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5.3 Amplifier Design Stages 217 5.3.3.3 Gain circles As mentioned in the previous section, when S12 is not negligible we may use simultaneous conjugate matching to achieve maximum small-signal gain but is there a way to "tune" the gain by tweaking our input or output matching networks as was possible in the case of unilateral matching? The answer is yes! In this section we will be looking at two techniques which allow us to achieve just that! 5.3.3.3.1 Operating Gain Circles Operating gain circles are a very useful graphical tool which allows us to design an amplifier with a specific gain when the unilateral assumption does not apply. These circles may be plotted on a Smith chart and indicate the loci of the terminations which we must present at the output of our transistor to achieve a specific gain (Figure 5.3-10). Figure 5.3-10 Operating Gain Circles Picking a termination along an operating gain circle corresponding to a specific gain value is only the first step of this procedure! Once a value for the output termination has been chosen, a matching network must be designed to transform our load impedance into such a termination. Once the output matching network is in place we must measure the S11 of the transistor yet again to obtain its new input impedance. We must then design a matching network to transform the source impedance into the complex conjugate of the transistor's own input impedance. Only then the gain that was specified by the circle on which we selected the output termination may be achieved! Notice how this technique may be applied to both stable and unstable devices. In the case of stable transistors, the circles will be fully contained within the Smith Chart whereas if the device is potentially unstable, part of the circles may lay outside the chart. This is illustrated in video tutorials 5.8 and 5.9. 0 1.0 1.0 -1.0 10.0 10.0 -10.0 5.0 5.0 -5.0 2.0 2.0 -2.0 3.0 3.0 -3.0 4.0 4.0 -4.0 0.2 0.2 -0.2 0.4 0.4 -0.4 0.6 0.6 -0.6 0.8 0.8 -0.8 Operating Gain Circles Swp Max 6000MHz Swp Min 6000MHz p4 p3 p2 p1 GPC_MAX(1,4) Stable Transistor p1: Freq = 6000 MHz G = 11.381 dB p2: Freq = 6000 MHz G = 10.381 dB p3: Freq = 6000 MHz G = 9.3815 dB p4: Freq = 6000 MHz G = 8.3815 dB Conquer Radio Frequency 217 www.cadence.com/go/awr