For purposes of this paper a sensor is defined as a transducer which detects a stimulus (motion, pressure, temperature, etc.) and outputs an electronic signal. The signal is usually a voltage but could also be a current, frequency or phase. An actor receives the output of the sensor and may – or may not – initiate an action based on the value of the signal from the sensor. Many actors may be tied to the output of a single sensor (for example several sprinklers might be activated based on the output of a single sensor which is detecting smoke or heat) or several sensors may provide input to a single actor (multiple sensors might detect the positioning of an item on an assembly line and activate a single robotic arm to perform when all the sensors agree the item is in the correct position). Digital oscilloscopes are excellent instruments for viewing, measuring, characterizing and troubleshooting the electrical signals produced by sensors. They can also examine the input signals to actors. Most design and test engineers own a digital storage oscilloscope (DSO). This paper will endeavor to give good advice on methods to apply the power of DSO’s to the types of signals typically produced/detected by sensors and actors starting with simpler examples and moving toward more complex ones. If an engineer is starting a new project which requires faster measurements or more precision than is provided by his current scope advice will be provided on choosing an oscilloscope.

Using Visual Tools

Typically the first thing an engineer wants to do when testing a sensor or actor is to look at the electrical signal to see if its shape is correct and that it meets some basic criteria. The fundamental oscilloscope properties that come into play are the bandwidth, sampling rate, memory length and display. Having enough bandwidth means the scope (and any probes that are used) have fast enough response to accurately track the shape of the signal. If the scope/probes have insufficient bandwidth the view of the signal will be distorted. For advice on “how much bandwidth is enough” see the final section of this paper. The sampling rate of an oscilloscope reflects how often the analog to digital convertor (ADC) measures the size of the signal. In order to get a good view of the signal shape, you want the scope to provide many sample points which “draw” a connect-the-dots picture of the signal amplitude vs time. Memory length is also important since longer memory allows the scope to provide lots of sample points spanning the duration of the signal of interest. Finally, the display is obviously an important tool for viewing signals since the signal shape is drawn on the screen. But there are also other considerations. One of those is the ability use the display to zoom in and view important details of the signal.

n Figure 1 channel 1 of a digital oscilloscope captures the output of a sensor (a force transducer) which detects an impulse from a short (about 1 msec) sharp impact. Channel 2 shows the output of another sensor (an accelerometer) located about 1 meter from the original point of impact. At this point, the original short, sharp impulse has been converted to a lower amplitude but much longer lasting ringing. Using just visual tools, an engineer can place cursors on the two waveforms to measure the time latency between the original impact and the first substantial peak of the transmitted ringing.

Figure 1:

C1 displays the output of a force transducer and C2 is the output of an accelerometer. C1 (the yellow trace with the highest peak) detects a sudden sharp impulse. C2 shows a delay, then a long ringing

The red box in the lower right corner of the figure outlines the readout from the cursors. In this example the tall peak on channel 1 is at 215 usec (measured relative to the trigger time of the scope) and the first large negative going peak on channel two is at 1.455 ms. This gives a “delta t” of 1.240 msec between the events on the two sensors. An engineer can get a better view – and a more accurate measurement – by using the simplest viewing tool in the digital oscilloscope – the zoom function.

In figure 2, the scope has two grids. On the top grid are the acquired waveforms and cursors. On the lower grid is a zoom of the front portion of the waveforms. Since the cursors have been placed near the front of the waveforms they also show up on the zooms. The first thing you might notice is that the visual placement of the cursors is not exactly on the top of the Channel 1 peak or on the bottom of the channel 2 peak. The zoom, in addition to allowing the user to see the details of the signal more clearly, also allows more accurate placement of cursors.

Figure 2:

The same signals as Figure 1 but now the lower grid shows zooms of both signals. Note the zoom shows the cursors that were placed using a view of the total signal are not quite on the sensor peaks

In Figure 3 the cursors have been repositioned and the oscilloscope shows a more accurate measurement of the elapsed time between the peaks of the two sensors to be 1.260 msec.

Figure 3:

The zoom view allows the user to see more details of the signal visually and also to place cursors more accurately

Simple Math – Reading the Cursor Output in Real World Units

Sensors convert the detection of a “real world” activity ( a change in temperature, acceleration, etc) into an electrical signal. In order to better understand what the sensor is saying it is often a good idea to convert the signal, usually in volts, into real world units that describe what the sensor has detected. This is a simple math equation y = mx+b where x is the sensor reading in volts, m is the conversion factor to real world units and b is any offset that is present. The result of this calculation, y, is a number that describes what is happening in the real world. For instance, if the accelerometer used in the previous examples has an output of one volt per 10 G of acceleration the conversion from “volts” to “G’s” is y = 10x. The simple math function that converts sensor voltage waveforms into physical units is called “rescale.” The voltage waveform is rescaled into units that have direct physical meaning. Figure 4 shows an example. The top trace is the voltage waveform from the output of a sensor. It is an accelerometer attached to the body of a fan. The bottom waveform has exactly the same shape, but all numbers in this waveform are ten times larger and the units of the 2nd waveform are in “gravity” rather than “volts.” A measure of the peak to peak amplitude of the upper waveform is 5.25 millivolts. For the bottom waveform it is 52.5 milligravities.

Figure 4:

The voltage waveform from a sensor (top waveform) is rescaled into physical units (bottom waveform)

Advanced Math

The ability to rescale a waveform into the physical units which the sensor detects also enables the digital oscilloscope to perform more advanced math operations that have useful meaning concerning the real world functioning of the sensor. A sensor that measures acceleration is measuring the mathematical derivative of velocity. And velocity is the derivative of position. So if an oscilloscope has a waveform that shows the output of an accelerometer over a period of time then the scope can integrate that waveform to obtain a new waveform that shows the moment by moment velocity experienced by the sensor over the same time period. If desired, the scope can integrate the velocity waveform to show the displacement in position as a function of time. Of course the oscilloscope will probably not know if the definition of “gravity” is earth standard of 32 ft/sec2 so the rescale function may need to be used again. An example of a math setup for double integration is shown in Figure 5.

Figure 5:

It is easy to perform math operations on the output of a sensor. Some digital oscilloscopes will allow two math operations to be “daisy chained” as shown above

Another common type of mathematical analysis is to look at the frequency domain view of a sensor reading. This is particularly true if the sensor shows some sort of repetitive structure in the value of its readout or if the user suspects there is some source of noise interfering with sensor operation. In this case an FFT of the sensor signal may give an indication of the source of the noise. In the case of the accelerometer signals shown in Figures 1-3 it may be interesting for the scope user to know the frequency spectrum of the ringing. The ringing behavior will be different for different types of coupling (i.e. protective materials) between the point of impact of an impulse and the sensor. If we did an FFT of the example shown in Figure 4 the frequency spectra would give insight into physical shaking of a fan. Figure 6 shows the setup of this type of frequency analysis using the same signal as was shown

Figure 6:

A Fourier transform is used to find the spectral components of the sensor readings from an accelerometer attached to a fan body

in Figure 4. Channel 1 of the oscilloscope captures the output of the sensor attached to the fan body. This is the upper trace. The math setup shows a rescale, then an FFT. The purpose of the rescale is to compute parameter P2 – the “max” of the rescaled math trace. This is the maximum acceleration detected by the sensor, 5.5009 milligravities.

The FFT could be performed on either the voltage vs time trace or the rescaled trace. Both traces have the same shape and the same spectral components. In this example the peak of the FFT is at 120 Hz as shown by the cursor reading toward the lower right of the screen image. Once the user has the math setup that is desired, the math menu can be closed so the entire viewing area of the screen can be used for examining the acquired waveform and the FFT. This is shown in Figure 7.

Figure 7:

The same signals as Figure 6 but the FFT setup menu has been closed. The signals can be viewed with better detail using the full screen

Testing Signal Parameters to Meet Specifications

Most products have to meet certain specifications, or should respond in a specified manner when subjected to a particular stimulus. A digital oscilloscope can help greatly in testing key signal characteristics or in documenting product response to a specified stimulus. All digital oscilloscopes measure signal parameters – some make more measurements, and more complex measurements, than others. Figures 4, 6 and 7 show some basic parameter measurements of peak-to-peak and maximum signal excursion. Oscilloscopes can also measure signal rise time, fall time, overshoot, pulse width, interval between two edges on a signal, the time between an edge on one signal and the arrival of an edge on a different signal and a host of other parameters. Sometimes the user just wants the oscilloscope to measure parameters for the acquisition that is shown on the screen. But in other cases it is necessary to test operation of a device over many iterations to prove the parameters of interest are always within specification. In Figure 8 the voltage waveform from an accelerometer is shown in the upper trace. The lower trace is the “rescaled” waveform using physical units (gravities). This example applies equally to any type of sensor for which the engineers wants to test certain key signal characteristics. In this particular example, the oscilloscope has acquired 238 acquisitions of the waveform (the “num” parameter near the bottom is the number of acquisitions).

Figure 8:

The upper trace is the voltage signal from a sensor. Below it is a rescaled trace using physical units. The parameters “mean”,”sdev”, and “pkpk” are computed on the rescaled trace. The parameter statistics are the result of 238 acquisitions of the signal. The green shapes below the statistics show the shape of the distribution of the parameter measurements

For each acquisition the scope computers the mean, standard deviation (rms difference from the mean) and peak-to-peak output of the sensor. The “value” at the top of the table is the parameter value for the most recent acquisition on the screen. The other statistical parameters are based on all 238 acquisitions. The green shapes at the bottom of the screen are “histicons” – icons showing thumbnail size views of the distribution of each parameter. The “mean” , P1, and peak-to-peak, P3, parameters have Gaussian-like distributions ( Gaussian shaped, but not true Gaussian since physical measurements do not extend to infinity). The sdev parameter, P2, is a Rayleigh distribution. If you are testing a sensor or actor to stress it for worst case conditions the parameters with statistics information is very useful. In particular the “max” and “min” will show the worst case extreme values of the sensor performance for a set of tests – as many as you want to administer. The “max” and “min” will also show if there is any intermittent very high or very low reading due to drop outs or other rare phenomena. The histicon shape is also quite useful. Most of the time the expected shape for the distribution of a parameter is known – for example a central value with some noise usually results in a Gaussian-like shape. If the oscilloscope shows some unexpected shape to the distribution of values for a parameter it is often a very good clue to use in troubleshooting a problem. You may see histicon shapes that are indicative of some sinusoidal modulation, or perhaps of the presence of two competing processes (two peaks in the histogram where only one was expected) or other types of unexpected phenomena. Not all oscilloscopes offer the ability to use parameter statistics or histicons. Figure 9 shows the setup menu for selecting which parameters to calculate and whether to display parameter statistics and histicons.

Figure 9:

The method for setting up the parameter measurements as shown in Figure 8. The user can choose six parameters to measure. Statistics and Histicons can be “checked” to have them displayed

It is easy to turn on the parameter statistics and histicons by checking a box.

Advanced Math – Filtering Signals to Obtain Higher Precision

Many types of sensors change their output values at a rate much slower than the sampling rate of modern digital oscilloscopes. In cases like this the oversampling can be used to obtain more precise measurement of the sensor value. As an extreme example, if the output of a sensor is DC only one sample would be needed to measure the voltage. More than one sample is oversampling. The ADC’s of an oscilloscope have integer steps. For an eight bit oscilloscope there are 256 possible output codes of the ADC. Maybe the hypothetical DC voltage from the sensor corresponds to 100.5 ADC counts. Since there are no half counts of the ADC, a single sample would be 100 or 101 counts. In fact, even if there is zero noise on the DC level of the sensor signal, the noise from the front end amplifier of the oscilloscope may push the reading to 99 or 102 counts. If the oscilloscope is set to capture 100 samples of the DC voltage, the average will probably be close to 100.5. The extra counts are used to “average out” the noise and also to obtain better vertical resolution. Figure 10 shows an example of using Enhanced Resolution (ERES) to add 2.5 bits of resolution when capturing a sensor signal.

Figure 10:

Enhanced Resolution is used to reduce noise and increase vertical resolution. Note in the red box an ERES noise filter has been set up which increases resolution by 2.5 bits but the tradeoff is reduced bandwidth. The lower trace is the signal captured at full bandwidth. The upper trace (which clearly has much lower noise) is the ERES view

ERES is a linear finite impulse response (FIR) filter. If the oscilloscope user wants to measure some slowly changing property of the sensor signal and wants to reduce the noise in the sensor signal (and also reduce front end noise from the oscilloscope), enhanced resolution is a useful tool. But the user needs to keep in mind that he has probably eliminated some portion of the real signal – the signal content that is above the bandwidth of the ERES filter.

Choosing the Right Oscilloscope

The preceding discussion shows a few of the many types of views, measurements and analysis which can be performed by digital oscilloscopes. Most engineers have several oscilloscopes in their labs – and there are even more available for purchase from oscilloscope vendors. The different instruments have varied capabilities for capture of signals, for viewing them, for making measurements and for producing documents such as test procedures or engineering progress reports. In order to select an oscilloscope that is a good match to the needs of an application there are a few basic properties to look for in the instrument.

First, consider what it is you want to measure. Maybe no measurements are required – you just need to view the signal. Or maybe only a few basic measurements are needed. But if you need to characterize the properties of a device or troubleshoot some sort of intermittent behavior that is causing odd signal performance then you may need a scope with more measurement capabilities. For example, the WaveAce line of oscilloscopes from LeCroy offers a basic selection of 32 parameter measurements. It can do basic math on waveforms such as +, -, x, / and FFT. In the same price class as the WaveAce oscilloscopes there are scopes from other companies offering anywhere from 11 to 23 parameter measurements – which might be just fine for some applications. But if you need to measure the time from an edge of signal 1 to an edge in signal 2 (on two different channels of the oscilloscope), you may wish that you had a WaveAce. On the other hand, if you want to be able to view the “histicons” shape of the distribution of a parameter value or if you want to perform advanced math such as integration, this is not possible on a WaveAce. You will need a WaveSurfer. The WaveSurfer is intended for applications where more types of measurements and troubleshooting will be performed. In addition to typical oscilloscope parameters and math, options are available for the WaveSurfer to decode serial data streams (USB, RS232, I2, etc.) and to add up to 36 digital channels for mixed signal operation.

Once you know the scope can measure what you need to measure the next step is to choose a model that can capture the signal of interest accurately. This means the front end of the scope needs a fast enough amplifier (and perhaps probes) to follow the shape of the signal, a fast enough sampling rate and a long enough memory. Amplifier bandwidth is the most common way in which oscilloscopes are rated. Typically a line of scopes offers several choices of bandwidth, so if you have found an instrument that makes all the measurements you need then you can select from among several choices of bandwidth. For example the WaveAce series has choices from 40 MHz to 300 MHz while the WaveSurfer spans the range from 200 MHz to 1 GHz. A 400 MHz scope can more accurately track the shape of fast edges than a 40 MHz scope. In general, to make measurements with reasonable accuracy you would like the risetime of your oscilloscope (which is closely related to its bandwidth) to be substantially faster than the risetime of the signals which are being captured. For oscilloscopes with bandwidths of 1 GHz and below it is a very reasonable approximation that the scope bandwidth and risetime are related by the equation BW x TR = .35 A 1 GHz scope will have a risetime around 0.35 nanoseconds. A 100 MHz oscilloscope will have a risetime about 10 times longer ; around 3.5 nsec. There are a variety of ways to determine how fast the ADC sample rate should be. Most vendors put ADCs into a scope that have fast enough sampling rate for the bandwidth of the amplifiers in that instrument. If the maximum ADC sampling rate is 10 times the bandwidth of the oscilloscope this is more than adequate. For example a max sampling rate of 1 GS/s for a 100 MHz oscilloscope. Finally, the scope needs to have enough memory to run at its maximum sampling rate for the length of time equal to the duration of your longest signal. If a scope can capture at 1 GS/s then it would need 1 Mpoint of memory to capture a signal duration of 1 msec while using the maximum sampling rate. If the memory length is too short then the ADC will still capture the 1 msec signal, but it will do so by slowing down the sampling rate so that the ADC samples stretch across a longer period of time.

There is much more that could be said about selecting an oscilloscope. In the end, perhaps the easiest way to shop for a scope is to call up a vendor, tell him the types of signals you want to capture, the types of measurements you need to make and get good advice from an expert.