5952-0292.pdf

Agilent

Spectrum Analysis Basics

Application Note 150

Table of Contents

Chapter 1 – Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

Frequency domain versus time domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

What is a spectrum? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

Why measure spectra? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

Types of measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Types of signal analyzers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Chapter 2 – Spectrum Analyzer Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

RF attenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

Low-pass filter or preselector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

Tuning the analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

IF gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Resolving signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Residual FM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

Phase noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

Sweep time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

Envelope detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25

Detector types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

Sample detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

Peak (positive) detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Negative peak detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Normal detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Average detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

EMI detectors: average and quasi-peak detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

Averaging processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

Time gating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38

Chapter 3 – Digital IF Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

Digital filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

The all-digital IF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45

Custom signal processing IC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47

Additional video processing features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47

Frequency counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47

More advantages of the all-digital IF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48

Chapter 4 – Amplitude and Frequency Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49

Relative uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52

Absolute amplitude accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52

Improving overall uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53

Specifications, typical performance, and nominal values . . . . . . . . . . . . . . . . . . . . . . .53

The digital IF section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54

Frequency accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56

Table of Contents

— continued

Chapter 5 – Sensitivity and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58

Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58

Noise figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61

Preamplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62

Noise as a signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65

Preamplifier for noise measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68

Chapter 6 – Dynamic Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69

Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

Dynamic range versus internal distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

Attenuator test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74

Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74

Dynamic range versus measurement uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77

Gain compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80

Display range and measurement range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80

Adjacent channel power measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82

Chapter 7 – Extending the Frequency Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83

Internal harmonic mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83

Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89

Amplitude calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91

Phase noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91

Improved dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92

Pluses and minuses of preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95

External harmonic mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96

Signal identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98

Chapter 8 – Modern Spectrum Analyzers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102

Application-specific measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102

Digital modulation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105

Saving and printing data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106

Data transfer and remote instrument control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107

Firmware updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108

Calibration, troubleshooting, diagnostics, and repair . . . . . . . . . . . . . . . . . . . . . . . . . .108

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109

Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110

Chapter 1

Introduction

This application note 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 we know some value of a sine wave (for example, peak

or average) and know the resistance across which we 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, we 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, we might

first ask ourselves: “Just what is a spectrum and why would we want to

analyze it?” Our normal frame of reference is time. We note when certain

events occur. This includes electrical events. We can use an oscilloscope to

view the instantaneous value of a particular electrical event (or some other

event converted to volts through an appropriate transducer) as a function

of time. In other words, we use the oscilloscope to view the waveform 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 tell us how

much energy is present at each particular frequency. With proper filtering,

a waveform such as in Figure 1-1 can be decomposed into separate sinusoidal

waves, or spectral components, which we can then evaluate independently.

Each sine wave 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 waves are separated in the frequency domain by 1/T, where

T is the period of the signal 2 .

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.

Figure 1-1. Complex time-domain signal

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, we 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 evaluated over all time, that is, over ± infinity.

However, in practice, we always use a finite 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 evaluation 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 wave transformed to the frequency domain

and back again could turn into a sawtooth wave if phase were not preserved.

What is a spectrum?

So what is a spectrum in the context of this discussion? A spectrum is a

collection of sine waves that, when combined properly, produce the

time-domain signal under examination. Figure 1-1 shows the waveform of a

complex signal. Suppose that we were hoping to see a sine wave. Although

the waveform certainly shows us that the signal is not a pure sinusoid, it

does not give us a definitive indication of the reason why. Figure 1-2 shows

our complex signal in both the time and frequency domains. The frequency-

domain display plots the amplitude versus the frequency of each sine wave

in the spectrum. As shown, the spectrum in this case comprises just two sine

waves. We now know why our original waveform was not a pure sine wave.

It contained a second sine wave, the second harmonic in this case. Does this

mean we have no need to perform time-domain measurements? Not at all.

The time domain is better for many measurements, and some can be made

only in the time domain. For example, pure time-domain measurements

include pulse rise and fall times, overshoot, and ringing.

Frequency domain

measurements

Time domain

measurements

Figure 1-2. Relationship between time and frequency domain

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