On the realization of immittance inverters with a minimum number of active components

It is proved that in a grounded 2-port (i.e., a 2-port in which both ports have a common terminal which can be grounded) containing resistors and either one operational amplifier (with differential input and grounded output) or one ideal transistor, the admittance parameters are such that If
y_{11}=0
then
y_{21} \leq 0
, and if
Y_{22}=0
then
y_{12}\leq 0
. One consequence of this is that a grounded positive inverter cannot be realized with only one operational amplifier or one ideal transistor (it is known that although the realization of a gyrator requires at least two amplifiers or two transistors, positive inverters can be realized with only one amplifier if only one port is grounded; it is not known whether single-transistor positive inverters are possible). Other consequences concerning the realization of various types of immittance inverters are also discussed.