low pass and high pass filters

[rhdwave]

Hey all, just a quick question about low and high pass filters:

I read the cook your own distortion article which was excellent and was looking at the explanation of the above.  Here's a link to the diagram provided (about halfway down the page):
http://privatewww.essex.ac.uk/~mpthak/Distortion/


my question: is a high pass filter simply having the cap come before the resistor and a low pass the opposite? is it dependent on which is going to ground?
Much thanks!

[Mark Hammer]

my question: is a high pass filter simply having the cap come before the resistor and a low pass the opposite? is it dependent on which is going to ground?   

In principle, yes, but remember that the filters shown in that article are the simplest possible form.  Doesn't mean they are not effective.  It's just that the summary statement about "going to ground" counts as a good description for this type of low/highpass filter, but not for all of them.

Note that:
a) When you have a capacitor and resistor in series going into an opamp or a transistor base, THEY act as a highpass filter, even though nothing is going to ground.
b) When you have a feedback resistor in an op-amp, and a capacitor in parallel with it, THEY act as a lowpass filter, even though nothing is going to ground.
c) When you have a resistor (or pot) and a cap in series, going from the '-' pin to ground on an op-amp, they act like a highpass filter.

[rhdwave]

Thanks for the reply!
So, is there a set of definitive rules for every situation or how do can u tell exactly if it's low pass or high pass filter based on the situation? Is this something you just need to memorize for each individual instance or is there a formula with frequency that you can use to determine the kind of filter that it is acting as?
Thanks again!

[Mark Hammer]

Capacitors always provide a lower-impedance path for frequencies above 0hz.  How much higher up than zero hz will depend on the value of the cap, and any resistors that provide an alternate path for different content to go.

The way to think about it in general, is to ask yourself "What would the consequences be if higher frequencies could pass along this path with greater efficiency?"

So, when the cap goes to ground, obviously there is a low-impedance path for high end, that low freqs don't have "access" to (or rather the same amount of access), and high end bleeds to ground.  Conversely, if the cap is in the signal path, then high-freqs have an easier time passing through than lower freqs.

It starts to get a little counter-intuitive when we're looking at op-amps. Keep in mind that the gain of an op-amp is set by how much negative feedback comes from the output back to the inputs to restrict/limit how much gain is created/applied.  When you run a capacitor between input and output pins on an op-amp, you've provided a low-impedance path for the high end portion of the negative feedback to find its way back to the beginning/input.  With more negative feedback, the gain is reduced.  So, even though there is no cap going to ground, beause it is "easier" for high freqs to get somewhere, the net effect is to have more gain for low-freqs than for higher-freqs, which is the same general outcome as having a lowpass filter where highs are bled to ground.

With transistor gain stages, you can also have counter-intuitive consequences that behave like filters.  You will often see a bipolar transistor that has a resistor and a capacitor going to ground from the emitter, or a FET that has the same components going to ground from the source pin.  If the capacitor is taken out of circuit, usually the gain is reduced.  You can adjust the gain by inserting a variable resistance in series with that cap.  There are now two paths to ground from the emitter/source, one of which is variable.  Typically, that cap value is chosen to provide a path for all frequencies to pass to ground, but what if we were to make it smaller?  If we provided such a low-impedance path to ground for only high frequenies, the transistor would actually boost the highs more than the lows. 

Weird, huh?  You started off asking if it was a question of low=cap-to-ground and high=cap-in-series, and now I've laid out two scenarios (cap in feedback path in op-amp, cap to ground for transistor) where it is producing the same outcome as a lowpass or highpass filter, but those caps are nowhere near where you expected them to be.

[rhdwave]

Thank you Mark for taking the time to explain this to me.  It's something that's been bothering me for a while now.  So basically the higher the cap value, the more frequencies can pass through easier.  If it's a low value, then only higher frequencies can bleed through, but as you increase the cap, lower and lower frequencies have more access.  So, in order to change the sound of say a booster one could adjust the input cap to allow differnt frequencies in easier.  Ok, things are starting to make more and more sense.  Now if you could bear with me for one more question, i'd be grateful ( i really should just get a good electronics or book on circuits i think):

I know resistors will provide impedence for the signal, so how does this affect things when they are in series with caps? Is it just an added assurance that only certain frequencies will filter through?

Thanks again, i really appreciate the patience and answers to these probably very basic questions! 

[Mark Hammer]

When a resistor is in series with a capacitor, or when you have a cap to ground with a resistor before it, the resistance value limits how much current can pass, and in turn, how quickly the cap can charge up.  Of course, if you use a hose and bucket analogy, where the cap is the bucket and the resistor is the hose, you can imagine that how fast the bucket "fills up" is a function both of how big the bucket is, and how much the hose lets pass.  A large diameter hose fills up both large and small buckets quickly.  A narrow hose can fill up a tiny bucket relatively efficiently, but takes a while to fill up a big bucket.

This is the build up to the basic principle that the rolloff frequency is going to be a function of both the capacitor value AND the resistor value.  The formula for calculating the corner/rolloff frequency for a single pole filter (like the ones you showed at the start, as well as the CR inputs to op-amps, the RC network to ground from op-amps, and the CR parallel combo in a feedback loop) is 1/(2*pi*R*C).  R is in megohms, and C is in microfarads.  So, if the feedback resistor in an op-amp was, oh, let's say 551k (the sum of the pot and resitor in the feedback loop of a Tube Screamer), and the capacitor was, say, 51pf, the treble would start to taper off around 1 / (2*pi*.551*.000051) = 5663hz.  Drop that resistance down to 301k (by reducing the pot to half its value), and the rolloff goes up to 1 / 2*pi*.301*.000051 = 10,367hz.

[rhdwave]

Hey thanks again for all the replies! Things are becoming clearer.