# Signals and Frequency

## Highlights

•     Electronic systems use voltage signals to exchange information
•     Voltage signals can be classified as digital or analog
•     Analog signals transmit information by varying continuously on a fixed interval
•     Digital signals switch on and off betwen discrete voltages
•     The “height” of the voltage signal is called the amplitude
•     The frequency of a singal is one divided by the time period between two peaks

## Notes

A signal is anything that conveys information about a process or phenomenon. Almost anything that is changing either in time, space or in both could potentially be a signal because if we measure it, we might be able to gain some sort of information from it.

Think of a signal as a message. When different components want to talk to one another, they communicate using signals. A very important type of signal is an electrical voltage signal. Electrical components talk to one another by varying the voltage a conductor like a wire. These fluctuations in the voltage let the component send and receive messages between different points in a circuit.

Since signals are changing in time, it is convenient to use some measures that describe how the signal changing in time. If a signal is cyclic – that is, as time passes the signal repeatedly returns to a given value, we refer to that signal as a type of wave. Each time the wave starts at a given value and then returns to that value, we say it has completed one cycle.

One important characteristic of a wave is its frequency. The frequency is the number of cycles the signal completes in a given amount of time. Usually, the units of frequency are Hertz (Hz). One Hertz is defined as one cycle per second.

What if we were to take the reciprocal of Hertz (a fancy name for 1/Hz). We would get seconds/cycle, or equivalently seconds per cycle. This quantity is called the period. The period is useful because if we want to know the frequency of a signal, we can measure the time it takes to complete one cycle, and then take the reciprocal of the result. This gives us the frequency we are looking for in Hz.

The amplitude of the wave is the biggest distance between the value of the signal at any given time in a cycle, and a reference point. This can be thought of as the “height” of the wave. All electronic devices use voltage signals to communicate messages and information. Take for example a microphone connected to a speaker. When you talk into the microphone, specialized components convert the sound into a voltage signal. The voltage in the microphone circuit goes up and down as the sound entering the microphone changes. On the other end of the wire, the speaker reads these changes in the voltage and reconstructs the same sound that was used to generate the voltage signal.

Voltage signals can be classified into two key types: analog and digital.

Analog signals transmit information by varying continuously on a fixed interval. This means that an analog voltage signal can take on any voltage between two limits such as +5V and −5V. The picture above depicts such an analog signal. Think of an analog signal as being similar to the volume on a pair of headphones. You can change the volume to any value you want between silent (volume of 0%) and the maximum volume (100%). In fact, the voltage driving a speaker is an analog voltage signal.

On the other hand, a digital signal is a signal that is only able to switch between two distant voltages. For example, many electronic devices operate using a digital voltage signal that changes between either 0V or +5V. We often describe the value of a digital signal as being either “on” or “off” where “on” corresponds to the greater of the two voltages, and “off”corresponds to the smaller of the two values. A digital signal transmits information by encoding the information into different patterns of voltages pulses. This is just like how Morse code encodes letters: depending on the length and number of “on” and “off” pulses and the sequence of these pulses, one person can send a message to another person. In a digital signal, we often refer to the signal as “high” when it is on and “low” when it is off.

There are many ways to encode information so that it can be transmitted via a digital signal. A common one called Pulse Width Modulation, or PWM for short, is used in many electromechanical systems. PWM works by sending a sequence of voltage pulses. A pulse is a single cycle of digital low to high, and then back to low. The pulses in PWM all have the same period, that is each one lasts for the same amount of time as the others. We call this the pulse width. PWM works by varying the percentage of the pulse width where the voltage is high. In other words, the message to be transferred by the PWM is encoded as a duration of time that the pulse width is “on”, hence the name pulse width modulation. The percentage of the pulse width that is “on” is called the duty cycle. For example, a desired motor speed of 100 RPM might correspond to a duty cycle of 10%, 200 RPM a duty cycle of 20%, 300 RPM a duty cycle of 30%, and so on. 