @OBW0549 wrote, there are a lot of variables and they vary case by case, or by design. I think simulation would give you a good idea of the practical response. Change component values randomly to higher and lower than nominal based on their tolerance. Choose different opamps if the design uses opamps.

 

I still do not have any quantifiable scale, like this to this is bad, this to this is fair, this to this is good, this to this is excellent, etc.

It isn't practical to define any such absolute scale, in part because filter performance requirements depend on the needs of the application. A level of performance that is "excellent" in one case may be absolutely unacceptable in another, and different applications may emphasize different aspects of filter performance (e.g., flatness of response in the passband, or amount of attenuation at some specific frequency in the stopband, or some aspect of the phase response or group delay).

@tsan made a good suggestion: use a simulator, such as LTSpice (or any other SPICE-based simulator) to model the behavior of a filter design with different component values to determine just how much deviation from ideal behavior you can expect. You can download LTSpice here.

 

Thank you very much, tsan and OBW0549.

 

OK! I am back on this old thread, Trying to understand this particular part of analog electronics through some practical examples.

Let's say I have a single-order, single-pole anti-aliasing R-C filter, which is showing a cut-off frequency very close to the ideal calculated value.

Now, what roll-off is expected from such a filter in practical scenarios?
I want to perform a qualitative analysis of this filter's health (effectiveness) as excellent, good, not-bad, bad, etc.

How am I suppose to do that? How should I proceed?

Regards,
Abbas.

 

A first-order RC filter will likely have a near perfect 20dB/decade rolloff above the passband, since there is no active circuitry and not much else that can cause it to deviate from the theoretical at typical antialiasing circuit frequencies in A/D converters.
But if it's a high frequency converter application, there may be stay circuit or component inductances that can affect the rolloff.
To calculate that you would need to determine what the stray inductances may be with the particular components and circuit layout being used.

 

OK! I am back on this old thread, Trying to understand this particular part of analog electronics through some practical examples.

Let's say I have a single-order, single-pole anti-aliasing R-C filter, which is showing a cut-off frequency very close to the ideal calculated value.

Now, what roll-off is expected from such a filter in practical scenarios?
I want to perform a qualitative analysis of this filter's health (effectiveness) as excellent, good, not-bad, bad, etc.
How am I suppose to do that? How should I proceed?
Regards,
Abbas.

My answer (sounds disappointing): It depends.....
The reason is that we have always several methods and/or design strategies for realizing filters. And each method has advantages and disadvantages. Even for first-order lowpass stages, there are several topologies, like
*passive RC
*passive RL
*Active RC with opamps
*Active RC with OTAs
*Active gmC (withOTAs).

Under IDEAL conditions, each method will produce the same response - however, the world of electronics is not ideal, hence, for each realization method we can observe different sorts of deviation from ideal response.

This situation will be, of course, more complex for higher order filters because the number of different realization methods (different filter topologies) is even larger than for first-order structures. And - for my opinion - the steepness of the roll-off is not the most important non-ideality to be observed for hardware realizations. More critical is, for example, the maximum attenuation the stopband can assume.

Example: One of the best known active second-order lowpass stage is the Sallen-Key block with a capacitor in the feedback path of the finite-gain opamp. When you measure or simulate (with a real opamp model) such a circuit you will see that the roll-off rate is as expected (40dB/dec) - however, the roll-off will stop at an attenuation level in the region of only -40 dB - and for further rising frequency the attenuation will even become worse (less damping).
The reason is the finite output impedance of the opamp because for rising frequencies we have three effects:
* An increasing portion of the input signal is DIRECTLY coupled to the opamp output (through the feedback capacitor which has a decreasing impedance) and will cause an unwanted output voltage at the ouput impedance,
* The wanted output voltage (delivered by the opamp) decreases due to the lowpass effect,
* The ouput impedance of the opamp is not constant but even goes up for rising frequencies...

For this reason, in many cases, such a lowpass stage cannot be used - however, there are enough alternatives which have - in this respect - better properties (but perhaps other deficencies). Hence, al always in electronics, a trade-off between conflicting requirements is necessary.

Just one remark regarding higher-order filters:
For filter orders n>4 it may be useful not to use a series combination of 2-nd order stages. Very often, an active realization of the well known passive RLC ladder structures has advantages.. These methods are based on active inductance simulation or FDNR blocks (artificial part called "Frequency Dependent Negative Resistor"). Both methods make use of a very versatile two-opamp combination: Generalized Impedance Converter (GIC).

 

Thanks a lot, LvW and crutschow.