1.1 Introduction


The field of Radio Frequency (RF) is an exciting field with a wide range of real world applications. Instrumentation in RF has introduced the ability to communicate, through data and voice, over large areas in real time. In the modern world, RF waves are omnipresent and increasing daily. RF is also present in space from naturally-occurring sources. This course will:

  • Give students a basic understanding of the fundamentals of RF
  • Take a look at some of the instrumentation and software used
  • Offer some basic guidance on testing RF
  • Explore some of today’s greatest challenges

You may skip around the class covering sections most interesting to you. The course will track your progress and save updates. You have no time limits and can refer to this course as often as you like.

A complete review of the course should take about 6 hours. You must complete the quiz and all sections to receive a Berkeley Nucleonics Completion Certificate. Your employer may provide up to 0.5 CEU units for this course.

The Basics: Time and Frequency Domain

It is common to measure events with respect to time. Time of flight, for example looks at the time that passes as an object (small element or large airplane) moves from point A to point B. This is considered a Time Domain measurement. Many of Berkeley Nucleonics’ first pulse generators resolved the time domain in nanoseconds, the time it takes light to travel about a foot.

In electronics, time domain measurements are extremely common. When a certain event occurs can be key to the success or failure of a design. While we don’t have the ability to observe some elements of our world at those high speeds, we now have equipment that can. Electrons, for example, are extremely useful, but notoriously small and hard to catch. To observe electronics we can use an Oscilloscope.

Oscilloscopes are one of the most common tools used to perform time domain measurements. In its simplest form, an oscilloscope plots a graph of the voltage at its input with respect to time.

Figure 1: Oscilloscope display showing 2 waveforms

The horizontal axis of the display is showing time and the vertical axis is displaying amplitude. The upper waveform is sinusoidal and the lower waveform is a square wave.

Note: Both waveforms contain elements that repeat with respect to time.

In this way, an oscilloscope can show when events occur, measure the amplitude of the event, and also measure the time between events. When discussing time-varying events, we often use terms from basic wave theory. Let’s take a look at a common wave function, the sine wave, and describe these basic elements in more detail.

The sinusoidal wave (sine) is a time-varying waveform with smooth transitions, that occurs quite frequently in electronics. The sine wave is mathematically represented as:

y(t) = A*sin(2πft + φ)

Where y(t) = A is the amplitude, the peak deviation of the function from zero; f is the frequency of oscillations (cycles) that occur each unit of time; and φ is the phase, specifying (in radians) where in its cycle the oscillation is at t = 0 (Figure 2a). When t is non-zero, the entire waveform waveform is shifted by the amount of φ/2πf seconds (Figure 2b).

Figure 2a: Two In-Phase Sinusoidal Waveforms

Figure 2b: Waveform 1 (yellow) is out-of-phase with respect to Waveform 2

Below is a video of 2 sine waves that are 90 degrees out of phase with each other


The period of a time-varying signal is the smallest amount of time that defines a fundamental repeating element of the waveform. The waveform in Figure 2a is a Sinusoidal Waveform showing the amplitude and one period of the waveform.

The Frequency is the number of such periods that occur during an amount of time. Time and Frequency are linked by the equation below:

f = 1/T

Where f is the Frequency in Hertz (Hz) and T is the waveform period in seconds. Hertz is a secondary unit that represents the inverse of the waveform period (1/s).

Let’s look at the voltage from our wall outlet. In the USA, if we measured the wall voltage with an oscilloscope, we would see that it has an amplitude of appx 110V and a period of 16.67ms. This means that every 16.67ms, the voltage values repeat. What is the frequency of the wall voltage in the USA?

f = 1/T = 1/16.67ms = 60Hz

So, a waveform can be described by its characteristics in the time domain as well as its characteristics in the frequency domain.


Learning the basics of periodic waveforms, like the sine wave, can provide extremely powerful tools that can be used to explain and understand more complex waveforms.

Figure 2a and 2b above show two sinusoidal waveforms with frequency of 10 MHz. Now, let's take a look at two waveforms with different frequencies:

Figure 3: An Oscilloscope displaying a two sine waves with different Frequencies. (10MHz yellow, 20MHz blue)

What happens when we add them together?

Figure 4: Oscilloscope displaying two sine waves (10 MHz yellow, 20 MHz blue) and a combined Resultant Wave (red)

Below is a video showing the addition of two waveforms:


The Waveform Changes

This is known as the superposition principle. You can add sine waves together and the resultant wave can have a drastically different shape than the original waveforms. To put it another way, any waveform can be constructed by the addition of simple sine waves.

Now, let’s discuss some basic terms. The fundamental frequency of the new waveform is the lowest repeated frequency. In this case, the fundamental frequency of the waveform is 10MHz.

The second harmonic is a waveform with a frequency that is twice the fundamental. In this case, the second harmonic is 20MHz (2 x 10MHz). You can continue on in this way to create any waveform. Let's take a look at a special case. If you continue to add odd harmonics (1, 3, 5, 7, 9, etc..), you will build a square wave.

Here is a waveform that was built using odd harmonics:

Figure 6: 10MHz Sine Wave (Yellow) and 10MHz Square Wave (Blue)

Note: The waveform is starting to look more square, but the frequency of the main shape is still 10MHz.

Below is a video showing the creation of a square wave from odd harmonics


If you are curious about oscilloscopes, the following is a basic datasheet on a typical 200MHz Touchscreen Oscilloscope. A cursory review is sufficient:


Frequency Domain

What would these waveforms look like in the frequency domain?

A spectrum analyzer is an instrument that displays the amplitude vs. frequency for input signals. Lets take a look at a 10MHz sine wave on a spectrum analyzer.

If we source a 10MHz Sine wave into a spectrum analyzer, we see a display like this:

Figure 6: 10MHz Sine wave displayed on a spectrum analyzer.

Now if we source a 10MHz Square wave into the spectrum analyzer, we see this displayed:

Figure 7: 10MHz Square wave showing frequency and power of each harmonic

You can see the fundamental frequency at 10MHz, the 3rd (3 x 10MHZ = 30MHz), 5th (5 x 10MHz = 50MHz), and 7th (7 x 10MHz = 70MHz) harmonics are also shown on the display.

The below video shows what the harmonics of a square wave look like when using the FFT function of an oscilloscope


By visualizing the signal in frequency domain, we can easily see what frequencies we are sourcing as well as the power distribution for each frequency. Spectral analysis is critical in designing and troubleshooting:

  • Communications circuits
  • Radio/broadcast
  • Transmitters/receivers
  • Electromagnetic Compliance (EMC) measurements.

In the following Sections, we will explain spectrum analyzer designs and techniques for using the instrument properly. You're off to a great start!