Energy Fundamentals of Radio

Chapter 4Noise in Communications Systems

Stepping out of the analytical weeds for a moment, it is fair to ask: Why should sending information require any energy at all?

It is a deep and interesting question that is hard to tackle in a completely general way. We can help ourselves out by being specific, and asking why communications using electronic equipment requires energy.¹ It turns out that our electronic communications engines, which internally represent information as voltages, require energy to run because (1) there is capacitance from every circuit node to ground, and (2) because noise is everywhere.

We looked deeply at the energy costs associated with driving capacitors in Chapter 3. To see how noise concerns might have an impact on our energy requirements, it is helpful to return to the resistor–capacitor $(RC)$ circuit of Figure 3.4. If there were no noise in the world, we could imagine using very accurate measurements of $v_0(t)$ to make this capacitor a memory cell of very high resolution. For example, if we wanted to encode one million possible values on the capacitor, we would be free to do so even if the source voltage was limited to a range of 0–1 V. In this case, we achieve our aim with discretization steps of $1\mathrm{\mu }\text{V}$, and the maximum energy we would ever need to store on the capacitor would be ${\displaystyle \frac{1}{2}}C{(1\mathrm{V})}^2$.

However, suppose that there is noise in the system. And by noise, what we mean is the following: If we take a large number of measurements of $v_0$ for a fixed $V_{\mathrm{A}}$, the ...