1. Prof. David R. Jackson Dept. of ECE Fall 2013 Notes 29 ECE 6340 Intermediate EM Waves 1

2. + - Mutual Impedance The mutual impedance Z 21 between two antennas is calculated. + - + - 2

3. The open-circuit voltage V 2 is put in the form of a reaction. Mutual Impedance (cont.) + - + - + - E 1 = field radiated by J 1 i in the presence of open-circuited antenna 2. 3

4. The equivalence principle is used to replace antenna 1 with its surface current. The antenna current J 1 ant is that excited on antenna 1 when it is in the presence of open-circuited antenna 2. Mutual Impedance (cont.) 4

5. Reciprocity is invoked, and then the equivalence principle. Mutual Impedance (cont.) 5 The antenna current J 2 ant is that excited by I 2 on antenna 2 when it is by itself (antenna 1 is absent).

6. Reciprocity is invoked one more time. Mutual Impedance (cont.) 6 The mutual impedance is then

7. Summary 7 Mutual Impedance (cont.) J s1 ant = current on antenna 1 when it is excited by I 1 in the presence of open-circuited antenna 2. J s2 ant = current on antenna 2 when it is excited by I 2 in the absence of antenna 1.

8. If the two currents come together to one surface, we have the self- impedance formula for a single antenna: 8 Self Impedance J ant = current on the antenna when it is excited by I. Note : This is a variational expression for the input impedance of an antenna.