Understanding Poles & Filters: Counting Capacitors & dB/decade

[Physixs]

Hello, I was reading over poles and filters, but I guess since I don't learn calculus, I don't learn transforms.

With that said, the definition of Poles in my text is a bit iffy... It talks about how the term poles means how many bypass capacitors are in a circuit.

I can't find ANY definitions even remotely close to that online.

However, if I google image filters, I can physically count capacitors to find out how many poles the filter is.

Can I always do that? Can I always look at a circuit, count the capacitors and know how many poles there are in that circuit? Is that legit?

For instance in the picture I provided, since I can see six bypass capacitors, does that mean it is a six-pole filter (I know the answer but wasnt sure if the method was ok)

Also, do you just ignore the low pass filter capacitor that is in the op amp itself (because it is not a bypass capacitor)?

Also, would it be safe to say that as a rule of thumb if you have 2 poles, your roll off will be double (-40dB/decade) and if you have 3 poles it will be triple (-60 dB/decade)?

Thanks so much

 

[analogdesign]

No you can't just "count capacitors" to determine how many poles there are. You can count "time constants" but that is a more advanced technique. Also what you show in the figure are not "bypass capacitors" they are in the signal path. A bypass capacitor is a capacitor connected between power and ground that shunts high-frequency noise from the supply to the ground (ideally the power supply is a small-signal ground so you want power and ground to be shorted at all frequencies above DC).

The main problem in "counting capacitors" is that sometimes a capacitor doesn't make a pole (which make the filter more low-pass) but sometimes it makes a zero (which makes a filter more high-pass).

In your circuit it is a coincidence that there are six capacitors. (as you said there are additional caps in the op amps for stability). In some very basic circuits (such as a series of RC stages) you can count capacitors but not always.

Lastly it is only "safe to say" that two poles --> -40dB/decade and so on if you don't have any zeros in your circuit. You can say if you have two more poles than zeros in your circuit there will be some point where the magnitude response is rolling off at -40dB/decade but where that region is depends on the locations of your poles and zeros.