2.2 Some Common Assumptions
The voltage symbol that we will use in this book implies an unlimited source of current with zero rise time. This perfect voltage source does not exist, but it will be used to avoid adding complications. An instantaneous voltage implies an instant electric field. Since this field stores energy, the generation of a field in zero time requires infinite power. Similarly, the instantaneous flow of current implies a magnetic field and again this field stores energy. The generation of field energy in zero time would again imply infinite power. If we are careful, we can use an ideal step voltage source or a step current, and we will not get into trouble.
The ideal switch does not exist. Even if the switch were mechanical, the capacitance before the moment of contact must get very large. If the switch is solid state, the closure is really a nonlinear dynamic impedance. We will use the ideal switch in our discussions even though it does not exist.1
A resistor at the end of a transmission line is called a termination. A resistor termination is a complex network because every resistor has a distributed series inductance, a parallel distributed capacitance, and skin effect. We use these circuit terms to make the point that every component is complex if examined closely. In microwave work, a wave guide termination is not a simple resistor. A valid terminating resistor must be planar in character and it must cover the entire end of the guide. We will often be terminating a transmission line with a resistor where picoseconds are of interest. One picosecond is one cycle at 1000 GHz, which is well above microwave frequencies. When we show a resistor on a schematic, we will assume it is a valid resistor at the frequencies of interest.2 It is important to keep in mind that we are always making assumptions. Ideal components do not exist except in our equations and maybe only in our minds. We need these ideal elements to simplify our analysis. We need these ideal elements to start any sort of discussion.