qr code vb.net library Fig. 285. Parallel connection of two-ports. in .NET framework

Drawer Code 128 in .NET framework Fig. 285. Parallel connection of two-ports.

Fig. 285. Parallel connection of two-ports.
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First, for the above parallel connection, note that both networks have the same input voltage V1 and the same output voltage V2 . Next, regarding currents, inspection of Fig. 285 shows that, for the parallel connection, I1 I1a I1b or, in matrix form, I1 I2 ! I1a I1b I2a I2b ! I1a I2a ! I1b I2b ! and I2 I2a I2b
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which, upon applying eq. (520) to each of the two right-hand matrices, can be written as ! ! ! ! ! I1 y11a y12a V1 y11b y12b V1 I2 y21a y22a V2 y21b y22b V2 and therefore I1 I2 ! y11a y11b y21a y21b y12a y12b y22a y22b ! V1 V2 ! 536
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Equation (536) shows that parallel-connected two-ports can be replaced, for analysis, with a single equivalent two-port whose y-parameters are equal to the sum of the corre-
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CHAPTER 11 Matrix Algebra. Networks
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sponding y parameters of the individual two-ports. This fact is summarized by writing that, for parallel-connected two-ports, y ya yb 537 where ya and yb are the admittance matrices of the individual parallel two-ports in the equation at the top of the page, and where y is the admittance matrix of the single equivalent two-port which appears in eq. (536). Note that, in accordance with the rule for the addition of matrices, the sum of the two admittance matrices in the equation at the top of the page does produce the admittance matrix of eq. (536), which is what eq. (537) says. It s also apparent that any number n of parallel two-ports can, for purposes of analysis, be replaced by a single equivalent two-port whose admittance matrix is equal to the sum of the admittance matrices of the n individual two-ports. If, in a given case, the values of the y-parameters are not known but the values of another set of parameters are known, then the values of the y-parameters can be found by inspection of the conversion chart of section 11.8. For example, if the values of, say, the g parameters are known, then inspection of the chart shows that y11 dg=g22 ; y12 g12 =g22 ; y21 g21 =g22 ; y22 1=g22
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SERIES-PARALLEL AND PARALLEL-SERIES CONNECTIONS OF TWO-PORTS
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In the series-parallel connection the two networks are connected in series on the input side and in parallel on the output side. This is illustrated in Fig. 286.
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Fig. 286. Series-parallel connection of two-ports.
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As will be shown in one of your practice problems, the series-parallel combination of Fig. 286 can be replaced, for purposes of analysis, by a single equivalent two-port network having h-parameters equal to the sums of the corresponding h-parameters of the individual two-ports. Thus (where subscript e denotes the h-parameters of the equivalent two-port) h11e h11a h11b h12e h12a h12b or, expressed in matrix notation, he ha hb h21e h21a h21b h22e h22a h22b
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Matrix Algebra. Networks
where ha and hb are the h-parameter matrices of the individual series-parallel two-ports, and where he is the h-parameter matrix of the equivalent two-port. It s also apparent that the above remarks apply to any number n of series-parallel connected two-ports. Next, in the parallel-series connection of two-port networks, the two networks a and b are connected in parallel on the input side and in series on the output side, as illustrated in Fig. 287.
Fig. 287. Parallel-series connection of two-ports.
It can be shown that the parallel-series connection of two-ports can be replaced, for purposes of analysis, by a single equivalent two-port having g-parameters equal to the sums of the corresponding g-parameters of the individual two-ports; thus, g11e g11a g11b g12e g12a g12b g21e g21a g21b g22e g22a g22b
where e denotes the g-parameters of the equivalent two-port. These remarks apply to any number n of parallel-series-connected two-ports.
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