Nested Miller Compensation - Page 1
Forum section: electronics / beginners

author: promach
author_rank: Frequent Contributor
timestamp: February 26, 2018, 01:12:01 am
content: Does anyone know how to derive the transfer function of nested miller compensated amplifier found at page 12 of this thesishttps://goo.gl/xJ8NgC?I have read several other books, yet no author present a step-by-step derivation usng small-signal model.

author: amspire
author_rank: Super Contributor
timestamp: February 26, 2018, 02:55:32 am
content: Quite often, the easiest way to derive the transfer function is to start out the output and work towards the input. Just alternate between solving for current and voltage.Going from the output to input gives you an ever increasing equation, but it is very systematic. You do not have to think past the voltage or current you are working on.If you redraw the circuit, you can make it a bit easier - like bundling the RCs together as one step in the chain of equations.You end up with an equation of the form Vin= big equation with a lot of Voutterms.You then have to wrangle the equation into a Vout/Vinform. You can use Matlab or the free Octave to simplify the algebraic manipulation. It can be done by hand, but mistakes are easy.

author: Wimberleytech
author_rank: Super Contributor
timestamp: February 26, 2018, 04:03:35 am
content: Here is the nodal admittance matrix (assuming I did not screw up).

author: danadak
author_rank: Super Contributor
timestamp: February 26, 2018, 01:05:36 pm
content: Si8gnal Flow Graph will save you a lot of time, and provide visual insight intocircuit behavior.https://sites.google.com/site/ahmedelmorsy89/projects-1/sfg-signal-flow-graphRegards, Dana.

author: Wimberleytech
author_rank: Super Contributor
timestamp: February 26, 2018, 02:37:20 pm
content: QuoteConfirmed this result with Symbolic Spice.Here is the SSPICE output for Vout/Vin [V4/V1]. I have further confirmed the approximation for the numerator but have not tackled the denominator.[0 ] [GMM1 sCM1+sC1+G1 0 -sCM1 ][V1 ][0 ]=[0 -GMM2 sCM2+sC2+G2 -sCM2 ][V2 ][0 ] [0 -sCM1 -sCM2+GMM3 +sCM2+sCM1+sC3+G3 ][V3 ][1 ] [1 0 0 0 ][V4 ]*nested millerNumerator of: v4/v1TERMS SORTED ACCORDING TO POWERS OF ss**2 terms:+ sCM2*sCM1*GMM1 + sCM1*sC2*GMM1s**1 terms:+ sCM2*GMM2*GMM1 + sCM1*GMM1*G2s**0 terms:- GMM3*GMM2*GMM1TERMS SORTED ACCORDING TO POWERS OF SS**0 terms:+ sCM2*sCM1*GMM1 + sCM2*GMM2*GMM1 + sCM1*sC2*GMM1+ sCM1*GMM1*G2 - GMM3*GMM2*GMM1************************************************Denominator of: v4/v1TERMS SORTED ACCORDING TO POWERS OF ss**3 terms:- sCM2*sCM1*sC3 - sCM2*sCM1*sC2 - sCM2*sCM1*sC1- sCM2*sC3*sC1 - sCM2*sC2*sC1 - sCM1*sC3*sC2 - sCM1*sC2*sC1- sC3*sC2*sC1s**2 terms:- sCM2*sCM1*GMM3 + sCM2*sCM1*GMM2 - sCM2*sCM1*G3- sCM2*sCM1*G2 - sCM2*sCM1*G1 - sCM2*sC3*G1 - sCM2*sC2*G1- sCM2*sC1*GMM3 - sCM2*sC1*G3 - sCM2*sC1*G2 - sCM1*sC3*G2- sCM1*sC2*G3 - sCM1*sC2*G1 - sCM1*sC1*G2 - sC3*sC2*G1- sC3*sC1*G2 - sC2*sC1*G3s**1 terms:- sCM2*GMM3*G1 - sCM2*G3*G1 - sCM2*G2*G1 - sCM1*GMM3*GMM2- sCM1*G3*G2 - sCM1*G2*G1 - sC3*G2*G1 - sC2*G3*G1- sC1*G3*G2s**0 terms:- G3*G2*G1

author: promach
author_rank: Frequent Contributor
timestamp: March 03, 2018, 10:30:13 am
content: @WimberleytechQuoteThe above is reply from the thesis author.I need some time to go through both the calculations made by you (on NMC amplifier) and the thesis author (on PFC amplifier).

author: Wimberleytech
author_rank: Super Contributor
timestamp: March 03, 2018, 10:01:47 pm
content: Quote from: promach on March 03, 2018, 10:30:13 amI believe the matrix and resulting transfer function I provided is accurate. In order to simplify, you need to make approximations likeS(C1 + C2) ~ C2 when C2 >> C1.It is that kind of approximation the author is referring to.For the numerator, you need to factor the third order into a second order and first order. I have not dont it yet, but it is that process that will reveal opportunities to eliminate terms by approximation.

author: promach
author_rank: Frequent Contributor
timestamp: March 04, 2018, 01:44:21 am
content: QuoteCould you show the above by a very simple example ?Besides, why do you invert the current direction polarity of -gm2*V1 as in the second KCL equation in the matrix ?

author: Wimberleytech
author_rank: Super Contributor
timestamp: March 04, 2018, 03:15:46 am
content: Quote from: promach on March 04, 2018, 01:44:21 amThe thesis states that Cm1, Cm2, CL >> Co1-3Therefore, whenever you see Cm1+any Co, ignore the Co term. Same for Cm2.He also ignores any factor containing the output conductance.Please apply these assumptions and modify the Symbolic spice V4/V1 output accordingly, and I will give you the next step.

author: promach
author_rank: Frequent Contributor
timestamp: March 04, 2018, 05:08:21 am
content: QuoteThis piece of software is not free and limited demo version is usable for up to only 6 nodes. Besides, I am using Linux OS.Let me do further reading first.

author: f5r5e5d
author_rank: Frequent Contributor
timestamp: March 04, 2018, 06:01:08 am
content: http://cirlab.det.unifi.it/Sapwin/may be helpful, outputs a Matlab .m file of the symbolic TFOctave is highly Matlab compatable, now includes a symbolics package wrapping Python's sympy if you want a free SW chain

author: promach
author_rank: Frequent Contributor
timestamp: March 04, 2018, 08:26:30 am
content: QuoteI still do not understand this. Would you mind shedding some light ?Is it because for -gm2 (example topology would be common source single-stage NMOS amplifier), impedance looking the drain is so much larger ??

author: Wimberleytech
author_rank: Super Contributor
timestamp: March 04, 2018, 03:06:55 pm
content: Quote from: promach on March 04, 2018, 08:26:30 amI replaced the triangles in Fig 2.5 with VCCS and did nodal analysis at node 2 by summing all currents OUT of the node. I ignored c02 because it was not necessary to address your gm2 question

author: Wimberleytech
author_rank: Super Contributor
timestamp: March 04, 2018, 04:40:05 pm
content: Quote from: promach on March 04, 2018, 05:08:21 amI did not intend for you to use SSPICE. I meant that you should analyze the output (which I provided) by hand.At any rate, if you were to use SSPICE, 6 nodes is plenty. I would not want to deal with anything beyond a 6x6 matrix.