By R.D. Richtmyer
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Additional info for 4th Int'l Conference on Numerical Methods in Fluid Dynamics
IM v1 +v2 + . . 2(b), as v1 = v2 = . . = vM i1 +i2 + . . + iM = 0 Both sets of constraints hold instantaneously and can be thought of as M-ports in their own right. In addition, both types of M-port are passive, and in fact lossless. 2), that M winst = M vj ij = i j =1 vj = 0 j =1 Losslessness of the parallel connection can be similarly demonstrated. It is possible to show, through the use of Tellegen’s Theorem , that a network made up of Kirchhoff connections of passive N -ports will behave passively as a whole.
1 N-ports Classical network theory  is partly concerned with the properties of connections of Nport devices. In the abstract, an N -port is a mathematical entity whose internal behavior is only accessible through its N ports. 1). The two terminals of any port must always be connected to the terminals of another port. A network is simply a collection of N -ports connected such that no port is left free1 . For lumped networks, the voltages, currents, and possibly element values in the networks are allowed to be real-valued functions of a sole real parameter t that is usually interpreted ...
In particular, we have that the analog DC frequency s = 0 is mapped to discrete DC z = 1, and that analog inﬁnite frequency is mapped to the Nyquist frequency. It should be clear that there will be signiﬁcant warping of the spectrum away from either extreme. 11) except for the factor 2/T . Although this factor is of little importance in ﬁltering applications, it is necessary here for the interpretation of such mapping as an integration rule. This should become clear in Chapter 3. 34 CHAPTER 2. 6: Spectral mapping corresponding to the trapezoid rule.
4th Int'l Conference on Numerical Methods in Fluid Dynamics by R.D. Richtmyer