# Measuring Frequency

Sections 1 and 2 helped to fill in details about waves, frequency, RF, and the electromagnetic spectrum. In the following sections, we are going to highlight common instrumentation that can be used to measure signals in the time and frequency domain and a closer look at spectrum analyzers and phase noise analyzers.

### Oscilloscopes

In many cases, looking at a signal in the time domain can provide indications about the performance of a particular design. You may be interested in how fast a signal achieves its maximum voltage (rise time) or its lowest (fall time), how two signals compare with one another versus time, or the duration of a signal. All of these measurements are ideally measured in the time domain.

We have introduced the Oscilloscope which measures voltage with respect to time. Then, it displays the graph of voltage (amplitude) vs. time, as shown below:

Figure 1: Oscilloscope display showing 2 wave forms. 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 that they contain elements that repeat with respect to time.

Figure 2: A 4 Channel Digital Oscilloscope

### Analog to Digital Oscilloscopes

Original oscilloscopes were strictly analog in nature. They utilized a Cathode Ray Tube (CRT) as a display. Very similar to the original television sets, these scopes would “draw” the incoming signal on the display. This was extremely helpful in visualizing the input signal, but it was difficult to perform any direct measurements and the data could only be saved by taking a picture of the display of the oscilloscope.

Fun Fact: In the 70's, scopes had no storage. Polaroid cameras with special shields were used to record signal waveforms

The advancement of digital technology led to fully digital oscilloscopes. With the raw voltage and time data digitized, the data could be saved as well as used to perform calculations directly within the scope itself. Modern oscilloscopes can now directly calculate rise time and fall time, frequency, period and duty cycle, pulse width and voltage amplitude, and more.

Figure 3: Digital Oscilloscope display showing all measurements for a 10MHz square wave input.

Some digital scopes can also display the amplitude of the incoming signal versus frequency by using Fast Fourier Transform (FFT) calculations. The FFT function of oscilloscopes can be useful in identifying the fundamental frequency as shown below:

Figure 4: Oscilloscope display showing an FFT a 10 MHz square wave input.

So, with a scope, we can read the phase information (in the time domain) and gather basic amplitude and frequency information in the frequency domain by using FFTs.

### Spectrum Analyzers

Unfortunately, oscilloscopes tend to have a noise floor that is much higher than traditional frequency measurement instrumentation like spectrum analyzers. This can make looking for small amplitude elements, like higher ordered harmonics, difficult.

They are also “wide band” instruments. This means that they detect a wide range of frequencies at the same time. This raises the noise floor and does not provide for an easy way to differentiate between signals that could have frequencies that are close together.

### The Real-Time Spectrum Analyzer

Real-Time Spectrum Analyzers are similar to oscilloscopes in that they first collect data in the time domain and then they calculate the frequency using FFT algorithms. In this way, they can collect a large number of data points over a broad range of frequencies, calculate the amplitude vs. frequency, and display them quickly in the frequency domain.

They differ from oscilloscopes in that they tend to offer lower noise floors as well as special filtering that can differentiate between signals that are close together. Real-Time Spectrum Analyzers are very useful in capturing quickly changing signals, especially in when working with digital communications.

Note: When compared to swept spectrum analyzers, real-time systems tend to have the ability to capture transients and fast signals faster, but they also have a higher noise floor and unit cost.

While Real-Time systems are gaining in popularity, they are still outnumbered significantly by the swept analyzer design. Let's take a closer look at the more common swept spectrum design.

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