Op Amp Calculations
in [Design]
|
From: Fred Bloggs on 4 Oct 2005 07:04 Terry Given wrote: > Fred Bloggs wrote: > >> >> >> Terry Given wrote: >> >>> Fred Bloggs wrote: >>> >>>> >>>> >>>> Terry Given wrote: >>>> >>>>> Fred Bloggs wrote: >>>>> >>>>>> >>>>>> >>>>>> Terry Given wrote: >>>>>> >>>>>>> >>>>>>> I recently built about 50,000 of this circuit, with a feedback >>>>>>> cap too (mathcad rather than mathematica, and a pencil to start >>>>>>> with for the analysis), and 15 inputs thru 100k resistors. the >>>>>>> effect of the 14 "grounded" resistors shifted the center >>>>>>> frequency by about 10% - Aol was about 50. power consumption (and >>>>>>> cost) constraints meant I couldnt use a faster opamp, so instead >>>>>>> I stopped assuming and started calculating :) >>>>>>> >>>>>> >>>>>> What was the transfer function you were shooting for, and which amp? >>>>>> >>>>> >>>>> a summing band-pass (ish) filter. 40 x TLV274. >>>>> >>>>> I didnt want to AC-couple the inputs (that would have cost me 240 >>>>> capacitors) so I used the bridged-T feedback network with an RC >>>>> shunt to give a DC gain of about 1/16 - any DC is basically >>>>> common-mode, and the next stage was AC coupled. 3 Rs and 2 Cs was a >>>>> whole lot cheaper than an RLC. But 100k/14 = 7k in parallel with >>>>> the -ve shunt arm, enough to move Fc 10% or so. >>>>> >>>>> SPICE clearly showed it, so I went back and re-did my opamp >>>>> analysis using Dostals approach (originally I did it using the >>>>> Woodgate approximation), and voila - out popped the same answer. Mr >>>>> HP3577 also agreed with spice and mathcad. Dostals method also >>>>> allowed me to directly calculate the phase margin. Since then, I >>>>> have analysed all opamp circuits thusly - but I use the Woodgate >>>>> approach with pencil & paper as a bullshit detector :) >>>>> >>>>> Cheers >>>>> Terry >>>> >>>> >>>> >>>> >>>> >>>> You can achieve a wild increase in effective GBW by going to current >>>> mode feedback. The peaking and rapid rolloff due to that low >>>> impedance -ve shunt is eliminated from any frequency bands usable >>>> with the voltage feedback circuit. The output gain of 2x deals with >>>> the CMR input range of the TLV274- requires about a volt of headroom >>>> to V+ - facilitation odds and ends not shown... >>>> View in a fixed-width font such as Courier. >>>> >>>> . >>>> . >>>> . >--[Ri]-+-------+------[R1]--+--[R2]------------+ >>>> . | | | | >>>> . o | | [R3] +--[R]---+-->Vout >>>> . | | +5V | | | >>>> . | | | C | | |\ | >>>> . o | | +-----||-+ +--|-\ | >>>> . | | | | | >--+ >>>> . | | +-----[Rc]-----+------|+/ >>>> . o | | | | | |/ >>>> . | | | | | >>>> . >--[Ri]-+ | +-----------+ | [R] >>>> . | | | | | | >>>> . >--[Ri]-+ +------|>|---+ | | | >>>> . | | | | | | | >>>> . >--[Ri]-+ +--------------------------+ >>>> . | | | | | | >>>> . | | | | | | >>>> . | | |\| c | | >>>> . | +-|+\ |/ | | OA TLV274 >>>> . | | >-+---| c | >>>> . 2.5V>-+-----|-/ | |\ |/ | >>>> . |/| | e+ c >>>> . | | |\ |/ >>>> . | [Rb] e+ >>>> . | | |\ >>>> . | | e >>>> . | | | >>>> . GND---------+--+-----------+------------ >>> >>> >>> >>> >>> I'll study that a bit later. unfortunately it also achieves a wild >>> increase in parts count and cost - this circuit is replicated many, >>> many times :) >> >> >> >> I can't comment on your application since only you know what that is. >> You may find this strange, but the idea is to overcome the limitations >> of low inverting input shunt impedance and not to improve your product. >> > > What about the typo? the 2nd transistor shorts out the +5V supply.... > > Cheers > Terry It is a common collector pre-drive for the third transistor which is CE. If extreme gain accuracy is not needed it can be pulled, the CE should be a high beta type at low Ic.
From: Terry Given on 4 Oct 2005 18:04 Fred Bloggs wrote: > > > Terry Given wrote: > >> Fred Bloggs wrote: >> >>> >>> >>> Terry Given wrote: >>> >>>> Fred Bloggs wrote: >>>> >>>>> >>>>> >>>>> Terry Given wrote: >>>>> >>>>>> Fred Bloggs wrote: >>>>>> >>>>>>> >>>>>>> >>>>>>> Terry Given wrote: >>>>>>> >>>>>>>> >>>>>>>> I recently built about 50,000 of this circuit, with a feedback >>>>>>>> cap too (mathcad rather than mathematica, and a pencil to start >>>>>>>> with for the analysis), and 15 inputs thru 100k resistors. the >>>>>>>> effect of the 14 "grounded" resistors shifted the center >>>>>>>> frequency by about 10% - Aol was about 50. power consumption >>>>>>>> (and cost) constraints meant I couldnt use a faster opamp, so >>>>>>>> instead I stopped assuming and started calculating :) >>>>>>>> >>>>>>> >>>>>>> What was the transfer function you were shooting for, and which amp? >>>>>>> >>>>>> >>>>>> a summing band-pass (ish) filter. 40 x TLV274. >>>>>> >>>>>> I didnt want to AC-couple the inputs (that would have cost me 240 >>>>>> capacitors) so I used the bridged-T feedback network with an RC >>>>>> shunt to give a DC gain of about 1/16 - any DC is basically >>>>>> common-mode, and the next stage was AC coupled. 3 Rs and 2 Cs was >>>>>> a whole lot cheaper than an RLC. But 100k/14 = 7k in parallel with >>>>>> the -ve shunt arm, enough to move Fc 10% or so. >>>>>> >>>>>> SPICE clearly showed it, so I went back and re-did my opamp >>>>>> analysis using Dostals approach (originally I did it using the >>>>>> Woodgate approximation), and voila - out popped the same answer. >>>>>> Mr HP3577 also agreed with spice and mathcad. Dostals method also >>>>>> allowed me to directly calculate the phase margin. Since then, I >>>>>> have analysed all opamp circuits thusly - but I use the Woodgate >>>>>> approach with pencil & paper as a bullshit detector :) >>>>>> >>>>>> Cheers >>>>>> Terry >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> You can achieve a wild increase in effective GBW by going to >>>>> current mode feedback. The peaking and rapid rolloff due to that >>>>> low impedance -ve shunt is eliminated from any frequency bands >>>>> usable with the voltage feedback circuit. The output gain of 2x >>>>> deals with the CMR input range of the TLV274- requires about a volt >>>>> of headroom to V+ - facilitation odds and ends not shown... >>>>> View in a fixed-width font such as Courier. >>>>> >>>>> . >>>>> . >>>>> . >--[Ri]-+-------+------[R1]--+--[R2]------------+ >>>>> . | | | | >>>>> . o | | [R3] +--[R]---+-->Vout >>>>> . | | +5V | | | >>>>> . | | | C | | |\ | >>>>> . o | | +-----||-+ +--|-\ | >>>>> . | | | | | >--+ >>>>> . | | +-----[Rc]-----+------|+/ >>>>> . o | | | | | |/ >>>>> . | | | | | >>>>> . >--[Ri]-+ | +-----------+ | [R] >>>>> . | | | | | | >>>>> . >--[Ri]-+ +------|>|---+ | | | >>>>> . | | | | | | | >>>>> . >--[Ri]-+ +--------------------------+ >>>>> . | | | | | | >>>>> . | | | | | | >>>>> . | | |\| c | | >>>>> . | +-|+\ |/ | | OA TLV274 >>>>> . | | >-+---| c | >>>>> . 2.5V>-+-----|-/ | |\ |/ | >>>>> . |/| | e+ c >>>>> . | | |\ |/ >>>>> . | [Rb] e+ >>>>> . | | |\ >>>>> . | | e >>>>> . | | | >>>>> . GND---------+--+-----------+------------ >>>> >>>> >>>> >>>> >>>> >>>> I'll study that a bit later. unfortunately it also achieves a wild >>>> increase in parts count and cost - this circuit is replicated many, >>>> many times :) >>> >>> >>> >>> >>> I can't comment on your application since only you know what that is. >>> You may find this strange, but the idea is to overcome the >>> limitations of low inverting input shunt impedance and not to improve >>> your product. >>> >> >> What about the typo? the 2nd transistor shorts out the +5V supply.... >> >> Cheers >> Terry > > > It is a common collector pre-drive for the third transistor which is CE. > If extreme gain accuracy is not needed it can be pulled, the CE should > be a high beta type at low Ic. > shouldnt there be something to limit current though? +5V...Vce...Vbe with nary a resistor in sight. ultimately the base current could be as high as the opamp output current (assuming negligible contribution from the summing junction).... nice artwork BTW Cheers Terry
From: Jim Thompson on 4 Oct 2005 18:08 On Wed, 05 Oct 2005 11:04:26 +1300, Terry Given <my_name(a)ieee.org> wrote: >Fred Bloggs wrote: >> >> >> Terry Given wrote: >> >>> Fred Bloggs wrote: >>> >>>> >>>> >>>> Terry Given wrote: >>>> >>>>> Fred Bloggs wrote: >>>>> >>>>>> >>>>>> >>>>>> Terry Given wrote: >>>>>> >>>>>>> Fred Bloggs wrote: >>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Terry Given wrote: >>>>>>>> >>>>>>>>> >>>>>>>>> I recently built about 50,000 of this circuit, with a feedback >>>>>>>>> cap too (mathcad rather than mathematica, and a pencil to start >>>>>>>>> with for the analysis), and 15 inputs thru 100k resistors. the >>>>>>>>> effect of the 14 "grounded" resistors shifted the center >>>>>>>>> frequency by about 10% - Aol was about 50. power consumption >>>>>>>>> (and cost) constraints meant I couldnt use a faster opamp, so >>>>>>>>> instead I stopped assuming and started calculating :) >>>>>>>>> >>>>>>>> >>>>>>>> What was the transfer function you were shooting for, and which amp? >>>>>>>> >>>>>>> >>>>>>> a summing band-pass (ish) filter. 40 x TLV274. >>>>>>> >>>>>>> I didnt want to AC-couple the inputs (that would have cost me 240 >>>>>>> capacitors) so I used the bridged-T feedback network with an RC >>>>>>> shunt to give a DC gain of about 1/16 - any DC is basically >>>>>>> common-mode, and the next stage was AC coupled. 3 Rs and 2 Cs was >>>>>>> a whole lot cheaper than an RLC. But 100k/14 = 7k in parallel with >>>>>>> the -ve shunt arm, enough to move Fc 10% or so. >>>>>>> >>>>>>> SPICE clearly showed it, so I went back and re-did my opamp >>>>>>> analysis using Dostals approach (originally I did it using the >>>>>>> Woodgate approximation), and voila - out popped the same answer. >>>>>>> Mr HP3577 also agreed with spice and mathcad. Dostals method also >>>>>>> allowed me to directly calculate the phase margin. Since then, I >>>>>>> have analysed all opamp circuits thusly - but I use the Woodgate >>>>>>> approach with pencil & paper as a bullshit detector :) >>>>>>> >>>>>>> Cheers >>>>>>> Terry >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> You can achieve a wild increase in effective GBW by going to >>>>>> current mode feedback. The peaking and rapid rolloff due to that >>>>>> low impedance -ve shunt is eliminated from any frequency bands >>>>>> usable with the voltage feedback circuit. The output gain of 2x >>>>>> deals with the CMR input range of the TLV274- requires about a volt >>>>>> of headroom to V+ - facilitation odds and ends not shown... >>>>>> View in a fixed-width font such as Courier. >>>>>> >>>>>> . >>>>>> . >>>>>> . >--[Ri]-+-------+------[R1]--+--[R2]------------+ >>>>>> . | | | | >>>>>> . o | | [R3] +--[R]---+-->Vout >>>>>> . | | +5V | | | >>>>>> . | | | C | | |\ | >>>>>> . o | | +-----||-+ +--|-\ | >>>>>> . | | | | | >--+ >>>>>> . | | +-----[Rc]-----+------|+/ >>>>>> . o | | | | | |/ >>>>>> . | | | | | >>>>>> . >--[Ri]-+ | +-----------+ | [R] >>>>>> . | | | | | | >>>>>> . >--[Ri]-+ +------|>|---+ | | | >>>>>> . | | | | | | | >>>>>> . >--[Ri]-+ +--------------------------+ >>>>>> . | | | | | | >>>>>> . | | | | | | >>>>>> . | | |\| c | | >>>>>> . | +-|+\ |/ | | OA TLV274 >>>>>> . | | >-+---| c | >>>>>> . 2.5V>-+-----|-/ | |\ |/ | >>>>>> . |/| | e+ c >>>>>> . | | |\ |/ >>>>>> . | [Rb] e+ >>>>>> . | | |\ >>>>>> . | | e >>>>>> . | | | >>>>>> . GND---------+--+-----------+------------ >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> I'll study that a bit later. unfortunately it also achieves a wild >>>>> increase in parts count and cost - this circuit is replicated many, >>>>> many times :) >>>> >>>> >>>> >>>> >>>> I can't comment on your application since only you know what that is. >>>> You may find this strange, but the idea is to overcome the >>>> limitations of low inverting input shunt impedance and not to improve >>>> your product. >>>> >>> >>> What about the typo? the 2nd transistor shorts out the +5V supply.... >>> >>> Cheers >>> Terry >> >> >> It is a common collector pre-drive for the third transistor which is CE. >> If extreme gain accuracy is not needed it can be pulled, the CE should >> be a high beta type at low Ic. >> > >shouldnt there be something to limit current though? +5V...Vce...Vbe >with nary a resistor in sight. ultimately the base current could be as >high as the opamp output current (assuming negligible contribution from >the summing junction).... > >nice artwork BTW > >Cheers >Terry Triple Darlington? Bah! Humbug! It'll fry! ...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.
From: Fred Bloggs on 4 Oct 2005 21:36 Terry Given wrote: > Fred Bloggs wrote: > >> >> >> Terry Given wrote: >> >>> Fred Bloggs wrote: >>> >>>> >>>> >>>> Terry Given wrote: >>>> >>>>> Fred Bloggs wrote: >>>>> >>>>>> >>>>>> >>>>>> Terry Given wrote: >>>>>> >>>>>>> Fred Bloggs wrote: >>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Terry Given wrote: >>>>>>>> >>>>>>>>> >>>>>>>>> I recently built about 50,000 of this circuit, with a feedback >>>>>>>>> cap too (mathcad rather than mathematica, and a pencil to start >>>>>>>>> with for the analysis), and 15 inputs thru 100k resistors. the >>>>>>>>> effect of the 14 "grounded" resistors shifted the center >>>>>>>>> frequency by about 10% - Aol was about 50. power consumption >>>>>>>>> (and cost) constraints meant I couldnt use a faster opamp, so >>>>>>>>> instead I stopped assuming and started calculating :) >>>>>>>>> >>>>>>>> >>>>>>>> What was the transfer function you were shooting for, and which >>>>>>>> amp? >>>>>>>> >>>>>>> >>>>>>> a summing band-pass (ish) filter. 40 x TLV274. >>>>>>> >>>>>>> I didnt want to AC-couple the inputs (that would have cost me 240 >>>>>>> capacitors) so I used the bridged-T feedback network with an RC >>>>>>> shunt to give a DC gain of about 1/16 - any DC is basically >>>>>>> common-mode, and the next stage was AC coupled. 3 Rs and 2 Cs was >>>>>>> a whole lot cheaper than an RLC. But 100k/14 = 7k in parallel >>>>>>> with the -ve shunt arm, enough to move Fc 10% or so. >>>>>>> >>>>>>> SPICE clearly showed it, so I went back and re-did my opamp >>>>>>> analysis using Dostals approach (originally I did it using the >>>>>>> Woodgate approximation), and voila - out popped the same answer. >>>>>>> Mr HP3577 also agreed with spice and mathcad. Dostals method also >>>>>>> allowed me to directly calculate the phase margin. Since then, I >>>>>>> have analysed all opamp circuits thusly - but I use the Woodgate >>>>>>> approach with pencil & paper as a bullshit detector :) >>>>>>> >>>>>>> Cheers >>>>>>> Terry >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> You can achieve a wild increase in effective GBW by going to >>>>>> current mode feedback. The peaking and rapid rolloff due to that >>>>>> low impedance -ve shunt is eliminated from any frequency bands >>>>>> usable with the voltage feedback circuit. The output gain of 2x >>>>>> deals with the CMR input range of the TLV274- requires about a >>>>>> volt of headroom to V+ - facilitation odds and ends not shown... >>>>>> View in a fixed-width font such as Courier. >>>>>> >>>>>> . >>>>>> . >>>>>> . >--[Ri]-+-------+------[R1]--+--[R2]------------+ >>>>>> . | | | | >>>>>> . o | | [R3] +--[R]---+-->Vout >>>>>> . | | +5V | | | >>>>>> . | | | C | | |\ | >>>>>> . o | | +-----||-+ +--|-\ | >>>>>> . | | | | | >--+ >>>>>> . | | +-----[Rc]-----+------|+/ >>>>>> . o | | | | | |/ >>>>>> . | | | | | >>>>>> . >--[Ri]-+ | +-----------+ | [R] >>>>>> . | | | | | | >>>>>> . >--[Ri]-+ +------|>|---+ | | | >>>>>> . | | | | | | | >>>>>> . >--[Ri]-+ +--------------------------+ >>>>>> . | | | | | | >>>>>> . | | | | | | >>>>>> . | | |\| c | | >>>>>> . | +-|+\ |/ | | OA TLV274 >>>>>> . | | >-+---| c | >>>>>> . 2.5V>-+-----|-/ | |\ |/ | >>>>>> . |/| | e+ c >>>>>> . | | |\ |/ >>>>>> . | [Rb] e+ >>>>>> . | | |\ >>>>>> . | | e >>>>>> . | | | >>>>>> . GND---------+--+-----------+------------ >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> I'll study that a bit later. unfortunately it also achieves a wild >>>>> increase in parts count and cost - this circuit is replicated many, >>>>> many times :) >>>> >>>> >>>> >>>> >>>> >>>> I can't comment on your application since only you know what that >>>> is. You may find this strange, but the idea is to overcome the >>>> limitations of low inverting input shunt impedance and not to >>>> improve your product. >>>> >>> >>> What about the typo? the 2nd transistor shorts out the +5V supply.... >>> >>> Cheers >>> Terry >> >> >> >> It is a common collector pre-drive for the third transistor which is >> CE. If extreme gain accuracy is not needed it can be pulled, the CE >> should be a high beta type at low Ic. >> > > shouldnt there be something to limit current though? +5V...Vce...Vbe > with nary a resistor in sight. ultimately the base current could be as > high as the opamp output current (assuming negligible contribution from > the summing junction).... > > nice artwork BTW > > Cheers > Terry You're dwelling on open loop anomalies- tie that collector to the rightmost transistor collector if it bothers you. There is no condition under which the TLV274 will put sustained maximum current into the base circuit- not even close- the output will rail at uA drive.
From: The Phantom on 5 Oct 2005 00:49
On Tue, 4 Oct 2005 11:44:53 +0200, "Fred Bartoli" <fred._canxxxel_this_bartoli(a)RemoveThatAlso_free.fr_AndThisToo> wrote: > >"The Phantom" <phantom(a)aol.com> a ?crit dans le message de >news:r7f3k19amd4737csli9d1c7c7c1d5engqn(a)4ax.com... >> On Mon, 3 Oct 2005 21:13:16 +0200, "Fred Bartoli" >> <fred._canxxxel_this_bartoli(a)RemoveThatAlso_free.fr_AndThisToo> wrote: >> >> >> >Well, you've forgotten the GBW in all that :-) >> >> >> >> No, I didn't forget at all; it's implicit in A. >> >> >> > >> >Well, yes, I somewhat figured that. >> >But not mentionning A(s) when you explicitly use s somewhere else might >lead >> >the not so careful to some error, i.e. forgetting its phase which is -90d >> >over almost the bandwidth. >> >> I think that anyone sufficiently well versed in complex arithmetic >> as used nowadays to write transfer functions will know that if they >> want the DC gain, they can just use the TF I gave with A constant, and >> if they want AC results, then of course they will know that A must be >> a function of frequency.. >> > >OK, fair enough. > >> > >> > >> >> >If we set WT=2.pi.GBW then we have >> >> > >> >> > -A - B p >> >> >----------------- with >> >> > 1 + C p + D p^2 >> >> > >> >> > A0(R4+R5) >> >> >A = ---------------- >> >> > R3(1+A0)+R4+R5 >> >> > >> >> > A0.C1(R4 R5 + (R4 + R5) R6) >> >> >B = ---------------------------- >> >> > R3(1+A0)+R4+R5 >> >> > >> >> > (A0(R3 + R4 + R5 ) + C1.WT((R3 + R4)R5 + R6(R3 + A0.R3 + R4 + >R5)) >> >> >C >= -------------------------------------------------------------------- >> >> > (R3 (1 + A0) + R4 + R5 ) WT >> >> > >> >> > >> >> > A0.C1 ((R3 + R4) R5 + (R3 + R4 + R5) R6) >> >> >D = ------------------------------------------ >> >> > (R3 + A0 R3 + R4 + R5) WT >> >> > >> >> > >> >> >Less than 2 min to work this out from scratch, incl. sign error >> >correction. >> >> >> >> What sign error is that? >> > >> >That was in the starting equations (wrong opamp gain sign). >> >> Did you notice that three different people contributed to the >> posting that you originally replied to? John Woodgate did the first >> ASCII schematic, John Fields did the second and provided an equation, >> viz: >> >> R4 + R5 Vcc R2 >> Vout = -Vin --------- + --------- >> R3 R1 + R2 >> >> All I (Phantom) posted was a couple of transfer functions. I didn't >> use John's equations, and I don't think there was a sign error in what >> I posted. Most of your reply was directed to me, so I thought you >> were suggesting I had made a sign error. >> >> It would make it easier for others to comment without ambiguity and >> misunderstanding on your posting if you would cut and paste in the >> equation you think is in error, perhaps even indicating what you think >> the correct equation should be. >> > >Oh, I see. >Sorry for the misunderstanding, I wasn't implying somebody made a sign >error. >It was just *me* that made the sign error when first writing the problem and >got obviously wrong results. >Error corrected in a snap. I understand now. > >By saying: >> >> >Less than 2 min to work this out from scratch, incl. sign error >> >correction. > >I was just emphasing how easy it is to correct such errors vs the >paper/pencil method. You're absolutely correct. It is really nice, having spent hours on a really complicated problem, discovering a stupid mistake that would entail more hours of computation after having discovered the mistake. to be able to just key in a small change, hit enter, and !bang!, the final result, a result derived from a large amount of algebraic drudgery! > > >> > >> > >> >> >> >> >Isn't that Mathematica lovely? ;-) >> >> >> >> Unfortunately, the result doesn't seem to be correct. Put the >> >> expressions for A, B, C (the numerator of the "C" expression seems to >> >> be missing a closing parenthesis), and D into the first expression, >> >> namely: >> >> >> >> -A - B p >> >> ----------------- >> >> 1 + C p + D p^2 >> >> >> >> Then when you have it written out in all it's glory, find the limit >> >> as A0 --> infinity, and then the limit as C1 --> infinity. You >> >> *should* get: -((r5*r6 + r4*(r5 + r6))/(r3*r6)) >> >> >> >> But, alas, you don't. >> >> >> > >> >But then I do :-) >> >I've doubled checked the results the brute force way, taking the A,B,C,D >> >directly from here back into mathematica and all the limits are OK. >> >> You set WT=2.pi.GBW, but you haven't indicated what kind of op amp >> model you're using. Was it the standard one pole model: >> >> A(s) = WT/(s + Wa) >> > >Yes it is. Except that you didn't use that particular formulation. You used a non-standard (in my experience) expression, namely; A(s) = WT/((WT/A0 + s)) and this caused your results to contain both A0 and WT. There's no need for this since WT incudes A0. (I'm going to use Wp for the pole frequency in the single pole model for an op amp in what follows.) A standard expression for op amp gain, (which is exactly equivalent to yours, but not involving *both* A0 and WT explicitly) such as found on page 19 of the classic Schaumann and Van Valkenburg, is: A(s) = WT/(s + Wp) another alternative would be: A(s) = (A0 Wp)/(s + Wp) Solving the circuit with either of these expressions gives results that explicitly display the effect of Wp, and only one variable that involves the DC gain of the op amp. (I personally like to use the expression: A(s) = A0/(1 + sT), where T is the time constant of the pole.) > > >> or something else? I can't comment further until you tell me your >> model, but I still think there is something out of kilter with your >> expression: >> >> -A - B p >> ----------------- >> 1 + C p + D p^2 >> >> after A, B, C and D are substituted. > >Well, you can't just make A0 and C1 go to the limit and expect the DC >response. Yes, you can, if you use the second version of the op amp gain I gave above. If you use the first, standard, expression for A(s), then you have to make WT go to infinity (but not A0 since it's no longer in the result expressions) and then C1. >You also have to either make WT go to the limit, Only if you have used an expression for A(s) which involves *both* A0 *and* WT, which is not necessary. >or make s=0. In your Mathematica program, you have these four lines (change mode temporarily from using s to using p :-) ): Limit[sol, A0 -> infinity] Limit[%, C1 -> infinity] Limit[%, WT -> infinity] Limit[%%, p -> infinity] The fourth limit operates on the result of the second limit, which expression already lacks the variable p, so of course the result of this limit is the same as the result of the second limit and therefore accidentally gives the correct DC gain; but, in general, just letting p -> 0 won't give the DC gain if capacitors are involved, as I explain. It is the admittance of the capacitor(s) we want to become infinite to get DC gain; that is, the product p*C1 must go to infinity. I notice that if you let p -> 0 first (with C1 still finite), and then let A0 go to infinity, the result is -(R4 + R5)/R3, because the product p*C1 has gone to zero. Letting both p -> 0 and C1 -> infinity would only work if p and C1 vary in such a way that the product p*C1 -> infinity. Thus, letting p -> 0 won't give the DC gain if C1 remains finite. But this is not a problem, since letting C1 -> infinity does the job. When I originally took your full expression involving A, B, C, and D and took the limit as A0 -> infinity and C1 -> infinity, I got the same result you got after the second limit (above) and I couldn't understand why WT was still in the result; that's why I initially thought your result was incorrect. Other than that unnecessary complication, your result is, of course, correct. The basic three equations are easy to write down by inspection as you did, and Mathematica did just what you told it to, and yes, Mathematica is indeed lovely. > >Then all goes fine. > >But then you can see that it's easy, even for someone "sufficiently well >versed in complex arithmetic > as used nowadays" (to take your words), to forget something in the process. >Hence my preference for writing A(s). It's just one thing less to remember. > >From some of your previous posts I believe you have mathematica, so you'll >find the code herewith. |