# Energy Consumption in Digital Systems

Computer Architecture Energy Electronics Energy Consumption Energy Efficiency Digital Systems Telecommunications

Power consumption refers to the amount of energy used per unit of time, and is of great importance in digital systems and, therefore, in computer architectures. Although the real world is analog, digital designers, engineers and electronic computer architects employ a discrete subset of possible signals, where binary variables operating with states 0 and 1 (LOW/HIGH, FALSE/TRUE) are of special relevance and popularity. All these systems are composed of logic gates, allowing to offer all kinds of states and operational combinations, generally built from CMOS transistors, behaving as electrically controlled switches.

Battery life in mobile and portable systems is strongly limited by their energy consumption, being one of the great challenges in mobile devices, embedded IoT appliances (Internet-of-Things), smartphones and all kinds of computer-electronic gadgets. This does not mean that in fixed systems and stationary devices it is irrelevant, as high energy consumption means an increase in electrical costs and promotes overheating problems.

Digital systems consume both static and dynamic power. Dynamic power is the power used to charge the capacitance as the signals change between 0 and 1. Static power, on the other hand, is the power used even when the signals do not change their values and the system is idle.

The logic gates and the wires that link them together provide a capacitance. The energy consumed by the power supply to charge capacitance C to voltage V is CV^2. If the capacitor voltage changes at a frequency f, that is, f times per second, it charges the capacitor \frac{f}{2} times and discharges another \frac{f}{2} times per second. Discharging does not consume power from the power supply, so the dynamic power consumed is as represented in the formula below:

P_{dynamic}\ =\ \cfrac{1}{2}\ C\cdot{}V^2_{DD}\cdot{}f

On the other hand, as mentioned, electrical systems consume current even if they are not in use. When transistors are OFF, they have a small current loss (leakage). The total static current, I, is also called leakage current or quiescent supply current, flowing between V and ground (GND). Static power consumption is proportional to the static current, as shown in the formula below:

P_{static}\ =\ I_{DD}\cdot{}V_{DD}

To understand these implications through a simplified example, consider a portable embedded device, e.g., a smartphone operating on a 16 Wh (watt-hour) battery at 0.944 V. When in use, it operates at 670 MHz, assuming an average on-chip capacitance of about 10 nF, for any given time and its state changes. In addition, when in use, it considers the broadcasting-propagation of the 4G waves as well as the establishment of protocols to ensure quality of service, consuming 1.1 W of power through its integrated antenna. Now, when the device is in power saving and airplane modes, the dynamic power practically drops to zero, as the signal processing and the necessary coprocessors are turned off and deactivated following power saving policies. Even so, the phone has an idle supply current of 53 mA, regardless of whether it is being used or not.

Thus, the battery life of the device has two variants depending on the use of the phone and its communications. If not in use and kept in airplane mode, the static power is 50 mW, making the battery last about 8 days:

\begin{aligned} P_{static}\ =\ 0.053\ \textrm{A}\cdot{}0.944\ \textrm{V}=\ \sim{}50\ \textrm{mW}\\ \\ {\small \textit{Battery\enspace{}life}_{idle}}\ =\ \frac{16\ \textrm{Wh}}{0.050\ \textrm{W}}\ =\ 320\ \textrm{hours} \end{aligned}

On the other hand, if the device is used, the dynamic power is 2.98 W. In addition, it is necessary to consider the static power (the same as in the previous case) and the propagation power by communications and its antenna, accumulating about 4.13 W of consumption, and therefore, limiting the useful life about 83 times, i.e., not even reaching 4 hours of duration.

\begin{aligned} P_{static}\ =\ 0.053\ \textrm{A}\cdot{}0.944\ \textrm{V}=\ \sim{}50\ \textrm{mW}\\ \\ P_{dynamic}\ =\ \frac{1}{2}\cdot{}10^{-8}\ \textrm{F}\cdot{}(0.944\ \textrm{V})^2\cdot{}6.7\cdot{}10^8\ =\ \sim{}2.98\ \textrm{W}\\ \\ {\small \textit{Battery\enspace{}life}_{use}}\ =\ \frac{16\ \textrm{Wh}}{2.98\ \textrm{W}\ +\ 0.050\ \textrm{W}\ +\ 1.1\ \textrm{W}}\ =\ \sim{}4\ \textrm{hours} \end{aligned}

Power consumption of the mobile device when in power saving (airplane mode) or being used in full-mode with 4G, reaching up to 4.13 W and limiting the battery lifetime to just under 4 hours.

These aspects are fundamental to grasp the importance of energy consumption and battery utilization, how electronic designs influence these characteristics, as well as some of the metrics to determine the possibilities for exploiting energy efficiency in our applications and devices.

Updated article: selectable and copyable formulas, vector graphics as a summary, as well as visualization and accessibility improvements.

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