## 1.1 Introduction

__Introduction__

__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)*

*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

*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**.

__Superposition__

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!

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