RF and Microwave Engineering: Fundamentals of Wireless Communications

6.6 Circulator

The previously discussed passive circuits (matching networks, filters) have two ports. We will now look at circuits with three ports. As discussed in Section 5.4.7 a three-port network cannot satisfy the following conditions simultaneously

• matching (at all ports),
• reciprocity and
• loss-lessness.

In order to construct a practical three-port network at least one condition must be dropped. If we allow losses we can build a power divider that is matched at all ports (see Section 6.7). Furthermore, an interesting non-reciprocal (s_ij ≠ s_ji) network that is matched at all ports is a circulator.

An ideal circulator transfers signals from port 1 to port 2, from port 2 to port 3 and from port 3 to port 1 as shown in Figure 6.32a. The signal flow graph shows that the forward transmission factors are s₂₁ = s₃₂ = s₁₃ = 1. All other scattering parameters are zero (Figure 6.32b). If we consider propagation delay, a more realistic term for the transmission coefficients includes a phase term e^−jφ. The corresponding scattering matrices are

6.45

A non-ideal circulator is usually described by non-zero reflection coefficients ρ, non-zero backward transmission coefficients σ and forward transmission coefficients τ with a magnitude of less than one. The corresponding signal flow diagram is shown in Figure 6.32c. The scattering matrix is given as

6.46

A typical application of a circulator ...