Overview

From APPLIED MICROWAVE & WIRELESS, VOL. 11, NO. 11, NOVEMBER 1999

This article describes an approach to the design of VHF lumped-element hybrid couplers that have broad bandwidth and do not require perfect magnetic coupling between the inductors. This design may be a useful alternative in cases where nearly ideal coupling cannot be achieved.

The classical design for a lumped-element VHF quadrature hybrid was described 20 years ago by Ho and Furlow [1, 2]. This circuit, shown in Figure 1, uses a pair of perfectly coupled inductors (i.e., having a unity coupling coefficient) and two capacitors.

Figure 1: Single (a) and multisection (b) couplers from references [1] and [2]. The inductors are assumed to have perfect magnetic coupling, and the transmission line impendance Z ₀ is equal to the port impendance.

The simple single-section coupler, however, is narrowband, but the bandwidth can be increased substantially by connecting two of them by transmission lines. Unfortunately, the transmission lines can be uncomfortably long, especially at low frequencies.

Design equations for this coupler are fairly simple. We first define the coupling ratio, k:

The design equations are:

where L and C are as shown in the figure, and ? is the center frequency.

Since the magnetic coupling must be perfect, the mutual inductance of the coupled inductors must equal the self inductance, L. In practice, tight coupling is achieved by winding the coils as a twisted pair of wires on a ferrite toroid.