8/24/2021 2A_3_ConnectingSourceandLoad.docx 1/9 Jim Stiles The Univ. of Kansas Dept. of EECS Connecting a Source and Load Say we wish to connect the output of one microwave network/component to the input of another microwave network/component. The terms “input” and “output” tells us that we wish for signal energy to flow from the output network to the input network. Microwave Network #1 Microwave Network #2 output port input port8/24/2021 2A_3_ConnectingSourceandLoad.docx 2/9 Jim Stiles The Univ. of Kansas Dept. of EECS Source delivers; load absorbs We can say that the output delivers signal power to the input, or equivalently, that the input absorbs power from the output. In this case, the first network is the source, and the second network is the load. The source delivers power to the load, or equivalently, the load absorbs power from the source. Each of these two networks may be quite complex, but we can always simply this problem by using equivalent circuits. Microwave Network #1 (source) Microwave Network #2 (load) Energy8/24/2021 2A_3_ConnectingSourceandLoad.docx 3/9 Jim Stiles The Univ. of Kansas Dept. of EECS Input impedance: The equivalent load For example, if we assume time-harmonic signals (i.e., eigen functions!), the load can be modeled as a simple lumped impedance, with a complex value equal to the input impedance of the network. inininVZI= in in inV ZI= L inZZ= inV+− inI Microwave Network #2 (load) inV+− inI8/24/2021 2A_3_ConnectingSourceandLoad.docx 4/9 Jim Stiles The Univ. of Kansas Dept. of EECS The equivalent source The source network can likewise be modeled using either a Thevenin’s or Norton’s equivalent. This equivalent circuit can be determined by first evaluating (or measuring) the open-circuit output voltage ocoutV: And likewise evaluating (or measuring) the short-circuit output current scoutI: ocoutV+− 0outI = Microwave Network #1 (source) 0outV+−= scoutI Microwave Network #1 (source)8/24/2021 2A_3_ConnectingSourceandLoad.docx 5/9 Jim Stiles The Univ. of Kansas Dept. of EECS Thevenin’s and Norton’s equivalent source From these two values ( and oc scout outVI) we can determine the Thevenin’s equivalent source: Or, we could use a Norton’s equivalent circuit: out g g outg outoutgV V ZIVVIZ= −−= ( )out g out gout gout gI IV ZV II Z= −= − ocg outocoutgscoutVVVZI==scg outocoutgscoutIIVZI==Ig Zg outV+− outI +− Vg Zg outV+− outI8/24/2021 2A_3_ConnectingSourceandLoad.docx 6/9 Jim Stiles The Univ. of Kansas Dept. of EECS A source and load equivalent Thus, the entire circuit: can be modeled with equivalent circuits as: Microwave Network #1 (source) Microwave Network #2 (load) V+− I LZ +− Vg Zg V+− I8/24/2021 2A_3_ConnectingSourceandLoad.docx 7/9 Jim Stiles The Univ. of Kansas Dept. of EECS Remember this? Please note that we have assumed a time harmonic source, such that all the values in the circuit above (Vg, Zg, I, V, ZL) are complex (i.e., they have a magnitude and phase). The time-averaged rate at which energy is absorbed (a real value!) by the complex load impedance is (remember??): { }1Re2absP VI∗= Joules/sec = Watts where * denotes the complex conjugate operator.8/24/2021 2A_3_ConnectingSourceandLoad.docx 8/9 Jim Stiles The Univ. of Kansas Dept. of EECS Power absorbed by the load… Analyzing the equivalent circuit, we find that the energy is absorbed by the load at a rate: { }221Re22gLabsgLVIVRPZZ∗= =+ Joules/Second where LR is the real (i.e., resistive) part of the load impedance: { } { }Re ReL LL LZ R jX R= += +− Vg Zg V+− I LZ8/24/2021 2A_3_ConnectingSourceandLoad.docx 9/9 Jim Stiles The Univ. of Kansas Dept. of EECS +− Vg Zg LZ delP absP …equals power delivered by the source From conservation of energy, this absorbed power is likewise that of the power delPdelivered by the source (i.e.,
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