The bandwidth of an amplifier is limited by both the frequency-dependent transconductance of the active device and by the device parasitics. The frequency-dependent transconductance is most significant with FETs as the basic operating control mechanism at the gate is the field produced at a capacitor. Thus the transconductance of a FET varies as the inverse of frequency. With unpackaged transistors, the device parasitics are capacitors. These are augmented by inductances and transmission line effects in packaged devices. Also the feedback capacitor between the collector/drain and base/gate becomes important at higher frequencies. Ignoring the feedback capacitance and thinking just about the input of the transistor, the input of the transistor is a capacitance sometimes in series and sometimes in parallel with a resistance, with the resistance describing the absorption of RF input power by the transistor.
There are two main approaches to wideband amplifier design. One is the synthesis of a matching network that provides a match over a bandwidth that is rarely more than one-half octave wide at microwave frequencies. One way of visualizing the design difficulty is to realize that a simple circuit comprising a resistor and a capacitor (this could represent the input and output equivalent circuits of an active deice) have a locus with respect to frequency that rotates clockwise on a Smith chart. Matching requires that the complex conjugate of the impedance be matched, so matching network design requires that a circuit be synthesized that has a counterclockwise rotation on the Smith chart. Such a circuit can be realized using a transmission line network, but matches over one-half octave of bandwidth are usually all that can be achieved. Another approach to wideband amplifier design is to use multiple active devices and incorporate the device parasitics into input and output transmission lines. This distributed amplifier approach can realize amplifier bandwidths of two or more octaves.
A third approach, which was considered through a case study, is to consider the design problem as a filter synthesis problem. Indeed, following the active device directly with a filter and bypassing the matching network can broaden the amplifier bandwidth by eliminating the bandwidth limiting effect of matching to a specific system impedance. The necessary impedance transformation is performed in the filter. That is, the doubly terminated filter network has one impedance at the first port (e.g., the lower output impedance of the amplifier) and another impedance, say the system impedance, at the second port.