SPECTRUM ANALYZER; Introduction

Introduction

This site is intended to explain the fundamentals of swept-tuned, superheterodyne spectrum analyzers and discuss the latest advances in spectrum analyzer capabilities.

At the most basic level, the spectrum analyzer can be described as a frequency-selective, peak-responding voltmeter calibrated to display the rms value of a sine wave. It is important to understand that the spectrum analyzer is not a power meter, even though it can be used to display power directly. As long as w know some value of a sine wav ( for example, peak or average) and know the resistance across which w measure this value, we can calibrate our voltmeter to indicate power. With the advent of digital technology, modern spectrum analyzers have been given many more capabilities. In this note, w shall describe the basic spectrum analyzer as well as the many additional capabilities made possible using digital technology and digital signal processing.

Frequency domain versus time domain Before we get into the details of describing a spectrum analyzer, w might first ask ourselves: Just what is a spectrum and why would w want to    analyze it? Our normal frame of reference is time. We note when certain events occur. This includes electrical vents. We can use an oscilloscope to view the instantaneous value of a particular electrical vent ( or some other event converted to volts through an appropriate transducer) as a function of time. In other words, w use the oscilloscope to view the wav form of a signal in the time domain.

Fourier 1 theory tells us any time-domain electrical phenomenon is made up of one or more sine waves of appropriate frequency, amplitude, and phase. In other words, we can transform a time-domain signal into its frequency- domain equivalent. Measurements in the frequency domain t ll us how much energy is present at each particular frequency. With proper filtering, a wav form such as in Figure 1-1 can be decomposed into separate sinusoidal waves, or spectral components, which w can then valuate independently. Each sine wav is characterized by its amplitude and phase. If the signal that we wish to analyze is periodic, as in our case here, Fourier says that the constituent sine wav s are separated in the frequency domain by 1/ T, where T is the period of the signal 2

Figure 1-1. Complex time-domain signal

1. Jean Baptiste Joseph Fourier, 1768-1830.
A French mathematician and physicist who discovered that periodic functions can be expanded into a series of sines and cosines.
2. If the time signal occurs only once, then T is infinite, and the frequency representation is a continuum of sine waves.
Some measurements require that we preserve complete information about the signal -frequency, amplitude and phase. This type of signal analysis is called vector signal analysis , which is discussed in Application Note 150-15, Vector Signal Analysis Basics . Modern spectrum analyzers are capable of performing a wide variety of vector signal measurements. However, another large group of measurements can be made without knowing the phase relationships among the sinusoidal components. This type of signal analysis is called spectrum analysis . Because spectrum analysis is simpler to understand, yet extremely useful, w will begin this application note by looking first at how spectrum
analyzers perform spectrum analysis measurements, starting in Chapter 2.


Theoretically, to make the transformation from the time domain to the frequency domain, the signal must be valuated over all time, that is, over ± infinity. How v r, in practice, we always use a finit time period when making a measurement. Fourier transformations can also be made from the frequency to the time domain. This case also theoretically requires the valuation of all spectral components over frequencies to ± infinity. In reality, making measurements in a finite bandwidth that captures most of the signal energy  produces acceptable results. When performing a Fourier transformation on frequency domain data, the phase of the individual components is indeed critical. For example, a square wav transformed to the frequency domain and back again could turn into a sawtooth wav if phase were not preserved.