Dual-Frequency Decoupling Networks for Compact Antenna Arrays

Table 1

Design equations for calculation of the parallel or series L-C circuit implementations of reactive elements in the decoupling and matching networks. Here, 𝜔_𝑗=2𝜋𝑓_𝑗 represents the angular frequency.

Network elements	Parallel/series	Component values
𝑋𝑖1, 𝑋𝑖2	Parallel	𝐶𝑖=(𝜔1/𝑋𝑖1−𝜔2/𝑋𝑖2)/(𝜔2^2−𝜔1^2)
		𝐿𝑖=(𝜔1/𝑋𝑖1+𝜔1^2𝐶𝑖)^−1
	Series	𝐿𝑖=(𝜔2𝑋𝑖2−𝜔1𝑋𝑖1)/(𝜔2^2−𝜔1^2)
		𝐶𝑖=(𝜔1^2𝐿𝑖−𝜔1𝑋𝑖1)^−1
𝐵𝑖1, 𝐵𝑖2	Parallel	𝐶𝑖=(𝜔2𝐵𝑖2−𝜔1𝐵𝑖1)/(𝜔2^2−𝜔1^2)
		𝐿𝑖=(𝜔1^2𝐶𝑖−𝜔1𝐵𝑖1)^−1
	Series	𝐿𝑖=(𝜔1/𝐵𝑖1−𝜔2/𝐵𝑖2)/(𝜔2^2−𝜔1^2)
		𝐶𝑖=(𝜔1^2𝐿𝑖+𝜔1/𝐵𝑖1)^−1