Oscilloscope Measurement Fundamentals: Frequency Domain Measurements (Part 3 of 3)

This is part three in a three part series in which we will examine oscilloscope measurements such as the ones available in hardware within the ZTEC family of modular oscilloscopes. Many oscilloscope users take advantage of only a small fraction of the powerful features available to them. In addition, selecting the right measurement from a catalog of possibilities and accurately interpreting the results can lead to confusion and mistakes. This series of articles is intended to help users understand oscilloscope measurements more completely in order to avoid common pitfalls. Digital storage oscilloscopes vary greatly among vendors in terms of form factor (stand-alone, PXI, VXI, PCI, etc), resolution (8-bit, 12-bit, 16-bit, etc), acquisition rates (1 MS/sec, 1 GS/sec, 40 GS/sec, etc), functionality (advanced triggering, deep memory, self-calibration, etc.), and more. One aspect that separates true oscilloscopes from most PC-based, modular digitizers is the ability to make measurements in hardware on an onboard processor. The available measurements also differ from one oscilloscope to another, although this paper will cover a large segment of them. In addition, the algorithms used to complete the measurements may differ slightly among vendors. This paper will focus on the measurements and algorithms used in ZTEC modular oscilloscopes, but most of these concepts are universal. Oscilloscope measurements can be sorted into the following three categories: • Vertical-Axis • Horizontal-Axis • Frequency Domain Part three of the series will focus on frequency domain measurements.

Frequency domain measurements involve translating a time-domain waveform with a fast Fourier transform (FFT), and then measuring the noise and distortion characteristics in the frequency domain. Frequency domain measurements provide magnitude and phase characteristics versus frequency.

Frequency Resolution and Accuracy

Using the FFT to quickly transform a signal into its frequency components is powerful, because it reveals signal characteristics that can’t be seen in the time-domain. The FFT used within ZTEC oscilloscopes returns complex IQ data which is then converted to magnitude and phase data. Figure 1 shows the result of calculating the FFT of a signal and a few of the measurements.

ZTEC oscilloscopes provide four FFT windows that can be applied as well. Windows are used to increase the spectral resolution in the frequency domain. The Rectangular Window provides the best frequency and worst magnitude resolution. It is almost the same as no window. The Blackman-Harris Window provides the best magnitude and worst frequency resolution. The Hamming Window provides better frequency and worse magnitude resolution than the Rectangular Window. It provides slightly better frequency resolution than the Hanning Window. The Hanning Window provides better frequency and worse magnitude resolution than the Rectangular Window.

Like some of the vertical- and horizontal-axis measurements discussed previously, the accuracy of the FFT can be improved by analyzing longer waveforms. Due to the nature of the calculations, the resolution is limited to half of the resolution of the onboard processor. In the case of the ZTEC ZT4611 oscilloscope, which uses a 64-bit processor, the accuracy would be limited to 32 bits of resolution. The FFT algorithm is binary in nature, so for the best performance it is wise to select a waveform size that is equal to 2^N.

Frequency Domain Measurements

Once a signal has been converted to the frequency-domain, five valuable measurements can be performed as explained in the following paragraphs. All of these measurements assume that the input signal is a perfect single-frequency sine wave and that all other frequency components are assumed to be harmonics or noise. All except the ENOB (bits) are expressed in decibels relative to carrier (dBc). THD is the only negative value.

The Signal-to-Noise Ratio (SNR) is the ratio of the RMS amplitude of the fundamental frequency to the RMS amplitude of all non-harmonic noise sources. SNR does not include the first nine harmonics as noise. In Figure 1, the SNR would be computed by dividing the magnitude of the fundamental by the sum of the magnitudes of all of the other frequency components, excluding the 2nd through the 10th harmonics. SNR is commonly used when only the narrow-band around the fundamental frequency is of concern and the harmonics will not have an effect on the system under test.

The Total Harmonic Distortion (THD) is the ratio of the RMS amplitude of the sum of the first nine harmonics to the RMS amplitude of the fundamental. In Figure 1, this would be calculated by summing the magnitudes of the 2nd through the 10th harmonics and then dividing that by the fundamental magnitude. THD is a concern when using active components such as amplifiers and mixers where the harmonics need to be minimized to reduce distortion.

The Spurious-Free Dynamic Range (SFDR) is the ratio of the RMS amplitude of the fundamental to the RMS amplitude of the largest spurious signal. This spurious signal can be a harmonic or noise frequency component. In Figure 1, the SFDR would be computed by dividing the magnitude of the fundamental by the magnitude of the 2nd harmonic, since it is the largest spurious signal. SFDR is used when there is a dominant spurious signal in relation to the other noise and distortion components.

The Signal-to-Noise and Distortion (SINAD) is the ratio of the RMS amplitude of the fundamental to the RMS amplitude of the sum of all noise and distortion sources. This is equivalent to the sum of the SNR and THD. In Figure 1, this would be calculated by dividing the magnitude of the fundamental by the sum of the magnitudes of all of the other frequency components, including harmonics and noise. SINAD is used in broad-band applications where all harmonics and noise will affect the signal.

The Effective Number of Bits (ENOB) is another way of expressing SINAD. It provides a measure of the input signal dynamic range as if the signal were converted using an ideal ADC. For instance, the ENOB of an 8-bit oscilloscope is often somewhere in the 6-7 bit range due to the noise and distortion affecting the instrument. The ENOB is calculated using the following equation:

High-Speed ADC Test Example

The specifications and test procedures of a high-speed Analog to Digital Converters (ADCs) are generally expressed in the frequency domain. The frequency measurements on a ZTEC oscilloscope can be used to mimic a more expensive spectrum analyzer to complete these tests. One test that is often used is a two-tone or multi-tone distortion test. This is completed because intermodulation distortion can occur when the ADC samples a signal composed of more than one sine wave. Figure 2 shows the FFT of an acquired ADC data record undergoing a two-tone test. Once the FFT is created, measurements such as THD and SINAD can be used to characterize the performance of the ADC.

This concludes the third and final installment of "The Fundamentals of Oscilloscope Measurements". Hopefully, these articles have provided our readers with a little deeper understanding of the waveform measurements available from an oscilloscope. This understanding can help users leverage the power of oscilloscopes more effectively and avoid potential pitfalls.

 

ZTEC Instruments in Biologically Inspired Acoustic Systems (BIAS)

Approaching the Capability of Bats and Dolphins

Bats and dolphins have developed very sophisticated means of object detection, location and characterisation. Their capabilities in the generation, reception and processing of acoustic signals go way beyond man’s current understanding. Current technology drivers in most scientific, military and industrial fields include increasing resolutions, lowering power consumption and improving material assessment and characterisation. Existing solutions often result in current technologies merely being driven harder, but new, novel technologies can be developed from a fresh view of the way bio-acoustic systems solve similar problems.

How bats and dolphins achieve such high levels of object detection, location and characterisation has been the focus of much research. One aim being to develop similar, ‘bio-mimetic’ systems, but it is still unclear the effort that is required to approach the capability of bio-acoustic systems. Recent experiences suggest that new research should be ‘bio-inspired’ and investigate the way in which energy is delivered to and returned from the source of investigation.

New Research: The BIAS Project

Researchers from the NERC British Geological Survey, the Universities of Southampton, Edinburgh, Leeds, Strathclyde, Leicester and Fortkey Ltd have formed the BIAS consortium to undertake research into the tools / techniques used routinely by nature that hitherto have not been embraced by man. Key challenges for a new approach include breaking the quarter wavelength barrier that currently limits spatial resolution, and the development of new signals for improved power efficiency and material property characterisation. The project will establish an experimental programme to be undertaken at three ultrasonic laboratory facilities:

• firstly, a waterborne, high frequency ultrasound facility focusing on medical physics applications
• secondly, a waterborne, low frequency ultrasound facility focusing on the physical characterisation of materials for geological applications,
• and thirdly, an airborne, low frequency ultrasound facility focusing on the characterising the effect of aspect angle on echo patterns.

Novel Ultrasonic Systems for New Coded Waveform Generation and Acquisition

A new study of the phase and magnitude of the echo-reflected wave is key to understanding the achievements of bats and dolphins. The Ultrasonics Research Laboratory at the British Geological Survey has commissioned Alba Ultrasound Ltd., Glasgow, UK to provide very wideband piezo-composite transducers to generate a new family of coded waveform signals to be used in this study. The bandwidths and efficiencies will be further improved when combined with new transducer matching networks commissioned by Blacknor Technologies, Portland, UK. The generation and detection of these new coded waveforms requires systems with very long memory lengths and high sampling frequencies at high dynamic ranges offered by ZTEC instrumentation.

ZTEC’s ZT530PXI-01 Arbitrary Waveform Generator has the voltage output capability to directly drive Alba Ultrasound’s wideband transducers. The ZT530PXI-01 offers sampling rates of up to 400MSs-1 at voltage levels of 20V peak to peak unlike many other competing products, which only offer 3V peak to peak.

ZTEC’s ZT530PXI-01 Arbitrary Waveform Generator can provide up to 4MSamples and the ZT410PXI-51 Digital Oscilloscope can acquire up to 16MSamples. Long memory lengths are vital for the generation and detection of signals such as wideband linear chirps. The linear upsweep above comprises 10, 000 samples at 10MSs-1 with a start frequency of 200kHz and an end frequency of 800kHz within 1ms, and is succeeded by a tail of 30, 000 points. The 200kHz to 800kHz upsweep was acquired with the ZT410PXI-51 with 125, 000 samples at 100MSs-1.

Step quantisation is a phenomenon that occurs when digitising analogue signals and can be seen as the staircase structure on the signals in the above figure. Step quantisation can introduce phase distortion to the signals, which can add unwanted phases for example when driving power amplifiers. Step quantisation can be reduced in the signal emitted from the ZT530PXI-01 using the interpolation feature to provide a smother signal input into the power amplifier.

Signal discrimination techniques can be much improved even if the transmitting transducer technology is bandwidth limited. For example, Barker code sequences can be sent to a transmitting transducer, each of which initiates a wave packet mainly containing damped oscillation at the resonant frequency of the transducer. The multiple reflections when returned to this transducer produce a composite signal that is the result of the convolution of all the echo returns from the various reflectors. Not only is the transmitted signal of long duration, but also the detection of pulse echoes requires a very long acquisition window. The ZT410PXI-51 with its combined 16MSample memory and very high sampling rate offers the capability of very high sampling rates of long duration events. This allows time delay measurements to very high resolution during pulse compression. The example below shows the deconvolution of an 11-point Barker code emitted from a piezoelectric transducer from a complicated pulse train comprising multiple echoes.

Bat and Dolphin Signals: Generation and Detection

Many bat species emit frequency modulated (FM) or combined FM and constant frequency (CF) signals, in pulse lengths ranging from 0.3 to 300 ms, with frequencies ranging from around 10 to 200 kHz. The figure below shows a complex chirp signal emitted from bat, and the time-frequency spectrogram shows that two FM signals are emitted, and, while one is delayed from the other, there is still some pulse overlap between the two signals.

The majority of dolphins emit clicks comprising a few cycles that don’t tend to change much in duration or shape, but where the frequency band appears to be related to signal intensity. High intensity signals tend to have centre frequency of 100 kHz or above and low intensity signals tend to have centre frequencies around 30 to 60 kHz, as shown below.

Recent research has shown that using this range of frequencies dolphins can detect differences in the wall thickness of metal cylinders of around 250 microns, or 1/50th of the wavelength. We cannot achieve anything like this at present but we hope to redress this balance with our new research programme.

Contributed by
David Gunn and Peter Jackson, British Geological Survey, Keyworth, Nottingham, UK
Said Assous and Clare Hopper, Leicester University, Leicester, UK

This work is being under taken as part of the Biologically Inspired Acoustic Systems (BIAS) project, which is funded by Research Councils UK via the Basic Technology Programme.

For more information, please visit http://www.biasweb.co.uk.

 

New Regional Sales Managers bring expertise and bandwidth to the ZTEC Team

ZTEC is excited to announce that Geoff Hoekstra and Manny Teran have joined the ZTEC sales team as Regional Sales Managers covering the United States and Latin America. Both Geoff and Manny bring a wealth of knowledge to ZTEC with prior work experience at National Instruments.  Please do not hesitate to contact them if you have any questions about ZTEC products or services. They are available for on-site product demonstrations, training sessions, and seminars.

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