Design of Reactance-to-Reactance Impedance Transformers Based on Conjugately Characteristic-Impedance Transmission Lines (CCITLs) and Meta-Smith Charts (MSCs)

Abstract

This paper proposes a novel technique to miniaturize the size of any reactance-to-reactance transformers (RRTs). These transformers are designed based on conjugately characteristic-impedance transmission lines (CCITLs)and Meta-Smith charts (MSCs). Note that the proposed technique can be effectively applied to popular microwave circuits; i.e., open-circuited and short-circuited tuning stubs as special cases. Numerical results are calculated, analyzed and compared with those of conventional stubs. In addition, the RRT prototype based on CCITLs is designed, simulated and measured to verify the proposed technique. It is found that the properly designed RRT prototype based on CCITLs can provide shorter electrical and physical lengths than those of the conventional RRT prototype indeed.

Generalized Complex-to-Complex Impedance Transformers Based on Conjugately Characteristic-Impedance Transmission Lines

“…A standard TL of length l, possessing the characteristic impedance (Z 0 ), propagation constant (β), and electrical length (θ), is employed to match between a complex output impedance (Z L = R L + jX L ) and a complex input impedance (Z in = R in + jX in ), where θ = βl. In Figure 1(a), the output (Γ L ) and input (Γ in ) reflection coefficients can be expressed as [11].…”

“…where Equations ( 1) and ( 2) are employed to obtain Equation (3). Similarly, Γ L and Γ in are related to the phase relationship in the case of θ in > θ L as [11] R…”

“…The CCIT implemented using a CCITL is shown in Figure 1(b) to match between a complex output impedance Z L to a complex input impedance Z in , where Z ± c , β c and θ c are the characteristic impedances, propagation constant, and electrical length of the CCITL, respectively. Note that Z ± c can be expressed as [11]…”

“…This paper proposes an alternative mathematical model of a generalized CCIT based on conjugate characteristicimpedance transmission lines (CCITLs) to achieve significant size reduction. Note that CCITLs have been introduced since 2004 [9][10][11]. In [9], the basic theory of CCITLs and the Meta-Smith charts (MSCs) were proposed, including their potential applications.…”

“…In [10], quarter-wave-like transformers (QWLTs) based on CCITLs were successfully applied for miniaturized resistance-to-resistance transformers. Recently, a novel reactance-to-reactance transformer (RRT) based on CCITLs and MSCs has been proposed for size reduction [11].…”