selecting a proper value for DC blocking cap

[tempus]

Hey all;

I was trying to figure out what values to use for my FX switcher, and came across this comment in a thread from mid summer:

Op amps usually have really low output impedance, which requires a large output cap to avoid bass roll off.  That is why you see 10uf and larger.  Other circuits have higher output impedance and may use .1uf.  Same with input.  The FF has low input impedance so you see large input caps.  Mosfets boosters have high input impedance and you see .01uf input caps and smaller.  As Mark pointed out, there are a variety of points thru out the circuits that can provide low or high roll off...   

Is this actually true or is that a typo? I've never heard that the output Z of the previous stage has any effect on what the low frequency rolloff will be for the next stage. Clearly, if the input of the next stage has a low Z, the cap needs to be higher, so I wonder if this is actually a typo.

Any thoughts?

[alanlan]

You can model it like this:
         RS          C
------/\/\/\------||-------
                                 |
                                 \
                                 /
                                 \   RL
                                 /
                                 |
                                 |
---------------------------

So output = RL / (RL + RS + 1/sC)

= sCRL/(1 + sC(RL + RS))

Typically RS will be a few ohms and RL could be say 10K so RS + RL is approx RL

Therefore RL dominates and determines what C should be for a given roll off.  The problem is you don't always know what RL might be.  it could be 1Meg or 10K.  Hence to cover all eventualities, it's usually best to use a higher value of C just in case.

With transistor output stages, RS will be larger generally and also, sometimes the output is taken directly from a volume pot, so at lower volumes RS is effectively greater and will start to play a part.

[GibsonGM]

Here's just a thought, tempus...to AC, I believe the previous stage's output Z works in PARALLEL with the input impedance of the next stage.  At least that's how it works for tubes ;o)   So, the ESR, or effective series resistance, of the coupling cap, is in fact involved in the relationship between those impedances.   Add in the Miller Effect, for those devices which demonstrate input capacitance, and we have ourselves a filter. 

That would explain your quote above: the capacitance working through the resistance/impedance present and forming a filter that will roll off low freq's.  And also explains why higher input impedance and lower output impedances are preferred, and why we have such trouble with low input impedances...

[darron]

i had always worked thinking that we put a larger cap on the output as i can't anticipate what circuit might be following it...

[R.G.]

Hey all;

I was trying to figure out what values to use for my FX switcher, and came across this comment in a thread from mid summer:

Op amps usually have really low output impedance, which requires a large output cap to avoid bass roll off.  That is why you see 10uf and larger.  Other circuits have higher output impedance and may use .1uf.  Same with input.  The FF has low input impedance so you see large input caps.  Mosfets boosters have high input impedance and you see .01uf input caps and smaller.  As Mark pointed out, there are a variety of points thru out the circuits that can provide low or high roll off...   

Is this actually true or is that a typo? I've never heard that the output Z of the previous stage has any effect on what the low frequency rolloff will be for the next stage. Clearly, if the input of the next stage has a low Z, the cap needs to be higher, so I wonder if this is actually a typo.

I hope it wasn't me that said that...    it's misleading. If it was me, I apologize, will find and dig through the discussion and correct it.

In general, a low output impedance is a Good Thing. There is no particular reason a low output impedance needs a large output cap to keep bass response up. I'm generally in agreement with alan's comments. Rs is so low that it can usually be ignored compared to the impedances of the output cap and load being driven. The only time this is not true is when you're trying to drive a current into a low impedance input. This does happen, but people will walk a long way around not to do it because of unfamiliarity.

On Gibson's comment - yes, everything is a capacitance, everything is a resistor and everything is an inductor. Calculating every possible effect gets mind numbing. This is why I'm always looking for rules of thumb about what matters and what doesn't. In general, a "side effect" which changes the main operation of something - anything! - can be neglected for a quick and dirty understanding if it only changes the main thing by less than +/-10%. Later, if you want a more accurate understanding, you can go back and calculate in the finer effects.

So when two things are in series, say two resistors, if one of them is less than 1/10th of the other, it's reasonable to neglect the little one. When two resistors are in parallel, what matters is the conductance (1/resistance), and in that case, what matters is the small resistance, which accounts for over 90% of the conductance.

Works with impedances too. In trying to understand bass rolloff of signal voltage, you're looking at what the relative effects of the source impedance, series capacitor, and load are. Strictly speaking, all of these may be modelled as being in series, so you have the source impedance, cap, and load resistor, and you're concerned with the value of voltage across the load resistor, which is the input impedance of the next stage in most cases. We know that there's a voltage divider effect going on here. The cap's impedance falls linearly with frequency rise. The bass rolloff is merely a reflection of the fact that the AC voltage is divided by the capacitor and load resistor. The bass rolloff is the frequency where the capacitive impedance equals the load resistor.

What effect does the source impedance have on this? If it's less than 1/10 of the load resistance, almost none. The difference between it being truly zero and being 1/10 of the load is neglegible on the load and capacitor. In fact, for all cases, the division of the signal voltage between cap and load resistor determines the frequency where the bass is rolled off.

Source impedance can be modelled by the Thevenin model, a voltage source in series with a resistor, or the Norton model, a current source in parallel with that same source resistance. The two representations are equivalent to all external measurments and connections.

i had always worked thinking that we put a larger cap on the output as i can't anticipate what circuit might be following it...

This is in fact the case. Not knowing the load resistor is the big question. The source impedance, as long as it's reasonably less than the load, can be neglected.

[tempus]

I hope it wasn't me that said that...

Don't worry RG, it wasn't. Thanks, though, to you and the others who replied, for affirming my thoughts on this. I see the logic in using a bigger cap to cover all eventualities, too. The piece I'm working on regarding this is a piezo pickup going to a JFET buffer to a 10K/150 transformer. I calculated my cap value (and raised it a bit to 2.2 uF) for the buffer to transformer stage based on a 10K R_in. Figuring the R_source was negligible, I didn't include it in my calculations, then I came across the above post, and thought I better double check. I doubt my JFET buffer will have an output Z of 100 ohms, but I'm pretty sure it'll be less than 1000 too, so I think I should be OK. For the piezo to the buffer, I figured a 0.1uF would do (and in this case I know that it won't be being connected to anything but the buffer). I'm not using an R_in for the buffer, and although my piezo has a whopping 1.3M Z at 100Hz, I would think the input Z of the JFET gate to source would be at least 10 times higher.

Thanks again