SELF

4 (appendix)

S.B. Karavashkin

If speaking, what you could try to determine on the basis of Reviewer's matrix, this is the input impedance of ladder filter. For it, you really could use the known regularity [1, p. 570] (I am writing in the Reviewer's symbols):

I agree, outwardly the structure of this solution looks a little like our solution (33):

But this is only an outward similarity. If we substitute to (29) the values of A-matrix from (12)- (15), the similarity will be immediately violated and we will yield basically other formulas, which cannot be thought similar by the simple reason - the delay phases will be different in them, nothing to say of the rest.

The second which you could try to do is to compare our solutions with those conventional for the transmission constant of the ladder filter as the whole. True, with it you would not need directly the expressions for all chains of filter, as you wrote in your letter, but let it.

The circuit with which you had to operate is shown in Fig. 3.

Fig. 3. Ladder filter with the load

In other words, you had to consider the circuit of sequential connection of two-ports, one of which is determined by the Reviewer's expression (1), and the second would have the matrix of the type [1, p. 562]:

"As the matrix of cascade connection of two-ports is the product of their transmission matrixes" [1, p. 563], then

First of all, it is easy to see from (32) that under

i.e. under mismatched load, the elements of the first column of matrix (32), after substituting (12)- (15) into them, will take the following form:

With it the A-matrix becomes similar to the Reviewer's matrix, but only under matched load. I would like to mention here, in my last letter I called the reviewer's solution conventionally correct, and this is well seen in (34). Should the Reviewer's solution be exact, in this expression we would see A_N   and C_N correspondingly. We can easily make sure that the Reviewer was mistaken, if in (26)- (28) of our paper we take the load impedance equal to the square root of product of two-port impedances. We will yield other expressions and other matrix elements which can be calculated on the basis of these results as well.

But if the load was mismatched, the transmission constant of this filter can be determined of the basis of the following standard expression:

Now let us compare (33) with the real situation. We have from (27)

And again the resulting expressions are fully different. And (35) can be reduced to (36) under no conditions.