How it Works
Tektronix
Loading...
AWG 2021
User Manual
36 pgs2.45 Mb0

Tektronix AWG 2021 User Manual

Signals and Measurements for Wireless Communications Testing
2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Analog Carriers and Modulation
1 Basic Sine Wave Amplitude Modulation (AM) . . . . . . . . . . . . . . .3
2 AM with Adjacent Carriers . . . . . . . . . . . . . . . . . . . . . . . . . .5
3 Multi-Tone Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
4 Frequency Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
5 FM with Dual-Tone Modulation . . . . . . . . . . . . . . . . . . . . . . . .10
7 Adding Noise to a Carrier Signal — AWG Noise Characteristics . . . . . . . . . . .14
Digital Modulation
12 Quadrature Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . .23
For More Information on Tektronix Instrumentation . . . . . . . . . . . . . . . . . .29
AWG 2000 Series Arbitrary Waveform Generators . . . . . . . . . . . . . . . .30
TDS 744A Digitizing Oscilloscope . . . . . . . . . . . . . . . . . . . . . . .31
Table of Contents
Note: Each signal and waveform screen in this application note originates from one of three types of instruments: an arbitrary waveform generator, a digital storage oscilloscope, or a spectrum analyzer. Each illustration is annotated with a symbol indicating its origin:
AWG
Oscilloscope (DSO)
Spectrum Analyzer
3
One of the most challenging tasks in designing wireless communications products is the develop­ment of a rational approach to characterizing and testing components, assemblies, and sub-systems. Baseband modulation and RF signal characteristics 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 gener­ators with limited modulation capabilities are inadequate and it is not always feasible to have a test department develop customized systems.
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 excel­lent 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.
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 sub­assemblies. Like a spreadsheet, the power of the AWG comes from the ability to define and re­define 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 record­playback technique. A live signal is recorded into the memory of a digital oscilloscope, and the record is transferred to the AWG for playback. This
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 date is as simple as retrieving it from memory— rather than re-cabling and re-configuring an assort­ment of interconnected generators.
Ironically, the flexibility of an AWG can make it difficult to select a model that fits a given applica­tion. 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 demon­strated 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.
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 capa­bilities, 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.
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 appro­priate RF signal sources available today, including products from Tektronix, Rohde & Schwarz, and others. For more information about RF sources, contact your local Tektronix representative.
Introduction
Signals and Measurements for Wireless Communications Testing
4
5
The best introduction to the AWG is to parallel the procedure of generating a carrier with a conventional signal generator. With a signal generator, one simply enters the carrier frequency and the output ampli­tude, such as 1000 kHz at 0 dBm. With an AWG, one creates a sequence of points to represent the waveform:
A sin
ωct
where A is the peak amplitude and ωcis the frequency. Since a 0 dBm sinusoid has a peak amplitude of 0.316 V (0.224 Vrms), the carrier is:
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
a single cycle sinusoid with a period of 1 µs that repeats every 1 µs. The unique or arbitrary part of the signal is a 1 µs series of points defined by the above equation. If amplitude modula­tion is enabled on a signal generator, one enters the tone modulation frequency and depth, such as 1000 Hz at 50%.
Similarly, with an AWG, one adds the modulation to the wave­form description:
(1+ k sin(ωmt)) A sin ωct ,
where k is the modulation depth between 0 and 1, and ωmis the sinusoidal modulation frequency. Thus, our example waveform becomes:
(1+ 0.5 sin(2π 1000 t) )
x 0.316 sin (2π 1000e3 t) Volts.
This waveform description can be entered in the AWG’s equa­tion editor to describe our 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 20,000 points is selected, keeping in mind the basic AWG relationship:
Record length (points)
= Waveform period (seconds)
x Sample rate (points/sec).
Basic Sine Wave Amplitude Modulation (AM)
1
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.
Analog Carriers and Modulation
6
A record length must be selected that has an adequate number of points to reconstruct the desired waveform. The waveform period is 1 ms and there are 1000 carrier cycles in this period. A record length of 20,000 points would allocate 20 points per cycle, which adequately over­samples the ideal waveform. Any sampling system must
sample at least twice as fast as 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.
The AWG equation compiler converts the waveform defini­tion 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 gener­ate a marker signal once per period on a separate output.
Figure 2. The AWG’s compiler converts the modu­lation 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.
7
A simple addition to the AM signal demonstrates the flexibility of equation-based waveform descriptions. A common task in evaluating receiver performance is to evaluate the effect of adja­cent carriers. For the basic AM signal, one can easily add modu­lated 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
modulation frequency of the adjacent carriers was changed to 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 normalization function (last line) is used to automatically scale the peak values encoun­tered in the equation to ensure that there is no clipping within the AWG when the signals are
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).
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.
AM with Adjacent Carriers
2
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.
8
Frequency (kHz
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
980 985 990 995 1000 1005 1010 1015 1020
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.
Magnitude (dBm)
9
Multi-Tone Testing
3
The logical extension of adjacent carrier testing is multi-tone test­ing. In addition to simulating multiple carriers in a multi­channel system, multi-tones can quickly test filter response when a scalar or network analyzer is not available, or they can iden­tify intermodulation products resulting from saturation or non­linearities in supposedly linear component stages. Traditionally, multi-tone testing requires assembling as many signal
generators as desired tones. And while the generators can be phase-locked to a common reference, the phase relationship between the independent signals is not absolute.
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 equa­tion editor specifying 11 tones centered at 70 MHz in 1 MHz steps (from 65 MHz through
75 MHz). In this case, the 1 MHz steps suggest a waveform period of 1 µs such that the record repeats at a 1 MHz rate. Thus, the 65 MHz tone is generated by 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.
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.
Frequency (MHz
-80
-70
-60
-50
-40
-30
-20
-10
0
60 65 70 75 80
Figure 8. Spectrum analyzer plot of the 11 carriers. The tone levels were flat to better than 0.25 dB.
Magnitude (dBm)
10
The 11 tone equation was then modified so that the last 5 tones (71 through 75 MHz) are 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-to­peak values are different. All eleven tones in the original signal added in-phase at t=0. This was not the case with the
second signal where 5 of the carriers were inverted at t=0. Thus, the crest factor (peak-to­rms ratio) of the two signals changed from 4.6 (original) to
3.4 (modified). This difference can have dramatic results when using multi-tones to test for satu­ration in transmitter or receiver stages. While both signals have the same power level, the peak levels are quite different.
Absolute control of phase rela­tionships 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 in­circuit performance characteri­zation since a scope can be triggered at the exact instant of the test signal’s peak value.
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.
Multi-tone signal
Inverted tones
Marker
11
Frequency modulation introduces control of the phase argument, Φ, in the basic carrier equation:
A sin (ωct + Φ ).
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:
A sin (ωct + k ∫ m(x) dx )
where k sets the peak frequency deviation. For the special case of
a modulating tone cos (ωmt), the phase argument becomes:
k/ωmsin (ωmt ),
where k is the peak frequency deviation and k/ωmis the FM modulation index.
The FM equation is entered directly into the AWG’s equation editor (Figure 10). The modula­tion tone is 1000 Hz, so the unique or arbitrary portion of the signal repeats every 1 ms. Choosing a common FM IF carrier frequency of 10.7 MHz, note that the carrier frequency is
a multiple of the modulating frequency. This means that the carrier signal will be phase continuous when the 1 ms record repeats.
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, J
0
(5.52), is zero.
Frequency Modulation
4
Frequency (kHz
-80
-70
-60
-50
-40
-30
-20
-10
0
10680 10685 10690 10695 10700 10705 10710 10715 10720
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.
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.
Magnitude (dBm)
Loading...
+ 25 hidden pages
Buy Points How it Works FAQ Contact Us Questions and Suggestions Privacy Policy Cookie Policy Terms of Use