Lesson 22

Waveforms and Measurements

A waveform is a graphic representation of a signal over time. The signal that shows on an oscilloscope can be a simple sine wave. It can also be more complex forms like a square, sawtooth or triangle. 

A sine wave is not pure, especially when modulated. For instance, the voltage may fluctuate up and down. To calculate the average voltage in a signal waveform use Root Mean Square or RMS. There are benefits to making voltage measurements using a true-RMS calculating meter. When you use a true-RMS calculating meter, RMS is measured for both sinusoidal and non-sinusoidal signals.  Sinusoidal is the term for a pure sine wave. Non-sinusoidal waves are sawtooth, square, or other waveforms. 

When analyzing a waveform, you can use a Fourier analysis. That will define the waveform in terms of mathematical functions. Here’s an example. A Fourier analysis demonstrates that a square wave is made up of a sine wave plus all its odd harmonics. 

Fourier analysis of square wave

Another complex waveform is an SSB phone signal. Signal power is an important measurement for SSB. We’ll evaluate the SSB signal power using PEP. 

The approximate ratio of PEP-to-average power in a typical single-sideband phone signal is 2.5 to 1.

PEP can vary from one ham to another based on your speech characteristics like your tone of voice and how you speak. Therefore, every waveform will be slightly different as well. Since everyone speaks a little differently, speech characteristics determine the PEP-to-average power ratio of a single-sideband phone signal.

Graph of SSB signal

 

Analog and Digital Interchanges

Remember that modern radios use a combination of analog and digital circuits. Signals are converted between the two modes in the radio or elsewhere. That’s done with ADC’s and DAC’s. Those are Analog to Digital Converters, and Digital to Analog Converters.

Microphones are analog devices. You speak into them and the vibrations are turned into voltage changes. To get that audio into my computer, I use an analog to digital converter or ADC. Typically, an ADC takes the analog signal’s voltage or current and converts it to a digital form. You know, to Ones and Zeros. Those can then be managed digitally. This ADC process might use successive approximation as one type of analog-to-digital conversion. With successive approximation the analog input is applied along with a clock signal. Then a binary search is performed. Finally, the output is converted to digital data.

Again, we’re going to show you some schematics to explain how these functions work. For this lesson, none of these will appear on the exam. 

ADC process diagram

Lots of analog data comes into a software defined radio. Your received signal, or your microphone input are examples. Your SDR needs to do quick conversions. Its ADC can use direct or flash conversion.   Direct or flash conversion is advantageous because their very high speed allows digitizing high frequencies. Remember this because high speed conversion happens in a flash!

Here are some terms to know related to analog to digital conversion.  

You remember “sample rate.” It determines the maximum receive bandwidth of an SDR. Sample size is the number of bits used to describe a sample, and we talked about the 10 bit minimum needed.   

Now let’s add “bit rate.” That’s the number of bits transmitted per second. Bit rate is very important. 

With 8-bit resolution, there are 256 different input levels that can be encoded by an analog-to-digital converter. Each bit is either 0 or 1. Take those two options and multiply them together, 2 times 2. Multiple 2×2 8-times, also known as 2 to the 8th power, and that’s how you get the answer of 256.   

Some ADC’s add a dither. A dither is a small amount of noise added to the input signal to allow more precise representation of a signal over time. A quality measure for an ADC is its total harmonic distortion.

Now let’s switch to talking about the Digital to Analog Converter or DAC. A DAC is used to convert digital signals from the world of 1s and 0s into the analog realm. Some examples of DAC’s include the headphone output on your mobile phone and the sound card for your PC’s speakers. They convert digital signals from your computer into analog waveforms that your ears and brain can understand.

Schematic of DAC circuit

You don’t want interference in the output of your DAC. Many DAC’s use a low-pass filter for noise management. The filter is there to remove spurious sampling artifacts from the output signal.

Spread Spectrum

Now, a deeper look at Spread Spectrum. Spread Spectrum functionality uses multiple frequencies in a band. It’s a function called frequency hopping. Frequency hopping is rapidly varying the frequency of a transmitted signal according to a pseudorandom sequence. There is a prerequisite to frequency hopping. The transmitting station and receiving station need to share a programming algorithm. That is how they get synchronized.

There are benefits to using frequency hopping. You can send parts of the data over a wider range when using multiple frequencies. That helps with interference and noise. Spread spectrum is resistant to some jamming or intentional interference. For this reason, spread spectrum has been used in military operations. It makes it significantly harder to jam signals when they go across a larger part of the spectrum, because they can’t just block a single frequency.

Why are received spread spectrum signals resistant to interference? Because signals not using the spread spectrum algorithm are suppressed in the receiver. The algorithm is like a secret code used between the transmitter and the receiver, suppressing all the signals except the correct ones.

One type of spread spectrum communications technique is called direct sequence. Direct sequence uses a high-speed binary bit stream to shift the phase of an RF carrier.

Two mass market uses of spread spectrum technology today are the global GPS system and home WiFi. A smaller example are IOT device networks like Zigbee and Bluetooth Low Energy.   

In ham radio a big use of spread spectrum is the ARDEN protocols. ARDEN stands for Amateur Radio Emergency Data Network. It creates WiFi-like networks. They are used in emergency situations or for public service events. Usually on frequencies around 2.4 GHz. Like your home WiFi, nodes in a mesh network have Internet Protocol (IP) addresses. The radios are often modified, off-the-shelf WiFi routers. They form up over RF using discovery and link establishment protocols. 

To find out more about ARDEN you can visit ardenmesh.org on the web.  

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