Tea break/ Network theorem: 3. Reciprocity theorem Definition: For linear two-port network which has no souree inside(no controlled souree also), no matter which port is for input, the ratio with the response from the other port is the Generally speaking The reciprocity network has the same transfer characteristic at the two transmission directions he reciprocity element has the same transfer characteristic for signals at the two transmission directions Network theorem: 3. Reciprocity theorem Network theorem: 3. Reciprocity theorem Definition: For linear two-port network which has no sourc Proof: also), no matter which port is used for input, the ratio with the response from the other port is the Circuit description I 工/M=L/V I /V =I/V Or if Va=Vsb I=Ib Assume la and Ib =V=1v vs① current method Because it is linear passive netwo 工 ifvs。= Vsh then:Ia=b So Ib/Vsa=I,/Vsb Network theorem: 3. Reciprocity theorem+ Network theorem: 3. Reciprocity theorem *l Definition: For linear two-port network which has no source inside(no controlled source also), no matter which port is used Because it is a linear passive network, and no controlled s inside. Nonreciprocal device Property: The Z and Y matrix is symmetric matrixes. The optical isolator is an optical passive device which only allows the light passes in one direction An isolator is a nonreciprocal device Since no matter which port is input. An attenuator is an reciprocal device Property2: The transfer characteristie is sy mmetric of both -Hg o)are the same for both directions. An ideal reciprocal phase shifter can introduce the same phase shift for both directions北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Tea break！ Tea break！ 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Definition: For linear two-port network which has no source inside (no controlled source also), no matter which port is used for input, the ratio with the response from the other port is the same. *** Generally speaking: The reciprocity network has the same transfer characteristic at the two transmission directions. The reciprocity element has the same transfer characteristic for signals at the two transmission directions Network theorem: 3. Reciprocity theorem 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Definition: For linear two-port network which has no source inside (no controlled source also), no matter which port is used for input, the ratio with the response from the other port is the same. *** linear passive No controlled source N - VSa + Ib a a’ b b’ linear passive No controlled Source N - VSb + a a’ b b’ Ia Circuit description 1: Ib/VSa = Ia/VSb if then: VSa = VSb Ia =Ib Network theorem: 3. Reciprocity theorem 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Proof: ∑= Δ = L k 1 Sk ki i V Z I Assume Ia and Ib is the loop current, from the loop current method, Sa ab b V Z I Δ = So: Sb ba a V Z I Δ = Because it is linear passive network, So Δba = Δab So Ib/VSa =Ia/VSb Network theorem: 3. Reciprocity theorem Ib/VSa = Ia/VSb Or if a b I = I Vsa Vsb = 无源线性 无受控源 - N VSa + Ib a a’ b b’ 无源线性 无受控源 N - VSb + a a’ b b’ Ia 无源线性 无受控源 - N VSa + Ib a a’ b b’ 无源线性 无受控源 N - VSb + a a’ b b’ Ia linear passive No controlled source N - VSa + Ib a a’ b b’ linear passive No controlled Source N - VSb + a a’ b b’ Form1: Ia 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Definition: For linear two-port network which has no source inside (no controlled source also), no matter which port is used for input, the ratio with the response from the other port is the same. *** Property1: The Z and Y matrix is symmetric matrixes. Because it is a linear passive network, and no controlled source inside, Property2: The transfer characteristic is symmetric of both directions. ——H(jω) are the same for both directions. Since no matter which port is input, Network theorem: 3. Reciprocity theorem 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Amplifier *** INPUT OUTPUT The optical isolator is an optical passive device which only allows the light passes in one direction. An attenuator is an reciprocal device. An isolator is a nonreciprocal device. An ideal reciprocal phase shifter can introduce the same phase shift for both directions. Phase shifter Nonreciprocal device Network theorem: 3. Reciprocity theorem