SELF

6 (appendix)

Correspondence

13 January 2004 2075

REVIEWER'S COMMENTS (for the Author)

This paper considers the analysis of electric filters composed of cascaded identical sections (with some slight changes at the beginning/end) based on comparison with corresponding mechanical systems.

Such types of filters were used many years ago (image-parameter filters) but because of poor performance (as confirmed in the present paper) and because of the arrival of filters based on network synthesis (Chebychev, maximally flat or elliptic functions type) were replaced by the latter type which have exact and predictable performance. There is thus very little interest in the type of problem considered in the present paper.

It is incorrect to state that the two-port method does not provide a complete and accurate result for the types of circuit studied in this paper. (What the authors quote is an incorrect application of the two-port method. For example in the circuit of Fig. 4, the transmission matrix (ABCD) of the ladder can be found in closed form and every property of the circuit can be found from this with any terminations. (A simple way to find this matrix is to write the recurrence relations for current and voltage in the ladder and solve this linear difference equations). A solution similar to the mechanical system is found this way, which is then written in the form of ABCD matrix.

Thus the results in this paper are already known and do not depend on using a mechanical analogy.

25.02.04

electric ladder filters"

1. When described the purpose of our manuscript, the referee emphasised that we are studying cascaded identical sections, only with some slight changes at the beginning/end. Pity, we cannot agree with it. These are not slight changes. In our calculation and experiment, the load resistance changes from 0 to 958 Ohm, i.e. by 3 orders, and load reactance changes from 10^-3 to 10⁴ mkF, i.e. by 7 orders (and this is not the limit of scope of our method - solutions are exact and have not the boundary of application in the load resistance). These changes, as we showed in our manuscript, considerably change the frequency dependence of input and output impedances of ladder filter, shift the peaks of resonances and change their amplitudes. Just because the filters are mismatched as to the load, they are out of domain of conventional two-port technique, as that theory is valid only for matched beginning/end. So, when the referee writes, we apply incorrectly the two-port method, this is not so. We quote the basic representation of this method. While to apply the two-port method to mismatched ladder filters - this is incorrect. This follows from the fact that when mismatched, we should not think the two-ports of ladder filter as identical, as in the ladder filter there will propagate a complicated process of standing and progressive waves. With it the input and output impedances of each chain will change in relation with its location in the filter. Conventional methods are unable to provide it and always say first of matching, then try to apply the two-port method, since under matched load there in the filter will excite only progressive waves. Only in this case we can think the chains of ladder filter as identical.

2. The author of review states the filters shown in our paper ineffective, as now more effective filters like Chebyshev, maximally flat or elliptic functions type are in use. I would like to mention, we yield our solution for impedances of two-ports of ladder filter of general type. Only when passing to experimental check, we have substituted the values of these impedances. Not in vain we took simple values of impedances. We wished to show in this way, on one hand, how theoretical calculations coincide with the experiment, and on the other hand, how will change the frequency pattern of a simple, as if clear for readers ladder filter under considerably mismatched load. We pity much that the referee as if did not notice this all. He surely cannot replicate the formula which we yielded, the more our frequency pattern which we have calculated theoretically and corroborated experimentally, despite seemingly simple circuit. Should we apply our result immediately to more complex two-ports of ladder filter, it would the more impede the understanding of our work. At the same time, nothing prevents the referee from substituting more complicated two-ports instead impedances, in that number m-type, and to yield much more complex frequency patterns. Besides, we noted in the paper, a homogeneous ladder filter is not the top of scope that our method offers. On the basis of mechanical problems which we already have solved, one can yield the analytical solutions for complicated filters having heterogeneous chains, resonance subsystems, cyclic, branched circuits etc. And the number of two-ports in our solutions is not limited, up to infinite filter. This is what considerably limits the matrix methods on whose basis specialists are unable at present to solve the problems with large number of two-ports of filter. The more they cannot solve the problems with limit passings from lumped to distributed filters, which is one of important advantages of analytical method.

3. The referee states, a simple way to find the matrix is to compose the recurrent relationships for currents and voltages in the ladder and in solving of yielded system of linear differential equations. We agree with this trivial true, the more that we also begin with recording these recurrent relationships and in standard way form the system of differential equations. But not in this is the novelty of paper! Is the referee sure, he can solve the system of n equations analytically? We would like much, the Editors to tell him our suggestion, he to show the technique, how we solved this system of equations. If he shows, how have we yielded these solutions in the form they are recorded, we will fully agree with his review. But if he cannot show this specific technique to yield these specific solutions, his conclusion that this result is already known is some beforehand. We would not limit his scope of techniques in it, let him use even numerical techniques. If he wants to do it with matrixes - let him. He only may want to account that we recorded our solution for arbitrary large number of two-ports of ladder filter. He can also apply the technique of zeros and poles on the complex plane and method of graphs - the main, he should yield our solution. If he prefers to use numerical techniques, we would ask him to do it for arbitrarily large n, and for general form of impedances that the two-port of ladder filter contains. This is a very important information for specialists in the circuit theory, as it shows general regularities of ladder filters of definite class and essentially helps in circuit synthesis. Numerical methods are basically unable to provide the information of such kind.

We will be sincerely thankful to the Editorial Board if you understand, why we are writing our objections, and pass our proposition to the referee as our natural reaction, when we reliably know, the considered classes of problems have not their solution in limits of conventional methods. The referee states opposite, though he certainly knows this what we do. When you Editors clarify the issue, whether this solution is known in frames of conventional methods, as the referee insists, this will show the importance of results presented in our manuscript. If the referee will not show this solution, he will corroborate in this way that the tremendous class of ladder filters with mismatched load is still out of the scope of calculation possibility. And this will corroborate itself for the Editorial Board, is it efficient for your journal to be the first who will publish the papers with solutions of such level. You surely will agree, the question raised by the referee exceeds the frames of publication decision. This is the matter of scientific principle. And we would like to ask you very much to understand us in it and to do so.

Sincerely yours,

Sergey Karavashkin

Olga Karavashkina

25.04.04

Dear Professor Scanlan,

As far as I can understand your silence, the Referee never gave you any substantiation that he can yield our formula, grounding on the existing calculation methods. However strange will it sound for you, for me this was obvious from the very beginning. I am not saying the existing methods wrong, but they do not note some features of dynamic electric circuits which we have noted in our paper. Of course, one can try to disregard it, and there is no secret that it is an usual practice in the scientific world. But our method already exists and, as you can see, it brings helpful results. Do not you agree?

Honestly, I would gladly leave aside the referee's ambition and the journal's regimentals and would discuss with you the essence of the subject. It seems, you will be interested in this discussion just as me.

Respectfully,

Sergey Karavashkin

29.06.04

The authors do not appear to have understood the comments in the previous review. The problem (in general) is to consider a cascade of N identical two-ports terminated arbitrarily at each end. If (ABCD) is the transmission matrix of one two-port then for the cascade (A_NB_NC_ND_N) is

From this any driving point or transfer function can be found by simple algebra.

(A_NB_NC_ND_N) can be found in several different ways for arbitrary two-ports (reciprocal or non-reciprocal, active or passive, lossy or lossless), e.g. by recurrence relations or diagonalization. One form of the result is, for reciprocal two-ports

Note: All terms are polynomial functions of (ABCD), as required.

The two-ports considered in this paper are reciprocal and the method of analysis based on mechanical analogy is not necessary.

04.07.04

Dear Professor Scanlan,

Thank you very much for your letter and the Referee's opinion which you kindly sent us. But regrettably, I have to distress you both. The Referee has not read thoroughly both our paper and respond to his review. In our respond to his review we emphasised that our paper studies the *mismatched* ladder filters, as you can see from the title. But the Referee again reduced it to the problem of matched ladder filter. You can clearly see it from the statement of problem in his version:

<< The problem (in general) is to consider a cascade of N identical two-ports terminated arbitrarily at each end. >>

No, this is not in general. It would be in general, if he introduced into his matrix an arbitrary load. He cannot do it correctly, and without this he cannot yield our solution.

So the Referee's solutions are not the explicit form of ours. You can easily check it, applying the Referee's matrixes at least to an LC-filter analysed in our paper. This will be far from any similarity to our solution. In fact, this second letter did not lift but only corroborated the basis of our previous objections. And it seems, you understand this no worse than we do. ;-)

The matter is just that the problem stated in our paper (in general) contains not only the ladder filter but the load in its most general appearance. With it we cannot already consider the filter as the homogeneous filter of N chains. If the load was active and equal to the wave impedance of filter, we can say the referee's solutions conventionally true, though less convenient than ours are. If they are not matched - and in practice you never find a filter matched in a range of frequencies - the Referee's solutions lose their sense. At the same time, our formula does work both in cases of matched and mismatched load. Also, we in our paper showed the solutions for complex load - and this even more worsens the situation for the two-port theory. While just the complex loads are typical for electric and radio engineering. One can yield these solutions only following our way of solving.

So I regret but cannot agree with the opinion of respectful Referee. I have to emphasise again, there is no analogue of our solutions in the existing theories and practice. Whilst practically all circuits are more or less mismatched and, as a rule, have a complex load. From this you can conclude, how much necessary this method is. Nothing to say that this method is highly necessary for the synthesis (of which I wrote you before) and for mechanical systems modelling with the help of electric circuits. There the match of filter with the load will be even worse, and the structure of filters will be more complicated. In particular, there often arises the necessity of composite filters consisting at the same time of discrete chains and long lines. And I can add, there is no analogue of our electromechanical analogy DEMA, this also is an original development. Namely because of lack of this analogy, the solutions for mechanical models still were behind the solutions for electric circuits.

Respectfully yours,

Sergey Karavashkin

14.07.04

Dear Dr Karavashkin,

Thank you for your message. I have carefully reviewed the points you make together with both sets of Reviewers comments and your original paper. (This is an area with which I am familiar).

There appears to be some confusion on your part in dealing with the Reviewers comments. Firstly the question of so-called "matched" loads does not arise. This concept was in common use in circuit theory forty and more years ago but in more recent years has become of no interest since it is usually physically unrealizable.

Analysis of two-ports is now based on (ABCD) or z or y or some similar set of parameters where the exact performance of any circuit can be calculated with an arbitrary source and load connected to the ports. (Results are of course in terms of ABCD, and the values of the load and source impedances and can be found in many text books). Your paper is concerned with a cascade of simple two-ports (shunt and series impedances) with load ZL and a current source. The Reviewer has given the correct formula for the ABCD matrix of the cascade, from which all formulas in your paper can be found using standard calculations. (I have personally checked your equations 26-28 which are the most general that you provide). The use of a circuit such as you consider, to form a filter has long ago been abandoned in favour of filters such as maximally flat and Chebychev, as pointed out by the Reviewer in his first comments. The reason is, of course, (as your analysis shows) that a "matched" load cannot be physically realized and with a realizable load there is no real control over the pass and stop bands. I regret therefore that your paper cannot be accepted for publication, since the results for such circuits are already available to circuit theorists and the mechanical analogy adds nothing new. Thank you for your interest in this Journal.

Yours sincerely,

J.O. Scanlan