6.10 Cross Junction

The cross junction and its equivalent circuit are illustrated in Figure 6.110. It is commonly used in matching and filter networks. As discussed in Sections 6.8 and 8.1.3 low impedance stubs suffer from the excitation of the first higher-order mode H _[10] ( HE ₁) on the stub. Although operating below cutoff the parasitic local wave can severely influence the quasi-TEM response. This can be avoided by replacing a low impedance stub by a cross junction with open-ended branches having twice the impedance value of the single stub, thus approximately doubling the cutoff frequency.

Figure 6.110: Cross junction and related equivalent circuit. (From [27], 1976 IEEE. Reprinted with permission.)

The following equations have been proposed by Garg and Bahl [40] for the equivalent circuit parameters referred to alumina substrate ( ? _r = 9.9).

(6.227)

(6.228)

(6.229)

where C ₊ relates to C by the relation C = C ₊/4. Accuracy is supposed to be within 5% in the following parameter range: C ₊: 0.3 ? w ₁/ h ? 3.0 and 0.1 ? w ₂/ h ? 3.0; L _v( v = 1, 2, 3): 0.5 ? ( w ₁/ h, w ₂/ h) ? 2.0. Normalized L ₂ can be calculated from (6.228) by interchanging w ₁ and w ₂. From Figures 6.111 to 6.113, the equivalent circuit parameters can be...