**4. Nonreciprocal devices**

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>45</sup> <sup>50</sup> <sup>55</sup> <sup>60</sup> <sup>65</sup> <sup>70</sup> <sup>75</sup> <sup>80</sup> −35

(a)

structure has been determined (see Fig. 17).

(bottom row) excitation calculated at *f*<sup>0</sup> = 8.2 GHz

Length (mm)

S11 S21 S31 S41

Phase difference (deg)

**Figure 16.** Scattering parameters of CFCL junction versus length of ferrite section: (a) magnitude and (b) phase

Similarly to the planar case presented in section 3.1, in order to illustrate the nonreciprocal properties occurring in the investigated CFCL junction, the power concentration along the

−3 −2 −1 <sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> −3

−3 −2 −1 <sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> −3

**Figure 17.** Power density and transversal field distribution in the CFCL section for even- (upper row) and odd-mode

Furthermore, the distributions of the electric and magnetic fields in the input (*z* = 0) and output ports (*z* = 26 mm) of FCL junction providing 45 ◦ Faraday rotation angle have been calculated. In the analysis, the even- and odd-mode excitations of the junction were assumed. The obtained results confirm the nonreciprocal behavior of the designed CFCL junction.

x (mm)

x (mm)

z = 0

z = 0

y (mm)

y (mm)

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>45</sup> <sup>50</sup> <sup>55</sup> <sup>60</sup> <sup>65</sup> <sup>70</sup> <sup>75</sup> <sup>80</sup> −20

(b)

(arg(S31)−arg(S41)) (arg(S32)−arg(S42))

> Re{E} Re{H}

> Re{E} Re{H}

y (mm)

y (mm)

Length (mm)

−3 −2 −1 <sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> −3

−3 −2 −1 <sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> −3

x (mm)

x (mm)

z = 26mm

z = 26mm

Re{E} Re{H}

Re{E} Re{H}

−30 −25 −20 −15 −10 −5 0

difference

Magnitude S (dB)

134 Advanced Electromagnetic Waves

In this section, the results of investigation of nonreciprocal devices made in both the planar and conformal line technology are presented. Section 4.1 presents the results of the three-port circulator realized in slotline technology. Section 4.2 presents the results of a double isolator realized in microstrip coupled lines technology. In Section 4.3, the results of the four-port circulator realized utilizing cylindrical ferrite coupled line section are discussed.
