ECE Student Success Toolkit – Thinking at the Speed of Light

Blog Post created by BradJolly on Nov 2, 2018

The previous blog post focused on generalized number bases – an essential concept of electrical and computer engineering (ECE) that is often not covered well at the high school level. Another area where pre-college preparation often falls short of college ECE expectations is the relationship between frequency, period, and wavelength for electromagnetic waves. This is often covered briefly in high school physics and chemistry courses, but those courses typically use scientific notation instead of engineering units. As a result, students cannot mentally translate among engineering units of frequency, period, and wavelength at conversational speeds.

Relationship between frequency, period, and wavelength

As a reminder, this table summarizes the basic relationships between frequency, period, and wavelength of electromagnetic waves in a vacuum.

 Frequency Period Number Word / Abbreviation Number Word / Abbreviation Wavelength 1 Hertz (Hz) 1 Second (s) 300,000 km 1,000 Kilohertz (kHz) 0.001 Millisecond (ms) 300 km 1,000,000 Megahertz (MHz) 0.000001 Microsecond (μs or us) 300 m 109 Gigahertz (GHz) 10-9 Nanosecond (ns) 300 mm 1012 Terahertz (THz) 10-12 Picosecond (ps) 300 μm 1015 Petahertz (PHz) 10-15 Femtosecond (fs) 300 nm

Applications – RF, circuit boards, and design validation

Engineers discussing wireless signals may talk about a 2.4-GHz signal, and it is helpful to be able to think of the associated period as being a bit more than 400 picoseconds. Similarly, a 5-GHz signal has a 200-picosecond period. Given the increasing diversity of radio frequency (RF) applications, especially those associated with the growing Internet of Things (IoT), an intuitive understanding of frequencies and their various physical properties is helpful to ECE students.

This concept is also critically important in designing circuit boards and interconnects. Electromagnetic waves propagate at approximately 3×108 meters per second (the “speed of light”), so the wavelength of a 1-GHz signal in a vacuum is 30 cm (about one foot). Depending on the physical material, the propagation speed of a signal in a circuit board or cable may be significantly slower, so seemingly minor changes in circuit layouts can cause significant propagation delays and timing challenges in high-frequency circuits.

Furthermore, understanding this concept is helpful in design validation. For example, suppose you need to measure a signal’s edge with a rise time of 15 nanoseconds. How fast must you sample that waveform to accurately catch that edge, including overshoot and any ringing that may occur? Facility with mental math will help you make correct test choices quickly.

Summary

The fundamental arithmetic of electromagnetic waves occurs with great frequency in ECE coursework and in professional practice after college. The high school student who becomes adept with the various relationships in engineering units will start ECE studies with a significant advantage.