Electromagnetic decoupling and complexity

Abstract

Abstract-In radio-frequency systems that drive coupled dissipative loads, the matching network between the amplifiers and their loads needs to account for the coupling. With N amplifiers driving N loads, a favorite choice is a "decoupling" network, which is a lossless reciprocal network that has N input ports connected to the sources and N output ports connected to the loads. The decoupling network transforms the coupled impedance of the loads into the uncoupled characteristic impedance of the sources. Any incident signal at the input ports of the network is transferred, without reflection, to the loads. Decoupling networks can be realized by generalized Π-networks of lumped and distributed impedances, depending on the design frequency. Although the impedance requirements of the network are unique, its realization is not, and networks that involve many impedances can be complex to lay out on circuit boards. In this paper, we establish that a decoupling network requires a minimum of N 2 +N impedances for N arbitrarily coupled loads, and provide a systematic method for realizing this lower bound.

Decoupling and Matching Strategies for Compact Antenna Arrays

“…In [13] a general method is outlined to design DMNs for arbitrary number of antenna elements. For a simple design approach the number of necessary circuit elements is given by 2N 2 + N , which can be reduced to N 2 + N with a more elaborate technique.…”

“…For a fair comparison of the three approaches we restrict the detailed analyses and simulation to an array of only two antennas elements. This is justified by the fact that the complexity of all DMN designs is unfortunately growing quadratically with the number of antenna elements N (it grows at least with N 2 + N as shown in [13]), the implementation of DMNs is limited to a low number of antenna elements, say 2, 3 or at most 4. Nevertheless these small arrays are still useful for massive MIMO, because they pave the way to implement a massively large array with a reasonable large number of such small subarrays, each of them with very few antennas, say 2 or 3.…”

A novel iterative method for simultaneously conjugate matching of N‐port networks

“…Assume the S matrix of the matching network is S M and the S matrix of the original network is S L . According to reference 14 the S parameters of the total network in Figure 1 should be: $$${S}_{\mathrm{new}}=A+B{S}_{L}{({I}_{N}-D{S}_{L})}^{-1}C,$$$where I N is the unity matrix with order N and A , B , C , D are N × N matrix divided from S M , as indicated in Equation (). It should be noticed that the inversion in Equation () always exits for any unconditionally stable networks 15 …”

“…Assume the S matrix of the matching network is S M and the S matrix of the original network is S L . According to reference 14 the S parameters of the total network in Figure 1 should be:…”

“…Arranging from fewer ports to more ports, a 2-port network, two 3-port networks, a 2 × 2 multiple input multiple output (MIMO) antenna array and a 10-port network will be matched. The optimization target is to minimize ε in (14), which is the maximum magnitude of diagonal elements of S new .…”