Print
PDFOverview
For an ideal signal generator, the generation of a pure analog sine wave would produce a single peak in the frequency domain. However, signal generators are fundamentally digital devices that are only able to approximate the ideal analog signal. As a result, it is important to determine the accuracy of this characterization using dynamic specification. In this tutorial, learn several common hardware specifications and gain insight into their relevance in various applications. This tutorial is part of the National Instruments Signal Generator Fundamentals series. Each tutorial in this series examines basic concepts about the architecture, features, or applications of signal generators. For more information about applications that commonly use signal generators, see the Signal Generator Applications Main Page.
Table of Contents
While specifications such as bit resolution and sample rate (see Introduction to High-Frequency Analog Signals) are used to differentiate signal generators, these factors alone cannot fully characterize the performance of a signal generator. Thus, this tutorial focuses on dynamic specifications such as passband flatness, spurious-free dynamic range (SFDR), total harmonic distortion (THD), the signal-to-noise-and-distortion ration (SINAD), effective number of bits (ENOB), intermodulation distortion (IMD), noise density, and phase noise to better characterize the analog performance of a signal generator.
Passband Flatness
Under ideal conditions, the amplitude of a stimulus remains constant even as it increases in frequency. However, due to nonideal characteristics of a signal generator's components, the amplitude of any given signal can vary slightly according to its frequency. The bandwidth of a given signal generator is the frequency at which the output signal is attenuated 3 dB relative to the amplitude of a DC or low-frequency signal. Again, the bandwidth of a signal source is limited by the output amplifier design or by filters in the analog output circuit. Bandwidth is one of the factors that determine the generator’s maximum output frequency.
In Figure 1, an NI 5421 generator specification is illustrated with a graph showing its frequency response.
Figure 1. NI 5421 – Passband Flatness (Direct Path)
As the graph illustrates, the output signal is typically attenuated by approximately -3 dB at greater than 43 MHz, the specified bandwidth for the device. From FIgure 1, you can see that the signal generator can reliably output signals with a frequency range of 0 to 40 MHz with less than 0.4 dB attenuation or less than 0.6 dB of amplification.
Passband flatness is a term expressed in decibels (dB) to specify the limits within which the amplitude of a signal varies across a given frequency range. Ideally a signal generator would have 0 dB passband flatness throughout its entire bandwidth. As Figure 1 shows, an NI 5421 guarantees a passband flatness of 1 dB for all signals between DC and 40 MHz. Moreover, you can see that the typical operation results in passband flatness of better than 0.2 dB up to 40 MHz.
Note that for some test applications, passband flatness is a crucial specification. For example, when characterizing the performance of an analog filter, the accuracy of the characterization test can only be as accurate as the passband flatness of the signal generator and digitizer used for conducting the test.
Spurious-Free Dynamic Range
SFDR is another crucial specification that you can use to characterize the dynamic performance of a signal generator. SFDR specifies the relationship between the amplitude of the fundamental frequency being generated and the amplitude of the most prominent harmonic. In an ideal world, the frequency domain of a pure analog signal has all power concentrated at the desired frequency. However, due to noise and the nonlinearity of components, even the best signal generators also generate frequency content at harmonics (or multiples) of the desired tone.
For example, when generating a 10 MHz sine wave, you can observe harmonics at 20 MHz, 30 MHz, and so on. These harmonics are also referred to as spurs.
The dynamic range between the fundamental tone and the largest spur is called spurious-free dynamic range (SFDR). SFDR is the measure of the ratio between the fundamental signal and the largest harmonically or nonharmonically related spur from the DC half of the sampling rate. You can calculate this specification visually by observing the graph in Figure 2.
Figure 2. Frequency Domain of SFDR Measurement
To measure the SFDR of a signal generator, a tone is generated a given frequency. A spectrum analyzer is then used to measure the amplitude of the fundamental tone and the amplitude of the next highest tone. Typically, this is one of the harmonics.
Given decibels, it is easy to calculate SFDR:
In Figure 2, the second harmonic is the second highest tone and the SFDR is approximately 70 dBc. As a matter of perspective, 70 dBc of SFDR means that the amplitude of spurious signals always is less than .00000001 times the amplitude of the fundamental frequency.
Given RMS voltages, you can calculate SFDR with the following equation:
For many applications requiring a clean sinusoid, it is important that a signal generator has a good SFDR performance. For example, consider analog-to-digital-converter (ADC) characterization (Figure 3).
Figure 3. Block Diagram of an ADC Characterization Test
For ADC characterization, it is important to measure the harmonic imperfections of the ADC. Thus, it is crucial that the stimulus to the device under test is as spectrally pure as possible.
Total Harmonic Distortion (THD)
Harmonic distortion is another specification used to characterize the harmonics of analog signals. Unlike SFDR, however, THD is used to quantify the distortion from all of the harmonics, not just the highest. Thus for signals with a large number of significant harmonic spurs, THD is a specification that you can use to adequately represent the effect these spurs have on the fundamental tone. As a good rule of thumb, a signal becomes visibly distorted when the THD approaches -30 dB.
You can calculate THD by summing the power in each of the harmonics and dividing by the total power of the fundamental. Thus, the equation for THD is:
As the equation above suggests, the THD specification evaluates the power in harmonic spurs from the second through the nth harmonic. Typically, a signal generator features THD specifications for harmonics two through six. For example, a 20 kHz sinusoid generated with an NI 5421 can be generated with -77 dBc or better of THD for the second through sixth harmonics. Figure 4 shows an example plot of this.
Figure 4. Frequency Domain of a THD Measurement
When choosing a signal generator, keep in mind that the THD generally deteriorates as the generated signal increases in frequency. Be sure to consider the THD throughout the bandwidth of the signal generator.
Signal-to-Noise-and-Distortion Ratio (SINAD)
The signal-to-noise-and-distortion ratio (SINAD) is a less commonly used specification for characterizing signal generator dynamic performance. It is defined as the ratio of the RMS signal amplitude to the RMS sum of all other spectral components, including the harmonics but excluding DC. Usually expressed in decibels, SINAD can be calculated with the following formula:
In the equation above, the amplitude for each variable is an RMS sum of all spectral components of the generated signal. Asignal represents the RMS value of the peak of the fundamental frequency. In addition, Anoise + distortion is the RMS value of each of the spurs and noise components. As you might expect, the higher the SINAD, the better the quality of the output signal.
Effective Number of Bits (ENOB)
Real-world digital-to-analog converters (DACs) must overcome challenges such as system noise and nonlinearity of analog components. As a result, one way to represent the resolution of a given signal generator is with a specification called effective number of bits (ENOB). Calculated directly from the SINAD specification, ENOB measures the actual performance of the DAC within a signal source after its various noise sources and nonlinearity are included. Real-world signal generators, however, suffer from noise and distortion for a variety of reasons including issues due to the DAC, multiplexing, impedance mismatches, and capacitor settling times.
The easiest way to measure ENOB is to use the SINAD specification, measured in decibels. Thus, the equation for ENOB is as follows:
As an example, an NI 5421 generator has a SINAD of 64 dB when generating a 1 MHz sinusoid. So the effective number of bits for this signal is:
Intermodulation Distortion (IMD)
Intermodulation distortion (IMD) is the ratio, in decibels, of the total RMS signal level of harmonic sum and difference distortion products to the overall RMS signal level. To make this measurement, you add two sine waves together and generate them. Because you added two sinusoids together, the IMD reveals nonlinearities under AC input signal conditions as opposed to relative accuracy, which reveals nonlinearities under DC input signal conditions.
This specification is most important for baseband I/Q or intermediate frequency (IF) generation. For these applications, a message signal is typically overlaid on a carrier; thus, the resulting signal contains frequency content at multiple frequencies.
Average Noise Density
The average noise density for a signal generator is a specification that characterizes the noise level in the generated signal. You also can think of it as the noise floor of the signal. This specification is affected by a number of factors, including the bit resolution of the DAC and the noise introduced by amplifiers used to create the various path options.
Thus, you can characterize the noise introduced by the DAC and other components with either a noise floor or average noise density specification. Consider an example where the average noise density of an NI 5421 is -148 dBm/Hz when generating a 0.1 Vptp signal using the direct path. However, various path options can introduce noise through the analog amplifiers that they implement.
Figure 5 shows the frequency domain of a 1 Vptp signal that has been generated with the high-gain path of an arbitrary waveform generator.
Figure 5. Frequency Domain of an Ideal 16-Bit DAC
As Figure 5 illustrates, the noise floor is well below -130 dBm/Hz. In addition, you can see the SFDR is about 90 dBc. Notice in this example that you are generating a 100 kHz tone. This frequency was chosen so you could take advantage of the full 24-bit resolution of the NI 5922 digitizer used to make this measurement.
Phase Noise and Clock Jitter
A final dynamic specification you can use to characterize the dynamic performance of a signal generator is phase noise. On NI signal generators, a voltage-controlled crystal oscillator (VCXO) is used to control the onboard clock of the instrument. While an ideal clock would be perfectly stable, clock sources have inherent jitter, which causes phase noise in the frequency domain.
Ideally, if the clock you use to generate a sinusoid was perfectly stable, a fast Fourier transform (FFT) of that signal would show a single spike at the desired frequency. However, clock jitter causes the power of the sinusoid to be distributed across a wider frequency range. Thus, you need to use a phase noise specification to characterize the degree to which clock jitter affects the dynamic performance. Figure 7 shows the effects of phase noise in the frequency domain.
Figure 7. The Effect of Phase Noise in the Frequency Domain
The left graph illustrates a single tone that has been generated with a simulated 16-bit DAC. Note that the figure shows a single spike at exactly 10 MHz and a noise floor at -148 dBc. The right figure shows a simulated signal where the clock signal has significant jitter. The power of the generated signal is spread across adjacent frequencies.
Thus, when measuring phase noise, it is important to specify both the offset and amplitude of frequency response. For high-performance signal generators, it is common to specify the phase noise at 10 kHz, 1 kHz, and 100 Hz. Note that for the simulated signal in Figure 7, you are observing significant phase jitter. For the simulated signal, you see that the phase noise is -95 dBc at a 1 kHz offset. By comparison, an NI 5421 offers a phase noise specification of -121 dBc at a 1 kHz offset.
Phase noise is an important specification for many applications. In particular, generation of baseband I/Q or intermediate frequency (IF) signals requires excellent phase noise. Because many of the modulation schemes used in digital communications transmit digital data with phase shifts, it is important that the phase of the baseband or IF signal remains stable. For example, consider the generation of digital communications signals using quadrature amplitude modulation. For reference, a constellation plot of 4-QAM is shown in Figure 8.
Figure 8. Constellation Plot of 4-QAM
As Figure 8 illustrates, you can characterize each symbol by both phase and amplitude. As a result, the phase error of the generated signal can distort the symbol representation. More specifically, better phase noise correlates directly to symbol generation with better modulation measurements such as error vector magnitude (EVM) and modulation error ratio (MER). For more information on how you can measure these specifications, see Modulation Error Ratio (MER) and Error Vector Magnitude (EVM).
Conclusion
Dynamic specifications are an important way to characterize the analog performance of a signal generator. Moreover, for some applications, your choice of a signal generator is critically important.
For more information on the applications that benefit from high-performance signal generators, see the Signal Generator Applications main page. In addition, for a thorough overview of the technology used to generate accurate analog signals, see Signal Generator Fundamentals.
Related Links
NI Signal Generators
NI Modular Instruments
Reader Comments | Submit a comment »
Expand IMD
Please expand on defining IMD.
- Albert Lysko, Lysko Consultings. lysko@lysko.com - Aug 1, 2007
Legal
This tutorial (this "tutorial") was developed by National Instruments ("NI"). Although technical support of this tutorial may be made available by National Instruments, the content in this tutorial may not be completely tested and verified, and NI does not guarantee its quality in any way or that NI will continue to support this content with each new revision of related products and drivers. THIS TUTORIAL IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND AND SUBJECT TO CERTAIN RESTRICTIONS AS MORE SPECIFICALLY SET FORTH IN NI.COM'S TERMS OF USE (http://ni.com/legal/termsofuse/unitedstates/us/).