Tektronix Stereo Receiver AWG 2021 User Manual

Signals and Measurements for  
Wireless Communications Testing  
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Signals and Measurements for  
Wireless Communications Testing  
Introduction  
One of the most challenging tasks in designing  
wireless communications products is the develop-  
ment of a rational approach to characterizing and  
testing components, assemblies, and sub-systems.  
method is expedient but has limited flexibility.  
Creating and editing a customized signal is a more  
powerful technique and is the focus of this note:  
once created, re-creating a complex signal at a later  
Baseband modulation and RF signal characteristics date is as simple as retrieving it from memory—  
are becoming increasingly complex as standards  
and common sense force more efficient use of the  
finite electromagnetic spectrum. In addition,  
manufacturers must often make equipment that is  
capable of switching between different modes with  
differing signal characteristics. As before, realistic  
test signals are needed to simulate nominal and  
worst case conditions. Yet traditional signal gener-  
ators with limited modulation capabilities are  
inadequate and it is not always feasible to have a  
test department develop customized systems.  
rather than re-cabling and re-configuring an assort-  
ment of interconnected generators.  
Ironically, the flexibility of an AWG can make it  
difficult to select a model that fits a given applica-  
tion. For example, you will not find a specification  
that explicitly defines an AWG’s ability to generate  
a particular modulation type. In general, an AWG’s  
ability to generate a specific signal must be demon-  
strated by example.  
In this paper, we begin with examples of basic  
AM-FM analog signals and introduce variations  
such as multiple carriers and multiple modulation  
signals (e.g., FM stereo). Then we demonstrate that  
digital modulation generation is a straightforward  
extension of basic analog modulation.  
Test equipment has historically allowed two  
approaches. If a standard has reached a threshold  
of maturity, then you could obtain a  
generator/analyzer that addresses that standard—  
from a traditional FM broadcast to a digital PCS  
system. Or you could concoct a combination of  
signal, RF, and pattern generators to simulate the  
desired test signal. The former approach is excel-  
lent for production and field service applications  
but lacks flexibility for development applications.  
The latter approach often turns into an expensive  
kluge providing both inconsistent performance and  
limited flexibility.  
Throughout this application tutorial, we have used  
the Tektronix AWG 2021 Arbitrary Waveform  
Generator as the signal source, and the Tektronix  
TDS 744A oscilloscope to capture and analyze  
signals. The AWG 2021 provides the signal capa-  
bilities, modulation features, and bandwidth  
essential to effective wireless communications  
testing. The TDS 744A is an ideal complement to  
the AWG 2021 and is unique in its ability to  
capture signal minutiae.  
More recently, test equipment manufacturers have  
filled the gap between the two approaches with the  
arbitrary waveform generator (AWG). The AWG is  
the signal generator equivalent to the computer  
spreadsheet; you can create limitless “what-if”  
waveforms to more thoroughly evaluate or test new  
concepts, prototype circuits, or production sub-  
assemblies. Like a spreadsheet, the power of the  
AWG comes from the ability to define and re-  
define a signal’s value as a function of time. But a  
blank spreadsheet is of little use—how do you get  
the first waveform to appear at the BNC connector?  
The most straightforward method is the record-  
playback technique. A live signal is recorded into  
the memory of a digital oscilloscope, and the  
record is transferred to the AWG for playback. This  
Certain test setups described in this book may  
require external RF generators to provide carrier  
signals, which are then modulated by the baseband  
signal from the AWG 2021. There are many appro-  
priate RF signal sources available today, including  
products from Tektronix, Rohde & Schwarz, and  
others. For more information about RF sources,  
contact your local Tektronix representative.  
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Analog Carriers and Modulation  
Basic Sine Wave Amplitude Modulation (AM)  
1
The best introduction to the  
AWG is to parallel the procedure period of 1 µs that repeats every  
a single cycle sinusoid with a  
This waveform description can  
be entered in the AWG’s equa-  
tion editor to describe our  
of generating a carrier with a  
conventional signal generator.  
With a signal generator, one  
simply enters the carrier  
frequency and the output ampli-  
tude, such as 1000 kHz at  
0 dBm. With an AWG, one  
creates a sequence of points to  
represent the waveform:  
1 µs. The unique or arbitrary  
part of the signal is a 1 µs series  
of points defined by the above  
equation. If amplitude modula-  
tion is enabled on a signal  
generator, one enters the tone  
modulation frequency and  
depth, such as 1000 Hz at 50%.  
modulated carrier (Figure 1).  
The unique or arbitrary part of  
the continuous waveform is now  
1 ms, so one defines a time range  
of 0 to 1 ms. For convenience,  
define several constants, k0, k1,  
and k2, so that the modulation  
parameters are easily altered.  
Finally, a record length of  
Similarly, with an AWG, one  
adds the modulation to the wave-  
form description:  
A sin ω t  
c
20,000 points is selected,  
keeping in mind the basic AWG  
relationship:  
where A is the peak amplitude  
and ω is the frequency. Since a  
(1+ k sin(ω t)) A sin ω t ,  
c
m
c
0 dBm sinusoid has a peak  
amplitude of 0.316 V  
Record length (points)  
= Waveform period (seconds)  
x Sample rate (points/sec).  
where k is the modulation depth  
between 0 and 1, and ω is the  
m
(0.224 Vrms), the carrier is:  
sinusoidal modulation frequency.  
Thus, our example waveform  
becomes:  
0.316 sin (2π 1000e3 t) Volts.  
For a continuous sinusoid this  
equation applies for all time, but  
the signal can also be defined as  
(1+ 0.5 sin(2π 1000 t) )  
x 0.316 sin (2π 1000e3 t) Volts.  
Figure 1. The AWG’s equation editor permits  
direct entry of the mathematical representation of  
the modulated carrier. Constants k0, k1, and k2  
are used to simplify alterations to modulation  
parameters. The user can directly specify the  
record length — 20,000 points in this case.  
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A record length must be selected sample at least twice as fast as  
The AWG equation compiler  
converts the waveform defini-  
tion to a 1 ms series of 20,000  
points (Figure 2). The AWG can  
repetitively generate this series  
to create the AM carrier in  
Figure 3. The TDS 744A scope  
captures the resulting waveform.  
To aid in scope triggering, the  
AWG was programmed to gener-  
ate a marker signal once per  
period on a separate output.  
that has an adequate number of  
points to reconstruct the desired  
waveform. The waveform period  
is 1 ms and there are 1000  
the analog bandwidth of the  
underlying signal (i.e.,  
1000 kHz). A sample rate of  
20 MHz meets this criterion and  
would require a record length of  
20,000 points. In general, to  
obtain reasonable results the  
sample rate should be at least 3  
times the analog bandwidth of  
the underlying signal.  
carrier cycles in this period. A  
record length of 20,000 points  
would allocate 20 points per  
cycle, which adequately over-  
samples the ideal waveform.  
Any sampling system must  
Figure 2. The AWG’s compiler converts the modu-  
lation equation into a series of points that will  
become the output record. The graphical display  
provides an oscilloscope-like overview of the  
record.  
Figure 3. This is a TDS 744A oscilloscope display  
of the modulated waveform; two complete AWG  
records are shown in this two millisecond display.  
The scope is triggered on one of the two marker  
outputs from the AWG. The marker output was  
programmed to generate a pulse once per record.  
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AM with Adjacent Carriers  
2
A simple addition to the AM  
modulation frequency of the  
signal demonstrates the flexibility adjacent carriers was changed to  
added together. The output level  
can be set as needed using the  
AWG’s setup menu (Figure 5). In  
this case the signal amplitude is  
set to 1 V peak-to-peak. The  
setup menu summarizes key  
waveform parameters such as  
the 20 MHz sampling rate and  
20,000 point record length. The  
resulting spectrum of the three  
modulated carriers is shown in  
Figure 6 (on the following page).  
of equation-based waveform  
descriptions. A common task in  
evaluating receiver performance  
is to evaluate the effect of adja-  
cent carriers. For the basic AM  
3 kHz for later identification,  
and the carrier frequencies were  
altered accordingly. In this case,  
the amplitudes are not explicitly  
selected, and the AWG’s  
signal, one can easily add modu- normalization function (last  
lated carriers 10 kHz above and  
below the original signal  
(Figure 4). One simply adds two  
copies of the basic AM equation  
to the original equation. The  
line) is used to automatically  
scale the peak values encoun-  
tered in the equation to ensure  
that there is no clipping within  
the AWG when the signals are  
Figure 4. Two additional carriers are added  
10 kHz above and below the original carrier. The  
“v” term in the equation is a place holder with the  
current value of the equation. This allows adding  
additional terms on separate lines in the equation  
editor. The cosine operator was used in this  
example. We can still use the 1 millisecond period  
since exactly 3 periods of the 3 kHz adjacent  
channel modulation tones occur in 1 millisecond.  
Figure 5. The AWG’s setup menu allows direct  
entry of the peak-to-peak waveform amplitude.  
The record of the 3-carrier signal is graphically  
displayed.  
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Figure 6. Spectrum analyzer plot of the 3 carriers.  
There are 3 kHz AM on the adjacent carriers and  
1 kHz AM on the original carrier. Note the low  
level of close-in spurious components.  
Frequency (kHz  
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Multi-Tone Testing  
3
The logical extension of adjacent generators as desired tones. And  
75 MHz). In this case, the 1 MHz  
steps suggest a waveform period  
of 1 µs such that the record  
carrier testing is multi-tone test-  
while the generators can be  
phase-locked to a common  
reference, the phase relationship  
ing. In addition to simulating  
multiple carriers in a multi-  
channel system, multi-tones can  
quickly test filter response when  
a scalar or network analyzer is  
not available, or they can iden-  
tify intermodulation products  
resulting from saturation or non-  
linearities in supposedly linear  
component stages. Traditionally,  
multi-tone testing requires  
repeats at a 1 MHz rate. Thus,  
between the independent signals the 65 MHz tone is generated by  
is not absolute.  
65 complete cycles in the 1 µs  
record. The 66 MHz tone is  
generated by 66 complete cycles  
in the record and so on. Thus,  
when the record repeats, all the  
tones are continuous in phase. A  
spectrum analyzer plot of the  
multi-tone signal is shown in  
Figure 8.  
When creating a multi-tone  
using an AWG, the relationship  
between carrier phase is implicit  
in the multi-tone equation.  
Figure 7 shows the AWG equa-  
tion editor specifying 11 tones  
centered at 70 MHz in 1 MHz  
steps (from 65 MHz through  
assembling as many signal  
Figure 7. Eleven tones are added together. The  
record length of 1024 points and a waveform  
period of 1 µs requires a sample rate of  
1.024 GHz. All the tones are in-phase such that  
the maximum value of the multi-tone occurs at  
t=0 (the beginning of the record) when all the  
cosine terms have a value of 1.  
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Figure 8. Spectrum analyzer plot of the 11  
carriers. The tone levels were flat to better  
than 0.25 dB.  
60  
65  
70  
75  
80  
Frequency (MHz  
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The 11 tone equation was then  
modified so that the last 5 tones  
(71 through 75 MHz) are  
second signal where 5 of the  
carriers were inverted at t=0.  
Thus, the crest factor (peak-to-  
rms ratio) of the two signals  
changed from 4.6 (original) to  
3.4 (modified). This difference  
can have dramatic results when  
Absolute control of phase rela-  
tionships means that the AWG  
can ensure repeatable worst case  
testing, which is not possible  
with a non-coherent collection  
of signal generators. The AWG’s  
marker output can simplify in-  
inverted. The two different  
multi-tone results are shown in  
Figure 9. The scope shows that  
the rms levels of the two signals  
are identical, but the peak-to-  
peak values are different. All  
eleven tones in the original  
signal added in-phase at t=0.  
This was not the case with the  
using multi-tones to test for satu- circuit performance characteri-  
ration in transmitter or receiver  
stages. While both signals have  
the same power level, the peak  
levels are quite different.  
zation since a scope can be  
triggered at the exact instant of  
the test signal’s peak value.  
Multi-tone signal  
Inverted tones  
Marker  
Figure 9. Scope plot of the original multi-tone  
(top trace) and multi-tone signal with five tones  
inverted (center trace). The rms levels are the  
same, but the peak-to-peak amplitudes differ.  
The bottom trace is the AWG marker output  
identifying the beginning of the record.  
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Frequency Modulation  
4
Frequency modulation introduces a modulating tone cos (ω t), the  
a multiple of the modulating  
frequency. This means that the  
carrier signal will be phase  
continuous when the 1 ms  
record repeats.  
m
control of the phase argument,  
phase argument becomes:  
Φ, in the basic carrier equation:  
k/ω sin (ω t ),  
m
m
A sin (ω t + Φ ).  
c
where k is the peak frequency  
FM is implemented by varying  
Φ in direct proportion to the  
integral of the modulating  
signal. Thus, for a modulating  
signal m(t), the FM signal can be  
written:  
deviation and k/ω is the FM  
m
Figure 11 shows a spectrum  
analyzer plot of the modulated  
signal. The peak deviation of  
5.52 kHz was selected because a  
modulation index of 5.52 causes  
the carrier component in the  
modulated signal to vanish. This  
is confirmed by noting that the  
0th order Bessel function for a  
modulation index of 5.52,  
modulation index.  
The FM equation is entered  
directly into the AWG’s equation  
editor (Figure 10). The modula-  
tion tone is 1000 Hz, so the  
unique or arbitrary portion of  
the signal repeats every 1 ms.  
Choosing a common FM IF  
A sin (ω t + k m(x) dx )  
c
where k sets the peak frequency  
deviation. For the special case of  
carrier frequency of 10.7 MHz,  
note that the carrier frequency is  
J0(5.52), is zero.  
Figure 10. AWG equation for FM single-tone  
modulation. The peak deviation is 5.52 kHz with a  
modulating tone of 1000 Hz. The carrier  
frequency is 10.7 MHz. A 1 ms period is used  
with a 32,768 point record length; this sets the  
AWG sampling rate to 32.768 MHz.  
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Figure 11. Spectrum analyzer plot of the FM  
signal. The carrier component vanishes for a  
modulation index of 5.52. The carrier would also  
vanish for indices of 2.40, 8.65, and 11.79. This  
is a simple way to verify that the peak deviation of  
an FM signal has been set properly.  
10680 10685 10690 10695 10700 10705 10710 10715 10720  
Frequency (kHz  
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FM with Dual-Tone Modulation  
5
While basic single-tone FM is a  
built-in function of virtually all  
conventional signal generators,  
the AWG waveform parameters  
must be carefully selected. The  
first step is to recognize that  
that takes on values between 0  
and 1 in direct proportion to the  
location within the 16.666 ms  
record. For example, the 17  
dual-tone FM modulation clearly 900 Hz and 1020 Hz are both  
contrasts the flexibility of the  
AWG approach. Dual-tone  
modulation tests can be used to  
measure intermodulation prod-  
ucts in a noise reduction  
integer multiples of 60 Hz. Thus  
a waveform period of 16.666 ms  
will exactly fit an integer  
number of cycles for each tone  
(15 and 17 respectively). The  
next step is to ensure that the  
carrier frequency itself is phase  
continuous in a 16.666 ms  
record. If one wants to inject at  
an IF frequency of 455 kHz, one  
must consider that 455 kHz is  
not an integer multiple of 60 Hz.  
However, with a carrier of  
cycles of the 1020 Hz tone can be  
expressed as sin(2π 17 x). This  
takes the time variable “t” out of  
the equation and is particularly  
useful for fitting exact numbers  
of cycles within an AWG record.  
First, the two tones are added to  
make the modulating signal.  
Next the modulating signal is  
integrated using the AWG’s inte-  
gration function. The integrated  
signal must be scaled by the time  
between each point since the  
integrator integrates point-to-  
point without regard to sample  
rate (which can be changed).  
With a record length of 32768  
points, the 16.666 ms period  
leads to a sample rate of  
compandor (compressor-  
expander) in FM receivers such  
as cordless phones. Standard  
dual-tone compandor test  
frequencies are 900 Hz and  
1020 Hz and a typical minimum  
requirement is that intermodula-  
tion products should be 26 dB  
below the per tone levels. This  
test used to be performed at  
454.98 kHz, exactly 7583 cycles  
of the carrier frequency fit in the  
audio frequencies since compan- 16.666 ms period. The 20 Hz  
dors work in the audio band. But error, less than 50 ppm, is irrele-  
highly integrated receivers may  
not offer direct access to the  
compandor circuit, so the dual-  
tone signal must be injected as a  
modulated IF signal.  
vant for all practical purposes.  
Figure 12 shows the waveform  
definition in the AWG’s equation  
editor. We take advantage of an  
equation compiler function  
1.966 MHz. Finally, the integrated  
modulating signal is inserted  
into the phase argument of the  
basic carrier equation with a  
peak deviation of 3 kHz per tone.  
The apparently odd combination which allows the parameter “x”  
of tone frequencies means that  
to represent a dummy variable  
Figure 12. Description of a dual-tone FM signal.  
The modulating tones are 900 Hz and 1020 Hz  
on a 455 kHz carrier. The record length is  
32,768 points, the waveform period is 16.666 ms,  
and the sample rate is 1.966 MHz. This FM signal  
is used to test the intermodulation distortion  
performance of a syllabic expander in an FM  
receiver.  
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Figure 13 shows the demodu-  
lated output from an FM  
receiver with the expander  
disabled and enabled. The top  
two-tone signal and its spectrum  
as calculated by the TDS 744A  
FFT function. The lower two  
traces show the same signals  
intermodulation products are  
now significant, with the first  
order products about 35 dB  
below the fundamental tones.  
two traces show the unexpanded with the expander enabled. The  
Demodulated output, unexpanded  
Unexpanded spectrum  
Demodulated output, expanded  
Expanded spectrum  
Figure 13. The TDS 744A shows the intermodu-  
lation performance with expanders disabled and  
enabled. There is no distortion with the expander  
disabled. The first order intermodulation products  
are about 35 dB below the fundamental tones  
with expanders enabled.  
13  
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FM Stereo  
6
A final example of conventional  
definition in the AWG’s equa-  
tion editor. This example uses a  
5 ms waveform period, a 32768  
point record, and a sampling  
rate of 6.5536 MHz. The carrier  
will be 455 kHz, which can be  
mixed externally to an appropri-  
ate IF frequency.  
carrier which is phase-locked  
(implicit in the equation defini-  
tion) to the 19 kHz pilot. Unlike  
the previous AM example,  
suppressed carrier modulation is  
used, where the carrier is  
suppressed if there is no modu-  
lating signal (the “1” term is  
absent from the modulation  
product term). The three terms  
are integrated to implement FM  
modulation; the integration  
output is scaled by the sampling  
rate as described earlier. Finally,  
the integrator output is inserted  
into the phase term of the sinu-  
soidal carrier with a peak devia-  
tion of 10 kHz per audio tone.  
analog modulation combines  
most of the above techniques to  
simulate the stereo modulation  
used in broadcast FM. The  
modulating signal consists of  
three components, 1) the  
composite audio which is the  
sum of the left and right (L+R)  
channels, 2) the stereo pilot  
signal which is a 19 kHz tone,  
and 3) the difference (L-R) signal  
which amplitude modulates a  
38 kHz carrier. These three  
components are summed  
The left channel signal is an  
800 Hz tone and the right chan-  
nel signal is a 1000 Hz tone. The  
composite audio signal (L+R) is  
made by summing the two tones.  
The 19 kHz pilot tone is then  
summed at half the amplitude of  
the audio tones. The (L-R) signal  
amplitude modulates a 38 kHz  
together and modulate the  
carrier using conventional FM.  
Figure 14 shows the waveform  
Figure 14. Definition of the stereo FM signal. The  
waveform period was 5 ms. All the modulating  
components have an integer number of cycles  
within the record (i.e., they are multiples of  
200 Hz) so the signal is phase continuous.  
14  
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The resulting 455 kHz signal is  
mixed up to the broadcast band  
and inserted into a stereo  
receiver. The stereo indicator is  
turned on, and the resulting left  
and right output signals are  
traces are the right channel  
cast is not unique. Higher sub-  
carriers are commonly used to  
encode specialized audio  
channels or pager data to take  
advantage of the coverage of  
commercial FM transmitters.  
(1000 Hz) signal and spectrum.  
The lower two traces are from  
the left channel (800 Hz). The  
stereo encoding was successful  
with the receiver separating the  
captured on the TDS 744A scope two tones by over 35 dB. The  
(Figure 15). The upper two 38 kHz sub-carrier in FM broad-  
Right channel and spectrum  
Left channel and spectrum  
Figure 15. After demodulation by an FM receiver,  
the TDS 744A displays the left and right channels  
and their spectra. The receiver separated the  
800 Hz and 1000 Hz tones by over 35 dB  
(spectrum scales are 250 Hz/div horizontal and  
20 dB/div vertical).  
15  
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Adding Noise to a Carrier Signal — AWG Noise Characteristics  
7
Although the removal of noise is  
a common design goal, a noise  
source can be an extremely  
definite implications for the  
spectral characteristics of the  
signal. The second property  
arises because an AWG noise  
waveform is simply another pre-  
calculated record that must  
eventually repeat to obtain a  
continuous signal.  
values, but circuit noise is better  
modeled with a Gaussian distri-  
bution. In practice, the AWG  
actually calculates a noise value  
by averaging 12 consecutive  
random numbers. Thus, by the  
central-limit theorem, the noise  
values will more closely approx-  
imate a Gaussian distribution  
than the underlying uniform  
distribution.  
useful test stimulus or signal  
impairment. The AWG 2041  
provides a built-in noise func-  
tion, but its characteristics are  
quite different than traditional  
sources such as noise diodes. An  
Calculating Noise  
1
AWG noise waveform is actu-  
The AWG provides a built-in  
function to calculate the noise  
waveform of a specified record  
length. In Figure 16, the AWG  
creates a 32768 point noise  
waveform. Digital random  
number generators typically  
produce uniformly distributed  
ally a calculated series of  
pseudo-random numbers. There  
are two key properties of the  
AWG noise function. First, the  
AWG noise signal is actually a  
series of voltages that changes  
once per clock period. This has  
The top trace in Figure 17 shows  
the resulting noise output. The  
key feature relating to the clock  
is that the waveform appears to  
be a staircase function. The  
sharp edges can be removed by  
Figure 16. The noise waveform is a built-in func-  
tion in the AWG. In this case, the 32768 point  
record length specifies a pseudo-random series  
of values. The values are approximately Gaussian  
in distribution with a crest factor of about 3 to 1.  
Pseudo-random noise sequence  
Filtered sequence  
Filtered and unfiltered spectra  
Figure 17. Upper waveform is a pseudo-random  
sequence with a 32.768 MHz clock. The second  
waveform is the same signal filtered by the  
AWG’s 10 MHz Bessel low-pass filter. The lower  
two traces are the calculated FFT spectra. The  
horizontal scale of the spectra is 10 MHz per  
division.  
1
AWG refers to Arbitrary Waveform Generator as opposed to Additive White Gaussian, an unfortunate coincidence in this context.  
16  
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the AWG’s 10 MHz low-pass  
filter (middle trace). The  
TDS 744A FFT spectra for the  
two signals are overlaid below  
the time domain waveforms. The  
salient characteristic of the  
unfiltered noise spectrum is that  
it rolls off with a (sin x)/x func-  
tion with the first null at the  
32.768 MHz clock frequency and  
subsequent nulls at multiples of  
the clock rate. If the goal is to  
add this noise waveform to the  
10.7 MHz FM carrier, then noise  
density is required only in the  
vicinity of 10.7 MHz. The  
account for the clock rate depen- option with pre-calculated AWG  
dent roll-off.  
waveforms, the effect of the peri-  
odicity can be reduced by  
Maximizing “Randomness”  
The second property to consider  
when using the AWG noise  
increasing the period of the  
noise waveform relative to the  
corresponding signal waveform.  
Figure 18 shows how the AWG’s  
sequence editor converts the  
32K point FM waveform into a  
256K point waveform which is  
simply 8 concatenated copies of  
the same waveform. Thus, if the  
same clock waveform of  
waveform is to observe that the  
noise waveform itself is a pre-  
calculated series of points that  
will repeat at each period of the  
record length. The period of the  
32K point noise waveform at a  
32.768 MHz sample rate is 1 ms  
and the exact noise waveform  
repeats at a rate of 1 kHz. This  
periodicity translates into the  
resulting noise spectrum. The  
ideal noise waveform would  
exhibit no periodicity (i.e., no  
repetition). While this is not an  
32.768 MHz is used, the resulting  
signal waveform is identical.  
However, if a 256K noise wave-  
form is generated, then the  
filtered noise signal is a suitable  
bandwidth-limited source. Thus,  
when using the AWG noise  
period of the noise waveform is  
increased by a factor of 8.  
function, one consideration is to  
Figure 18. The 32K point FM waveform can be  
converted to a 256K point waveform by simply  
sequencing or concatenating 8 copies of the  
original 32K waveform. This expansion means  
that a 256K noise waveform can be added to the  
FM waveform instead of a 32K noise waveform.  
17  
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The AWG’s graphical waveform  
editor provides a variety of  
mathematical operators for exist- waveform and the 256K point  
ing waveforms. Waveforms can  
be combined with other  
waveforms, or a waveform can  
be squared, scaled, differenti-  
ated, integrated, etc.  
waveform editor (Figure 19).  
The spectra of the 32K point  
waveforms with the minimum  
number of record points, noise  
waveforms should be created  
with the maximum number of  
record points! The two objec-  
tives are resolved by creating a  
longer version (to match the  
noise record length) of the signal  
waveform by sequencing multiple  
copies of itself.  
waveform are overlaid in  
Figure 20. Recall that the period  
of the 32K point waveform is  
1 ms. You can see that the noise  
“floor” of the spectrum of the  
32K point waveform is a series  
of discrete components spaced  
1 kHz apart. Thus, even though  
the objective is to define signal  
Combining the Noise  
with the Carrier  
The signal and noise waveforms  
are summed using the AWG’s  
Figure 19. The 32K point FM waveform is added  
to the 32K point noise waveform.  
-20  
-30  
-40  
-50  
-60  
-70  
-80  
-90  
Figure 20. Spectrum analyzer plots of the  
32K point FM carrier plus noise (lighter) and the  
256K point FM carrier plus noise. Longer noise  
waveforms repeat less often so the noise density  
characteristics will be flatter.  
10670  
10680  
10690  
10700  
10710  
10720  
10730  
Frequency (kHz  
18  
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Digital Modulation  
Digital Phase Modulation — PSK  
8
The modulating signals in the  
foregoing examples have been  
sinusoidal or continuous wave-  
forms. A simple step to digital  
by rounding and scaling the  
continuous waveform to the  
nearest eighth. This quantized  
modulating pattern is then  
modulation is made with a slight directly inserted in the phase  
variation to sinusoidal modula-  
tion. Figure 21 shows one cycle  
of a sinewave that has been  
quantized into steps between  
–0.5 and +0.5. The equation  
defining these steps is shown in  
Figure 22. The second line  
argument of a cosine carrier.  
Thus, the phase argument takes  
on values between –π to +π in  
π/4 steps. If the polar graphical  
representation of the signal is  
used, a family of eight points of  
equal magnitude is defined,  
spaced around the circle in π/4  
simply quantizes a cosine wave  
or 45° phase increments.  
Figure 21. The sinusoidal modulating pattern is  
quantized into discrete steps. The steps are  
equally spaced in amplitude and will shift the  
phase of the carrier in π/4 or 45° increments.  
19  
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Figure 22. The equation defining the quantized  
1 MHz modulating pattern and its subsequent  
insertion into the phase argument of the 50 MHz  
carrier. The modulating pattern shown in Figure  
21 is the result of the rounding definition.  
The record length of 1024 points  
and a waveform period of 1 µs  
requires a sampling rate of  
1.024 GHz. The resulting carrier  
frequency is 50 MHz. Since each  
level represents one of eight  
states or symbols, 3-bits of data  
can be transmitted per symbol.  
Of course, no data per se is  
Figure 23 shows the resulting  
AWG output. The top trace is  
the marker output generating a  
scope trigger pulse once per  
record. The second trace is the  
phase modulated waveform. The  
third trace is the carrier wave-  
form without the phase modula-  
tion. That is, the phase argument  
was removed from the final  
equation line on the AWG in  
Figure 22, leaving just the  
associated with this particular  
modulating pattern since a  
sinusoid was quantized without  
regard to the symbol or baud rate. expression cos (2*pi*50*x). This  
waveform was captured sepa-  
rately by the TDS 744A but is  
synchronized to the same trigger  
Marker (trigger)  
Phase modulated waveform  
Carrier waveform  
Product  
Figure 23. Scope plot of the marker output (top  
trace) and the phase modulated 50 MHz carrier  
(2nd trace). The 3rd trace is the carrier without  
the modulation. The bottom trace is the product  
of the unmodulated carrier (constant Φ=0) and  
the modulated carrier.  
20  
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Baseband Digital Patterns  
9
Before continuing with exam-  
be used by altering more than  
one bit at each record point. In  
addition to direct data entry, the  
AWG can automatically generate  
pseudo-random data streams.  
Figure 25 shows the setup for a  
length = 9 linear feedback shift  
16,352 points.  
ples of digital modulation, it is  
important to establish a method  
of creating arbitrary test data  
patterns. Figure 24 shows direct  
entry of a 28-bit binary pattern.  
In this case, the 0 or 1 value of  
In some applications, the data  
pattern itself is the desired  
output signal for the AWG. For  
example, the data pattern can be  
the baseband modulation signal  
to an external RF generator or  
modulator. However, the  
following examples use the  
simple 28-bit, 28,000 point  
record as the baseband signal in  
demonstrating several digital  
modulation techniques.  
each data bit is repeated for 1000 register that repeats only after  
points in the record, which  
requires a record length of  
28,000 points. A binary data  
pattern requires only one bit of  
the AWG’s dynamic range.  
Multi-level digital encoding can  
511 data bits. As with direct  
entry, the number of record  
points per data bit can be speci-  
fied. In this case, each bit  
repeats for 32 data points,  
requiring a record length of  
Figure 24. A binary or hex (4-bit) data pattern  
can be directly entered from the keypad. The  
AWG directly translates a variety of encoding  
formats such as NRZ, RZ, and NRZI. The number  
of record points that each bit interval occupies  
can be specified.  
Figure 25. The pseudo-random generator  
supports register lengths from 2 to 32 bits. The  
binary output stream from the generator can be  
assigned to a specific bit in the output range or to  
one of the marker bits.  
21  
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Digital AM — OOK and BPSK  
10  
The simplest example of digital  
(middle) to produce the modu-  
lated carrier (bottom). Since  
If the data pattern is simply  
shifted vertically so that it takes  
on bipolar values of –1 and +1,  
instead of 0 and 1, then the  
modulation inverts the sign of  
the carrier. Since inverting the  
sign is equivalent to shifting the  
phase argument of the carrier by  
π, this implements two-state or  
binary phase-shift keying  
modulation is to turn the carrier  
on or off, depending on the state  
of the modulation data. On-off  
keying (OOK) can be directly  
implemented by multiplying a  
carrier by the 1 or 0 value of the  
data pattern. This example uses a  
10.7 MHz carrier created in a  
28,000 point record to match the  
record length of the data pattern.  
The AWG sampling rate is  
40 MHz so the record period is  
700 µs. Since each of the 28 data  
values occupies 1000 record  
points, the data rate is 40 kbaud.  
Figure 26 shows how the AWG’s  
dual waveform math capability  
multiplies the data pattern (top  
display) and the 10.7 MHz carrier  
10.7 MHz is a popular receiver IF  
frequency, these signals can be  
directly injected at the appropri-  
ate receiver point to characterize  
demodulator performance. The  
AWG’s sequencing and triggering  
capabilities are particularly  
useful in OOK remote-control  
device simulations. The AWG  
can generate single or occasional  
bursts with varying parameters  
(BPSK). Figure 27 illustrates the  
same AWG setup except that the  
modulating pattern is offset  
such as carrier frequency offset or using the shift and scale func-  
data rate. The burst itself can be  
amplitude modulated with  
tions. The resulting BPSK has a  
constant envelope since the  
another waveform to simulate the magnitude of the multiplier is  
power ramping found in many  
battery-powered transmitters.  
always 1.  
Data pattern  
Carrier  
Modulated carrier (output signal)  
Figure 26. OOK: The “1” and “0” values of the  
data pattern turn the carrier on and off. The  
carrier frequency is 10.7 MHz. The data rate is  
40 kbaud.  
Data pattern  
Carrier  
Modulated carrier (output signal)  
Figure 27. BPSK: The 28-bit data pattern is  
shifted and scaled to generate a bipolar pattern.  
This implements BPSK modulation when multi-  
plied by the carrier. The BPSK waveform has a  
constant envelope.  
22  
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Digital FM — FSK  
11  
The modulating data alters the  
carrier frequency in  
frequency-shift keying (FSK). A  
digital modulation index of 0.5  
the AWG’s mathematical preci-  
sion. First, a second 28-bit data  
pattern is generated which is the  
1’s complement of the original  
pattern. Then two 28,000 point  
carriers are generated at  
10.690 MHz and 10.710 MHz.  
Note that the carriers are phase  
continuous since exactly 7483  
and 7497 cycles, respectively, of  
the carriers fit in the 700 µs  
record. The upper waveform is  
the 10.690 MHz carrier  
multiplied by the original data  
pattern, and the middle wave-  
form is the 10.710 MHz carrier  
multiplied by the complemented  
pattern. If the two waveforms are  
added (bottom trace), then the  
carrier shifts between the two  
frequencies exactly at the data  
transitions. The spectra of the  
two unmodulated carriers and  
the modulated FSK signal are  
shown in Figure 29.  
is used in this example; that is,  
1
the frequency shift will be ⁄  
2
the  
40 kbaud data rate or 20 kHz. If  
the carrier remains centered at  
10.7 MHz, this results in the two  
data frequencies of 10.710 MHz  
and 10.690 MHz. Figure 28  
shows one way to implement  
binary FSK to take advantage of  
Carrier x data pattern  
Carrier x data complement  
Sum  
Figure 28. FSK: Upper waveform is the  
10.690 MHz carrier amplitude modulated by the  
data pattern. Middle waveform is the 10.710 MHz  
carrier modulated by the complemented pattern.  
The sum of the two waveforms shifts between the  
two frequencies at data transitions.  
0
-10  
-20  
-30  
-40  
-50  
-60  
-70  
-80  
-90  
Figure 29. Spectrum analyzer plots of the two  
unmodulated carriers, at 10.690 MHz and  
10.710 MHz, and an overlay of the FSK signal  
with the 28-bit modulation.  
10650  
10670  
10690  
10710  
10730  
10750  
Frequency (kHz  
23  
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As previously mentioned, the  
AWG’s two binary marker  
real time with the AWG’s main  
signal output. The third trace is  
the FSK modulated signal with  
no indication of modulation  
since it is a constant envelope  
waveform. However, a coherent  
copy (using a marker pulse at  
the same record point) of the  
10.710 MHz unmodulated  
carrier. When the data is 0, the  
FSK signal is at 10.710 MHz and  
the coherent demodulation  
yields a positive-only compo-  
nent. When the data is 1 (e.g,  
between the cursors), the  
frequencies are not equal and a  
constant frequency difference  
during the interval generates a  
beat component at 20 kHz. Note  
that the time between peaks, or  
the period of the beat product, is  
50 µs or 20 kHz.  
output signals can be modulated  
with a data pattern. Figure 30  
shows how this can be used as a  
tool for testing or troubleshooting  
digital receivers. One marker  
output is programmed to  
generate a trigger pulse at the  
beginning of each 700 µs record  
carrier is captured and saved in  
(top trace). The second marker is the TDS 744A reference  
programmed with the 28-bit data memory. The lower trace is the  
pattern (second trace). The two  
marker signals are generated in  
real-time product of the FSK  
signal and the coherent reference  
Trigger pulse  
28-bit data pattern  
FSK modulated signal  
Reference copy of unmodulated carrier  
FSK signal x carrier  
Figure 30. The TDS 744A triggers on AWG’s once  
per record marker output (top trace). The TDS  
744A multiplies the FSK signal by one of the  
reference frequencies (lower trace). The data  
pattern can be demodulated by inspection and  
verified by the actual data pattern generated by  
the AWG’s second marker output (second trace).  
24  
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Quadrature Modulation  
12  
Multi-level data modulation  
an orthogonal quadrature  
Signal impairments are easily  
generated with this approach.  
The cosine or sine carrier (before  
modulation) can be altered  
relative to each other in phase or  
amplitude to simulate errors in  
the modulated signal. For exam-  
ple, the cosine carrier could be  
splits the amplitude, frequency,  
or phase of the carrier into more  
than two discrete states. 8-PSK  
previously demonstrated direct  
control of the phase Φ in the  
component (Q). Thus, if we  
select 16 equally spaced points  
to send 4 bits of information per  
symbol, then we can easily  
transmit the symbols by ampli-  
tude modulation of two carriers.  
equation A cos(ω t + Φ); A was  
c
constant. The eight symbols  
were equally spaced points  
around the polar axes.  
Alternatively, the I-Q mapping  
can be used by noting the  
relationship:  
For example, the I component  
altered from cos(ω t) to  
c
3
1
1
3
could be – ⁄4, – ⁄4, ⁄4, or 4 times  
cos(ω t+δ) where δ is a small  
c
cos(ω t). The Q component  
c
offset to move the two carriers  
out of quadrature. Or the levels  
of the baseband data pattern can  
be altered in the waveform  
would be one of the same  
multipliers applied to sin(ω t).  
c
Figure 31 illustrates a 28-symbol  
pattern, each with one of these  
four multipliers. Each quadra-  
ture component carries 2 bits of  
information. Figure 32, on the  
following page, illustrates the  
creation of the quadrature ampli-  
tude modulated carrier using the  
AWG’s waveform editor. The top  
waveform is the I pattern modu-  
lating the 10.7 MHz cosine  
A cos(ω t + Φ)  
c
editor to corrupt the uniform  
spacing of the 16 symbols. To  
accomplish quadrature modula-  
tion at appropriate frequencies,  
it may be necessary to couple  
the AWG with a specialized  
dual-input RF signal generator  
designed to handle I and Q  
information. Figure 33 depicts  
the interconnection of the two  
instruments, as well as the other  
elements of the test setup.  
= A cos Φ cos(ω t) – A sin Φ sin(ω t)  
c
c
That is, any symbol location can  
be expressed as a vector sum of  
an in-phase (I) component and  
carrier. A separate 28-symbol  
Q pattern was created and  
modulates the 10.7 MHz sine  
carrier in the middle waveform.  
The two waveforms are  
combined in the third pattern.  
Figure 31. The AWG’s waveform editor was used  
to generate this 28-symbol data pattern which  
has four potential uniformly spaced levels per  
symbol.  
25  
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I pattern x carrier  
Q pattern x carrier  
Sum  
Figure 32. Quadrature amplitude modulated  
(QAM) signal generated by combining an  
amplitude modulated cosine carrier (upper) and  
an amplitude modulated sine carrier. There are  
16 symbols, so this is 16-QAM.  
Controller (PC)  
Oscilloscope (DSO)  
AWG  
Ch. 1 Out  
Ch. 2 Out  
Discrete I Signal  
Discrete Q Signal  
Figure 33. This block  
diagram shows the  
setup for quadrature  
modulation. For more  
information about  
suitable RF sources,  
contact your local  
Tektronix  
I In  
Q In  
DUT  
I/Q Modulated RF Out  
RF Generator  
representative.  
26  
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Filtering Out Unwanted Sidebands  
13  
One effect of the edge transitions AWG directly performs the  
equal to 0.31/B, where B is the  
filter bandwidth in Hz. Figure 35  
shows the implementation in the  
AWG’s equation editor. The key  
parameter to select is the half-  
width. This example uses a BT  
parameter of 0.5, where B is the  
filter bandwidth and T is the  
data period (25 µs). This means  
the bandwidth must be 20 kHz  
in digital modulation patterns is  
a wider than desired occupied  
spectrum of the transmitted  
signal. The solution is to filter  
the baseband digital signal  
before it modulates the carrier.  
The two most common filter  
types for this application are  
Gaussian and Nyquist filters.  
Application of the Gaussian  
filter is illustrated here, though  
the process for applying any  
filter type is the same. The base-  
band modulating pattern is  
filtered by convolving it with the  
impulse response of the desired  
filter in the time-domain. The  
convolution function. Figure 34  
shows the convolution setup.  
The upper left waveform is the  
28,000 point data pattern, while  
the lower left waveform is the  
2000 point Gaussian impulse  
response. The result of the  
convolution process is shown at  
the right.  
and the PW = 15.5 µs. By trial  
50  
The impulse response of the  
Gaussian filter is defined by:  
and error it is determined that a  
50 µs total pulse interval defines  
the total response so that both  
tails drop to zero within the  
interval. For the sample rate of  
40 MHz, this requires a record  
length of 2000 points.  
2
2
h(t) = exp {–t /2s },  
where s = PW /(2 (2 ln(2)).  
50  
PW is the half-width for the  
50  
pulse and is approximately  
Data pattern  
Resulting convolved signal  
Gaussian impulse response  
Figure 34. The data pattern (upper left) is  
convolved with the Gaussian impulse response  
(lower left). The result is the filtered data pattern.  
The convolution of the two waveforms produces a  
new waveform that is 30,000 points long. This is  
the sum of the two individual waveform lengths  
and is a by-product of the convolution process.  
Figure 35. The Gaussian impulse response is  
defined by the pulse half-width, which is approxi-  
mately equal to 0.31/B, where B is the –3 dB filter  
bandwidth. The constant k1 offsets the peak of  
the impulse response to the center of the record.  
27  
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The convolution result is 30,000  
points long. Note that the  
impulse response is 2000 points  
long, which is longer than the  
1000 points per data bit. This  
means that each data bit affects  
created by adjoining copies of  
discontinuities when concate-  
the same waveform record. What nated.  
is to be done with the extra 2000  
Of course this was a selected  
example. The general solution to  
insuring that a convolved  
points? In the example, a data  
pattern was selected in which  
the last two bits are 00. This  
pattern can be concatenated is to  
add extra bits to the ends of the  
pattern before convolution. The  
extra bits simply duplicate the  
bits that would be there for a  
repeating pattern. In other  
words, add the first few bits of  
the data pattern to the end of the  
pattern. The number of bits to  
add depends on the length of the  
impulse response.  
more than the 1000 points that it means that the last two bits  
immediately occupies. Hence, a  
possible anomaly must be  
(2000 points) do not contribute  
to the convolved response, and  
accounted for in the convolution it matches the convolution  
process. The AWG assumes that  
assumption that the data before  
the data before and after the data the first bit in the pattern is 0.  
pattern is 0. It does not “know”  
that the data pattern is to repeat  
over and over. However, a  
Thus, the 2000 points can be  
simply removed from the 30,000  
point record, and the 28,000  
point record will not have any  
continuous signal is being  
Unfiltered data pattern  
FFT of unfiltered data  
Filtered data pattern  
FFT of filtered data  
Figure 36. The TDS 744A captures the filtered and  
unfiltered data patterns and calculates their FFT  
spectra. The data rate is 40 kbaud, and the  
Gaussian filter has a 20 kHz bandwidth. The hori-  
zontal scale on the spectra is 25 kHz per division.  
Filtered data pattern  
Carrier (10.7 MHz)  
Product  
Figure 37. BPSK with filtered data: The AWG  
waveform editor performs the BPSK modulation  
of the 10.7 MHz carrier with the Gaussian filtered  
28-bit data pattern. Compare to Figure 27 where  
the data was unfiltered: the transition time  
between the two complementary phases has been  
dramatically increased.  
28  
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Figure 36 compares the original  
and filtered data patterns. The  
upper two traces are the unfil-  
tered data pattern and its spec-  
trum. The lower two traces are  
the filtered data pattern and its  
spectrum. Note how the spec-  
trum of the filtered version rolls  
off more quickly. The spectrum  
of a modulated carrier shows the  
same results. Figure 37 shows  
the filtered baseband pattern  
modulating (BPSK) the  
10.7 MHz carrier, as in Figure 27. of the symbol period. Using the  
Figure 38 shows the difference  
in their spectra.  
clock output defines the center  
marker output as a data clock  
provides a convenient reference  
when characterizing the perfor-  
mance of symbol timing recov-  
ery circuits. Careful attention  
was given to wrapping data at  
the ends of the data patterns so  
that the convolution result  
would be continuous across the  
seams.  
The convolution operator can be  
applied to multi-level patterns.  
Figure 39 shows Gaussian  
filtered I and Q baseband  
patterns for the 16-QAM signal  
in Figure 32. (The unfiltered I  
pattern is shown in Figure 31.)  
The falling edge of the data  
0
-10  
-20  
-30  
-40  
-50  
-60  
-70  
-80  
Figure 38. Spectrum analyzer plots of unfiltered  
(upper) and BT=0.5 Gaussian filtered (lower)  
BPSK carriers at 10.7 MHz. The data rate is  
40 kbaud. Compare the roll-off to the baseband  
roll-off in Figure 35.  
10500 10550 10600 10650 10700 10750 10800 10850 10900  
Frequency (kHz  
AWG data clock output  
I baseband pattern  
Q baseband pattern  
Figure 39. Gaussian filtered multi-level baseband  
modulation is shown. The AWG generated a data  
clock output on one of its marker outputs. The  
bottom trace is the other AWG marker output  
generating a once per pattern pulse for scope  
triggering.  
29  
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Direct Sequence Spread Spectrum  
14  
The final example of digital  
modulation spreads the energy  
in a BPSK signal by amplitude  
modulating the carrier with a  
spreading pattern. In the same  
way that the baseband data  
pattern spreads the energy of an  
unmodulated carrier, a spread-  
ing pattern further spreads the  
energy of a modulated carrier.  
Pseudo-random sequences are  
generally used as the spreading  
pattern, with a bit rate or chip-  
ping rate that is much higher  
than the data bit rate. The  
511-bit pseudo-random  
sequence generated in Figure 25  
is used as the spreading  
Figure 40 shows how the AWG’s  
waveform editor can horizontally  
interpolate a waveform into  
sequence—the assumption being another record size. The spread-  
that a receiver would use the  
same sequence to de-spread the  
signal. Since the data pattern is  
28 bits, one can directly imple-  
ment a chipping rate to data rate  
ratio of 18.25 or (power reduc-  
tion of 12.6 dB) by simply  
ing is implemented by using the  
AWG waveform editor to multi-  
ply the spreading sequence and  
the modulated BPSK carrier  
from Figure 37. The spectra of  
the original and spread signals  
are shown in Figure 41. The first  
null in the spread signal occurs  
at the chipping rate of 730 kHz,  
which is 18.25 times the 40 kHz  
data rate.  
mapping the 511-bit sequence  
into 28,000 AWG record points.  
Figure 40. The AWG waveform editor performs  
horizontal scaling of the 511-bit spreading  
sequence. The original record length was  
16,352 points. A “new” size of 28,000 points is  
entered, and the AWG expands and interpolates  
the waveform by a factor of 1.71.  
0
-10  
-20  
-30  
-40  
-50  
-60  
-70  
-80  
Figure 41. Spectrum analyzer plots of the BPSK  
carrier at 10.7 MHz before and after a 511-bit  
pseudo-random spreading sequence. The data  
rate is 40 kbaud and the chipping rate is 730 kHz.  
The original spectrum is the same as the filtered  
spectrum in Figure 38, but it is displayed here at  
a wider span.  
9700  
10200  
10700  
11200  
11700  
Frequency (kHz  
30  
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For More Information on Tektronix Instrumentation  
Tektronix offers a broad line of signal sources and electronic measurement products for engineering,  
service, and evaluation requirements in virtually every industry.  
For detailed information about the Tektronix tools used in developing this booklet, consult the  
appropriate brochures and data sheets for the respective products:  
Signal Sources brochure . . . . . . . . . . . . . . . . . . . . . . . . . . .11252  
AWG 2005 data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11372  
AWG 2021 data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11561  
AWG 2041 data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11371  
AFG 2020 data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11297  
Signals and Measurements for Disk Drive Design . . . . . . .11478  
TDS 700A family brochure . . . . . . . . . . . . . . . . . . . . . . . . .11483  
TDS 700A family data sheet . . . . . . . . . . . . . . . . . . . . . . . .11031  
To order any of these documents:  
From within the U.S.A., call 1-800-426-2200; when prompted press “3” and ask for Code 454.  
Outside of the U.S.A., call the nearest Tektronix sales office.  
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AWG 2000 Series Arbitrary Waveform Generators  
Tektronix AWG Arbitrary  
of the AWG’s standard wave-  
forms, or define your own from  
scratch. Using their powerful  
editing tools, you can edit the  
waveform right on the screen,  
then clock it out at rates up to  
1 GS/s.  
record formats are identical to  
those of the benchtop unit. As  
such, the VX4792 allows easy  
movement of waveforms and  
instructions from the design lab  
to the production line.  
Waveform Generators give the  
most extensive capabilities for  
editing waveforms, with 8 or 12  
bits of vertical resolution and  
waveform frequencies to  
500 MHz. AWGs contain a high  
speed, high resolution digital to  
analog convertor with sophisti-  
cated triggering and mode  
Where the utmost signal purity  
For computer-controlled produc- is required, the AFG 2020  
tion test applications demanding Arbitrary Function Generator  
high throughput, the AWG 2021  
is available in VXI format as the  
VX4792. This uncompromised  
signal source delivers the same  
bandwidth and accuracy as the  
AWG 2021, and its waveform  
offers direct digital synthesized  
waveforms with exceptionally  
low distortion and high  
frequency agility.  
settings, plus up to 4 megabytes  
of internal memory in which to  
create and edit waveforms.  
You can import a waveform  
from a scope or disk, select one  
AWG 2041  
AWG 2021  
250 MS/s  
125 MHz  
AWG 2005  
20 MS/s  
Clock Rate  
1 GS/s  
Max Output Waveform Frequency 500 MHz  
10 MHz  
Region Shift  
Yes  
Yes  
Yes  
Direct Waveform Transfer  
from DSOs  
TDS, 2000 Series, 11000 Series,  
DSA, RTD 700 Series, and others  
Same as AWG 2041  
Same as AWG 2041  
External Clock  
Clock In & Out  
Same as AWG 2041  
Same as AWG 2041;  
Same as AWG 2041  
Graphical Waveform Editing  
Draws, Timing Table, Equation;  
Same as AWG 2041;  
FFT (Opt. 09), Digital Word/Pattern  
Generator (Opt. 03)  
TTL Digital Word Generator  
(Opt. 03)  
Digital Word/Pattern Generator option  
not available  
Max P–P Amplitude into 50  
Memory: Execution per Channel  
Memory: Non-Volatile  
External Modulation  
2 V  
5 V  
10 V  
1 MB; expandable to 4 MB (Opt. 01)  
256 kB per channel  
64 kB per channel  
512 kB  
AM  
512 kB  
AM  
512 kB  
AM  
Output Channels  
1 Analog & Complement;  
8 ECL Digital (Opt. 03)  
1 Analog;  
2 Analog (Opt. 02);  
12 ECL Digital (Opt. 03);  
24 TTL Digital (both Opt. 02 and 04)  
2 Analog;  
4 Analog (Opt. 02);  
24 TTL Digital (Opt. 04);  
Predefined Waveforms  
Sweep  
Synthesized, 10 MHz  
Synthesized, 2.5 MHz  
Same as AWG 2041  
Synthesized, 2.5 MHz  
Sequencer and Equation Editor  
used to create sweep  
Linear; Log; User-defined (Opt. 05)  
Time Base Accuracy  
Vertical Resolution  
Built-In Floppy Drive  
1 ppm  
8 bits  
Yes  
50 ppm  
12 bits  
Yes  
5 ppm  
12 bits  
Yes  
32  
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TDS 744A Digitizing Oscilloscope  
The TDS 744A represents the  
acquisitions per second—a rate  
2,500 times faster than the most  
advanced DSOs available.  
sophisticated documentation  
capability.  
next generation of digitizing  
scope performance. This versa-  
tile general-purpose instrument  
With its long record length and  
high bandwidth, the TDS 744A  
is an ideal complement to the  
2000 Series AWGs for wireless  
communications testing.  
Other TDS 744A features  
include advanced triggering,  
graphical user interface,  
high-speed signal processing,  
complementary probing, and  
introduces Tek’s new InstaVu  
acquisition feature and sets a  
benchmark in waveform capture  
rate for DSOs. The TDS 744A  
can display more than 400,000  
TDS 744A  
Bandwidth  
500 MHz  
4
Input Channels  
Sample Rate per Channel  
1 channel  
2 GS/s  
2 channels  
1 GS/s  
3 or 4 channels  
500 MS/s  
Vertical Resolution  
8 bits;  
> 12 bits with Hi-Res;  
11 bits with Averaging  
Record Length  
500 to 50,000 points per channel  
Max. 500,000 points (optional)  
DC Gain Sensitivity  
Vertical Sensitivity  
± 1.0%  
1 mV to 10 V/div;  
50 : 1 mV to 1 V/div  
Automatic Measurements  
Triggering System  
25  
Edge, Pulse (Width, 1 ns Glitch, Runt, and Slew Rate),  
Logic (Pattern, State, and Setup and Hold Time  
Violation), HDTV Video (optional)  
Special Features  
InstaVu, Dual Window Zoom, FFT, Differentiation,  
Integration, Color Monitor, 3 ⁄2" Floppy Drive  
1
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For further information, contact Tektronix:  
World Wide Web: http://www.tek.com; ASEAN Countries (65) 356-3900; Australia & New Zealand 61 (2) 888-7066; Austria, Eastern Europe, & Middle East 43 (1) 7 0177-261; Belgium 32 (2) 725-96-10;  
Brazil and South America 55 (11) 3741 8360; Canada 1 (800) 661-5625; Denmark 45 (44) 850700; Finland 358 (9) 4783 400; France & North Africa 33 (1) 69 86 81 08; Germany 49 (221) 94 77-400;  
Hong Kong (852) 2585-6688; India 91 (80) 2275577; Italy 39 (2) 250861; Japan (Sony/Tektronix Corporation) 81 (3) 3448-4611; Mexico, Central America, & Caribbean 52 (5) 666-6333;  
The Netherlands 31 23 56 95555; Norway 47 (22) 070700; People’s Republic of China (86) 10-62351230; Republic of Korea 82 (2) 528-5299; Spain & Portugal 34 (1) 372 6000; Sweden 46 (8) 629 6500;  
Switzerland 41 (41) 7119192; Taiwan 886 (2) 765-6362; United Kingdom & Eire 44 (1628) 403300; USA 1 (800) 426-2200  
From other areas, contact: Tektronix, Inc. Export Sales, P.O. Box 500, M/S 50-255, Beaverton, Oregon 97077-0001, USA (503) 627-1916  
Copyright © 1997, Tektronix, Inc. All rights reserved. Tektronix products are covered by U.S. and foreign patents, issued and pending. Information in this  
publication supersedes that in all previously published material. Specification and price change privileges reserved. TEKTRONIX and TEK are registered  
trademarks of Tektronix, Inc. All other tradenames referenced are the service marks, trademarks or registered trademarks of their respective companies.  
4/97 WCI  
76W–10555–1  
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