# Evaluating Oscilloscopes (Part 2)

This is Part 2 of my mini-series on selecting an oscilloscope. Rather than a completely thorough guide, it’s more a “collection of notes” based on my own research. But I hope you find it useful, and it might cover a few areas you hadn’t considered.

Last week I mentioned the differences between PC-based and stand-alone oscilloscopes and discussed the physical probe’s characteristics. This week I’ll be discussing the “core” specifications: analog bandwidth, sample rate, and analog-to-digital converter (ADC) resolution.

Topic 1: Analog Bandwidth
Many useful articles online discuss the analog oscilloscope bandwidth, so I won’t dedicate too much time to it. Briefly, the analog bandwidth is typically measured as the “half-power” or -3 dB point, as shown in Figure 1. Half the power means 1/√2 of the voltage. Assume you put a 10-MHz, 1-V sine wave into your 100-MHz bandwidth oscilloscope. You expect to see a 1-V sine wave on the oscilloscope. As you increase the frequency of the sine wave, you would instead expect to see around 0.707 V when you pass a 100-MHz sine wave. If you want to see this in action, watch my video in which I sweep the input frequency to an oscilloscope through the -3 dB point.

Figure 1: The bandwidth refers to the “half-power” or -3 dB point. If we drive a sine wave of constant amplitude and increasing frequency into the probe, the -3 dB point would be when the amplitude measured in the scope is 0.707 times the initial amplitude.

Unfortunately, you are likely to be measuring square waves (e.g., in digital systems) and not sine waves. Square waves contain high-frequency components well beyond the fundamental frequency of the wave. For this reason the “rule of thumb”  is to select an oscilloscope with five times the analog bandwidth of the highest–frequency digital signal you would be measuring. Thus, a 66-MHz clock would require a 330-MHz bandwidth oscilloscope.

If you are interested in more details about bandwidth selection, I encourage you to see one of the many excellent guides. Adafruit has a blog post “Why Oscilloscope Bandwidth Matters” that offers more information, along with links to guides from Agilent Technologies and Tektronix.

If you want to play around yourself, I’ve got a Python script that applies analog filtering to a square wave and plots the results, available here. Figure 2 shows an example of a 50-MHz square wave with 50-MHz, 100-MHz, 250-MHz, and 500-MHz analog bandwidth.

Figure 2: This shows sampling a 50-MHz square wave with 50, 100, 250, and 500 MHz of analog bandwidth.

Topic 2: Sample Rate
Beyond the analog bandwidth, oscilloscopes also prominently advertise the sample rate. Typically, this is in MS/s (megasamples per second) or GS/s (gigasamples per second). The advertised rate is nearly always the maximum if using a single channel. If you are using both channels on a two-channel oscilloscope that advertises 1 GS/s, typically the maximum rate is actually 500 MS/s for both channels.

So what rate do you need? If you are familiar with the Nyquist criterion, you might simply think you should have a sample rate two times the analog bandwidth. Unfortunately, we tend to work in the time domain (e.g., looking at the oscilloscope screen) and not the frequency domain. So you can’t simply apply that idea. Instead, it’s useful to have a considerably higher sample rate compared to analog bandwidth, say, a five times higher sample rate. To illustrate why, see Figure 3. It shows a 25.3-MHz square wave, which I’ve sampled with an oscilloscope with 50-MHz analog bandwidth. As you would expect, the signal rounds off considerably. However, if I only sample it at 100 MS/s, at first sight the signal is almost unrecognizable! Compare that with the 500 MS/s sample rate, which more clearly looks like a square wave (but rounded off due to analog bandwidth limitation).

Again, these figures both come from my Python script, so they are based purely on “theoretical” limits of sample rate. You can play around with sample rate and bandwidth to get an idea of how a signal might look.

Figure 3: This shows sampling a 25.3-MHz square wave at 100 MS/s results in a signal that looks considerably different than you might expect! Sampling at 500 MS/s results in a much more “proper” looking wave.

Topic 3: Equivalent Time Sampling
Certain oscilloscopes have an equivalent time sampling (ETS) mode, which advertises an insanely fast sample rate. For example, the PicoScope 6000 series, which has a 5 GS/s sample rate, can use ETS mode and achieve 200 GS/s on a single channel, or 50 GS/s on all channels.

The caveat is that this high sample rate is achieved by doing careful phase shifts of the A/D sampling clock to sample “in between” the regular intervals. This requires your input waveform be periodic and very stable, since the waveform will actually be “built up” over a longer time interval.

So what does this mean to you? Luckily, many actual waveforms are periodic, and you might find ETS mode very useful. For example, if you want to measure the phase shift in two clocks through a field-programmable gate array (FPGA), you can do this with ETS. At 50 GS/s, you would have 20 ps resolution on the measurement! In fact, that resolution is so high you could measure the phase difference due to a few centimeters difference in PCB trace.

To demonstrate this, I can show you a few videos. To start with, the simple video below shows moving the probes around while looking at the phase difference.

A more practical demonstration, available in the following video, measures the phase shift of two paths routed through an FPGA.

Finally, if you just want to see a sine wave using ETS you can check out the bandwdith demonstration  I referred to earlier in the this article. The video (see below) includes a portion using ETS mode.

Topic 4: ADC Resolution
A less prominently advertised feature of certain oscilloscopes is the ADC bit resolution in the front end. Briefly, the ADC resolution tells you how the analog waveform will get mapped to the digital domain. If you have an 8-bit ADC, this means you have 28 = 256 possible numbers the digital waveform can represent. Say you have a ±5 V range on the oscilloscope—a total span of 10 V. This means the ADC can resolve 10 V / 256 = 39.06 mV difference on the input voltage.

This should tell you one fact about digital oscilloscopes: You should always use the smallest possible range to get the finest granularity. That same 8-bit ADC on a ±1 V range would resolve 7.813 mV. However, what often happens is your signal contains multiple components—say, spiking to 7 V during a load switch, and then settling to 0.5 V. This precludes you from using the smaller range on the input, since you want to capture the amplitude of that 7-V spike.

If, however, you had a 12-bit ADC, that 10 V span (+5 V to -5 V) would be split into 212 = 4,096 numbers, meaning the resolution is now 2.551 mV.  If you had a 16-bit ADC, that 10-V range would give you 216 = 65,536 numbers, meaning you could resolve down to 0.1526 mV. Most of the time, you have to choose between a faster ADC with lower (typically 8-bit) resolution or a slower ADC with higher resolution. The only exception to this I’m aware of is the Pico Technology FlexRes 5000 series devices, which allow you to dynamically switch between 8/12/14/15/16 bits with varying changes to the number of channels and sample rate.

While the typical ADC resolution seems to be 8 bits for most scopes, there are higher-resolution models too. As mentioned, these devices are permanently in high-resolution mode, so you have to decide at purchasing time if you want a very high sample rate, or a very high resolution. For example, Cleverscope has always advertised higher resolutions, and their devices are available in 10, 12, or 14 bits. Cleverscope seems to sell the “digitizer” board separately, giving you some flexibility in upgrading to a higher-resolution ADC. TiePie engineering has devices available from 8–14 bits with various sample rate options. Besides the FlexRes device I mentioned, Pico Technology offers some fixed resolution devices in higher 14-bit resolution. Some of the larger manufacturers also have higher-resolution devices, for example Teledyne LeCroy has its High Resolution Oscilloscope (HRO), which is a fixed 12-bit device.

Note that many devices will advertise either an “effective” or “software enhanced” bit resolution higher than the actual ADC resolution. Be careful with this: software enhancement is done via filtering, and you need to be aware of the possible resulting changes to your measurement bandwidth. Two resources with more details on this mode include the ECN magazine article “How To Get More than 8 Bits from Your 8-bit Scope” and the Teledyne LeCroy application note “Enhanced Resolution.” Remember that a 12-bit, 100-MHz bandwidth oscilloscope is not the same as an 8-bit, 100-MHz bandwidth oscilloscope with resolution enhancement!

Using the oscilloscope’s fast Fourier transform (FFT) mode (normally advertised as the spectrum analyzer mode), we can see the difference a higher-resolution ADC makes. When looking at a waveform on the screen, you may think that you don’t care at all about 14-bit accuracy or something similar. However, if you plan to do measurements such as total harmonic distortion (THD), or otherwise need accurate information about frequency components, having high resolution may be extremely important to achieve a reasonable dynamic range.

As a theoretical example I’m using my script mentioned earlier, which will digitize a perfect sine wave and then display the frequency spectrum. The number of bits in the ADC (e.g., quantization) is adjustable, so the harmonic component is solely due to quantization error. This is shown in Figure 4. If you want to see a version of this using a real instrument, I conduct a similar demonstration in this video.

Certain applications may find the higher bit resolution a necessity. For example, if you are working in high-fidelity audio applications, you won’t be too worried about an extremely high sample rate, but you will need the high resolution.

Figure 4: In the frequency domain, the effect of limited quantization bits is much more apparent. Here a 10-MHz pure sine wave frequency spectrum is taken using a different number of bits during the quantization process. (CLICK TO ZOOM)

Coming Up
This week I’ve taken a look at some of the core specifications. I hope the questions to ask when purchasing an oscilloscope are becoming clearer! Next week, I’ll be looking at the software running the oscilloscope, and details such as remote control, FFT features, digital decoding, and buffer types. The fourth and final week will delve into a few remaining features such as external trigger and clock synchronization and will summarize all the material I’ve covered in this series.

Author’s note: Every reasonable effort has been made to ensure example specifications are accurate. There may, however, be errors or omissions in this article. Please confirm all referenced specifications with the device vendor.

# Build an Inexpensive Wireless Water Alarm

The best DIY electrical engineering projects are effective, simple, and inexpensive. Devlin Gualtieri’s design of a wireless water alarm, which he describes in Circuit Cellar’s February issue, meets all those requirements.

Like most homeowners, Gualtieri has discovered water leaks in his northern New Jersey home after the damage has already started.

“In all cases, an early warning about water on the floor would have prevented a lot of the resulting damage,” he says.

You can certainly buy water alarm systems that will alert you to everything from a leak in a well-water storage tank to moisture from a cracked boiler. But they typically work with proprietary and expensive home-alarm systems that also charge a monthly “monitoring” fee.

“As an advocate of free and open-source software, it’s not surprising that I object to such schemes,” Gualtieri says.

In February’s Circuit Cellar magazine, now available for membership download or single-issue purchase, Gualtieri describes his battery-operated water alarm. The system, which includes a number of wireless units that signal a single receiver, includes a wireless receiver, audible alarm, and battery monitor to indicate low power.

Photo 1: An interdigital water detection sensor is shown. Alternate rows are lengths of AWG 22 copper wire, which is either bare or has its insulation removed. The sensor is shown mounted to the bottom of the box containing the water alarm circuitry. I attached it with double-stick foam tape, but silicone adhesive should also work.

Because water conducts electricity, Gualtieri sensors are DIY interdigital electrodes that can lie flat on a surface to detect the first presence of water. And their design couldn’t be easier.

“You can simply wind two parallel coils of 22 AWG wire on a perforated board about 2″ by 4″, he says. (See Photo 1.)

He also shares a number of design “tricks,” including one he used to make his low-battery alert work:

“A battery monitor is an important feature of any battery-powered alarm circuit. The Microchip Technology PIC12F675 microcontroller I used in my alarm circuit has 10-bit ADCs that can be optionally assigned to the I/O pins. However, the problem is that the reference voltage for this conversion comes from the battery itself. As the battery drains from 100% downward, so does the voltage reference, so no voltage change would be registered.

Figure 1: This is the portion of the water alarm circuit used for the battery monitor. The series diodes offer a 1.33-V total drop, which offers a reference voltage so the ADC can see changes in the battery voltage.

“I used a simple mathematical trick to enable battery monitoring. Figure 1 shows a portion of the schematic diagram. As you can see, the analog input pin connects to an output pin, which is at the battery voltage when it’s high through a series connection of four small signal diodes (1N4148). The 1-MΩ resistor in series with the diodes limits their current to a few microamps when the output pin is energized. At such low current, the voltage drop across each diode is about 0.35 V. An actual measurement showed the total voltage drop across the four diodes to be 1.33 V.

“This voltage actually presents a new reference value for my analog conversion. The analog conversion now provides the following digital values:

Table 1 shows the digital values as a function of battery voltage. The nominal voltage of three alkaline cells is 4.75 V. The nominal voltage of three lithium cells is 5.4 V. The PIC12F675 functions from approximately 2 to 6.5 V, but the wireless transmitter needs as much voltage as possible to generate a reliable signal. I arbitrarily coded the battery alarm at 685, or a little above 4 V. That way, there’s still enough power to energize the wireless transmitter at a useful power level.”

 Battery Voltage ADC Value 5 751 4.75 737 4.5 721 4.24 704 4 683 3.75 661

Gaultieri’s wireless transmitter, utilizing lower-frequency bands, is also straightforward.

Photo 2 shows one of the transmitter modules I used in my system,” he says. “The round device is a surface acoustic wave (SAW) resonator. It just takes a few components to transform this into a low-power transmitter operable over a wide supply voltage range, up to 12 V. The companion receiver module is also shown. My alarm has a 916.5-MHz operating frequency, but 433 MHz is a more popular alarm frequency with many similar modules.”

Photo 2: These transmitter and receiver modules are used in the water alarm. The modules operate at 916.5 MHz, but 433 MHz is a more common alarm frequency with similar modules. The scale is inches.

Gualtieri goes on to describe the alarm circuitry (see Photo 3) and receiver circuit (see Photo 4.)

For more details on this easy and affordable early-warning water alarm, check out the February issue.

Photo 3: This is the water alarm’s interior. The transmitter module with its antenna can be seen in the upper right. The battery holder was harvested from a \$1 LED flashlight. The box is 2.25“ × 3.5“, excluding the tabs.

Photo 4: Here is my receiver circuit. One connector was used to monitor the signal strength voltage during development. The other connector feeds an input on a home alarm system. The short antenna reveals its 916.5-MHz operating frequency. Modules with a 433-MHz frequency will have a longer antenna.

# Client Profile: Pico Technology

Pico Technology
320 North Glenwood Boulevard
Tyler, TX 75702

Contact: sales@picotech.com

Embedded Products/Services: Pico Technology’s PicoScope 5000 series uses reconfigurable ADC technology to offer a choice of resolutions from 8 to 16 bits. For more information, visit www.picotech.com/picoscope5000.html.

Product information: The new PicoScope 5000 series oscilloscopes have a significantly different architecture. High-resolution ADCs can be applied to the input channels in different series and parallel combinations to boost the sampling rate or the resolution.

In Series mode, the ADCs are interleaved to provide 1 GB/s at 8 bits. In Parallel mode, multiple ADCs are sampled in phase on each channel to increase the resolution and dynamic performance (up to 16 bits).

In addition to their flexible resolution, the oscilloscopes have ultra-deep memory buffers of up to 512 MB to enable long captures at high sampling rates. They also feature standard, advanced software, including serial decoding, mask limit testing, and segmented memory.

The PicoScope 5000 series oscilloscopes are currently available at www.picotech.com.

The two-channel, 60-MHz model with built-function generator costs \$1,153. The four-channel, 200-MHz model with built-in arbitrary waveform generator (AWG) costs \$2,803. The pricing includes a set of matched probes, all necessary software, and a five-year warranty.

# CC280: Analog Communications and Calibration

Are you an analog aficionado? You’re in luck. Two articles, in particular, focus on the November issue’s analog techniques theme. (Look for the issue shortly after mid-October, when it will be available on our website.)

Data from the base adapter is sent by level shifting the RS-232 or CMOS serial data between 9 and 12 V. A voltage comparator at the remote adapter slices the signal to generate a 0-to-5-V logic signal. The voltage on the signal wire never goes low enough for the 5-V regulator to go out of regulation.

These adapters use a combination of tricks. A single pair of wires carries full-duplex serial data and a small amount of power to a remote device for tasks (e.g., continuous remote data collection and control). The digital signals can be simple on/off signals or more complex signals (e.g., RS-232).

Dick Cappels, a consultant who tinkers with analog and mixed-signal projects, presents a design using a pair of cable adapters and simple analog circuits to enable full-duplex, bidirectional communications and power over more than 100 m of paired wires. Why bother when Power Over Ethernet  (PoE), Bluetooth, and Wi-Fi approaches are available?

“In some applications, using Ethernet is a disadvantage because of the higher costs and greater interface complexity,” Cappels says. “You can use a microcontroller that costs less than a dollar and a few analog parts described in this article to perform remote data gathering and control.”

The base unit including the 5-to-15-V power supply is simple for its functionality. The two eight-pin DIP ICs are a voltage comparator and the switching regulator.

Cappels’s need for data channels to monitor his inground water tank inspired his design. Because his local municipality did not always keep the tank filled, he needed to know when it was dry so his pumps wouldn’t run without water and possibly become damaged.
“Besides the mundane application of monitoring a water tank, the system would be excellent for other communication uses,” Cappels says, including computer connection to a home weather station and intrusion-detection systems. Bit rates up to 250 kHz also enable the system to be used in two-way voice communication such as intercoms, he says.

Retired engineer David Cass Tyler became interested in writing his series about calibration while working on a consulting project. “I came to realize that some people don’t really know how to approach the issue of taking an analog-to-digital value to actual engineering units, nor how to correct calibration factors after the fact,” Tyler says

In Part 1 of his article series, Tyler notes: “Digital inputs and digital outputs are pretty simple. They are either on or off. However, for ADCs and DACs to be accurate, they must first be calibrated. This article addresses linear ADCs and DACs.” Part 2, appearing in the December issue, will discuss using polynomial curve fitting to convert nonlinear data to real-world engineering values.

In addition to its analog-themed articles, the November issue includes topics ranging from a DIY solar array tracker’s software to power-capped computer systems.

Editor’s Note: Learn more about Circuit Cellar contributors Dick Cappels and David Cass Tyler by reading their posts about their workspaces and favorite DIY tools.

# Data Acquisition Instrument

The DI-145 USB data acquisition instrument features four ±100-V analog channels and two dedicated digital inputs. The included DATAQ WinDaq data acquisition software (DAS) enables you to display and record data to a PC hard drive in real time. Once recorded, data can be played back, analyzed, or exported to an array of data acquisition and spreadsheet formats.

DATAQ also provides access to the DI-145 data protocol, which enables access to the DI-145 on any Windows, Linux, or MAC OS. In addition, .NET control is available to Windows users who wish to use a third-party programming language (e.g., Microsoft’s Visual Basic or National Instruments’s LabVIEW) to interface with the DI-145.

The four ±10-V fixed differential channels are protected from transient spikes up to ±150 V peak (±75 V, continuous). A 10-bit ADC provides 19.5-mV resolution across the full-scale measurement range. Digital inputs are protected up to ±30 VDC/peak AC. The digital inputs enable you to use a switch closure or TTL signal to remotely insert event marks or record data to disk.

The DI-145 measures 1.53” × 2.625” × 5.5” (3.89 cm × 6.67 cm × 13.97 cm) and weighs 3.6 oz. The data acquisition instrument costs \$29 and includes a mini screwdriver, a USB cable, WinDaq/Lite DAS, access to the data protocol, and .NET control.

DATAQ Instruments, Inc.
www.dataq.com