Subject: [NEXTEL-1] Agilent Spectrum Analysis Basics

From: [email-masked]
Date: Wed, 12 May 2004 14:59:23 -0400

Agilent Spectrum Analysis Basics
Application Note 150

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.

Fourier1 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
frequencydomain 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
signal2.

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
frequencydomain 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.

More: http://cp.literature.agilent.com/litweb/pdf/5952-0292.pdf

--
    "NEXTEL-1 IT'S NOT JUST NEXTEL"
  Note The New address
Subscribe to Nextel-1: http://www.groups.yahoo.com/subscribe/NEXTEL-1

  "NEXTEL2 FOR iDEN SOFTWARE DEVELOPERS"
Subscribe to Nextel2: http://www.groups.yahoo.com/subscribe/NEXTEL2

  "WIRELESS FORUM HOMELAND SECURITY GROUP"
     The Complete Resource for Wireless Homeland Security.
Subscribe to WFHSG:  http://www.groups.yahoo.com/subscribe/WFHSG

------------------------ Yahoo! Groups Sponsor ---------------------~-->
Make a clean sweep of pop-up ads. Yahoo! Companion Toolbar.
Now with Pop-Up Blocker. Get it for free!
http://us.click.yahoo.com/L5YrjA/eSIIAA/yQLSAA/61FxlB/TM
---------------------------------------------------------------------~->

-- 
    "NEXTEL-1 IT'S NOT JUST NEXTEL"
  Note The New address 
Subscribe to Nextel-1: http://www.groups.yahoo.com/subscribe/NEXTEL-1

  "NEXTEL2 FOR iDEN SOFTWARE DEVELOPERS"
Subscribe to Nextel2: http://www.groups.yahoo.com/subscribe/NEXTEL2

  "WIRELESS FORUM HOMELAND SECURITY GROUP"
     The Complete Resource for Wireless Homeland Security.
Subscribe to WFHSG:  http://www.groups.yahoo.com/subscribe/WFHSG

Yahoo! Groups Links

<*> To visit your group on the web, go to:
     http://groups.yahoo.com/group/NEXTEL-1/

<*> To unsubscribe from this group, send an email to:
     [email-masked]

<*> Your use of Yahoo! Groups is subject to:
     http://docs.yahoo.com/info/terms/