Understanding scope-based spectrum analysis

With the ever-expanding adoption of wireless in embedded systems of all types, there’s no question that having spectrum analyzer capability in an oscilloscope is a time-savings convenience for designers. Traditionally, test equipment manufacturers have used scope-based fast Fourier transforms (FFT) to provide RF capabilities, but this often falls short of requirements for modern RF designs, forcing designers to turn to standalone spectrum analyzers in addition to their oscilloscopes.

Now, mixed-domain oscilloscopes that offer improved spectral fidelity throughout the signal path have come on the market. But how does an MDO achieve these improvements compared to typical FFT algorithms on oscilloscopes? How does an integrated oscilloscope-based spectrum analyzer compare to a standalone spectrum analyzer?  

Mixed-domain use cases

Recent research shows more than 45% of oscilloscope users now use a spectrum analyzer multiple times per month, and more than 40% of embedded design projects include some form of wireless capability. These facts alone make a compelling case for the integration of time-domain and frequency-domain analysis in a single instrument.  

A particular challenge is that modern wireless communications such as 802.11n are using increasingly wide bandwidth modulation schemes to provide greater data throughput. To effectively measure these modern wireless technologies, it often is necessary to capture the entire channel bandwidth at a single point in time.

But use cases for an integrated oscilloscope are not limited to just pure RF applications. Even for designs without wireless technologies, engineers are facing EMI, crosstalk, and noise-related issues that are easier to diagnose in the frequency domain than in the time domain. Understanding the emissions profile of a product under test at all test frequencies often requires the capability to see those frequencies at the same time to avoid missing a critical event.  

Scope-based FFT

Most oscilloscopes have the capabilities of calculating and displaying an FFT of the acquired time-domain signal. On the surface, this would seem to provide adequate frequency-domain analysis capabilities for many users. However, the typical oscilloscope, even with FFT capability, is a poor substitute at best for a spectrum analyzer when it comes to looking at spectral information.

To make spectral measurements, an input capable of measuring high-frequency signals is required. Many modern communications signals operate in the ISM bands at 2.4 GHz and 5.8 GHz. Even making measurements on a relatively low-frequency 900-MHz system requires an input frequency range of 2.7 GHz to examine the third harmonic.

While oscilloscopes are available with bandwidths that can measure these signals, the spectrum is limited to the bandwidth of the oscilloscope—potentially forcing purchase of a more expensive scope than might otherwise be required for time-domain analysis of analog or digital signals. Additionally, since signal amplitude gradually rolls off to -3 dB at the oscilloscope’s rated bandwidth, RF measurements made anywhere near the rated bandwidth of the oscilloscope are attenuated significantly.

Of equal importance when making RF measurements is signal fidelity. The most important measure of fidelity in a spectrum analyzer is spurious free dynamic range (SFDR). This multifaceted specification indicates the capability for a spectrum analyzer to detect and measure small signals in the presence of large signals. Because of their general-purpose nature, oscilloscopes provide ~45 dBc SFDR, much worse than the ~60 dBc provided by spectrum analyzers. Low noise performance is important for measuring low-level signals and out-of-band emissions for transmitters.

Another downside of using an FFT on an oscilloscope for making frequency-domain measurements is that the oscilloscope’s user interface is understandably optimized for time-domain measurements. This makes it quite difficult to make typical spectrum analyzer adjustments, such as center frequency, span, and RBW. Adjusting the display typically involves manual calculations of the time-domain parameters of sample rate, record length, and FFT window shape. It also is often impossible to get exactly the desired settings. 

Spectral analysis with a scope FFT is limited compared to a spectrum analyzer. Manual cursors typically are required to identify the frequency and amplitude of peaks in the spectrum. Typical spectrum analyzer trace types such as max hold, min hold, and average are not available, nor are typical spectral measurements like channel power or occupied bandwidth. 

MDOs 

An MDO avoids the limitations of scope FFT by incorporating a modern spectrum analyzer to provide much improved spectral fidelity and usability. At the same time, MDOs leverage oscilloscope acquisition technology to provide unprecedented wide capture bandwidth, a performance advantage over entry-level spectrum analyzers.

The integrated spectrum analyzer of an MDO has a dedicated pathway and input for the spectrum analyzer as shown in Figure 1, providing the required performance for typical RF signals without requiring the traditional oscilloscope channels to equal that performance. Some instruments also have a dedicated A/D converter to allow simultaneous time and frequency-domain acquisitions. 

As a result, adequate performance levels are achieved on both analog and RF channels while keeping the price of the instrument in line with a bench oscilloscope. The RF channel in the MDO has flat frequency response across the entire frequency range leading to more accurate measurements and an SFDR rating of up to -65 dBc (typical).

From a usability perspective, an MDO provides an experience similar to that of a spectrum analyzer. The MDO automatically optimizes acquisition parameters for the frequency domain when making spectral measurements. It also offers a complete set of spectrum analyzer controls for most common adjustments including center frequency, span, reference level, RBW, and markers. 

An MDO also provides a more complete set of analysis capabilities when compared to an oscilloscope FFT. Typical spectrum analyzer trace types are supported including normal, max hold, min hold, and average as well as typical spectrum analyzer detection methods including +peak, -peak, average, and sample. A range of automated measurements also is available including channel power, adjacent channel power ratio, and occupied bandwidth.

But an MDO is not exactly the same as a standalone spectrum analyzer—it takes advantage of the wide bandwidth architecture of an oscilloscope to offer notable improvements.  

The spectrum analyzer was first developed in an era when frequency-domain analysis was done on RF signals that were stable over time and had simple narrowband modulation schemes like AM or FM. Signals used in today’s digital communications, however, vary significantly with time, using sophisticated digital modulation schemes and, often, transmission techniques that involve RF bursts. These modulation schemes can be very wide bandwidth as well. 

Traditional swept or stepped spectrum analyzers are ill-equipped to view these types of signals since they are only able to look at a small portion of the spectrum at any one time. Most spectrum analyzers on the market today have 10-MHz capture bandwidths, sometimes with expensive options to extend that to 20, 40, or even 160 MHz in some cases.

By taking advantage of oscilloscope technology, an MDO is able to acquire the entire spectrum of interest with up to 3.75-GHz capture bandwidth. As you might expect, this provides much better insight into the spectral content of today’s modern wideband RF signals.

Synchronized acquisition 

Performance MDOs have an A/D converter dedicated to the spectrum analyzer input. This enables them to display both the time and frequency domain at the same time. A universal trigger system in the MDO acquisition system integrates all channels. A trigger can be set on any one of the analog, digital, or RF channels. When the trigger event occurs, the MDO captures all channels simultaneously. As a result, all signals are time-correlated for accurate analysis. 

Figure 2 shows a synchronized acquisition of multiple channels including RF. Since all waveforms are time synchronized, it is possible to see the RF spectrum at the same point in time that a significant event occurred on an oscilloscope channel, such as a specific serial bus pattern or ripple on a power rail. 

Higher performance MDOs provide deep acquisition memory to allow a long time period of the RF signal to be acquired, making it possible to see the precise spectrum at any point in time in the time-domain acquisition. By simply moving spectrum time (the orange bar in Figure 2) through the acquisition, it is possible to see how the RF spectrum changes over time or device state. This enables accurate measurements of key radio parameters such as turn-on time and settling time.

Under the covers

There’s no question that the integration of a dedicated spectrum analyzer into an oscilloscope offers significant advantages over an oscilloscope-based FFT as well as advantages over traditional spectrum analyzers for capture of wide-bandwidth rapidly changing signals. But making this work in practice requires careful engineering.

As shown in Figure 3, at the core of the MDO is an 8-bit A/D converter. After data is acquired to memory, a combination of hardware and software techniques is used to perform a digital downconversion (DDC) to greatly enhance signal fidelity. Further spectral processing using a discrete Fourier transform (DFT) allows the display of spectral data. This essentially is the same architecture used by modern spectrum analyzers with one major difference. The A/D in the MDO runs at 10 GS/s, orders of magnitude faster than typical spectrum analyzers. This is what enables the MDO’s exceptionally wide capture bandwidth.

Process gain 

There might appear to be an inconsistency between the use of an 8-bit A/D converter and the need to view signal details that can be more than 100 dB below full scale. This inconsistency stems from the formula that relates A/D resolution to the signal-to-noise ratio (SNR):  

SNR = 6.02N + 1.76 dB 

where: N = number of bits of resolution 

For an 8-bit A/D converter, the noise floor is, at best, about 50 dB below full scale. This would seem to eliminate any possibility of viewing signals below this level.

However, the noise predicted by this equation is broadband and typically spread uniformly across the bandwidth of the A/D converter. By using a combination of DDC and DFT to reduce the bandwidth of the data that actually is processed and displayed, the noise floor is lowered, allowing visibility of small signals. This effect is called process gain and improves the SNR as follows:

where:
f_s = sample rate
RBW = resolution bandwidth of the DFT 

As an example, for a 10-MHz span and an RBW of 10 kHz (given a sample rate of 10 GS/s), this improves SNR by roughly 57 dB to about 107 dB.

It is interesting to note that with an A/D sampling at 20 MS/s, which is typical for an entry-level spectrum analyzer, it would require at least 12.5 bits of resolution to achieve this same SNR performance.

The displayed average noise level (DANL) specification for a spectrum analyzer is given in units of dBm/Hz. This is because the system noise is broadband. The level of noise seen at a particular setting is determined by the RBW setting. This phenomenon is demonstrated on a typical spectrum analyzer where the noise floor is reduced by 10 dB for every 10x reduction in the RBW. Process gain is simply a manifestation of this phenomenon.

Another important point in understanding noise performance is that in a typical spectrum analyzer (using a 14 or 16-bit A/D), the downconverter noise output is well above the A/D noise floor. This is due to the high gain between the mixer and the A/D converter. The high gain is required because the downconverter mixer input level has to be kept low to keep its distortion below that of the high-resolution A/D. In an MDO, the input level of the downconverter can be higher because its distortion only has to be kept below that of the 8-bit A/D. In this case, the noise floor is much closer to the A/D converter itself. The net result is that the DANL specification for an MDO is very similar to a typical spectrum analyzer.

Dither improves SFDR

There also appears to be an inconsistency between the use of an 8-bit A/D and the high SFDR needed for spectral measurements. In an A/D converter, differential nonlinearity (DNL) errors show up as spurs in the frequency domain. Lower resolution A/D converters generally have higher DNL errors, resulting in a correspondingly lower SFDR.

In a typical A/D converter, the DNL errors are not uniformly distributed but, rather, affect only a subset of the A/D codes. Because of this, dither can be used to significantly reduce DNL errors and improve SFDR. Dither is a random signal that is added to the input signal to smear its energy across multiple A/D codes, effectively averaging the individual DNL errors across all the codes. The result of adding dither is that the spurs, caused by DNL errors, are pushed closer to the noise floor.

 

MDO benefits 

MDOs with an integrated spectrum analyzer represent a significant advance compared to oscilloscope-based FFTs. As shown in Table 1, MDOs offer performance comparable to a basic or bench spectrum analyzer with the added benefit of a single, cost-effective instrument with ultra-wide capture bandwidth.

To be sure, using oscilloscope technology to build a high-fidelity spectrum analyzer represents a significant break from tradition and required a number of innovations. These included the use of a dedicated spectrum analyzer input to improve fidelity, use of DDC and DFT techniques to leverage process gain for improved sensitivity, and the use of dither to improve SFDR.

About the author

Gina Bonini is a technical marketing manager for Tektronix. She has worked in various test-and-measurement positions for more than 16 years, including product planning, product marketing, and business and market development. Bonini holds a BSChE from the University of California, Berkeley, and an MSEE from Stanford University.
[email protected]