Tektronix Fundamentals Of Real-Time Spectrum Analysis User Manual

Fundamentals of Real-Time Spectrum Analysis

Primer

Table of Contents

Chapter 1: Introduction and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

The Evolution of RF Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Modern RF Measurement Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

A Brief Survey of Instrument Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Swept Spectrum Analyzers:

Traditional Frequency Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Vector Signal Analyzers: Digital Modulation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Real-Time Spectrum Analyzers: Trigger, Capture, Analyze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Key Concepts of Real-Time Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Samples, Frames, and Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Real-Time Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Seamless Capture and Spectrogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Time-Correlated Multi-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2: How a Real-Time Spectrum Analyzer Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Digital Signal Processing in Real-Time Spectrum Analyzers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

IF Digitizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Digital Down-Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

I/Q Baseband Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Decimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Time and Frequency Domain Effects of Sampling Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Real-Time Triggering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Triggering in Systems with Digital Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Trigger Modes and Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

RSA Trigger Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Constructing a Frequency Mask. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Timing and Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Baseband DSP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Calibration/Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Timing, Synchronization, and Re-sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Fast Fourier Transform Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

FFT Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Windowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Post-FFT Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Overlapping Frames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Modulation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Amplitude, Frequency, and Phase Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Digital Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Power Measurements and Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Chapter 3: Real-Time Spectrum Analyzer Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Frequency Domain Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Real-Time SA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Standard SA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

SA with Spectrogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Time Domain Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Frequency vs. Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Power vs. Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Complementary Cumulative Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

I/Q vs. Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Modulation Domain Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Analog Modulation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Digital Modulation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Standards-Based Modulation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Codogram Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Chapter 4: Frequently Asked Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Chapter 5: Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Acronym Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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Fundamentals of Real-Time Spectrum Analysis

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Chapter 1: Introduction and Overview

The Evolution of RF Signals

Engineers and scientists have been looking for innovative new uses

for RF technology ever since the 1860s, when James Clerk Maxwell

mathematically predicted the existence of electromagnetic waves

capable of transporting energy across empty space. Following

Heinrich Hertz’s physical demonstration of “radio waves” in 1886,

Nikola Tesla, Guglielmo Marconi, and others pioneered ways of

manipulating these waves to enable long distance communications.

At the turn of the century, the radio had become the first practical

application of RF signals. Over the next three decades, several

research projects were launched to investigate methods of transmit-

ting and receiving signals to detect and locate objects at great

distances. By the onset of World War II, radio detection and ranging

(also known as radar) had become another prevalent RF application.

Due in large part to sustained growth in the military and communi-

cations sectors, technological innovation in RF accelerated steadily

throughout the remainder of the 20th century and continues to do

so today. To resist interference, avoid detection, and improve capac-

ity, modern radar systems and commercial communications net-

works have become extremely complex, and both typically employ

sophisticated combinations of RF techniques such as bursting,

frequency hopping, code division multiple access, and adaptive

modulation. Designing these types of advanced RF equipment and

successfully integrating them into working systems are extremely

complicated tasks.

At the same time, the increasingly widespread success of cellular

technology and wireless data networks has caused the cost of basic

RF components to plummet. This has enabled manufacturers out-

side of the traditional military and communications realms to embed

relatively simple RF devices into all sorts of commodity products. RF

transmitters have become so pervasive that they can be found in

almost any imaginable location: consumer electronics in homes,

medical devices in hospitals, industrial control systems in factories,

and even tracking devices implanted underneath the skin of live-

stock, pets, and people.

As RF signals have become ubiquitous in the modern world, so too

have problems with interference between the devices that generate

them. Products such as mobile phones that operate in license

spectrum must be designed not to transmit RF energy into adjacent

frequency channels, which is especially challenging for complex

multi-standard devices that switch between different modes of

transmission and maintain simultaneous links to different network

elements. Simpler devices that operate in unlicensed frequency

bands must also be designed to function properly in the presence of

interfering signals, and government regulations often dictate that

these devices are only allowed to transmit in short bursts at low

power levels.

In order to overcome these evolving challenges, it is crucial for

today’s engineers and scientists to be able to reliably detect and

characterize RF signals that change over time, something not easily

done with traditional measurement tools. To address these problems,

Tektronix has designed the Real-Time Spectrum Analyzer (RTSA), an

instrument that can trigger on RF signals, seamlessly capture them

into memory, and analyze them in the frequency, time, and modula-

tion domains. This document has been written to describe how the

RTSA works and provide a basic understanding of how it can be

used to solve many measurement problems associated with

capturing and analyzing modern RF signals.

Modern RF Measurement Challenges

Given the challenge of characterizing the behavior of today’s RF

devices, it is necessary to understand how frequency, amplitude, and

modulation parameters behave over short and long periods of time.

In these cases, using traditional tools like swept spectrum analyzers

(SA) and vector signal analyzers (VSA) might provide snapshots of

the signal in the frequency domain and the modulation domain, but

this is often not enough information to confidently describe the

dynamic RF signals produced by the device. The RTSA adds another

crucial dimension to all of these measurements – time.

Consider the following common measurement tasks:

Transient and dynamic signal capture and analysis

Capturing burst transmissions, glitches, switching transients

Characterizing PLL settling times, frequency drift, microphonics

Detecting intermittent interference, noise analysis

Capturing spread-spectrum and frequency-hopping signals

Monitoring spectrum usage, detecting rogue transmissions

Compliance testing, EMI diagnostics

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Figure 1-1: The swept spectrum analyzer steps across a series of frequency

segments, often missing important transient events that occur outside the current sweep band highlighted in yellow.

Analog and digital modulation analysis

Characterizing time-variant modulation schemes

Troubleshooting complex wireless standards using

domain correlation

Performing modulation quality diagnostics

Each measurement involves RF signals that change over time, often

unpredictably. To effectively characterize these signals, engineers

need a tool that can trigger on known or unpredictable events,

capture the signals seamlessly and store them in memory, and

analyze the behavior of frequency, amplitude, and modulation

parameters over time.

A Brief Survey of Instrument Architectures

The Real-Time Spectrum Analyzer (RTSA) is an innovative measure-

ment tool designed by Tektronix to address the emerging RF meas-

urement challenges described above. To learn how the RTSA works

and understand the value of the measurements it provides, it is

helpful to first examine two other types of traditional RF signal

analyzers: the swept spectrum analyzer (SA) and the vector signal

analyzer (VSA).

The Swept Spectrum Analyzer: Traditional Frequency Domain Analysis

The swept-tuned, superheterodyne spectrum analyzer is the tradi-

tional architecture that first enabled engineers to make frequency

domain measurements several decades ago. Originally built with

purely analog components, the swept SA has since evolved along

with the applications that it serves. Current generation swept SAs

includes digital elements such as ADCs, DSPs, and microproces-

Figure 1-2: Typical swept spectrum analyzer architecture.

sors. However, the basic swept approach remains largely the same

and is best suited for observing controlled, static signals.

The swept SA makes power vs. frequency measurements by

downconverting the signal of interest and sweeping it through the

passband of a resolution bandwidth (RBW) filter. The RBW filter is

followed by a detector that calculates the amplitude at each fre-

quency point in the selected span. While this method can provide

high dynamic range, its disadvantage is that it can only calculate

the amplitude data for one frequency point at a time. Sweeping the

analyzer over a span of frequencies takes time – on the order of

seconds in some cases. This approach is based on the assumption

that the analyzer can complete several sweeps without there being

significant changes to the signal being measured. Consequently, a

relatively stable, unchanging input signal is required.

If there is a rapid change in the signal, it is statistically probable

that the change will be missed. As shown in Figure 1-1, the sweep

is looking at frequency segment Fa while a momentary spectral

event occurs at Fb(diagram on left). By the time the sweep arrives

at segment Fb, the event has vanished and does not get detected

(diagram on right). The SA does not provide a way to trigger on this

transient signal, nor can it store a comprehensive record of signal

behavior over time.

Figure 1-2 depicts a typical modern swept SA architecture. It

supplements the wide analog resolution bandwidth (RBW) filters

inherited from its predecessors with digital techniques to replace

the narrower filters. Filtering, mixing, and amplification prior to the

ADC are analog processes for bandwidths in the range of BW1,

BW2, or BW3. When filters narrower than “BW3” are needed, they

are applied by digital signal processing (DSP) in the steps following

the analog-to-digital conversion.

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The job of the ADC and the DSP is rather demanding. Non-linearity

and noise in the ADC are a challenge, although some types of errors

that can occur in purely analog spectrum analyzers are eliminated.

Vector Signal Analyzers: Digital Modulation Analysis

Traditional swept spectrum analysis enables scalar measurements

that provide information only about the magnitude of the input signal.

Analyzing signals carrying digital modulation requires vector measure-

ments that provide both magnitude and phase information. The vector

signal analyzer is a tool specifically designed for digital modulation

analysis. A simplified VSA block diagram is shown in Figure 1-3.

The VSA is optimized for modulation measurements. Like the

Real-Time Spectrum Analyzer described in the next section, a VSA

digitizes all of the RF energy within the passband of the instrument

in order to extract the magnitude and phase information required

to measure digital modulation. However, most (but not all) VSAs are

designed to take snapshots of the input signal at arbitrary points in

time, which makes it difficult or impossible to store a long record

of successive acquisitions for a cumulative history of how a signal

behaves over time. Like a swept SA, the triggering capabilities are

typically limited to an IF level trigger and an external trigger.

Within the VSA, an ADC digitizes the wideband IF signal, and the

down-conversion, filtering, and detection are performed numerically.

Transformation from time domain to frequency domain is done using

FFT algorithms. The linearity and dynamic range of the ADC are crit-

ical to the instrument’s performance. Equally important, there must

be sufficient DSP processing power to enable fast measurements.

The VSA measures modulation parameters such as Error Vector

Magnitude (EVM) and provides other displays such as the

constellation diagram. A standalone VSA is often used to supplement

the capabilities of a traditional swept SA. In addition, many modern

instruments have architectures that can perform both swept SA and

VSA functions, providing non-correlated frequency and modulation

domain measurements in one box.

Real-Time Spectrum Analyzers: Trigger, Capture, Analyze

The Real-Time Spectrum Analyzer is designed to address the

measurement challenges associated with transient and dynamic

RF signals as described in the previous section. The fundamental

concept of real-time spectrum analysis is the ability to trigger on

an RF signal, seamlessly capture it into memory, and analyze it in

multiple domains. This makes it possible to reliably detect and

characterize RF signals that change over time.

Figure 1-4 shows a simplified block diagram of the RTSA architec-

ture. (A more detailed diagram and circuit description appears in

Chapter 2). The RF front-end can be tuned across the entire frequen-

cy range of the instrument, and it down-converts the input signal to

a fixed IF that is related to the maximum real-time bandwidth of the

RTSA. The signal is then filtered, digitized by the ADC, and passed to

the DSP engine that manages the instrument’s triggering, memory,

and analysis functions. While elements of this block diagram and

acquisition process are similar to those of the VSA architecture, the

RTSA is optimized to deliver real-time triggering, seamless signal

capture, and time-correlated multi-domain analysis. In addition,

advancements in ADC technology enable a conversion with high

dynamic range and low noise, allowing the RTSA to equal or surpass

the basic RF performance of many swept spectrum analyzers.

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Figure 1-4: Typical real-time spectrum analyzer architecture.

Figure 1-3: Typical vector signal analyzer architecture.

Fundamentals of Real-Time Spectrum Analysis

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Figure 1-5: Samples, frames, and blocks: the memory hierarchy of the RSA.

For measurement spans less than or equal to the real-time band-

width, the RTSA architecture provides the ability to seamlessly

capture the input signal with no gaps in time by digitizing the RF

signal and storing the time-contiguous samples in memory. This has

several advantages over the acquisition process of a swept spectrum

analyzer, which builds up a frequency domain image by serially

sweeping across the frequency span. The remainder of this

document discusses these advantages in detail.

Key Concepts of Real-Time Spectrum Analysis

Samples, Frames, and Blocks

The measurements performed by the RTSA are implemented using

digital signal processing (DSP) techniques. To understand how an RF

signal can be analyzed in the time, frequency, and modulation

domains, it is first necessary to examine how the instrument

acquires and stores the signal. After it is digitized by the ADC, the

signal is represented by time domain data, from which all frequency

and modulation parameters can be calculated using DSP. These

concepts are discussed in detail in Chapter 2.

Three terms—samples, frames, and blocks—describe the hierarchy

of data stored when an RTSA seamlessly captures a signal using

real-time acquisition. Figure 1-5 illustrates the sample-frame-block

structure.

The lowest level of the hierarchy of data is the sample, which

represents a discrete time-domain data point. This construct is

familiar from other applications

Figure 1-6: Real-time spectrum analyzer block acquisition and processing.

of digital sampling, such as a real-time oscilloscopes and PC-based

digitizers. The effective sample rate which determines the time

interval between adjacent samples depends on the selected span. In

the RTSA, each sample is stored in memory as an I/Q pair contain-

ing magnitude and phase information.

The next step up is the frame.A frame consists of an integer number

of contiguous samples and is the basic unit to which the Fast Fourier

Transform (FFT) can be applied to convert time domain data into the

frequency domain. In this process, each frame yields one frequency

domain spectrum.

The highest level in the acquisition hierarchy is the block,which

is made up of many adjacent frames that are captured seamlessly

in time. The block length (also referred to as acquisition length) is

the total amount of time that is represented by one continuous

acquisition. Within a block, the input signal is represented with no

gaps in time.

In the real-time measurement modes of the RTSA, each block is

seamlessly acquired and stored into memory. It is then post-

processed using DSP techniques to analyze the frequency, time,

and modulation behavior of the signal. In standard SA modes, the

RTSA can emulate a swept SA by stepping the RF front end across

frequency spans that exceed the maximum real-time bandwidth.

Additional information can be found in Chapter 4.

Figure 1-6 shows block acquisition mode, which enables real-time

seamless capture. Each acquisition is seamless in time for all the

frames within a block, though not between blocks. After the signal

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Fundamentals of Real-Time Spectrum Analysis

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processing of one acquisition block is complete, the acquisition of

the next block will begin. Once the block is stored in memory any

real-time measurements can be applied. For example, a signal

captured in real-time SA mode can then be analyzed in demod

mode and time mode.

The number of frames acquired within the block can be determined

by dividing the acquisition length by the frame length. The acquisi-

tion length entered by the user is rounded so the block contains an

integer number of frames. The maximum acquisition length ranges

from seconds to days and depends on the selected measurement

span and the memory depth of the instrument. Examples for specific

RTSAs are given in Chapter 4.

Real-Time Triggering

Useful triggering has long been a missing ingredient in most

spectrum analysis tools. The RTSA is the first mainstream spectrum

analyzer to offer real-time frequency domain triggering and other

intuitive trigger modes in addition to simple IF level and external

triggers. There are many reasons that the traditional swept

architecture is not well suited for real-time triggering, most signifi-

cantly that in a swept SA a trigger event is used to begin a sweep.

The RTSA, on the other hand, uses a trigger event as a reference

point in time for the seamless acquisition of the signal. This enables

several other useful features, such as the ability to store both pre-

trigger and post-trigger information. An in-depth discussion of the

real-time triggers of the RTSA can be found in Chapter 2.

Another significant capability of the RTSA is the real-time frequency

mask trigger, which allows the user to trigger an acquisition based

on specific events in the frequency domain. As illustrated in

Figure 1-7, a mask is drawn to define the set of conditions within

the analyzer’s real-time bandwidth will generate the trigger event.

The flexible frequency mask trigger is a powerful tool for reliably

detecting and analyzing dynamic RF signals. It can be also used to

make measurements that are impossible with traditional spectrum

analyzers, such as capturing low-level transient events that occur in

the presence of more powerful RF signals (as shown in Figure 1-8)

and detecting intermittent signals at specific frequencies within a

crowded frequency spectrum (as shown in Figure 1-9).

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Figure 1-8: Using the frequency mask to trigger on a low level burst in the

presence of a large signal.

Figure 1-7: Real-time frequency domain triggering using a frequency mask.

Figure 1-9: Using the frequency mask to trigger on a specific signal in a

crowded spectral environment.

Fundamentals of Real-Time Spectrum Analysis

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Figure 1-10: Spectrogram display.

Seamless Capture and Spectrogram

Once the real-time trigger conditions have been defined and the

instrument is armed to begin an acquisition, the RTSA continuously

examines the input signal to watch for the specified trigger event.

While waiting for this event to occur, the signal is constantly

digitized and the time domain data is cycled through a first-in,

first-out capture buffer that discards the oldest data as new data

is accumulated. This enables the analyzer to save pre-trigger and

post-trigger data into memory when it detects the trigger event.

As described in the sections above, this process enables a seam-

less acquisition of the specified block, within which a signal is

represented by contiguous time domain samples. Once this data has

been stored in memory, it is available to process and analyze using

different displays such as power vs. frequency, spectrogram, and

multi-domain views. The sample data remains available in random

access memory until it is overwritten by a subsequent acquisition,

and it can also be saved to the internal hard drive of the RTSA.

The spectrogram is an important measurement that provides an

intuitive display of how frequency and amplitude behavior change

over time. The horizontal axis represents the same range of fre-

quencies that a traditional spectrum analyzer shows on the power

vs. frequency display. In the spectrogram, though the vertical axis

represents time, and amplitude is represented by the color of the

trace. Each “slice” of the spectrogram corresponds to a single fre-

quency spectrum calculated from one frame of time domain data.

Figure 1-10 shows a conceptual illustration of the spectrogram of a

dynamic signal.

Figure 1-11: Time-correlated views: power vs. frequency display (left) and

spectrogram display (right).

Figure 1-11 shows a screen shot displaying the power vs. frequency

and spectrogram displays for the signal illustrated in Figure 1-10.

On the spectrogram, the oldest frame is shown at the top of the

display and the most recent frame is shown at the bottom of the

display. This measurement shows an RF signal whose frequency is

changing over time, and it also reveals a low level transient signal

that appears and disappears near the end of the time block. Since

the data is stored in memory, a marker can be used to scroll “back

in time” through the spectrogram. In Figure 1-11, a maker has been

placed on the transient event on the spectrogram display, which

causes the spectrum corresponding to that particular point in time

to be shown on the power vs. frequency display.

Time-Correlated Multi-Domain Analysis

Once a signal has been acquired and stored in memory, it can be

analyzed using the wide variety of time-correlated views available in

the RTSA, as illustrated in Figure 1-12 (next page).

This is especially useful for device troubleshooting and signal

characterization applications. All of these measurements are based

on the same underlying set of time domain sample data, which

underscores two significant architectural advantages:

Comprehensive signal analysis in the frequency, time, and

modulation domains based on a single acquisition.

Domain correlation to understand how specific events in the

frequency, time, and modulation domains are related based on

a common time reference.

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Fundamentals of Real-Time Spectrum Analysis

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In real-time spectrum analysis mode, the RTSA provides two time-

correlated views of the captured signal: the power vs. frequency

display and the spectrogram display. These two views can be seen

in Figure 1-11.

In the other real-time measurement modes for time domain analysis

and modulation domain analysis, the RTSA shows multiple views of

the captured signal as illustrated in Figures 1-13 and 1-14. The

window in the upper left is called the overview, and it can display

either power vs. time or the spectrogram. The overview shows all of

the data that was acquired in the block, and it serves as the index

for the other analysis windows.

The window in the upper right (outlined in purple) is called the sub-

view, and it shows the same power vs. frequency display that is

available in Real-Time Spectrum Analyzer mode. Just like the dis-

play in Figure 1-11, this is the spectrum of one frame of data, and

it is possible to scroll through the entire time record to see the

spectrum at any point in time. This is done by adjusting the spec-

trum offset, which is found in the Timing menu of the RTSA. Also

note that there is a purple bar in the overview window that indicates

position in time that corresponds to the frequency domain display in

the purple subview window.

The window in the bottom half of the screen (outlined in green) is

called the analysis window, or mainview, and it displays the results

of the selected time or modulation analysis measurement.

Figure 1-13 shows an example of frequency modulation analysis,

and Figure 1-14 shows an example of transient power vs. time

analysis. Like the subview window, the green analysis window can

be positioned anywhere within the time record shown in the

overview window, which has corresponding green bars to indicate

its position. In addition, the width of the analysis window can be

flexibly adjusted to lengths less than or greater than one frame.

Time-correlated multi-domain analysis provides tremendous

flexibility to zoom in and thoroughly characterize different parts of

an acquired RF signal using a wide variety of analysis tools. An

introduction to these measurements can be found in Chapter 3.

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Figure 1-14: Multi-domain view showing spectrogram, power vs. frequency,

and power vs. time.

Figure 1-13: Multi-domain view showing power vs. time, power vs.

frequency, and FM demodulation.

Figure 1-12: Illustrations of several time-correlated measurements available

on RTSA’s.

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Fundamentals of Real-Time Spectrum Analysis

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Chapter 2: How a Real-Time Spectrum Analyzer Works

Modern Real-Time Spectrum Analyzers can acquire a passband, or

span, anywhere within the input frequency range of the analyzer. At

the heart of this capability is an RF down-converter followed by a

wideband intermediate frequency (IF) section. An ADC digitizes the

IF signal and the system carries out all further steps digitally. An

FFT algorithm implements the transformation from time domain to

frequency domain, where subsequent analysis produces displays

such as spectrograms, codograms, and more.

Several key characteristics distinguish a successful real-time

architecture:

An ADC system capable of digitizing the entire real-time BW with

sufficient fidelity to support the desired measurements.

An integrated signal analysis system that provides multiple

analysis views of the signal under test, all correlated in time.

Sufficient capture memory and DSP power to enable continuous

real-time acquisition over the desired time measurement period.

DSP power to enable real-time triggering in the frequency

domain.

This chapter contains several architectural diagrams of the main

acquisition and analysis blocks of the Tektronix Real-Time Spectrum

Analyzer (RSA). Some ancillary functions (minor triggering-related

blocks, display and keyboard controllers, etc.) have been omitted to

clarify the discussion.

Digital Signal Processing in Real-Time Spectrum Analyzers

Tektronix’ RSAs use a combination of analog and digital signal

processing to convert RF signals into calibrated, time-correlated

multi-domain measurements. This section deals with the digital

portion of the RSA signal processing flow.

Figure 2-1 illustrates the major digital signal processing blocks

used in the Tektronix RSA Series. An analog IF signal is bandpass

filtered and digitized. A digital down-conversion and decimation

process converts the A/D samples into streams of in-phase (I) and

quadrature (Q) base band signals. A triggering block detects signal

conditions to control acquisition and timing. The baseband I and Q

signals as well as triggering information are used by a baseband

DSP system to perform spectrum analysis by means of FFT,

modulation analysis, power measurements, timing measurements

as well as statistical analyses.

IF Digitizer

Tektronix RSAs typically digitize a band of frequencies centered

around an intermediate frequency (IF). This band or span of fre-

quencies is the widest frequency for which real-time analysis can

be performed. Digitizing at a high IF rather than at DC or baseband

has several signal processing advantages (spurious performance,

DC rejection, dynamic range, etc.) but can require excessive compu-

tation to filter and analyze if processed directly. Tektronix RSAs

employ a digital down-converter (DDC), Figure 2-2 and a decimator

to convert a digitized IF into I and Q baseband signals at an effec-

tive sampling rate just high enough for the selected span.

Figure 2-1: Real-time spectrum analyzer digital signal processing

block diagram.

Figure 2-2: Digital down-converter block diagram.

Fundamentals of Real-Time Spectrum Analysis

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Span Decimation (n) Effective Time

Sample Rate Resolution

15 MHz 2 25.6 MS/s 39.0625 ns

10 MHz 4 12.8 MS/s 78.1250 ns

1 MHz 40 1.28 MS/s 781.250 ns

100 KHz 400 128 KS/s 7.81250 s

10 KHz 4000 12.8 KS/s 78.1250 s

1 KHz 40000 1.28 KS/s 781.250 s

100 Hz 400000 128 S/s 7.81250 ms

Figure 2-3: Information in the passband is maintained in I and Q, even at

half the sample rate.

Digital Down Converter

The IF signal is digitized with sample rate FS. The digitized IF is then

sent to a DDC. A numeric oscillator in the DDC generates a sine and

a cosine at the center frequency of the band of interest. The sine

and cosine are numerically multiplied with the digitized IF, generating

streams of I and Q baseband samples that contain all of the informa-

tion present in the original IF. The I and Q streams then pass through

variable bandwidth low-pass filters. The cutoff frequency of the low-

pass filters is varied according to the selected span.

I and Q Baseband Signals

Figure 2-3 illustrates the process of taking a frequency band and converting it to baseband using quadrature down-conversion. The original IF signal is contained in the space between three halves of the sampling frequency and the sampling frequency. Sampling produces an image of this signal between zero and one-half the sampling frequency. The signal is then multiplied with coherent sine and cosine signals at the center of the passband of interest, generating I and Q baseband signals. The baseband signals are real-valued and symmetric about the origin. The same information is contained in the positive and negative frequencies. All of the modulation contained in the original passband is also contained in these two signals. The minimum required sampling frequency for each is now half of the original. It is then possible to decimate by two.

Table 2-1: Selected span, decimation and effective sample rates.

(Tektronix RSA3300A Series and WCA200A Series)

Decimation

The Nyquist theorem states that for baseband signals one need only sample at a rate equal to twice the highest frequency of interest. Time and frequency are reciprocal quantities. To study low frequencies it is necessary to observe a long record of time. Decimation is used to balance span, processing time, record length and memory usage.

The Tektronix RSA3300A Series, for example, uses a 51.2 MS/s

sampling rate at the A/D converter to digitize a 15 MHz bandwidth,

or span. The I and Q records that result after DDC, filtering and

decimation for this 15 MHz span are at an effective sampling rate

of half the original, that is, 25.6 MS/s. The total number of samples

is unchanged: we are left with two sets of samples, each at an

effective rate of 25.6 MS/s instead of a single set at 51.2 MS/s.

Further decimation is made for narrower spans, resulting in longer

time records for an equivalent number of samples. The disadvan-

tage of the lower effective sampling rate is a reduced time resolu-

tion. The advantages of the lower effective sampling rate are fewer

computations and less memory usage for a given time record, as

shown in Table 2-1.

Time and Frequency Domain Effects of Sampling Rate

Using decimation to reduce the effective sampling rate has several consequences for important time and frequency domain measurement parameters. An example contrasting a wide span and a narrow span is shown in Figures 2-4 and 2-5. A more through discussion and additional examples can be found in the FAQ in Chapter 4.

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A wide capture bandwidth displays a broad span of frequencies with relatively low frequency domain resolution. Compared to narrower capture bandwidths, the sample rate is higher, and the resolution bandwidth is wider. In the time domain, frame length is shorter, and time resolution is finer. Record length is the same in terms of the number of stored samples, but the amount of time represented by these samples is shorter. Figure 2-4 illustrates a wide bandwidth capture, and Table 2-2 provides a real-world example.

In contrast, a narrow capture bandwidth displays a small span of frequencies with higher frequency domain resolution. Compared to wide capture bandwidths, the sample rate is lower, while the resolution bandwidth is narrower. In the time domain, the frame length is longer, time resolution is coarser, and the available record length encompasses more time. Figure 2-5 illustrates a narrow bandwidth capture, and Table 2-2 provides a real-world example. Note the scale of the numbers such as frequency resolution — they are several orders of magnitude different from the wideband capture.

Real-Time Triggering

The Real-Time Spectrum Analyzer adds the power of the time domain to spectrum and modulation analysis. Triggering is critical to capturing time domain information. The RSA offers unique trigger functionality, providing power and frequency-mask triggers as well as the usual external and level-based triggers.

The most common trigger system is the one used in most oscilloscopes. In traditional analog oscilloscopes, the signal to be observed is fed to one input while the trigger is fed to another. The trigger event causes the start of a horizontal sweep while the amplitude of the signal is shown as a vertical displacement superimposed on a calibrated graticule. In its simplest form, analog triggering allows events that happen after the trigger to be observed, as shown in Figure 2-6(next page)

Fundamentals of Real-Time Spectrum Analysis

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Figure 2-4: Wide capture bandwidth

example.

Figure 2-5: Narrow capture

bandwidth example.

Instrument Settings Wide span Narrow span

Span 15 MHz 1 kHz

Sample Rate 51.2 MS / second 51.2 MS / second

Decimation 2 32000

Effective Sample Rate 25.6 MS / second 1.6 kS / second

Time Domain Effects

Time Domain Resolution (sample) 39.0 nanoseconds 625 microseconds

Spectrogram Time Resolution (frame length) 40.0 microseconds 640 milliseconds

Maximum Record Length (256 MB memory) 2.56 seconds 11.4 hours

Frequency Domain Effects

Frequency Resolution (FFT bin width) 25.0 kHz 1.56 Hz

NBW (noise bandwidth) 43.7 kHz 2.67 Hz

Equivalent Gaussian RBW 41.2 kHz 2.52 Hz

Table 2-2: Comparison of time and frequency domain effects of changing the span setting. (Tektronix RSA3300A Series and WCA200A Series)

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