3-Lesson_Notes_Lecture31_ee205

# 3-Lesson_Notes_Lecture31_ee205 - EE 205 Dr A Zidouri E...

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EE 205 Dr. A. Zidouri - 1 - E le ctric Circuits II Two-Port Circuits Hybrid and Transmission Parameters Lecture #31

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EE 205 Dr. A. Zidouri - 2 - The material to be covered in this lecture is as follows: o The Two-Port Hybrid parameters o The Two-Port Transmission parameters o Relationships Among the Two-Port Parameters o Reciprocal Two-Port Circuits After finishing this lecture you should be able to: ¾ Determine the Two-Port Hybrid Parameters ¾ Determine the Two-Port Transmission Parameters ¾ Derive all the Other Sets from a Known Set of Parameters ¾ Recognize Reciprocal and Symmetric Two-Port Circuits
EE 205 Dr. A. Zidouri - 3 - H yb rid pa ram e te rs The z and y parameters of a two-port network do not always exist. There is a need for developing another set of parameters. Hybrid Parameters ( h-parameters ): 11 1 2 2 22 1 1 2 2 2 Vh Ih V I hI hV =+ (43-1) or in matrix form: 1 1 2 1 1 2 2 2 h I I hhV ⎡⎤ ⎡ ⎡⎤ = ⎢⎥ ⎢ ⎢⎥ ⎣⎦ ⎣ ⎣⎦ [] 1 2 I h V = (43-2) The h-parameters are very useful for describing electronic devices such as transistors. It is much easier to measure experimentally the h-parameters of such devices than to measure their z or y parameters. In fact an ideal transformer for example does not have z -parameters as it is impossible to express the voltages in terms of the currents or vice versa. See Fig. 43-1 12 1 VV n I nI = = −

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EE 205 Dr. A. Zidouri - 4 - The values of the parameters can be evaluated by setting I 1 =0 (input port open-circuited) or V 2 =0 (output port short-circuited). Thus, 11 11 12 12 22 21 22 21 , 00 , VV hh IV VI II == = = = = (43-3) The parameters h 11 , h 12 , h 21 , h 22 represent an impedance, a voltage gain, a current gain, and an admittance respectively. This is why the h -parameters are called the hybrid parameters: ¾ h 11 = short-circuit input impedance ¾ h 12 = Open-circuit reverse voltage gain ¾ h 21 = short-circuit forward current gain ¾ h 22 = Open-circuit output admittance The following example illustrates the determination of the h- parameters for a resistive circuit. Example 43-1 Find the hybrid parameters for the two-port network of Fig. 43-2 Solution: To find h 11 and h 21 , we short circuit the output port and connect a current source I 1 to the input port as shown in Fig. 43-3a Fig. 43-2 Circuit for Example 43-1
EE 205 Dr. A. Zidouri - 5 - ( ) 11 1 236 4 VI I =+= hence 1 11 1 4 V h I = =Ω and by current division, 21 1 62 63 3 I II −= = + hence 2 21 1 2 3 I h I = =− To find h 12 and h 22 , we open circuit the input port and connect a voltage source I 2 to the input port as shown in Fig. 43-3b. By voltage division 12 2 3 VV V == + hence 1 12 2

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• Spring '09
• profsyed
• Thévenin's theorem, Electronics terms, Two-port network, Admittance parameters, Impedance parameters, Dr. A. Zidouri

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3-Lesson_Notes_Lecture31_ee205 - EE 205 Dr A Zidouri E...

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