Delays are an essential part of electronics such that a set of instructions can be executed in a specific order. There are two main categories of delays: critical and non-critical. Critical delays are delays associated with systems that require high accuracy, such as an MCU’s crystal oscillator operating at 32 MHz, which oscillates with a period of 31.125 ns, i.e., a HIGH delay period of 15.625 ns and a LOW delay period of 15.625 ns. Non-critical delays are delays associated with systems that do not require high accuracy, such as switching an LED ON for a HIGH delay period of 1000 ms, followed by switching the LED OFF for a LOW delay period of 1000 ms. Another method of establishing a non-critical delay is to use a Resistor-Capacitor (RC) delay circuit, as shown in Figure 1.

Figure 1: RC Delay Circuit

There are four fundamental elements: power source (VDD), resistor (R), capacitor (C), and output voltage (VCAP). Before the VDD voltage is applied to the RC circuit, the capacitor’s voltage remains at 0 V, assuming it is fully discharged. Equation 1 describes the voltage across a capacitor in an RC delay circuit, whilst Equation 2 represents the rise time (𝜏).

\begin{equation}
\tag{1}
V_{CAP}{(t)}= V_{DD}(1-e^{-\frac{t}{{𝜏}}})
\end{equation}

\begin{equation}
\tag{2}
𝜏= RC
\end{equation}

The rise time is the time it takes for the capacitor to go from 10% to 90% of the supply voltage (VDD). There are a couple of reasons why the rise time is not taken from 0% to 100% of VDD. The first reason is because as soon as the power supply to supply VDD is switched ON, the initial voltage is at 0 V. The second reason is due to the fact that a capacitor can never be charged to VDD, due to its exponential charging nature. Ninety percent of VDD is “close enough”.