The resistor you add in your gyrator to "tame the peaking" related to the finite GBW of the op-amps... I'd like to understand and/or derive the value you use, R=2/(2*pi*GBW*C). Any pointers on how do go about doing so? I'm thinking that if I go through the math for a regular integrator using an op-amp with finite gain and a single pole (i.e., dominant pole assumption), the resistor you add will have some "obvious" effect on the transfer function that causes it to move somewhat closer to 1/sC.
I know at one time I read one of your comments about this resistor to the effect that its usage was well known?
It adds "lead" just at the point where excess phase kicks in.
More detail tomorrow... my wife says to get my ass out of the office ;-)
...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice:(480)460-2350 | |
| E-mail Address at Website Fax:(480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
Often in analyses where effects of GBW of op amps are considered, a single pole op amp rolloff is used, namely A/(1+st), with A the DC gain and t the time constant of the pole. If this is the model you use in your analysis, Jim, would you give us the values of A and t you use? Or if your model is more complex, could you give us the op amp transfer function in a similar form, such as A/p(s), with P(s) being a polynomial in s?
My OpAmp model is more complex... it's modeled like a real device... current driven capacitor forms the pole, and controls the slew-rate. It also has an excess-phase element. It is excess-phase that causes the need for the peak-taming resistors.
(Otherwise, most OpAmp models just have a constant ninety degree phase shift.)
You can obtain a copy of the OpAmp model from my website.
...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC\'s and Discrete Systems | manus |
| Phoenix, Arizona Voice:(480)460-2350 | |
| E-mail Address at Website Fax:(480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
I believe that. I spent awhile reading Schaumann/Van Valkenburg last night, and he goes through the analysis of "the effects of finite A(s)" on a bunch of op-amp topologies. In the case of the regular old integrator, he ends up with the transfer function being approximately -1/sRC * 1/(1+s/w_t) (where w_t is supposed to be omega-sub-t, the unity gain bandwidth). Hence, by changing the capacitor into a series resistor 'r' and capacitor, he changes 1/sRC into (srC+1)/sRC. After some straightforward algebra, he uses this newfound zero (phase lead) to cancel the 1+s/w_t pole. The end result is r=1/(w_t*C), which is obviously similar to your value of 2/(w_t*C) ... but of course you're not using a pure integrator, but rather a gyrator that's trying to produce something more like 1-1/sC out of the "would be" integrator op-amp.
Interestingly, he goes through a similar analysis for the Antoniou gyrator, but his analysis leads him in the direction of finding component value ratios that ideally eliminate the loss term in the simulated inductor rather than adding compensation to the op-amps themselves.
Back to the regular old (Miller) integrator, he also shows the technique of sticking a unity gain op-amp in the feedback loop of the integrator ("active compensation") with guidance that this approach allows some pole/zero cancellation (assuming matched op-amps) which can be preferable in that w_t is a widely varying parameter and therefore you might find yourself having to tweak passive compensation resistors a little. What do you think? Worth the effort?
Thanks,
---Joel
P.S. -- Sorry for the typo in your last name in the subject line! :-)
Does she want you to pick up the donkey crap as well?
"Passive and Active Network Analysis and Synthesis" by Aran Budak is a very helpful book. It was the text for a very helpful class I took as a grad student -- it was at the same time a lifesaving gut class because the Estimation and Detection class I was taking was murder, and at the same time it was very informative with in-depth information that I've used ever since so it wasn't a waste of time. At any rate, the book discusses how to analyze filters with non-ideal op-amps. The basic technique is to make a feedback loop of it, and substitute a high-gain integrator (or other appropriate model) for the op-amp.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Interesting... I'll look into it. Reminds me... I have a paper by Geiger and Bailey, "Integrator Design for High-Frequency Active Filter Applications", IEEE Transactions on Circuits and Systems, Vol. CAS-29, No. 9, September 1982, that addresses using multiple OpAmps as compensation.
No problem, I do it myself... typing two fingers on each hand... one hand gets ahead of the other ;-)
...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC\'s and Discrete Systems | manus |
| Phoenix, Arizona Voice:(480)460-2350 | |
| E-mail Address at Website Fax:(480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
I have a copy (hooray for re-issues!), I'll take a look. From your description, it sounds like he's analyzing non-ideal op-amps the same way as Van Valkenburg; it'll be interesting to compare results.
Van Valkenburg must have at least a dozen repetitions of "the op-amp is really an integrator!" in his book.
The OP27 DOES have excess phase in it, but the better version is "Op-Amp-Config.zip " on the Subcircuits & Symbols page.
...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC\'s and Discrete Systems | manus |
| Phoenix, Arizona Voice:(480)460-2350 | |
| E-mail Address at Website Fax:(480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
Are you saying that the peaking is caused by the excess phase shift? So that if we remove the excess phase shift from the op amp model, the peaking will go away?
For the closed loop response of an op-amp you have the standard T(f)=A(f)/(1+A(f)b), where A(f) is the open loop gain and b is the feedback ratio, which I've assumed to be something like ideal resistors that aren't frequency dependent. As f goes from zero to the unity gain frequency w_t of the op-amp, A(f) goes from some large real value to magnitude 1, angle "180 degrees minus the phase margin," which is something starting to approach -1. In other words, with zero phase margin, the op-amp would be an oscillator, and with some phase margin you get peaking with the amount of peaking be inversely proportional to the phase margin. One thing to note from the T(f)=... equation is that the peaking is worst with the lowest gains (b approaches 1); witness the availability (and desirability) of uncompensated op-amps require gains >1 (or an external compensation network) to maintain stability.
This is explained in much more detail in many books, including "Intuitive IC Op-Amp Design."
I wasn't looking for an explanation of the theoretical basis for peaking, but rather examination of the actual behavior of the Thompson gyrator bandpass as shown in the .pdf file, "GyratorFilters-BP-LP-HP", on Jim's website.
It doesn't seem to. It would be interesting if you or someone else would run the simulations I describe below and see what results are obtained.
I simulated Jim's bandpass filter with and without the excess phase block he uses in his OP27 model. That excess phase block doesn't start to add excess phase until you get up to about 1 MHz, so I was wondering how it could cause peaking down at 20 kHz, which is the center frequency of the bandpass filter. After I got the model working, I decided to try to duplicate the family of response curves shown on page 3 of the .pdf file. I swept the GBW with smaller steps and noticed even more peaking at frequencies that Jim didn't show. In fact, with certain op amp parameters, you can get peaking of greater than 130 db (I got peaking of a factor of 3.5 million!). Just set the op amp DC gain to 1000000, the GBW to
279069.248 Hz and you should see a huge peak at 17437.0011 Hz (this is without excess phase in the op amp model). With excess phase, the huge amount of peaking remains, but is
*slightly* changed in frequency.
I swept the GBW from 25 kHz to 100 MHz and plotted the results, with and without excess phase; I used the excess phase block from Jim's OP27 model. I see two regions of substantial peaking. I've posted the plots over on ABSE.
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