Two Port Network. Ram Prasad Sarkar
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1 Two Port Ram Prasad Sarkar 0
2 Two Post : Post nput port Two Post Fig. Port Output port A network which has two terminals (one port) on the one side and another two terminals on the opposite side forms a two port network. One port functions as input and the other as output to the network. The networks may composed of active or passive elements, but we are not concerned with its internal functioning and simple we assumed as a black box From above fig. it is noted that there are four variable,,, of the four, any two can be dependent and other two independent, which gives rise to different parameters (a) mpedance parameters or Z parameters. (b)admittance parameters or Y parameters. (C) Hybrid parameters or h parameters (d)transmission parameters. () Reason why to study two port network: (a) Such networks are useful in communication, control system, power systems and electronics. (b) Knowing the parameters of a two port network enables us to treat it as a black box when embedded within a larger network. (a) mpedance parameters or Z parameters. Linear Fig.
3 mpedance parameters are commonly used in the synthesis of filters and also useful in the design and analysis of impedance matching networks and power distribution networks., are dependent variables., are independent variables. The defining equations are = z z...() = z z...() n matrix form as: z z =....(3) z z To obtain Z parameters, we alternatively open circuit the output and input ports. Thus z = = 0 z = = 0 z z = = = 0 = 0 These parameters are as follows: z Open circuit input impedance z Open circuit transfer impedance from port to port z Open circuit transfer impedance from port to port z Open circuit output impedance When z=z, the network is said to be symmetrical. When the network is linear and has no dependent sources, the transfer impedances are equal (z=z), the network is said to be reciprocal.
4 This means that if the input and output are switched, the transfer impedances remain the same. Any twoport network that is composed entirely of resistors, capacitors, and inductors must be reciprocal Since, the Z parameters are obtained by opening the input or output port, they are also called the open circuit impedances. Z and Z are called driving point impedances and Z and Z are called transfer impedances. Z Parameters for a T Fig.3 Z = ZA ZC Z = Z =Zc Z =ZB ZC in which, Z = Z as in case in above T network are called reciprocal networks. f ZA =ZB, the network is symmetrical. Equivalent circuit for the Z parameters is here under 3
5 Z Z Z Z Fig.4 (b)admittance parameters or Y parameters. Linear Fig. Fig.5 Y Parameter also called admittance parameter and the units is Siemens (S)., are independent variables., are dependent variables. The defining equations are y y = y y t is represented as a circuit as follows 4
6 Y Y Y Y Fig.6 This is a voltage controlled (dependent) current source (CCS) n the matrix form y y = y y To obtain the Y parameters, we alternatively short circuited the input and output ports. Thus Y = Y = = 0 = 0 Y = Y = = 0 = 0 These parameters are as follows: y Short circuit input admittance y Short circuit transfer admittance from port to port y Short circuit transfer admittance from port to port y Short circuit output admittance The impedance and admittance parameters are collectively called the immitance parameters. 5
7 Since, the Y parameters are obtained by short circuiting the input or output, therefore they are also called the short circuit admittance parameters. Y parameters for π network Y C Y B Y A Fig.7 Y parameters can also be obtained from the Z parameters [] = [Z][] or, [] = [Z] [] Therefore Y Y Z Z = Y Y Z Z Z Where Z Reciprocal network = determinant of Z Symmetrical condition (C) Hybrid parameters or h parameters 6
8 Fig.8 Linear Fig., are independent variables., are dependent variables the, defining equations are = h h = h h n the matrix form h = h h h The h terms are known as the hybrid parameters, or simply hparameters. The name comes from the fact that they are a hybrid combination of ratios. These parameters tend to be much easier to measure than the z or y parameters. They are particularly useful for characterizing transistors.transformers too can be characterized by the h parameters. The h parameters are obtained from above equations by setting =0 i.e output port short circuited and =0 i.e input open circuited. h = h = = 0 = 0 h = h = = 0 = 0 The parameters h, h, h, and hrepresent an impedance, a voltage gain, a current gain, and an admittance respectively. 7
9 The hparameters correspond to: h Short circuit input impedance h Open circuit reverse voltage gain h Short circuit forward current gain h Open circuit output admittance n a reciprocal network, h=h. The equivalent network is shown below: The inverse of hybrid parameters are called g parameters, inverse hybrid parameters = g g = g g The values of the g parameters are determined as: g = g = = 0 = 0 g = g = = 0 = 0 The equivalent model is shown below: h h h h Fig.9 The g parameters correspond to: 8
10 g Open circuit input admittance g Short circuit reverse current gain g Open circuit forward voltage gain g Short circuit output impedance (d)transmission parameters or ABCD parameters: Linear Fig.0 Fig. T parameter or ABCD parameter is a set of parameters relates the variables at the input port to those at the output port. T parameter also called transmission parameters because this parameter are useful in the analysis of transmission lines because they express sending end variables ( and ) in terms of the receiving end variables ( and ). The equation is: = A B...() = C D...() n matrix form is: A B = C D The T parameter that we want determine are A, B, C and D where A and D are dimensionless, B is in ohm (Ω) and C is in Siemens (S). The values can be evaluated by setting 9
11 = 0 (input port open circuit) = 0 (output port short circuit) Thus; A = B = = 0 = 0 C = D = = 0 = 0 n term of the transmission parameter, a network is reciprocal if; ADBC= and for symmetrical A=D. Condition for reciprocity and symmetry: Parameters Condition of Reciprocity Condition of symmetry [Z] Z=Z z=z [Y] Y=Y Y=Y [h] h=h hhhh= [g] g=g gggg= [ABCD] ADBC= A=D nterconnections of s Often it is worthwhile to break up a complex network into smaller parts. The subnetwork may be modeled as interconnected two port networks. From this perspective, two port networks can be seen as building blocks for constructing a more complex network. These connections may be in series, parallel, or cascaded. ()Series Connection Two port networks with ABCD parameters are A,B,C,D and A,B,C,D are connected in series as shown in fig below 0
12 A B C D Fig. A B = A B and = C D C D Here = and = A B A B = C D C D Thus the overall transmission matrix for two port networks in tandem is the matrix product of individual transmission network matrix. When two port networks are connected in series, the Z parameter of the combination is equal to the sum of the individual Z parameters. Z Z Z Z Z Z a a b b = Z Z Z Z Z Z a a b b ()Parallel Connection Two port networks are in parallel when their port voltages are equal and the port currents of the larger network are the sums of the individual port currents. Consider the network shown
13 a a a a a a b b b b Fig. a=b=, =ab, =ab []=[YaYb][]. the Y parameter of the parallel network is equal to the sum of the individual network s Y parameter. [Y]=[Ya][Yb] (3)SeriesParallel Connection: n this connection the input ports are connected in series while the output ports are connected in parallel. The connection requires that =ab, =a=b and =a=b, =ab a a a a b b b b Fig.3 The overall hparameters of the combined seriesparallel connection can be obtained by adding their individual hparameters.
14 So, overall we have h h h h h h a a b b = h h h h h h a a b b (4) ParallelSeries connection. n this connection the input ports are connected in parallel while the output ports are connected in series. The connection requires that =a=b, =ab and =ab, =ab a a a a a b b b b b Fig.4 The overall inverse hparameters or gparameters of the combined parallel series connection can be obtained by adding their individual gparameters. So, overall we have g g g g g g a a b b = g g g g g g a a b b mage mpedance: 3
15 n a two port network, if two impedances Zi and Zi are such that Zi is the driving point impedance at port with impedance Zi connected across port and Zi is the driving point impedance at port with impedance Zi connected across port, then impedances Zi and zi are called the image impedances of the network. For symmetrical network image impedances are equal to each other i.e Zi=Zi and is called the characteristic or iterative impedance Zc. Two port Zi Z i Fig.a Zi Z i n fig.a Z = =driving point impedance at port. i n fig.b Z = = driving point impedance at port. i T to π Transformation: Z Z Y c Z 3 Y a Y b 4
16 mpedances Z, Z, and Z3 of the above fig.a T network are known and it is require to calculate equivalent admittances Ya, Yb and Yc of the π network in the fig.b Y Z a = Z Z Z Z 3 Z 3 Z π to T Transformation: Y Z = Z Z Z Z Z Z 3 3, b Z3 and Yc = Z Z Z Z Z Z 3 3 Y c Z Z Y a Y b Z 3 n this case, admittances Ya,Yb,and Yc of the above fig.a π network are known and it is require to calculate equivalent impedances Z,Z and Z3 of the T network in the fig.b Y Z = b YaY Y Yc YcY b b a, Y a Z = YaY Y Yc YcY b b a Y c and Z3 = YaY Y Yc YcY b b a 5
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