GENERAL DESCRIPTIONThe 90°hybrid is widely used in many applications, such as phase shifters, balanced mixers, IQ modulators etc., and implemented either by means of distributed or lumped elements. In this paper a lumped-element 90°hybrid is built using active inductances to achieve a controllable attenuator/amplifier in the 5.8-GHz ISM band.The selected topology for the 90°hybrid is shown in Figure 1. This is a well known structure, widely discussed in the literature [1,2]. The elements' values are dimensioned according to the following formulae:The problem encountered in designing a 90°hybrid with lumped components resides, mostly, in the losses introduced by the planar inductors. The most obvious detriment introduced by the losses is the reduced coupling factor at the coupled ports. Another important effect is the shift of the natural resonant frequency of the structure with a degradation in the hybrid performances.In our case, the attractive property of this topology lies in the fact that it uses grounded inductors only, allowing therefore the use of the grounded active inductor reported in [3].The basic idea is to implement such inductors in active form and let two of them have adjustable positive/negative resistance in order to achieve a variable attenuation (Figure 2). In fact, assuming that the loading at the coupled ports is the same, input and output matching at the mutually insulated ports is perfect. As is well known, by choosing reflective terminations, the power associated to the input signal is devolved to the load connected to the isolated port. Conversely, if the loads connected to the coupled ports are made to be progressively more absorbing, the portion of the input signal that reaches the isolated port is accordingly reduced as the dissipation at the coupled ports increases. Finally, if a load with some moderate negative resistance is connected to the coupled ports, a reflection coefficient greater than unity is achieved and the loaded hybrid acts as an amplifier. The value of the negative resistance must not be excessive in order to avoid circuit instability.
THE ACTIVE INDUCTORA simple configuration for the active inductors ensures compactness and low power consumption. As demonstrated in [3], an active inductor with very high Q can be implemented with a few components, making use of a common-gate PHEMT with the gate connected to the ground by a short transmission line or a lossy planar inductor. In Figure 3 the basic scheme of such an inductor is reported.Provided that the operating conditions are satisfied, as stated in [1], the active inductor exhibits approximately the following input impedance: One attractive capability of such an active inductor is the possibility to vary the quality factor without changing the inductance value. This can be achieved by controlling the transconductance of the PHEMT g m , for example, by directly varying the dc bias voltage. As already anticipated, a negative resistance can be associated to the active inductance when biased beyond a specified dc voltage....