(57) where is the magnetic flux and is the induced voltage. In our setup, the relationship between and is (58) because is parallel to the “measurement” solenoid coil which has turns and cross-sectional area . When we substitute the above into Eq. (57), we have (59) because is a constant. is found by integrating the above (60) Finally, we can substitute the above into Eq. (56) to get (61) which, in principle, is the equation that is used to determine the relative permeability of the garnet. This equation will have to be modified to include the correction for the air gap between the garnet and the coils. This correction will be discussed in section 16.1.4. The witness pieces and measurement setup Each garnet ring is made up of eight sectors glued together with a 3 mm thick alumina ring base. See Figure 50 and Figure 51. Witness samples have been paired with each sector piece and individually numbered by the manufacturer. The samples are 17.8 mm in diameter and 16 mm long. Figure 124 shows an example of a witness sample. The samples are tested in an apparatus designed to provide a uniform magnetic field within the sample throughout the tested range of bias current between 0 to 19.1 A. Figure 125 shows the garnet witness sample test stand at different stages of assembly. The witness sample sits in a box made of MN-60 ferrite as a flux return. MN-60 has a high permeability of 6000. The high permeability of the box ensures that the H-fields are concentrated in the sample. Fig. ?? shows the distribution of B-fields. Figure 125 shows how the witness piece and ferrite box are assembled. An excitation coil and a measurement coil were wound to fit inside the measurement box with the excitation coil surrounding the measurement coil, which fits as closely around the sample as possible. The excitation coil is wound with 183 turns of #14 (0.62 mm) insulated copper wire, and the measurement coil with 80 turns of #34 (0.16 mm) insulated copper wire. The measurement coil has been
(57) where is the magnetic flux and is the induced voltage. In our setup, the relationship between and is (58) because is parallel to the “measurement” solenoid coil which has turns and cross-sectional area . When we substitute the above into Eq. (57), we have (59) because is a constant. is found by integrating the above (60) Finally, we can substitute the above into Eq. (56) to get (61) which, in principle, is the equation that is used to determine the relative permeability of the garnet. This equation will have to be modified to include the correction for the air gap between the garnet and the coils. This correction will be discussed in section 16.1.4. The witness pieces and measurement setup Each garnet ring is made up of eight sectors glued together with a 3 mm thick alumina ring base. See Figure 50 and Figure 51. Witness samples have been paired with each sector piece and individually numbered by the manufacturer. The samples are 17.8 mm in diameter and 16 mm long. Figure 124 shows an example of a witness sample. The samples are tested in an apparatus designed to provide a uniform magnetic field within the sample throughout the tested range of bias current between 0 to 19.1 A. Figure 125 shows the garnet witness sample test stand at different stages of assembly. The witness sample sits in a box made of MN-60 ferrite as a flux return. MN-60 has a high permeability of 6000. The high permeability of the box ensures that the H-fields are concentrated in the sample. Fig. ?? shows the distribution of B-fields. Figure 125 shows how the witness piece and ferrite box are assembled. An excitation coil and a measurement coil were wound to fit inside the measurement box with the excitation coil surrounding the measurement coil, which fits as closely around the sample as possible. The excitation coil is wound with 183 turns of #14 (0.62 mm) insulated copper wire, and the measurement coil with 80 turns of #34 (0.16 mm) insulated copper wire. The measurement coil has been
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