Designing an effective low noise amplifier (LNA) requires a high-performance transistor. But most suitable devices are potentially unstable at microwave frequencies, leading to oscillation. Fortunately, resistive loading at the input or output of the transistor can prevent oscillation at the frequency of interest for all passive source and load terminations, ^{1- 4} but stability at other frequencies remains problematic, and out-of-band oscillations are possible.

Work reported in 1992 detailed a single stability parameter, µ, to characterize amplifier stability and prove that the condition µ > 1 is necessary and sufficient for unconditional amplifier stability. ⁵ This parameter can be defined by:

where:

Δ= S₁₁S₂₂—S₁₂S₂₁ Parameter µ serves as a figure of merit with increasing values of µ indicating greater stability. As an example, Fig. 1 shows µ computed from manufacturer's scattering parameters (S-parameters) for a model FHR02X HEMT amplifier from Fujitsu Compound Semiconductor. ⁶ It also shows the regions where the amplifier is unconditionally stable and potentially unstable (over most of its frequency range).

To understand the effect of resistive stabilization over a broad range of frequencies, it is necessary to determine the equivalent transmission parameters of a cascaded two-port system that includes the transistor and any stabilizing resistor networks. Figure 2 offers an example, where the first and last two-ports in the cascade each represent one element, either a series or parallel resistor, or a through connection, while the center two-port represents the transistor with transmission parameters computed from its scattering parameters. The stability of an overall network of this type can be found by cascading the transmission parameters, converting from transmission to scattering parameters, and then applying Eq. 1 to determine the value of µ for the overall configuration. Eight different input/output combinations are available for investigation with this technique depending upon whether resistors are connected in series or parallel to one or both of the active device's ports (see table).

Once an amplifier is unconditionally stable, it is possible to determine the maximum transducer power gain, G_Tmax. Parameter G_Tmax is defined as the ratio of the power delivered to the load by the amplifier to the power available from the source under the condition that the amplifier's input and output impedances are conjugately matched, usually through the appropriate design of input and output matching networks. ⁷ The table shows value for G_Tmax for the eight resistor combinations computed at 2 GHz. Increasing the stability factor beyond unity directly reduces the maximum transducer power gain, G_Tmax. For the other six cases equal stability factors lead to equal power gains, as predicted in ref. 8.

Figure 3 shows µ as a function of frequency from 0.10 to 30 GHz, for the nine cases in the table: with no, one, and two stabilization resistors. Networks containing two resistors introduce an additional degree of freedom into the problem. As a consequence, use of a systematic search algorithm is necessary to find input and output resistance combinations that stabilize the transistor. A typical search algorithm for obtaining resistor values consists of a pair of nested loops, with the input resistance value in the outer loop and the output resistance value in the inner loop. Initial resistance values are incremented or decremented, depending on whether the resistor in question is connected in series or in parallel. If the pair of resistors results in an unconditionally stable amplifier, i.e., the stability factor µ, is greater than unity for every frequency examined, the routine reports the resistance values along with the frequency where the minimum value of µ occurs and plots the results as a function of frequency (as in curves 6 to 9 of Fig. 3).

For this work, the search algorithm was designed to identify resistor combinations that stabilize the transistor at all frequencies while providing a stability factor as close to unity at 2 GHz as possible (curves 6 through 9 of Fig. 3). For this particular transistor, it proves possible to adjust the minima of µ for the parallel resistance input/series resistance output (curve 6) and parallel resistance input/parallel resistance output (curve 8) to approximately 10 GHz. The minima of µ for the series resistance input/parallel resistance output (curve 7) and series resistance input/series resistance output (curve 9) combinations was not adjustable.

Figure 3 shows that amplifiers with the parallel resistance input/series resistance output (curve 6) and parallel resistance input/parallel resistance output (curve 8) are stabilized over the entire frequency range without gain penalty at 2 GHz as compared with the four series only/parallel only single resistor combinations that provide stability only over a limited frequency range.

The results of this section demonstrate that, in the particular case of the FHR02X HEMT, all of the eight resistive networks are able to stabilize the amplifier over at least a restricted range of frequencies. In order to apply the technique in a more general way, the stability of a number of other resistively loaded microwave amplifiers were examined by applying the technique presented in this section with all eight resistive networks using manufacturer provided scattering parameters for the different transistors. Most of the results for the eight resistor networks obtained from this investigation are similar to those presented in Fig. 3. For one or two of the resistor networks in the case of some of the transistors, however, no single resistance or combination of resistances was found to result in a value of µ greater than unity at any frequency for the overall resistively loaded amplifier. Thus, the stability improvement due to resistive loading depends strongly on the characteristics of the individual transistors as well as the values of the resistors themselves.

Noise performance is often a critical-factor for microwave amplifiers. While noise is unavoidable, and adding resistance to amplifiers inevitably decreases the output signal-to-noise ratio, different resistive network configurations can have significantly different effects on noise performance. For this reason, it is important to predict the effect of the various resistive stabilization techniques on the overall noise figure of the amplifier in order to facilitate design trade-offs between amplifier stability, gain, and noise performance. A network approach with scattering parameters is feasible because the noise performance of active devices is described in terms of system reflection coefficients. This is illustrated by Fig. 4, which models the resistors as lossy, mismatched two-ports in a cascade network. Amplifier noise is increased by the resistive two-ports as a result of signal attenuation and the impedance mismatch between the cascade-connected ports.

In Fig. 4, considering signals propagating to the right, an input matching network (IMN) transforms the source impedance Z_g into the appropriate source reflection coefficient Γ_S while an output matching network (OMN) transforms the load impedance Z_L into the appropriate load reflection coefficient Γ_L. These matching networks are designed to provide the appropriate impedance transformations necessary to achieve maximum transducer gain, minimum noise figure, or any other amplifier specifications as necessary to meet system requirements.