(Editor's note : This is the “golden” (#50) installment of the Signal Chain Basics series; click here for a complete, linked list of all previous installments of the series.)
High-speed analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) typically are characterized using continuous wave (CW) signals. There are several reasons for this practice: 1) for ADCs, CW signals are easier to cleanly generate using CW generators and narrow bandpass filters; 2) for DACs, CW signals are easier to analyze; and 3) they provide a standard reference tests that can be unambiguously compared across devices.
However, most real world systems use high-speed data converters for sampling modulated waveforms. Bridging the differences between specifications based on CW measurements and system requirements for modulated signals can be a challenge.
(Note : see the box below the “About the author” section, for a very brief tutorial on CW and modulated signals.)
There are two differences between CW and modulated signals that can affect the behavior of high-speed data converters:
First , a CW signal has no bandwidth – the energy is confined to a single frequency; whereas a modulated signal has a bandwidth and the energy is spread across a range of frequencies.
One result is that while distortion of a CW signal causes CW harmonics at another frequency, distortion of a modulated signal causes harmonics and intermodulation with a wider frequency range than the signal: 2 × for the second harmonic, 3 × for the third harmonic, etc. The spreading in the energy results in a lower integrated distortion energy in a band equal in bandwidth to the modulated signal.
Second , most modulated signals (the exception being phase only modulation schemes such as GMSK used in GSM) modulate amplitude, which results in a lower average power than maximum power. For comparison, a CW signal has a constant power. The difference is demonstrated in Figure 1 ,which shows the power versus time for modulated long term evolution (LTE) signal. The average power is approximately seven percent of the maximum power, or 11 dB lower.
Figure 1 : Power versus time for a modulated LTE signal.
In most devices, harmonic distortion products increase with increasing signal power. For example, the third-order harmonic products increases 3 dB for every 1 dB increase in signal power. So, a CW signal at maximum power has significantly more distortion than a modulated signal with a lower average power. This is illustrated in Figure 2 , which compares the third-order harmonic distortion for a CW signal at maximum power to a modulated LTE signal.
Figure 2 : Harmonic distortion CW and modulated LTE signals.
The distortion model used was a simple polynomial:
Vout = Vin + coeff × Vin3
where the harmonic distortion coefficient coeff was arbitrarily chosen to demonstrate a significant amount of distortion.
The CW signal generates a third-order distortion product 42 dB below the CW signal, while the LTE signal generates a third-order distortion product 56 dB below the LTE signal. Note that the power in Figure 2 has been normalized to the maximum power for each signal.
Therefore, using a maximum power CW signal to estimate the harmonic distortion of a modulated LTE signal in our theoretical device has over-estimated the LTE signal distortion by 14 dB.
What would be a more accurate CW test? A CW test will never be able to capture the exact same effects of a modulated signal, and the distortion of a modulated signal will depend on the statistical distribution of signal power. In our example, a CW signal at –7 dB below maximum power would have generated the same third harmonic distortion level as the LTE signal (see Figure 2). Since the average power of the modulated LTE signal is ~11 dB below the maximum or peak power, this corresponds to setting the CW signal power at 4 dB above the average power of the modulated signal.
A quick rule of thumb for a more accurate estimate of modulated signal performance would take the modulated signal peak to average power ratio in dB and set the CW power at 2/3 below maximum power. For example, if the modulated signal PAR is 6 dB, the CW signal should be set at –4 dB below the maximum power and the harmonic distortion measured relative to the signal power. This rule works well for a variety of modulated signal types like OFDM, WCDMA and QAM.
For more information on data converters, visit http://www.ti.com/dataconverters-ca.
About the Author
Robert Keller is the Systems and Applications Manager for High-Speed Data Converters. He has nine years experience supporting high-speed products in wireless infrastructure communication, test and measurement, and military systems. He received a B.A. in Physics and Mathematics from Washington University, St. Louis, and a Ph.D. in Applied Physics from Stanford University. He has 10 US patents in networking and sensor applications. Robert can be reached at .
Tutorial: Continuous waveforms versus modulated signals
In his classic textbook Detection, Estimation, and Modulation Theory, Volume 1, Harry L. Van Trees identified three classes of signal-capture and recovery problems:
- Detection : Finding a known signal in noise; where “known” means the signal is binary and you just want to know if it if there or not (absent/present), or which of the two binary values it has. This is the easiest challenge.
- Estimation : Assessing the one-time value of an unknown signal in noise, where the value is analog and its value can be anywhere within a specified range.
- Continuous estimation (modulation) : where the challenge is to demodulate a randomly modulated, unknown (analog) signal, again in noise. This continuous-waveform problem is the most difficult one of the three.
Keep these distinctions and differences in mind when you are developing a signal-capture circuit and system, as they bound the scope of your problem.—Bill Schweber, Planet Analog Editor