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48 DESIGN007 MAGAZINE I OCTOBER 2019 will be sqrt(1-0.01) ~0.995, and this matches what we get from the simulated response. The second example is fundamentally dif- ferent. The simple fact that we included a series resistor in the circuit made the cir- cuit lossy. Though the conservation of ener- gy principle still applies, now in the power sum, we would also need to include the pow- er lost by dissipation across the series resis- tor. We could follow this approach to calcu- late the signal magnitude at the output, but we can also use some other simple tricks to get an answer. In Figure 4, looking into the T 1 transmis- sion line on the left, its input impedance is 50 ohms, regardless of the frequency, because we deal with the input impedance of a matched- terminated lossless transmission line. Based on this realization, we can draw a simplified equivalent circuit (Figure 6). Looking into the circuit from the left, we see the sum of R s and Z 02 , or 55 ohms. From the 2V source voltage, together with the 50-ohm source impedance, this input impedance creates a 2*55/(55 + 50) = 1.0476 ~1.05 V signal, just as we see in Figure 4. From this input signal, the 50/(55 + 50) voltage attenuator produces approximately 0.95 V, again, as we see in Figure 4. The previous two examples represent the bounding limits we have to deal with in prac- tice when we have lossy or lossless passive networks. These two extreme conditions can simply be plotted in spreadsheets in a normal- ized fashion. Figure 7 can be applied to cas- es similar to Figure 2. The fact that the cir- cuit does not dissipate power is represented by a (lossless) reactance in series to the lossless transmission line. Figure 6: Simplified equivalent circuit of the network shown in Figure 4. Figure 7: Calculated return loss (RL) and insertion loss (IL) of circuits similar to shown in Figure 2.