Using resistive load to enhance LNA stability (Part 1)

        This paper presents a new method to predict the improvement in stability and noise figure by adding resistive loads to the input and output ports of an amplifier. The method is effective over a wide frequency range and can be used for both low noise amplifiers (LNAs) and broadband amplifiers. 
        
        Designing an effective low noise amplifier (LNA) requires high performance transistors. However, most suitable devices are potentially unstable at microwave frequencies, leading to oscillations. Fortunately, resistive loading of the transistor input or output prevents oscillations in all passive and load terminals at the target frequency band, while problems exist at other frequencies, making out-of-band oscillations possible. A 

        separate stability parameter ? represents the stability of the amplifier. ?>1 is necessary and sufficient for the amplifier to be unconditionally stable. This parameter can be defined as follows: 
        The ? parameter is a quality factor, with increasing ? values ​​indicating improved stability when: Δ = S11S22 - S12S21. For example, Figure 1 shows the ? values ​​calculated from the scattering parameters (S-parameters) of a Fujitsu Semiconductor Manufacturing Company FHR02X HEMT amplifier. The figure also shows the regions where the amplifier is unconditionally stable and potentially unstable (covering most of its frequency band). 

        To understand the effect of resistive stability over a wide frequency range, the equivalent transfer parameters of the cascaded two-port system containing the transistors and the stabilizing resistor must be determined. 
        Figure 2 provides an example where the first and last two-port networks in the cascade each represent a component, either in series or parallel, or straight through, and the middle two-port represents a transistor whose transmission parameters are calculated from discrete parameters. The overall stability of this type of network can be obtained from the cascade parameters, and from the conversion from transmission parameters to discrete parameters, the value of ? for the entire configuration is determined using Equation 1. A total of eight different input-output combinations can be used to investigate this technique, depending on whether the resistor is connected in series or parallel to one or both of the active device ports (see table). 
        Once the amplifier is unconditionally stable, it is possible to determine the maximum value of the transducer power gain, Gtmax _. Gtmax _is defined as the power an amplifier can deliver to its load relative to the power it can absorb from the source when the amplifier input and output impedances are conjugate matched, usually achieved by properly designed input and output matching networks. The table shows the calculated values ​​for the eight resistor combination at 2GHz. Increasing the stability factor above 1 directly reduces the maximum transconductance gain Gtmax _. For the other six cases, the same stability factor results in the same power gain. 
        Figure 3 shows ? as a function of frequency from 0.10 to 30 GHz for the nine cases in the table: no, one, and two stabilizing resistors. The inclusion of two stabilizing resistors in the network introduces an extra degree of freedom into the problem. As a result, a systematic search algorithm must be used to find the input-output impedance combination that stabilizes the transistor. The typical search algorithm for obtaining the values ​​assumes a pair of nested loops, with the input resistor values ​​in the outer loop and the output resistor values ​​in the inner loop. The resistor values ​​tried are either increasing or decreasing, depending on whether the resistors under consideration are in series or in parallel. If the resistor pair results in an unconditionally stable amplifier, that is, the stability factor ? is greater than 1 at any frequency considered, the program reports the resistance and frequency values ​​at which the ? value is maximum, and the results are plotted as a function of frequency (curves 6 to 9 in Figure 3). 
        In this paper, the search algorithm is designed to find the resistor pair that provides stability for the transistor over the entire frequency band while keeping the stability factor as close to 1 as possible at 2 GHz (curves 6 to 9 in Figure 3). For this particular transistor, the program proves that it is possible to adjust the value of ? to the minimum over a range of about 10 GHz for parallel-in-series-out (curve 6) and parallel-in-parallel-out (curve 8). The minimum value of ? is not adjustable for series-in-parallel-out (curve 7) and series-in-series-out (curve 9). 

        Figure 3 shows that the amplifier with parallel-in-series-out (curve 6) and parallel-in-parallel-out (curve 8) stabilizing resistors is stable over the entire frequency range with no gain loss at 2 GHz, while the other four combinations of all series or parallel only provide stability over a limited frequency range. 

        This section shows that for the specific case of the FHR02X HEMT, all eight resistive networks can stabilize the amplifier at least over a limited frequency range. In order to apply the technique in a more general case, the network stability for all eight resistive networks is investigated for a series of other resistively loaded microwave amplifiers, applying the techniques presented in this section and the discrete parameters of transistors from different manufacturers. Most of the results for the eight resistive networks are similar to those shown in Figure 3. However, in some cases for some transistors, it was not possible to find a single or paired resistor that gave the overall amplifier a value greater than 1 at all frequencies for one or two of the resistive networks. Therefore, the improvement in stability caused by the resistive load is strongly dependent on the characteristics of the specific transistor, as well as the resistors themselves.