V.2 No 1

5 (appendix)

Respond to Dr Scanlan on ladder filters

As I already wrote and as this was reflected in our paper, the cause is that the method of two-ports is unable to take into account the dynamic processes in ladder filters with mismatched load - in particular, the multiple reflections within the filter and at its boundaries. And this relates not to some specific variation of the method of two-ports. This method is basically applicable exceptionally to matched filters, i.e. to the conditions of full identity of transmission constants of the filter chains. When we introduce the load, it basically changes the situation. Looking at the example of filter in Fig. 3, we could already see that mismatched load first of all changes the transmission matrix of the two-port and introduces the dependence between its input and output impedances. Due to this, we have already to take into account that

as now the input impedance will be

because, in accordance with the circuit in Fig. 3, the double two-port is open; this allows us to write (38), doing not turning the load impedance into infinity, as it is now the internal element of the two-port.

And if now we consider the ladder filter consisting of such double two-ports as in Fig. 3, with (37) the general circuit of this filter will be as shown in Fig. 4:

Fig. 4. The ladder filter, taking into account the input impedances of chains

It is seen from Fig. 4 that at

all two-ports will be identical and the Reviewer's record of A-matrix will be true. But if

given (38), all chains of filter will be mismatched. Our solutions take this disbalance into account, and Reviewer's solutions do not. This is just what I wrote in my previous letter. And as I showed in this brief study, it is impossible to improve the situation in limits of matrix method, as we have to know the pattern of change of disbalance from chain to chain. With the matrix formalism, and in general form, it is impossible to get this to know.

So, with all your and Reviewer's wish, you basically could not pass from (1) to our solutions, (26)- (28) of our paper, and I know what I am saying. And this is not exactly so as you are saying that this subject was topical 40 years ago and is not now. This subject did not and could not lose its importance, as you agreed, practically all filters working in the range are mismatched. Simply in the lack of methods to yield exact analytic solutions of problems of such class, scientists took a "rude" way and omitted the basic principles on which the two-port conception has been constructed. And they outwitted themselves, having yielded, on one hand, some expressions in which the load impedance is present, but on the other hand, these solutions do not describe the practice. You know no less than I do, practical engineers say frankly, it is useless to calculate the ladder filters with standard formulas. They only select the parameters experimentally.

You have a possibility to change my opinion in only one way which I suggested you in the beginning of our discussion - please show the matrix formula which by commonly known, standard transformation could be reduced to our solutions. Unfortunately, the Reviewer have not shown such formula. As I said in my previous letter and showed in this present, it is basically impossible to pass from his matrix to our solutions. You in your last letter have confirmed the Reviewer's opinion, but also did not show such matrix solution.

Out of this, the issue, to publish or not, is rather the matter of scientific principle, of ethics, but not of the paper itself. Until the Reviewer showed a grounded alternative, our method remains unique, and you just corroborated in your last letter, how topical is this subject.

In this connection, I would be very grateful, if you showed me the way you went from the Reviewer's (1) to (26)- (28) of our paper. As our discussion is the matter of principle, this would bring us to a simple decision, and you surely will agree with me at this point.

Yours sincerely,

Sergey B. Karavashkin

Reference:

1. Kugushev, A.M. and Golubeva, N.S. Foundations of radio electronics. Energy, Moscow, 1969, 880 p. (Russian)