Network Synthesis i.e. converting transfer functions to real circuits - Page 1
Forum section: electronics / projects

author: InterestedTom
author_rank: Regular Contributor
timestamp: July 15, 2016, 05:33:20 pm
content: I am interested in learning about network synthesis, that is converting an s-plane impedance function into a circuit that is either an exact implementation of the transfer function or, where this is not possible/practical, a good approximation to it. Ideally I would be learning about this over the next few days and then putting it into practice by the beginning of next week.As far as my experience and aptitude is concerned I am a 3rd Year Undergraduate Electronic Engineer and acheived good grades in my Maths module (and maths and further maths A-levels) so this is something I should be able to learn in the timescale with the appropriate textbook and/or guidance.My current application is for Passive Network Analysis i.e. converting a transfer function into an RLC circuit so this is what I would most like to learn about.What I really want is some reccomendations for textbooks for learning Network Synthesis or Passive Network Synthesis. Through my University I have online access to"Theory and Synthesis of Linear Passive Time-Invariant Networks" By Dante C. Youlabut it's quite heavy going. Going for £20 on Amazon is"Network Analysis and Synthesis: A Modern Systems Theory Approach" by Brian D O Anderson. Does anyone have any opinions on these books or any others I should consider?ThanksP.S. as a bit of background I have designed and manufactured a compact electromagnet for which I have collected frequency response data for Input voltage and output Magnetic Flux Density (which should be roughly proportional to input current over the range assessed) the impedance is resistive, inductive and a little capacitive. Using Matlab's non-linear regression model in the curve fitting toolbox I have come out with an equation in terms of angular frequency which describes a line of best fit through the data-points, I now want to convert this equation back into an RLC circuit that represents the frequency response of the Electromagnet.

author: uncle_bob
author_rank: Unknown
timestamp: July 15, 2016, 11:47:19 pm
content: HiNormally this is part of a masters program in circuit synthesis. It is based on having completed an undergraduate program already. You do it in about two or three semesters in most schools. Start today / done early next week either means you followed a cookbook or just did something trivial.Bob

author: alterbaron
author_rank: Contributor
timestamp: July 16, 2016, 01:27:58 am
content: Quote from: InterestedTom on July 15, 2016, 05:33:20 pmI was interested in learning about this stuff awhile back as well (in particular, synthesis of resistively-terminated LC ladder networks). I found the following paper a rather easy read and a nice launching-off point for further reading:"A Review and Modern Approach to LC Ladder Synthesis"LINKBest of luck!

author: danadak
author_rank: Super Contributor
timestamp: July 16, 2016, 01:46:37 am
content: It was an undergrad course for me, Kuo was author, "Network Analysis and Synthesis",get second edition, first was printed with some missing pages. My book is 1962, I gottabelieve there is a new author maybe with some more practical examples with active elementsthan this has. But book is good, step by step, w/o trying to make you prove 1 = 1......Largely techniques of PFE on f()'s, all normalized of course, so the last stepwas un-normalizing to get actual values..Regards, Dana.

author: uncle_bob
author_rank: Unknown
timestamp: July 16, 2016, 02:00:02 am
content: HiSyntesis of simple systems is an undergraduate course. Synthesis of arbitrary plots into N dimensional circuits ... that's a grad course. Same is true of releasability.Bob

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 16, 2016, 02:47:06 am
content: If you have a rational (pole-zero) expression, you can represent it exactly with a circuit. Further, you can implement it with real components if it is causal (no poles with positive real frequencies)The standard ladder network design consists of addition (series elements) and reciprocals (parallel elements), which constructs the transfer function as a continued fraction.Naturally, finding the roots of the polynomial, and the network, isn't the simplest task... but that's what computers are for.As for arbitrary functions, as long as the frequency response obeys suitable laws (while phase and amplitude can be whatever, the group delay has to be greater than some amount, which depends upon how sharply the amplitude changes, i.e. dH/dw). You may further find it beneficial to work with minimum-phase systems, which contains no added phase shift (all-pass) or delay elements beyond that. In that case, you can approximate the transfer function by adding poles and zeroes, in an iterative process.This is practical, for example, to simulate diffusion elements over a finite error and range. A chain of RC networks (either a series chain of (R||C), or a parallel stack of (R+C)) is scaled geometrically (the R value and RC time constant per pair) to match the f^(1/2) slope. I think around six RCs can give < 0.5dB error over three decades of frequency, not bad.Tim

author: f5r5e5d
author_rank: Frequent Contributor
timestamp: July 16, 2016, 04:13:29 am
content: probably easier to find previously developed purpose built models closely matching your constructionsomewhat more complete parasitic models of multilayer coils, possibly eddy current losses and magnetic material losses can be found in the literaturecertainly many practical inductors, transformers, solenoids, DC machinery are well modeled - likely even electromagnets in the Power Engineering litof course when ferromagnetic material are involved the linear modeling is of limited use with nonlinear and even hysteresis effects dominating the calcs

author: danadak
author_rank: Super Contributor
timestamp: July 16, 2016, 10:28:51 am
content: Synthesis and Realizability was an undergrad course at UCD in 1972.I found it fascinating because finally one had the tools to take a relationship,meeting certain constraints, and convert it to real component solutions.Regards, Dana.

author: InterestedTom
author_rank: Regular Contributor
timestamp: July 16, 2016, 12:11:14 pm
content: Thanks for all the replies.The best fit line for my data-points is a ratio of two 4th order polynomials:(p1x4+ p3x2+ p5)/(x4+ q2x2+ q4)where x = ?/8498this can be reduced further to an expresssion for R/(R + X(?)) and then each polynomial can then be solved and reduced to imaginary root pairs.I think I will carry on using the textbook I have online access to and persevere with that.I realise now that it would have been useful to collect phase shift data as well as magnitude data for the frequency response, however I no longer have access to the Electromagnet or a Gaussmeter/Teslameter so I will have to do what I can with the data I have.Quote from: danadak on July 16, 2016, 01:46:37 amThe first book I mentioned was published in 2015 I think ("Theory and Synthesis of Linear Passive Time-Invariant Networks" By Dante C. Youla) but that focuses on passive systems. I feel like I should be able to work through the algorithms to find which one suits my system.The material I used is Moly-Permalloy aka EFI Alloy 79, which should have a low magnetic remanence so the Alternating component of the Flux density should dominate.

author: danadak
author_rank: Super Contributor
timestamp: July 16, 2016, 10:32:16 pm
content: Then there is always interesting stuff like this, passive G, attached.Regards, Dana.