The first step is to construct the lattice network. UHPFRC is considered to be composed of two phases, that is, the matrix and fibers .
After the lattice network construction, the mechanical properties of all the beams have to be assigned.
At every step, a prescribed force or displacement is applied on the lattice network, and the stresses in the beams can be calculated.
In the lattice network, the arrow pointed nodes at the bottom were fixed, and a prescribed displacement was imposed on the arrow pointed nodes at the top for every step.
Since the main goal in designing double-Y baluns is to provide a transition between balanced and unbalanced transmission lines without an impedance transformation, the first case analyzed is when [Z.sub.bal] = [Z.sub.unbal] = [Z.sub.0], that is, when the equivalent circuit of the double-Y baluns is a symmetrical lattice network with Z-parameters
Due to the reciprocal normalized impedances [Z.sub.a]/[Z.sub.0] and [Z.sub.b]/[Z.sub.0] (-jcot[Theta] * jtan[Theta] = 1), this type of symmetrical lattice network is known as a constant-resistance network.(7) When terminated with a characteristic impedance [Z.sub.0], this lattice has an input impedance that is a pure resistance equal to [Z.sub.0].
The structure is analyzed as a symmetrical lattice network with serial impedance [[Z.sup.*].sub.a] and parallel impedance [[Z.sup.*].sub.b] as
Four different realizations of double-Y baluns are shown in Figure 1: microstrip-to-slotline,(3) CPW-to-slotline,(4) [CPW.sub.FGP]-to-CPS(5) and [CPW.sub.FGP]-to-parallel microstrip baluns.(6) According to the equivalent circuit,(5) double-Y baluns are symmetrical lattice networks with equal characteristic impedances of the balanced and unbalanced lines.