AC/DC-Feedback

Not related to the well know rock band! :grin:

Look at this schemo: [removed]

I've seen this on very few designs and would love to know more about the math behind it. The idea is to use separate feedback paths for AC (the 10k in the schemo) and DC (R1 + R2). This allows to use smaller ('lytic) caps which have lower leakage.

Now my questions:

* how do I determine R1, R2, C1, C2 and C3? From what I've seen, Rx=25k and Cx=100 uF should be OK, right?

* what's the math behind the low freq roll off (i.e. the -3 dB point)? Is the roll off 1st or 2nd order?

* If R1>>RGain, R1 and R2 do not influence AC gain, right?

* if used in the first stage of an instrumentation amp (three opamp config), it would be wise to connect C2 not to ground but to the opposite cap - similar as we would do it with RGain?

* why is this not used more often? Seems to be a neat trick that does not only improve performance but could save money as well (smaller caps).

Thanks for the help and sorry for so many Qs!

Samuel

Messy messy...but...

If you want to know more about it, slog through writing down the transfer function (it will be ugly). And then play with values and ratios.

Good insight about R1 >> Rgain---and you did that without having to run to a simulator---bravo.

If all you are concerned about is reducing output offsets due to amp input offests, then sure it works. But if there is significant input bias current then R1 and R2 large will give you offset due to that.

Why have C3? Also, what do you mean by Rx and Cx?

....rumination delay here...

In any event, it is a complex response however you cut it---you can get some crazy peaking with the (im)proper choide of values. You can tune the response but I don't think ever make it appetizing, by playing with C3.

The circuit looks a bit like part of a popular second-order shelving circuit as it is---if Rgain is open, noninv input is grounded and an input network similar to the feedback network is attached to the inv input.

Although the comment regarding bias current erros still applies, a config with a single pole response and unity d.c. gain just is the circuit with C3 shorted, C2 open and R1 R2 a single resistor; for R1' >>10k>> Rgain, your gain is the usual ni gain and rolloff is simply set by the C1 R1 tau. Simpler and trouble-free I think.

Brad

As I can see this is nothing more than a non invertent amplifier at AC (or to be more precise at a frequency for wich the Z of the capacitors is trascurable in respect of the resistors) that (given that r1 >> rgain and r1>>R 10K ) has a gain of 1+10K/Rgain.
This because C2 shorts to ground the signal coming trought R2 so that it can't reach the input by R1 thus escluding R1 and R2 from the feedback path.

At DC the capacitors left apart the Rgain and R10k so that there is only r1 and r2. this mean that the circuit has a dc gain of 1.

I think that the same thing could be obtained using a simple non inverting configuration where a capacitor is inserted between the ground and the feedback resistor.

When I have a little bit of time i would check how does it work with spice.


Alessio

Thanks for the answers! Let me add that I found this idea on the (unfortunately no longer available) Barry Porter homepage and in this schemo: F110_schem2.PDF

slog through writing down the transfer function

Click to expand...

Hm, hard work for a computer scientist! I'll give it a try (but don't be afraid to jump in here :wink: ).

what do you mean by Rx and Cx?

Click to expand...

Rx={R1, R2}
Cx={C1, C2, C3}

a config with a single pole response and unity d.c. gain just is the circuit with C3 shorted, C2 open and R1 R2 a single resistor

Click to expand...

If we short C3, we'll have the output offset of the amp on RGain which defeats the purpose of having low leakage caps, no?

I think that the same thing could be obtained using a simple non inverting configuration where a capacitor is inserted between the ground and the feedback resistor.

Click to expand...

True, but we need very big caps for high gains (and low impedance feedback networks). These caps have high leakage, which will make gain changes noisy.

Samuel

OK---I didn't realize that you were concerned about switching gains here, hence the desire to minimize any d.c. on the 10k-Rgain combo. However, even without C3 you are at least reducing the d.c. offset to that of the intrinsic offset voltage of the op amp block, again adding algebraically to the bias current times R1 + R2 combination. This will be better by far most of the time than a two-resistor d.c. coupled feedback network at least.

But, with your suggested vaues for all save the 10k, and with Rgain = 1k, the resulting response is a one-pole highpass with a resonant peak of alpine proportions: about 25dB above the nominal 20dB of midband gain, centered at 215 mHz (milli- not Mega-) and a Q of about 71! The rolloff below that resonance is eventually 20dB/decade, i.e., single-pole.

Imagine now the step response and associated settling time! As the hapless phrasebook user says in the Monty Python Flying Circus skit, "Bouncy bouncy." As well, 1/f noise, likely large at that frequency to begin with, will continue to excite the resonance even without further external stimulation.

Brad

Thanks, Brad, for your calculation! Did you end up with the transfer function?

resonant peak of alpine proportions

Click to expand...

I'm swiss, so I'm used to alpine proportions! :grin:

Seriously: what are values that would work? I guess R1 and R2 need to be lower, at least they are on the schemo I mentioned. C1 is bigger.

Samuel

PS: Correction to last reply---I had forgotten that I had changed the configuration to inverting to see some issues more clearly. With the circuit driven noninverting it falls to merely unity gain below the big peak, as all such stages must, before it has a chance to fully assume a 20dB/decade rolloff.

I looked at the original schematic and notice that it is not really in the configuration you have drawn. I see your C2 and C3, and your R1 and R2, but the remaining components are somewhat differently arranged. BTW I hope the value of R22 on the mic pre schematic is a misprint, and that R30 is a trimpot and not a gain adjust used in normal operation. Then there is R26, unnecessary at that point in the circuit and the wrong value for bias current compensation anyway...

But having said that, the actual mic pre's central stage circuit works much better. There are some inflection points in the rolloff towards unity gain but no horible peaking. At max gain of about 42 dB the -3dB point is at about 6 Hz.

Brad

PPS: If it is any consolation, it is possible to get back to alpine peakiness with C6 (mic pre schematic) large enough.

I don't have the courage or the time to attempt to scale the north face of the transfer function. Those readers with a good command of Mathcad or Matlab etc. should find it a trivial exercise, but of course that is cheating.

Brad

I looked at the original schematic and notice that it is not really in the configuration you have drawn. I see your C2 and C3, and your R1 and R2, but the remaining components are somewhat differently arranged.

Click to expand...

I think the only thing that is changed is C1, it is moved to between RGain and ground. Does this changes things completely?

Samuel

Well---enough to make the response of the mic pre circuit work reasonably well for the values in the schematic. As I say, with large enough C (your C2, mic pre C6), the serious amount of peaking comes back.