### Section 4: Observations

The reader has just gone through many steps to create a simulation (with practice, this is a quick simulation to set up). At this point, it is useful to shift focus away from learning how to perform the simulation, and consider what we are simulating. In particular, we are performing an RF analysis of the same circuit that we analyzed for steady state voltages in the previous lesson.

By selecting a transmission line that is 90˚ at our frequency of interest, 1GHz, we have created a “quarter-wave transformer”. In particular, when the transmission line's impedance is the geometric mean of the source and load impedance, then at that frequency the reflection will be minimized. The geometric means is:

Looking at Figure 3.15, we observe that at 1GHz, the system is perfectly matched. No energy is reflected back to the source, and Figure 3.16 shows us that all of the energy is delivered to the load. We could have gotten this result (at a single frequency) with a Wave Bounce Diagram using complex voltage waves. However, in about the time it would take to do the Wave Bounce diagram at a single frequency, we have the match versus frequency. Looking at Figure 3.15, we can quickly observe that the match stays pretty good from 0.8GHz – 1.2GHz, or a 40% bandwidth.

**Main
Point**

Even if one has certain expectations of
how an RF circuit should behave, simulating the circuit can provide
greater insights and will generally be less error prone than solving
by hand.