2.8: Trading Off Gain, Noise, and Stability in Amplifier Design

The design of small signal amplifiers requires a trade-off of gain, stability, and noise figure. This can be further complicated by the bandwidth requirement. So first consider the trade-offs in narrowband amplifier design with input and output matching networks and with no feedback network between the output and input of a transistor. The amplifier consists of three cascaded two-ports, one of which (the transistor two-port) can produce a potentially unstable situation. Whether the amplifier is stable or not depends on the impedance seen looking from the transistor into the output matching network and the impedance seen from the transistor looking into the input matching network. Even in narrowband amplifier design, the designer must be concerned about stability out of band. The amplifier must also be stable no matter what the values of the load or source impedances. This is because in nearly every situation there is a severe penalty if the amplifier becomes unstable and oscillates. The instrument or device in which the amplifier is embedded certainly will not work, but in the case a communication system, the entire communication system could be corrupted and system operation not restored until the offending device is tracked down and turned off.

The impedance presented to the output of the transistor is not the load impedance, it will be modified by the output matching network and by losses in cabling and filters (if any), between the output of the amplifier and the load. As far as stability is concerned, this loss helps as it reduces the range of effective loads presented to the amplifier. Ignoring loss, the amplifier load could be a short circuit, an open circuit, a match, or any combination. Thus on a Smith chart the load could be anywhere. If the output matching network is lossless and of any topology, then the impedance presented to the output of the transistor could be anywhere on the Smith chart. Now if constraints are placed on the matching network, then the region of the effective load on the Smith chart could be constrained, but this involves a more sophisticated design and is something only very experienced amplifier designers would exploit.

This discussion is designed to provide convincing evidence that the amplifier should be designed for unconditional stability. So if the load can be any value, the stability circle on the input plane defines the values of \(\Gamma_{S}\) (the reflection coefficient looking into the input matching network from the transistor) that result in unconditional stability. The matching network must be designed to provide a \(\Gamma_{S}\) that ensures stability no matter what happens to the load. Only in extreme circumstances, say at very high frequencies (where design becomes very difficult) or where there is considerable loss, say in subsequent filtering, would an experienced designer consider designing an amplifier that is not unconditionally stable. Even then design would begin with the unconditionally stable situation and morph into the potentially less stable situation.

The stability discussion above concerns designing for stability no matter what happens to the load. The discussion is similar for designing the output matching network no matter what happens to the source. So there is an apparent flaw in the stability argument. In designing the input and output matching networks for unconditional stability, the procedure described above considers the load being corrupted on its own independent of whether the source is corrupted (e.g. by the failure of a previous stage). If something goes wrong at both the source and the load, then the amplifier could be unstable even after best efforts have been undertaken in design. It is unlikely that both the load and source would be compromised simultaneously.

Now consider the trade-off between gain and the noise figure. This could be a difficult trade-off, but a simple design procedure has been adopted. If the amplifier is the first stage in a cascade of amplifiers, then the preferred choice is that the emphasis for the first stage is to design it for the minimum noise figure and ensure that at least some gain is obtained. In subsequent stages the emphasis is on gain and the noise figure is given little consideration. This trade-off is based on Friis’s formula for the noise figure of cascaded systems, which indicates that if the gain of the first stage is high, then the noise figure of the first stage dominates the system noise figure. A better overall trade-off can be achieved using the optimizer provided in a microwave design tool. However, the manually directed design must be done first or the optimization problem is too difficult.

With wideband designs of a half-octave bandwidth amplifier, the additional problem of achieving stability and the minimum noise figure, or stability and maximum gain, over the frequency band is a further complicating factor. Here the inventive aspect of design is developing a matching network that has the desired frequency response.

Further complicating this is that efficiency and distortion must be considered as well. Even with a small signal, distortion is a concern, as a design goal is minimizing DC power consumed. This is because reducing distortion usually results in increased DC power consumption.