8.1Relationship Between 2 Sets of Port Parameters:Since a single set of network parameters characterizes the linear circuits completely at the input and output terminals, it is possible to derive other network parameters from this set.Example: Consider the z and y parameter characterization of a given circuit with noindependent sources:vvz zz zii1211 1221 2212iiy yy yvv1211 1221 2212Show that:z zz zy yy yyy y y yyy y y yyy y y yyy y y y11 1221 2211 1221 2212211 22 21 121211 22 21 122111 22 21 121111 22 21 12 y yy yz zz zzz z z zzz z z zzz z z zzz z z z11 1221 2211 1221 2212211 22 21 121211 22 21 122111 22 21 121111 22 21 12 Example: Consider the abcd and h parameter characterization of a given circuit with no independent sources:8.2via bc dvi2211vih hh hiv1211 1221 2212Show that:h hh hba aad bcaca11 1221 221a bc dhhhhhhh hh112111222122122 1112Solving for Terminal Currents and Voltages from Port Parameters:Once the port parameters are known, no other information from the circuit is required to determine the behavior of the currents and voltages at the terminals.Example: Given the z-parameter representation of a circuit, determine the resulting terminal voltages and currents when a practical source with internal resistance Rs8.3and voltage Vs is connected to the input (terminal 1) and a load RL is connected to theoutput (terminal 2):vvz zz zii1211 1221 2212 Show vz R V z Rz R V R R z RR R R z Rz R R R z RL s sL s L s sL s L sL L s s111 1221 221222 22 and vR R R z R Vz R z R VR R R z Rz R R R z RL s L L sL L sL s L sL L s s21122 211222 22Combinations of Two-Port Networks:VsRsRL+v2-+v1-i1-i2-8.4Consider circuits A and B described by their abcd-parameters (assume independent sources zero).If A and B are connected in series, show that the abcd parameters for the new two-port (from v1a to v2b) is given by:via a b c a b b dc a d c c b d dvibbb a b a b a b ab a b a b a b aaa2211 Combinations of Two-Port Networks:Consider circuits A and B described by their y parameters (assume independent sources zero).+v2a-+v1a-i1a-i2a-A+v2b-+v1b-i1b-i2b-B8.5If A and B are connected in parallel, show that the y parameters for the new two-port (from v1a to v2b) is given by:iiy y y yy y y yvva b a ba b a b1211 11 12 1221 21 22 2212 AB+v2a-+v1a-i1a-i2a-+v2b-+v1b-i1b-i2b-+v2-+v1-i1-i2-8.6Two-Port Characterizations of Phasor Circuits:When energy storage elements are present in the system, the network parameters become transfer functions.Example: Find the h-parameters of the circuit below.RC VIH HH HIV1211 1221 2212Show H HH HRCp11 1221
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