- Admittance parameters
Admittance parameters or Y-parameters are properties used in
electrical engineering ,electronics engineering , and communication systems engineering describe the electrical behavior oflinear electrical network s when undergoing various steady state stimuli by small signals. They are members of a family of similar parameters used in electronics engineering, other examples being:S-parameters , [Pozar, David M. (2005); "Microwave Engineering, Third Edition" (Intl. Ed.); John Wiley & Sons, Inc.; pp 170-174. ISBN 0-471-44878-8.]Z-parameters , [Pozar, David M. (2005) (op. cit); pp 170-174.]H-parameters ,T-parameters orABCD-parameters . [Pozar, David M. (2005) (op. cit); pp 183-186.] [Morton, A. H. (1985); " Advanced Electrical Engineering";Pitman Publishing Ltd.; pp 33-72. ISBN 0-273-40172-6]The General Y-Parameter Matrix
For a generic multi-port network definition, it is assumed that each of the ports is allocated an integer 'n' ranging from 1 to N, where N is the total number of ports. For port n, the associated Y-parameter definition is in terms of input voltages and output currents, V_n, and I_n, respectively.
For all ports the output currents may be defined in terms of the Y-parameter matrix and the input voltages by the following matrix equation:
:I = Y V,
where Y is an N x N matrix the elements of which can be indexed using conventional matrix notation. In general the elements of the Y-parameter matrix are
complex number s.The phase part of an Y-parameter is the "spatial" phase at the test frequency, not the temporal (time-related) phase.
Two-Port Networks
The Y-parameter matrix for the
two-port network is probably the most common. In this case the relationship between the input voltages, output currents and the Y-parameter matrix is given by::I_1 choose I_2} = egin{pmatrix} Y_{11} & Y_{12} \ Y_{21} & Y_{22} end{pmatrix}{V_1 choose V_2} .
where
:Y_{11} = {I_1 over V_1 } igg|_{V_2 = 0} qquad Y_{12} = {I_1 over V_2 } igg|_{V_1 = 0}
:Y_{21} = {I_2 over V_1 } igg|_{V_2 = 0} qquad Y_{22} = {I_2 over V_2 } igg|_{V_1 = 0}
Admittance relations
The input admittance of a two-port network is given by:
:Y_{in} = y_{11} - frac{y_{12}y_{21{y_{22}+Y_L}
where YL is the admittance of the load connected to port two.
Similarly, the output admittance is given by:
:Y_{out} = y_{22} - frac{y_{12}y_{21{y_{11}+Y_S}
where YS is the admittance of the source connected to port one.
Converting Two-Port Parameters
The two-port Y-parameters may be obtained from the equivalent two-port
S-parameters by means of the following expressions.:Y_{11} = {((1 - S_{11}) (1 + S_{22}) + S_{12} S_{21}) over Delta_S} ,
:Y_{12} = {-2 S_{12} over Delta_S} ,
:Y_{21} = {-2 S_{21} over Delta_S} ,
:Y_{22} = {((1 + S_{11}) (1 - S_{22}) + S_{12} S_{21}) over Delta_S} ,
Where
:Delta_S = (1 + S_{11}) (1 + S_{22}) - S_{12} S_{21} ,
The above expressions will generally use complex numbers for S_{ij} and Y_{ij}. Note that the value of Delta can become 0 for specific values of S_{ij} so the division by Delta in the calculations of Y_{ij} may lead to a division by 0.
S-parameter conversions into other matrices by simply multiplying with e.g. Z_0 = 50Omega are only valid if the characteristic impedance Z_0 is not frequency dependent.
Conversion from
Z-parameters to Y-parameters is much simpler, as the Y-parameter matrix is basically thematrix inverse of the Z-parameter matrix. The following expressions show the applicable relations::Y_{11} = {Z_{22} over Delta_Z} ,
:Y_{12} = {-Z_{12} over Delta_Z} ,
:Y_{21} = {-Z_{21} over Delta_Z} ,
:Y_{22} = {Z_{11} over Delta_Z} ,
Where
:Delta_Z = Z_{11} Z_{22} - Z_{12} Z_{21} ,
In this case Delta_Z is the
determinant of the Z-parameter matrix.Vice versa the Y-parameters can be used to determine the Z-parameters, essentially using thesame expressions since
:Y = Z^{-1} ,
And
:Z = Y^{-1} ,
References
Bibliography
*David M. Pozar, "Microwave Engineering", Third Edition, John Wiley & Sons Inc.; ISBN 0-471-44878-8
ee also
*
Scattering parameters
*Impedance parameters
*Two-port network
*Hybrid-pi model
*Power gain
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