In this series on strain gauges, we’ve looked at quarter- and half-bridge configurations. In this final part, we will look at a full-bridge implementation with four active elements.

Q: Where do these active elements get placed on our test specimen?
A: Figure 1 shows one possibility. With stress applied in the direction of the arrow, the red elements on top, each of length l in the unstressed state, will expand by Dl, and the blue ones of the same initial unstrained length will contract by Dl.

Q: How do we connect these elements?
A: Figure 2 shows these elements connected in the Wheatstone-bridge circuit, where VEX is the excitation voltage, and V_O is the output voltage proportional to strain e.

Q: How do we derive strain from VO?
A: We basically have two voltage dividers with the voltages at the positive and negative terminals of our voltmeter as follows:

Then, V_O is V₊–V_–:

Given a gauge factor (GF), we want to find V_O as a function of strain. From part 3, we know we can substitute R(GF)e  for DR:

For GF = 2, the Figure 3 traces show V_O as a function of e  for full-, half-, and quarter-bridge circuits along with the corresponding equations. Note that for the quarter-bridge case, the equation represents a linear approximation (black trace) of the actual nonlinear response (dashed black trace) that we calculated in part 2. Note that as we double the number of active elements, V_O doubles, thereby increasing our measurement sensitivity.

Figure 4. Lead resistance RL can drift with ambient temperature (a), but an additional sense lead can provide compensation (b). (Image: Rick Nelson)

Q: Couldn’t we also increase sensitivity by increasing the excitation voltage?
A: Yes, increasing the excitation voltage would increase the sensitivity and signal-to-noise ratio. However, this approach has a downside: it increases power dissipation in each strain-gauge element, with power increasing with the square of the excitation voltage. As power increases, the gauge becomes susceptible to self-heating, which can cause the gauge to expand and contract relative to the test specimen [1], thereby introducing a thermal error that is difficult to compensate for. Consequently, the excitation voltage should remain as low as possible while maintaining an adequate signal-to-noise ratio.

Q: What about lead-length resistance while measuring strain on large structures such as wide-body airframes?
A: As illustrated in Figure 4 in a quarter-bridge configuration, our strain gauge R_X attaches to our data-acquisition system through two leads, Lead 1 (red) and Lead 2 (blue), of resistance R_L each, so our meter will respond as if R_X=R_X+2R_L. If we know R_L, we can compensate, but R_L will vary with ambient temperature, making it difficult to know its value exactly.

The gold-standard approach for compensating for lead resistance is to use a four-wire Kelvin measurement, but that incurs additional cost. With the Wheatstone bridge, however, we only need to add one additional sense lead and make a minor wiring change, shown in orange in Figure 4b. Note that with this approach, we’ve moved the Lead 1 resistance from the bottom right of the bridge to the top right, while the Lead 2 resistance remains in the bottom right. Consequently, the bridge will cancel out any resistance changes due to temperature, as described in an earlier article. Of course, the sense lead has some resistance, but it’s negligible compared to the voltmeter’s impedance.

Reference

[1] Strain Gauges: Selecting an Excitation Voltage, Siemens

Related EEWorld Online content

Defining and measuring strain: part 1
The basics of Kelvin connections
Making sense of test circuits with Kirchhoff’s laws: part 4
What’s the difference between 2-, 3-, & 4-wire RDT sensing?
Stress & Strain, Part 1: fundamental principles
How to avoid errors in low-voltage measurements

The post Defining and measuring strain: part 4 appeared first on Test & Measurement Tips.

In this series, we’ve been looking at the strain gauge, a type of sensor that can measure how a test specimen deforms as a function of applied stress. In part 2 of this series and in an earlier article on the Wheatstone bridge, we looked at how a single active strain-gauge element coupled with a passive element in a half-bridge configuration can measure tensile and compressive axial strain while providing temperature compensation. In this article, we’ll look at the use of two active strain-gauge elements.

Q: Could we first review the basic Wheatstone bridge topology?
A: Yes, and in fact, this is a good time to update one of our labels. Figure 1 shows the basic Wheatstone-bridge circuit. So far, our unknown resistance of interest has been R_X on the lower right. With multiple active strain-gauge elements, however, we can have multiple unknown resistances in our bridge, so I’ll rename R_X as R₄ to emphasize that it’s not the only potential unknown. Note also that V_EX is the excitation voltage, and V_O is the output voltage, with V_O varying with strain e.

Q: So how do we make use of multiple strain-gauge elements?
A: We concluded part 2 of this series with a figure similar to Figure 2a, with strain gauges mounted on the top and bottom of a test specimen, and with the long sense conductors aligned in parallel with the direction of axial strain. Both will increase in resistance when in tension and decrease in compression. This, in and of itself, can be useful, but first let’s look at a slightly different configuration. In Figure 2b, our test specimen becomes a cantilever subjected to a bending stress, as shown by the red arrow. Here, the top strain-gauge element of length l increases in length by Dl, and the bottom element decreases in length by the same amount.

Q: How do we connect this to our bridge?
A: Figure 3 shows one possibility. Let’s say the fixed resistors and the unstrained resistance values of our strain gauges are all equal to R. We can see immediately that the voltage at the negative terminal of our V_O meter is V_EX/2, and the stressed resistances of the R₂ and R₄ strain gauges are R–DR and R+DR, respectively. Note that this configuration retains the temperature-compensation characteristic of our previous implementation with one active and one dummy element.

We can then calculate V_O:

From part 1, we know that

And therefore:

We can now substitute R(GF)e  for DR in our equation for V_O:

The Figure 4 trace in blue plots V_O vs e  for the Figure 3 circuit. The red trace shows the relationship for our circuit from part 2 with the single active element. Note that for a given e, the voltage for the two-active-element circuit approximately doubles, boosting measurement sensitivity.

Q: Why say “approximately doubles”?
A: The equation above for V_O for two active elements is clearly linear, and the equation for the single-element version is nearly linear over the ranges of strain found in many applications, especially ones with metallic test specimens. However, if we look at a wider range of strain, as shown in Figure 5, we see that the single-active-element response is actually nonlinear—the dashed trace is a straight line connecting the end points of the red trace. Because of the nonlinearity of one of our traces, it wouldn’t be accurate to say the blue trace voltage is exactly double the red trace voltage for any value of strain.

Q: What else should we know about strain gauges?
A: We will conclude this series with a look at full-bridge implementations as well as considerations regarding excitation voltage levels.

Related EEWorld Online content

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Defining and measuring strain: part 1
Making sense of test circuits with Kirchhoff’s laws: part 1
Quantifying and measuring non-electrical phenomena: Heat

The post Defining and measuring strain: part 3 appeared first on Test & Measurement Tips.

Welcome to the April edition of Engineering Deep Dive — a curated selection of the most engaging technical threads from the Electro-Tech-Online community’s Electronic Projects Design/Ideas/Reviews category. Questions are selected based on view counts, reply depth, and educational value. Each entry below has been expanded with context, key concepts, and suggestions for further exploration.

Questions at a glance

Q1  Why Does My Window Comparator Output Stay ON at 0V Input Despite Correct Threshold Voltages?
Q2 Does Cable Velocity Factor Affect Pulse Propagation Delay or Only Phase Shift?
Q3  How Does Pulse Ignition and Flame Rectification Work in Gas Water Heater Ignition Systems?
Q4  How Do You Identify Whether a PCB Failure Is Caused by Design Errors or Manufacturing Defects?
Q5  Why Is Reflection Cancellation Still Considered Resonance in Time-Domain Analysis?
Q6  How Can You Measure and Isolate PCB Trace S-Parameters Without RF Connectors?
Q7  What Is the Most Convenient Way to Implement Real-Time Audio FFT Analysis?

Q1  Why does my window comparator output stay on at 0V input despite correct threshold voltages?

A window comparator circuit based on the LM339 is behaving unexpectedly — the output LED stays ON even when the input voltage is 0V, despite threshold voltages appearing correct. This thread walks through threshold calculation, LM339 open-collector output behavior, and systematic troubleshooting of component failures that cause latched outputs.

Key technical topics covered

• Window comparator design with LM339 (open-collector output stage)
• Upper and lower threshold voltage calculation
• Diagnosing latched or stuck outputs caused by faulty components
• Pull-up resistor selection and LED drive circuit

Why It Matters | Window comparators appear in battery monitors, motor-speed controllers, temperature alarms, and ADC over-range detectors. Misunderstanding open-collector outputs is one of the most common LM339 pitfalls for beginners.

Topic tags

Circuit Design | LM339 | Comparator | Troubleshooting

Supporting data: Circuit schematic image

Community thread: Thread link

Q2  Does Cable velocity factor affect pulse propagation delay or only phase shift?

When feeding a digital pulse into a coaxial or transmission-line cable, does the cable’s velocity factor (VF) introduce a propagation delay, or does it only shift the phase of a sinusoidal signal? This thread distinguishes group velocity (relevant to pulse delay) from phase velocity (relevant to sinusoidal phase shift) and explains why both are numerically identical in non-dispersive media.

Key technical topics covered

• Velocity factor and its physical origin (permittivity of the dielectric)
• Group velocity vs. phase velocity — when they differ
• Propagation delay calculation: t_d = length / (VF × c)
• Practical impact on digital timing in long cable runs

Why It Matters | Signal integrity engineers designing high-speed serial links, RF engineers building phased arrays, and hobbyists working with long cable runs all need to understand how VF affects their signals.

Topic tags

Signal Integrity | Transmission Line | RF | Digital Timing

Supporting data: Oscilloscope waveform image

Community thread: Thread link

Q3  How Does Pulse Ignition and Flame Rectification Work in Gas Water Heater Ignition Systems?

This thread goes beyond simple ignition spark generation to explore how a flame rectification sensor confirms combustion. The discussion covers the ionization current produced by a gas flame, how it is used as a half-wave rectifier in the safety circuit, and the risks of DIY modifications to gas appliance electronics.

Key technical topics covered

• High-voltage spark generation via a pulse ignition module
• Flame rectification: DC bias through an ionized gas column
• Safety interlocks and why repeated ignition failures must not be bypassed
• Troubleshooting the sensor electrode (fouling, misalignment, cracked ceramic)

Why It Matters | Gas appliance faults can be dangerous. Understanding the intended safety logic helps technicians and advanced hobbyists diagnose faults responsibly, without disabling protective interlocks.

Topic tags

Power Electronics | Safety Systems | Sensors | Gas Ignition

Supporting data: Module photograph

Community thread: Thread link

Q4  How do you identify whether a PCB failure is caused by design errors or manufacturing defects?

When a PCB batch fails, the root cause might be in the Gerber/drill files or in the fabrication process itself. This thread provides a structured methodology: cross-referencing design files with fab specifications, identifying tell-tale defect signatures (trace opens, plating voids, layer misregistration), and communicating findings to the PCB house.

Key technical topics covered

• DFM (Design for Manufacturability) review checklist before ordering
• Common fab defects: plating voids, trace opens, drill inaccuracies, solder-mask misalignment
• Layer misregistration detection via cross-section or X-ray inspection
• How to document and report defects to get boards replaced or credited

Why It Matters | PCB fabrication failures are costly in both money and schedule. A systematic approach reduces finger-pointing between design and manufacturing teams and speeds up root-cause resolution.

Topic tags

PCB Design | DFM | Manufacturing | Quality Assurance

Supporting data: PCB microscopy image

Community thread: Thread Link

Q5  Why Is Reflection Cancellation Still Considered Resonance in Time-Domain Analysis?

Resonance is traditionally taught in the frequency domain as a sharp peak at a natural frequency. This thread unpacks the conceptual bridge to the time domain: how delayed reflections, constructive/destructive interference, and oscillating energy exchange between inductance and capacitance all manifest as what we still call ‘resonance’, regardless of domain.

Key technical topics covered

• Time-domain view of resonance: energy oscillating between L and C
• Reflections on transmission lines and how they create standing waves
• Fourier duality: why time-domain oscillation maps to a frequency-domain peak
• Practical examples: stub resonance, via resonance in PCBs

Why It Matters | Signal integrity engineers and RF designers often switch between domains. Understanding why the same physical phenomenon appears as both a time-domain ringing and a frequency-domain peak prevents analysis errors.

Topic tags

Signal Integrity | RF Theory | Frequency Domain | Time Domain

Supporting data: Simulation waveform image

Community thread: Thread Link

Q6  How can you measure and isolate PCB trace S-parameters without RF connectors?

Characterizing a PCB interconnect with a VNA is straightforward when SMA connectors are available — but what if there are none? This thread covers probe-based measurement, the de-embedding process to remove fixture and pad parasitics, and the 2x-Thru method for extracting a single trace’s S-parameters from a back-to-back structure.

Key technical topics covered

• Probe landing and transition de-embedding concepts
• 2x-Thru and Short-Open-Load-Through (SOLT) calibration strategies
• Reducing fixture discontinuities with careful pad geometry
• Software tools: IDEM, OpenDEKit, or VNA manufacturer utilities

Why It Matters | As PCB speeds push into multi-GHz territory, accurate S-parameter extraction without connectors is essential for channel simulation, equalizer design, and compliance testing.

Topic tags

RF Measurement | S-Parameters | PCB | Signal Integrity

Supporting data: VNA measurement image

Community thread: Thread Link

Q7  What is the most convenient way to implement real-time audio FFT analysis?

Real-time FFT analysis of audio turns a time-domain waveform into a live frequency spectrum. This thread compares hardware (dedicated FFT modules, FPGA), microcontroller (ARM CMSIS-DSP, ESP32 FFT), and PC-based (Python, MATLAB) approaches, weighing latency, cost, and complexity.

Key technical topics covered

• FFT fundamentals: window functions, bin resolution, sample rate requirements
• Microcontroller options: ARM CMSIS-DSP library, ESP32 FFT example
• Dedicated modules: MSGEQ7 7-band analyzer IC, OpenMusicLabs FHT
• PC/software approaches: Python (numpy.fft), MATLAB, Audacity spectrum view

Why It Matters | Audio FFT is used in music visualizers, hearing aid design, acoustic testing, and voice-command pre-processing. Choosing the right platform depends on the required resolution, update rate, and available hardware.

Topic tags: Audio DSP | FFT | Embedded Systems | Signal Processing

Supporting data: N/A — community discussion

Community thread: Thread Link

Join the conversation

If any of these questions sparked an idea or you have hands-on experience with a related problem, jump into the thread — the community benefits most when engineers at all levels contribute. You can also start your own question in the Electronic Projects Design/Ideas/Reviews category on Electro-Tech-Online.

Browse all categories: electro-tech-online.com

The post Engineering deep dive-monthly forum highlights April edition appeared first on Test & Measurement Tips.

The Arbitrary Waveform Generators from Spectrum Instrumentation now include a new Sequence Restart Mode for the 65xx and 66xx series, allowing the full sequence of looped and linked waveforms to restart automatically on a trigger event with fixed trigger-to-output timing. The mode is intended for automated test environments where repeatable sequence control can help reduce test time and improve measurement efficiency. The feature is available at no additional charge through the latest driver installation and is supported on Windows and Linux, with programming examples for Python, MATLAB, C++, and LabVIEW as well as a high-level Python API.

The post New AWG mode restarts sequences on trigger appeared first on Test & Measurement Tips.

The update expands NI Nigel AI with prompt-based code generation in the LabVIEW+ Suite and extends AI-assisted capabilities across FlexLogger, InstrumentStudio, TestStand and SystemLink. The tools are designed to support engineers throughout the test lifecycle, offering context-aware suggestions for development, debugging, validation and system reuse.

According to Emerson, the AI features are built specifically for test engineering environments, where traceability, repeatability and system visibility are required. Engineers retain control over generated code and workflows while using AI to reduce manual effort.

The NI platform combines modular instrumentation hardware with open software and a shared data framework, enabling teams to manage diverse signal types, scale test systems and reuse data across projects and locations.

In internal use, Emerson reports reductions in some test development and troubleshooting tasks from hours or days to minutes. Availability of the new capabilities is expected later in 2026.

The post Emerson adds AI-assisted code generation and workflow support to NI test platform appeared first on Test & Measurement Tips.

Emerson announced updates to its NI test software portfolio, adding AI-assisted features designed to improve test development efficiency and system integration. The NI Nigel AI technology will expand to include prompt-based code generation in LabVIEW+ and broader support across tools such as FlexLogger, InstrumentStudio, TestStand, and SystemLink.

The updates are intended to help engineers develop, validate, and deploy tests more quickly while maintaining visibility into system behavior. Nigel AI is designed for test environments, providing context-aware suggestions across the workflow, from development and code reuse to validation and deployment.

The NI platform combines modular hardware, open software, and a shared data framework to support complex test requirements. Engineers can configure systems to handle a range of signals, manage large data sets, and integrate evolving computing technologies over time.

According to internal testing, AI-assisted workflows reduced some development and troubleshooting tasks from hours or days to minutes. The platform is used in industries including aerospace, semiconductor, and transportation, where reliability, traceability, and performance are critical.

The post Emerson introduces AI capabilities for test automation at NI Connect 2026 appeared first on Test & Measurement Tips.

In Part 1 of this series, I discussed how to use near-field probes to help identify high-frequency harmonic energy sources on PC boards. Characterizing each energy source, such as processors, memory, and power conversion, helps identify the source of coupled EMI being radiated from your product. This is “Step 1” of my three-step process for troubleshooting radiated emissions issues and has been pretty well documented in other articles and industry application notes.

What has not been as well covered is my “Step 2”, how to use RF current probes to further characterize attached cable harmonic currents and reveal “red flags” in your designs. The ability to identify potential coupling mechanisms from observing harmonic energy on attached cables is an important part of the troubleshooting process. In Part 2 of this series, I’ll show how I use one of my most important tools for troubleshooting radiated emissions issues.

RF current probes

I suspect most product designers are familiar with the smaller current probes designed for oscilloscopes or digital multimeters (DMMs). These typically have smaller apertures that fit a wire or small cable and generally extend from DC to 100 MHz, at best. There are also current probes for electrical measurements with larger apertures that range up to only a few MHz and are really designed for mains frequencies.

RF current probes, on the other hand, are designed to measure microamps of RF current from kHz to hundreds of MHz flowing on I/O and power cables. They usually have a hinged aperture that can accept everything from a single wire to large-diameter cables (Figure 1). When their 50Ω port is connected to a spectrum analyzer, you’ll observe an RF spectrum similar to that when using a near-field probe. Many manufacturers make these probes, but for this article, we’ll use the affordable Tekbox Model TBCP2-750 ($879). See [2].

Cable radiation is usually the dominant reason for radiated emission failures. The problem is that the various harmonic energy sources measured on your circuit boards or system can couple to any attached cables, resulting in high-frequency harmonic currents that now create an antenna effect, causing radiated emissions.

We’ll use the RF current probe to characterize and reduce these coupled RF currents by clamping it around each I/O and power cable in turn and recording the spectral characteristics for each. The typical RF current probe is sensitive enough to measure µA of RF current, and only 6 to 8 µA of harmonic current can fail the FCC class B limit.

If cables are the dominant cause of emission failure, then I often leave the probe connected and fixed in place while I’m trying various mitigations back in the PC board or system. Observing changes in real time is quite efficient!

RF current probe measurements

The RF current probe is merely a current transformer that measures RF currents in the primary (wire or cable to be measured) and couples that to the secondary, which is loaded by the 50Ω input impedance of the spectrum analyzer (Figure 2). This produces a voltage across 50Ω that is usually in terms of dBµV. Switching the MXO38 spectrum display from the default dBm to dBµV allows us to calculate and directly compare to the emissions limits, as you’ll see further on.

I usually insert a bit of “bubble wrap” within the probe aperture to keep the wire or cable centered and away from the metal probe case in order to minimize measurement errors.

Because of resonances on cables, it’s best to slide the RF current probe back and forth on the cable or wire in order to maximize the dominant harmonic or harmonics. Once the larger harmonics are maximized, I tape the probe down to the table to minimize variables while trying different mitigations to reduce cable coupling from the board.

Mitigations could include rerouting internal cables, improved bonding of cable shields to chassis or digital return plane, adding or improving common mode filtering at the I/O or power connectors, shielding energy sources using local shields, etc.

Caution

RF current probes are so sensitive that when clamped around a wire or cable, that cable tends to act as a receiving antenna. Ambient transmissions, like AM/FM broadcast stations, two-way communications, digital TV, and cellular phones, can confuse measurements from the equipment under test (EUT). It is important to be aware of certain bands in the RF spectrum where these services reside, so they can be differentiated from product emissions.

To ease this confusion, I usually clamp the current probe around the cable under test with the EUT turned off. You’ll like to see at least the FM broadcast stations in the region 88 to 108 MHz. Placing these captured signals in Max Hold mode provides an initial plot of current ambient signals. On the MXO3, this can be saved as a “reference” trace, as you’ll see in the next section.

Making a measurement

We’ll be measuring the common-mode harmonic currents on the power input cable of a 1 MHz GaN buck converter. This converter has a strong 230 MHz ring frequency that I use to demonstrate how ring frequency can manifest as a broad peak in the frequency spectrum. We’ll use a Fair-Rite 43 material snap-on choke to demonstrate a reduction in harmonic currents in the cable. Figure 3 shows the test setup.

As mentioned above, when using the RF current probe to test common mode cable emissions outside of a shielded chamber, I first perform an ambient measurement with the EUT off. This will record and save the specific RF environment so you can better differentiate EUT emissions from ambient signals.

First, connect the current probe to channel 1 (C1) and set the Termination to 50Ω. Leave all other settings to their defaults. Turn on the EUT in order to set up the oscilloscope for an acceptable time domain signal. I usually just press Auto-set at first.

Then turn on the Spectrum mode (Menu > Spectrum), turn On the Display, set the Source to C1, touch Start/Stop and set the frequency limits to Start = zero, Stop = 1 GHz, Normally, the EMC standards have you set the resolution bandwidth to either 100 kHz (military) or 120 kHz (commercial), but I find 1 MHz may have a cleaner averaged signal for troubleshooting purposes. Turn off Auto BW and set RBW for 1 MHz. Press Max Hold to save the ambient plot.

Now, switch the Menu to Apps > Reference and select R1 (reference waveform 1), turn Show = On, and select Source = S1MaxH. Select Create/Update and Save As “Ambient”. This will save the ambient Max Hold plot as reference 1 (R1).

Note that every time you reopen the Reference screen, the Source keeps defaulting to C1, so you’ll need to keep selecting S1MaxH, or it will save a time domain reference for C1. This messed me up several times when trying to add reference waveforms to the spectrum display.

Next, turn on the EUT and select Max Hold, then save this as R2 [2]. This will become the saved “before” spectrum case. You can change the default color by going to Settings > Appearance, Category = Reference, and Color Source = R2. Go ahead and set the color as desired. For this article, I set it to light blue. In a similar fashion, save this as reference 2 (R2) and name it “EUT_On”.

You should end up with a screen capture as in Figure 4 with the ambient in default grey, EUT-On (“before case”) in the color of your choice, and the real-time waveform in the default yellow. From here, you can try various mitigations and compare the resulting spectrum with the saved reference 2 (R2) waveform. The ambient spectrum (R1) may be used to differentiate the ambient RF signals from the “live” signals.

The blue trace is the measurement with the EUT turned on and shows the broad peaks at the ring frequency of 233 MHz and board resonance at 558 MHz. Now, with the saved reference plots, you can commence troubleshooting and applying various mitigations while observing immediate results!

Estimating pass/fail

One important use for the RF current probe is to provide an estimate of passing or failing specific emission test limits. By knowing the dominant currents in an I/O or power cable, we can calculate the E-field at the test distance per the standard used (usually 3m or 10m for commercial products). While this won’t necessarily be precise, it still gives us a “ballpark” estimate to which we can compare with the test limit at that frequency.

Commercial RF current probes come with a calibration chart of transfer impedance versus frequency (Figure 5). Using Ohm’s Law, we can use this chart to calculate the measured common mode current in the wire with respect to the voltage measured at the probe output port, assuming a 50Ω system. This is based on work by Dr. Clayton Paul [3] and further refined by Henry Ott [4]. There are example calculations in [5] and [6].

Let’s assume we measure one of the dominant harmonics in a cable as 28 dBµV at 120 MHz at the spectrum analyzer. We can also read of a transfer impedance of 20 dBΩ at 120 MHz from the calibration chart in Figure 5.

Using Ohm’s Law, we can calculate the common mode current (Icm) in the cable:

Icm (A) = E (V) / R (Ω), or, in converting to terms using log identities,

Icm (dBµA) = Vprobe (dBµV) – 20 dBΩ = 28 – 20 = 8 dBµA

Now using the E-field equation from Paul and Ott:

where

Ec is the calculated E-field in V/m due to common-mode current flowing on the cable,

Ic is the current through the wire or cable (A),

f is the harmonic frequency being measured (Hz),

L is the length of the cable in meters and

d is the measured distance during the compliance testing (usually 3 or 10m).

Converting the measured values to basic units and plugging into the E-field equation, we get 1.26E-4 (V/m). Converting this back to log units, we get 42.03 dBµV/m. Comparing this with the FCC class B limit at 120 MHz (43.5 dBµV/m) indicates we may be just under the limit by only 1.47 dB. Typically, we’d want at least a 6 dB margin, so this is probably not good enough.

To streamline all these calculations, I developed a simple Excel spreadsheet, which may be downloaded from my website [7]. Figure 6 shows an example calculation. By entering the specific probe transfer impedance, the frequency of concern, the cable length, and test distance (typically 3 or 10m), the E-field in dBµV/m is calculated and may be compared to the appropriate test limit.

Summary

The RF current probe is not only a useful tool for general troubleshooting, but may be used to determine potential passing or failing due to harmonic currents on a radiating cable. While they may be a bit pricy, I find the RF current probe is one of my most-used tools for troubleshooting emissions.

Most importantly, if you know that cables are the dominant radiating source, all the troubleshooting can be done in-house with an RF current probe. No need to run back and forth between your facility and the 3rd-party test lab to perform this troubleshooting, saving cost and time!

I also have a short video showing how to use these RF current probes in [8].

With its fast acquisition update rate, the MXO38 spectrum feature works extremely well for general bench-top EMC troubleshooting and debugging, and it’s become one of my favorite bench-top tools. The ease of setting up the analyzer is a step ahead of other leading manufacturers. Once saved, the reference waves stay in memory along with the instrument setup, so if you have to move locations, everything is preserved.

References

[1] Rohde & Schwarz
[2] Tekbox current probes
[3] Paul, Introduction to Electromagnetic Compatibility (2nd Edition), Wiley Interscience, 2006, pages 518-532.
[4] Ott, Electromagnetic Compatibility Engineering, Wiley, 2009, pages 690-693.
[5] Wyatt, Workbench Troubleshooting EMC Emissions (Volume 2), Amazon.
[6] Wyatt, The RF Current Probe: Theory and Application, Interference Technology
[7] Wyatt, E-Field Calculator (scroll down to find it)
[8] Wyatt, Current Probe Demo, Current Probe Demo

The post R&S MXO3 Oscilloscope for EMC measurements: part 2 appeared first on Test & Measurement Tips.

Rohde & Schwarz has released a Pulsar signal simulation option for the R&S SMBV100B and R&S SMW200A vector signal generators, adding support for the LEO satellite navigation service from Xona for receiver development and production testing. The software allows engineers to simulate next-generation positioning, navigation and timing signals alongside existing GNSS services such as GPS, helping validate compatibility as Pulsar deployment scales. The option is intended for manufacturers developing navigation receivers and other PNT-enabled devices that need test coverage for stronger signals with improved resilience to threats and interference.

The post New LEO signal simulation speeds receiver validation appeared first on Test & Measurement Tips.

Q: In Figure 1, it looks like you’ve changed some of the labels.
A: Right. I had been using V_DMM to emphasize that we are using a modern digital multimeter (DMM) instead of a 19th-century galvanometer, which would have been used in early Wheatstone bridges. 19th-century galvanometers were quite useful in detecting zero current and voltage conditions, with applications extending to the decoding of transmitted signals in early trans-Atlantic telegraphy. However, such galvanometers were not good at quantifying non-zero levels, which modern instruments can do easily and accurately. In Figure 1, I’m using labels commonly found in strain-gauge literature. For example, I’ve changed V_DMM to V_O, for output voltage. In addition, I changed V_IN to V_EX, for excitation voltage. Finally, in the setup from our earlier series, V_DMM varied inversely with R_X. In Figure 1, I have reversed the meter polarity, so V_O varies directly with R_X and hence strain e.

To review, in Figure 1, R_X is an active strain gauge, and R₂ is a dummy strain gauge used for temperature compensation. Note that the long, thin wires of R₂ are mounted perpendicular to the direction of tension, so their resistance is relatively unaffected by the strain.

Q: So, how do we calculate strain given V_O?
A: From our previous series, we demonstrated how to calculate R_X based on the voltage reading, with the DMM or output voltage equaling V_V – V_X. For the configuration shown in Figure 3 with the polarity switch,

We can rearrange this equation as follows:

Then we can calculate R_X as a function of V_O:

Q: And how does strain relate to R_X?
A: From part 1 of this series, we know that given a gauge factor GF, strain is

We also see that DR is R_X – R₂, where R₂ equals the unstrained resistance of R_X, or 120 W. So, given V_O and a GF value of 2, we can directly calculate strain:

Figure 2 plots this equation for values of V_O from -10 mV to +10 mV.

Q: Can we design a bridge configuration where both strain-gauge elements are active, and if so, what would be the advantages?
A: Figure 3 shows an alternative arrangement to Figure 1, with one strain gauge depicted in red placed at the top of a test specimen, while another depicted in blue is placed at the bottom, with the sense wires in both aligned with the direction of stress, so both are active.

Next time, we’ll take a look at how to apply this configuration and describe its benefits.

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Making sense of test circuits with Kirchhoff’s laws: part 4
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Things to know about multimeters
The first undersea transatlantic cable: An audacious project that (eventually) succeeded, Part 2
Wheatstone bridge, Part 1: Principles and basic applications
Stress & Strain, Part 1: fundamental principles

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The CP1000 supports up to 1000 A rms continuous and peak currents up to 1400 A. But the specification that generated the most conversation was bandwidth. Most competitive products in this current range top out around 10 kHz. The CP1000 goes from DC to 1.5 MHz, which matters more than it might seem at first glance. Additional specs worth noting: rise time is 235 ns typical, AC noise at 20 MHz bandwidth limit is 10 mA, and the probe offers two output voltage settings at 0.005 V/A and 0.05 V/A with a minimum sensitivity of 100 mA/div. The 6-meter cable gives engineers some practical flexibility when working around large power setups.

The Teledyne LeCroy team explained it this way: when engineers calculate switching losses, they multiply the current and voltage waveforms. If the current probe’s bandwidth is too narrow, it artificially slows the rise time, making losses appear larger than they actually are. As one engineer at the booth put it, “By having a higher bandwidth probe, you can get a more accurate representation of how fast you’re switching, and you can make better efficiency measurements and loss measurements.”

That point connects to a broader issue the team raised about oscilloscope measurements generally: “A lot of people who are doing oscilloscope measurements have this assumption that what I’m seeing on the oscilloscope is what’s happening on my system. We spend a lot of time explaining to people that’s not what you’re seeing in your system. That’s what you’re seeing after it goes through the probe, after it goes through what’s happening on the front end of the oscilloscope. It’s a total system measurement. Engineers don’t care about that. They want to know what’s happening.”

The CP1000 uses Hall effect technology, so there’s no need to break the line, unlike current transformers or Rogowski coils, which remain the workaround most engineers are using today. The maximum conductor diameter the probe can accommodate is 33 mm. It connects via Teledyne LeCroy’s ProBus interface for automatic scaling, degauss, and autozero functions on compatible oscilloscopes, and it’s available now at a list price just under $9,000.

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Today’s designs are more complex than ever. Signal frequencies are climbing, package sizes are shrinking, and the range of bus types and standards that engineers need to support continues to expand. A scope that checks the bandwidth box but falls short on noise performance, probing capability, or analysis software can slow you down when it matters most.

The right approach starts with the measurement problem, not the spec sheet. Power integrity work demands low-noise front ends and high vertical resolution. Serial data conformance testing adds requirements around jitter analysis and de-embedding. Embedded system troubleshooting calls for strong trigger systems and protocol decode capability. RF and wireless applications require high-performance FFTs and spectrogram display support.

On April 16, EE World Online is hosting a webinar that tackles exactly this. Industry veteran Chris Loberg will walk through a practical framework for oscilloscope selection across all four application areas, with plenty of time for audience questions.

Do you have questions now you would like us to address during the webinar? Email those to akalnoskas@wtwhmedia.com.

Beyond Bandwidth: How Engineers Should Really Choose an Oscilloscope takes place Thursday, April 16, at 2:00 PM EDT. Register here.

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PicoRaptor combines high bandwidth with high insertion count, using a single elastomer for consistent contact force while allowing a slight wiping action. Its Advanced Contact Finish (ACF) technology stabilizes contact resistance (Cres), limits solder migration, and extends load board life. PowerRaptor includes a contact wipe for Cres stability and an optional Airtherm integration for rapid, accurate pin temperature conditioning. Both variants are engineered to increase Mean Time Between Assist (MTBA) across demanding test environments.

The post ATE contactors combine kelvin configuration with thermal pin conditioning appeared first on Test & Measurement Tips.

In a previous series, we investigated the Wheatstone-bridge circuit topology and described how strain-gauge elements could be used in the bridge legs.

Q: At that point, I asked the question, what is strain, and what are its units?
A: Right, so we’ll take up that question in this new series. Figure 1 at the top shows a specimen under test of length l. In the center image, we apply an axial stress in the form of tension to the specimen, and it lengthens by an amount Dl. The strain, indicated by a lower-case epsilon, is

In addition, as shown at the bottom, if you apply axial compression to a specimen, it shrinks in length, and you’ll have a negative strain.

Like the radian, strain is a ratio of lengths and is therefore dimensionless. It can be helpful, however, to think of it in units such as meters per meter. You’ll also see strain expressed in microstrain, abbreviated µe, which is 1 millionth of e. If you have a specimen 1 meter long and you apply tension that expands its length by 1 micron, you’ll have a strain of 1 µe.

Q: OK, given that we’ve defined strain, what’s an effective way to measure it?

A: Just as we can use a thermocouple to measure temperature or an accelerometer to measure vibration, we can use a metallic strain gauge to measure strain. The metallic strain gauge consists of a conductive foil pattern on a flexible insulating backing, such as the one shown in Figure 2, with the conductive foil shown in black and the insulating backing, called a carrier, shown in blue. The image on the left shows the strain gauge in an unstrained state, for which it has a resistance R. When a test specimen on which the gauge is mounted undergoes tension, as shown in the center, the vertical conductive elements of the pattern elongate and become thinner, and their resistance increases by an amount DR. Conversely, under compression, as shown on the right, the resistance decreases by DR.

Q: How do we relate strain-gauge resistance changes to test-specimen length changes?
A: Your strain gauge will have a parameter called gauge factor, abbreviated GF, which you will find on the data sheet. GF, usually about 2 for a metallic strain gauge,^[1] relates to gauge resistance and specimen length as follows:

Now we can solve for strain as a function of the resistances and gauge factor:

Q: So we just glue the strain gauge to the specimen, and we are all set.
A: Right, but you’ll need to use a special adhesive, such as cyanoacrylate, methacrylate, or epoxy resin, that can accurately transfer your specimen’s deformation to the strain gauge. Factors that influence which adhesive you use include the strain and temperature ranges.^[2]

Q: How do we measure strain using the Wheatstone bridge?
A: Figure 3 is an alternate view of Figure 2 from part 4 of our previous series. Here, R_X is an active strain gauge, and R₂ is a dummy strain gauge used for temperature compensation. Note that the long, thin wires of R₂ are mounted perpendicular to the direction of tension, so their resistance is unaffected by the strain, and you will not need a special adhesive. However, if you use two different adhesives, you should ensure that their thermal properties are similar.

Q: So how do we calculate strain?
A: We’ll look at the details of the calculation next time, after which we’ll discuss some additional strain-gauge considerations. For example, Figure 3 shows a half-bridge application with one active strain-gauge element, but other configurations are possible. We’ll also look at optimizing the excitation voltage (V_IN in Figure 3). Finally, strain-gauge applications often involve large structures, such as wide-body airframes, antenna towers, stadiums, buildings, or bridges, so we’ll look at lead-resistance and signal conditioning considerations.

References

[1] Measuring Strain with Strain Gages, Emerson
[2] How to Select the Right Adhesive for your Strain Gauge Installation, HBK

Related EEWorld Online content

Why are analog signal conditioners important?
Sensors expert talks data acquisition, IoT, wearables, and AI
If you are working with antennas, here are some tools to consider, Part 1
Making sense of test circuits with Kirchhoff’s laws: part 1
How to choose analog-signal-chain components: part 1
How does a thermocouple work, and do I really need an ice bath? part 1

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The DDS option adds frequency and amplitude slopes, flexible command sequencing, and real-time signal adaptation without large data transfers or complex waveform calculations. These capabilities address applications including network stimulation, filter and amplifier testing, vibration shaker control for mechanical resonance testing, and simulation of power fault conditions for circuit fault detection. Software support covers Windows and Linux, with programming interfaces for Python, MATLAB, C++, and LabVIEW, plus a no-code DDS CONTROL GUI for direct signal generation. All products include lifetime technical support from Spectrum Instrumentation’s engineering team and free software and firmware updates.

Link to video

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Moku:Delta is a meaningful hardware upgrade over its predecessor, featuring eight channels instead of four, a larger FPGA, improved analog input noise performance, and QSFP ports that support high-speed data streaming up to 80 Gbps. The device runs eight instruments simultaneously at 2 GHz, consolidating significant test-and-measurement capability into a single unit.

Generative Instrumentation is an AI-powered tool that writes HDL/Verilog code on behalf of the engineer, removing the steep learning curve traditionally associated with custom FPGA instrument development. Engineers describe what they need, the tool generates and compiles the code, and the entire process remains fully auditable in real time. Auto-generated plain-language documentation accompanies each build. Public release is slated for later this spring.

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At first glimpse, you may not realize the common thread in the three sketches in Figure 1. The left (a) shows a transmission-line symbol. The middle (b) shows a fraction of a schematic, potentially depicting two components on a power-distribution network (PDN). The right (c) shows a satellite communications example. Basic physics tells us that you can view all three in the context of characteristic impedance and propagation delay.

Signal Integrity Perspective

SI engineers are familiar with the fundamental equations that describe the Z₀ characteristic impedance and t_pd propagation delay of uniform interconnects. If we ignore losses, these equations became a function of per-unit-length inductance (L) and per-unit-length capacitance (C) of the transmission line.

The center schematic snippet may represent the simplified impedance of a DC source (R₁ and L) and a bulk capacitor (C and R₂) in the frequency range where the DC source becomes inductive, and the bulk capacitor’s impedance flattens out. PI engineers would know that if we want a smooth transition between the two impedances, we need to ensure the following:

We also know that the f_c resonance frequency between the capacitor and inductor is:

Though this is just a one-port lumped circuit, we can notice that (3) and (4) have essentially the same form of expressions as (1) and (2).

We may also wonder what is the corresponding item in Figure 1a to R₁ and R₂ in Figure 1b? Figures 2 and 3 explain and illustrate the connection. In short, when R₁ and R₂ in (3) are the same, they represent what we may call the lumped characteristic impedance of this circuit, making the impedance of the circuit frequency independent, just as terminating a lossless transmission line with its characteristic impedance makes its input impedance frequency independent.

Figure 2 shows the input impedance magnitude of a lossless 50-Ω transmission line with 2.5 ns propagation delay with different values of load resistance (R_load). At low frequencies, where the transmission line is electrically very short, the input impedance magnitude equals the load resistance. At higher frequencies, we notice the familiar periodic fluctuation of the input impedance. Notice the logarithmic frequency scale that compresses the sinusoidal variation as a function of frequency. As the load resistance approaches the characteristic impedance, the impedance peaks and valleys come closer and eventually, when the load resistance equals the characteristic impedance, the curve becomes a straight line. This shows what SI engineers know well: terminating the transmission line with its characteristic impedance eliminates reflections over a wide range of frequencies.

Power Integrity Perspective

Figure 3 illustrates how this relates to PI. We use the schematics from Figure 1 to look at the combined impedance of the parallel-connected R₁–L and C–R₂ network. The component values on the left illustrate potentially a medium-power DC source (this is the R₁–L leg) interacting with the bulk capacitor, represented by the C–R₂ leg. We vary only one component value, R₂, which in this example represents the equivalent series resistance (ESR) of the capacitor.

On the impedance plot in Figure 3, the black line represents the R1–L leg, the red lines show the impedance of the C–R₂ leg for the three C–R₂ values (short dashed line: R₂_max, solid line R₂_nom, long-dashed line: R₂_min) and the blue lines represent the combined impedance magnitude for the three R₂ values. We can see that when R₁ equals R₂ (and it also equals the

L/C = 10 mΩ value), the impedance magnitude plot becomes frequency independent, similar to the input impedance of a matched-terminated lossless transmission line. Another similarity is that pushing R₂ lower than the optimum value required for flatness actually creates an impedance peak at the LC resonance frequency.

To make the connection between the SI and PI illustrations in terms of cutoff frequency and propagation delay as well. Figure 4 and Figure 5 compare the frequency-domain and time-domain behavior of two circuits: a transmission line with Z₀ = 10 mΩ and t_pd = 1 µs propagation delay. For this, take the SI illustration circuit from Figure 2 and rerun that simulation with the characteristic impedance, LC values, and relative load impedance steps around 10 mΩ nominal value. Though a transmission line with 10 mΩ characteristic impedance is not practical for our typical signaling tasks, it matches the component values in our PI example in Figure 3.

Figure 5 shows the result of using extreme termination and looking at the response with fast step excitations. We take the transmission lines from Figure 2 and the equivalent transmission line from Figure 4 and apply a fast voltage source with a 0 V to 1 V swing.

Both waveforms show a damped periodic square-wave ringing, where the period of the ringing equals four times the propagation delay: 10 ns for the 50-Ω transmission line and 4 µs for the transmission line approximating the power circuit. (The 4x multiplier comes from the well-known quarter-wave resonator structure, since we have low impedance at one end and high impedance termination at the other end.)

Another way to view these circuits is to stay with the lumped circuit equivalent of the power circuit. The 10 nH inductance and 100 µF capacitor could be considered as the inductance and capacitance of a single-lump LC approximation of a transmission line. This leads us to the schematics shown on the left of Figure 6. We use the same source and load conditions we used on Figure 5: 1 mΩ source resistance and 100 mΩ load resistance.

From these figures, we can summarize that the lowest resonance frequency in a distributed transmission line occurs at the quarter-wave resonance:

The resonance frequency of the lumped LC circuit from Figure 6 was given in (4). Though the constant in the formula is slightly different, both expressions rely on the square root of the LC product.

EMC Perspective

Recall that Figure 1 includes an EMC case, where electromagnetic waves travel through a dielectric medium, most often through free space. In free space, we cannot speak about the medium’s capacitance and inductance. Instead, we can look at the permittivity and permeability material constants, which are proportional to capacitance and inductance when conductors form terminals. The permittivity of free space is ε₀ = 8.85 pF/m, and the permeability of free space is µ₀ = 4π × 10^-7 H/m. If we substitute L and C with these material constants and units, we get the very familiar results: the 120π= 377 Ω impedance of free space (in the far field) and the inverse of the speed of light: c = 3 × 10⁸ m/s.

Summary

From these examples, I’ve shown how the three disciplines — SI, PI, and EMC — are related. Even though they were introduced at different times and were motivated by seemingly different practical concerns, they share the same roots. PI engineers tend not to think about reflections during the design of lumped power distribution circuits. SI people tend to think of interconnects as conductor-bound distributed transmission lines, even though their behavior can also be described using lumped expressions. EMC people consider electromagnetic waves bouncing around in space. You can see how propagating waves connect transmission lines and lumped circuits through basic formulas. Once you understand their common roots, you can appreciate that distance along the signal propagation comes with finite delay and can be associated with inductance, no matter which discipline you look at. You can also see that the lumped equivalent circuit of a power distribution network can relate to reflections, commonly used in the context of transmission lines. Knowing these common roots helps you make more effective and better designs.

The post How physics relates signal integrity, power integrity, and EMC appeared first on Test & Measurement Tips.

R&S sent me a model MXO38, the eight-channel version with built-in 50 MHz single-channel AWG and two optional 8-bit digital channels. At just 15-in. wide x 9-in. tall x 6-in. deep, the MXO3-series is scaled down to fit most lab benches [1]. I’ve been using their larger MXO4 for a few months, so I was immediately familiar with the user interface, which is laid out intuitively and just the same. The MXO4-series is an inch wider and an inch taller with the same 6″ depth. The smaller MXO3 just seems more at home on my test bench. The base price for the four-channel model is $5,890, while the base price for the eight-channel model is $13,800.

As Figure 1 shows, R&S reduced the size when designing the MXO-series compared to the MXO4, yet kept most of the basic specs. The 1 mV low-noise vertical sensitivity, 12-bit resolution, 500 Msamples memory depth, and 21 ns trigger re-arm allow a terrific FFT spectrum display. The waveform capture is 4.5 million waveforms per second, providing real-time capture of up to 99%. From an EMC perspective, this provides a nearly real-time spectrum capture.

The 11.6-in. full HD touch screen provides plenty of room for multiple waveforms. For this EMC engineer, a big advantage is the ability to display up to four independent spectral displays simultaneously.

The MXO3 menu system is straightforward, and the keyboard is well laid out. Top to bottom, the front panel includes triggering, horizontal, vertical, and various modes: Autoset, Preset, cursor control, and screen capture buttons (Figure 2).

In use, I found the default backlight was too bright for my office lab. This can be adjusted via Menu > Settings > Display > then touch the Backlight button and use the universal control knob (lower panel) to set the level.

Ports located on the rear include the usual communications connections, plus an HDMI port for connecting an external monitor (Figure 3). You’ll also find Trigger In and Trigger Out connectors, as well as the 50 MHz arbitrary waveform generator (AWG) RF output. The AWG is controlled from the front and can be set to several normal waveforms, including sample ECG and EEG.

Figure 4 shows the two 8-channel digital input ports. Being an EMC engineer, I did not test the digital ports. Attaching the cables could potentially pull on the connectors, causing reliability issues.

Setting up the MXO38 for EMC measurements

When I’m looking for clock harmonics on a PCB or cable, I’ll set the vertical sensitivity to the most sensitive: 1 mV/division. For larger signals such as power conversion circuits, I’ll use the Autoset button to get me in the general range, then adjust trigger level, horizontal, and vertical adjustments to obtain the best viewable display.

Next, I turn on the spectrum analyzer by either selecting Menu > Spectrum or simply pressing the “Spec” button in the vertical section of the front panel. You’ll obtain the menu selections shown in Figure 5.

I usually prefer to set the Start and Stop frequencies manually, so press Start/Stop, then double-tap the Start and manually enter the desired start frequency. I usually leave this at the default “zero”. Repeat this by double-tapping the Stop button and manually setting the frequency. Sometimes, I will leave this at the default 1 GHz if I wish to see the whole spectrum.

Next, I like to turn off Auto resolution bandwidth (RBW), so I can manually set it to 100 kHz or 120 kHz (MIL or commercial, respectively), depending on what the appropriate standard requires for frequencies below 1 GHz.

I set the Window Type to the default Blackman-Harris setting. Note that there are four capture modes: Normal, Min Hold, Max Hold, and Average. For general probing, you should leave this set to Normal. For intermittent or broadband signals, I often use Max Hold to capture the signal envelopes for a few seconds.

The last steps include pressing Scale and choosing dBµV from the default dBm. Usually, I didn’t have to change the default scale factors, but you can change them as needed. This setup was far easier than I’ve seen on other manufacturers’ oscilloscopes.

The spectrum analyzer menu includes a feature that automatically adds peak markers (Peak List; Figure 6) to spectral peaks. These labels include frequency and amplitude for each peak, as you’ll see later. You can add annotations (text, arrows, boxes, etc.) to the display. The oscilloscope stores screen captures in its internal memory or on a USB thumb drive, if installed. You can save and recall setups as well.

EMC measurements

Let’s try it out on some basic EMC characterization measurements on an Arduino Due Version R3 embedded processor, as there’s plenty to see. Let’s dive in!

This older model Arduino Due R3 is ideal for testing because it includes a conventional DC-DC converter with a switch inductor easily accessible (Figure 7). It is based on an Atmel ATSAM3X8E ARM Cortex 32-bit processor clocking at 84 MHz (12 MHz clock oscillator). The DC-DC converter runs at about 500 kHz and USB at 16 MHz. We’ll see all those signals clearly. I had to order mine from eBay, as the newest versions of the board do not include the same type of power conversion circuit.

Let’s make some real measurements. A proper characterization of a product for radiated emissions requires three steps. I discuss this in detail in volume 2 of my EMC Troubleshooting Trilogy books [2]. We’ll demonstrate the first step in this article.

1. Near-field probing to characterize the spectral response for all high-energy components
2. Characterization of high-frequency cable harmonic currents for all attached cables
3. Measurements a short distance away (~1 m) to confirm the harmonics that actually radiate

I used an R&S H-field probe (1 cm loop) for all the measurement points (Figure 8). Near-field probing of a PC board or cable should always be the first step. We want to identify each high-energy component and document its spectral characteristics.

A loop probe couples nicely to the switch inductor of the DC-DC buck converter, which allows us to observe many important waveforms and spectral displays (Figure 9).

Using cursors and measuring the distance between switched waveforms confirms the converter is switching at a little over 500 kHz. There is ringing due to operating in discontinuous conduction mode (DCM). This ringing will manifest as a broad peak at the ring frequency, in this case, 4.2 MHz. You can observe this peak in Figure 10. I describe this concept in more detail in [3]. We can observe that each frequency spike occurs at 500 kHz intervals.

Now, let’s look at the 12-MHz crystal oscillator, shown in Figure 11. Probing near the oscillator confirms the 12-MHz harmonics. Here, we’ve increased the upper frequency limit to 500 MHz.

Note the use of Peak List to identify major harmonics. The adjustments, Max Results, Threshold, and Peak Excursion can be varied to automatically label just the most important peaks. Note that the delta difference in adjacent peaks in Figure 12 is exactly 12 MHz and that some harmonics extend out to 500 MHz, or more.

Next, let’s measure the 16-MHz USB clock.

Again, I coupled the probe to the USB IC and its 16-MHz clock oscillator in Figure 13. Note that the delta difference in adjacent peaks is exactly 12 MHz and that some harmonics extend out to 400 MHz, shown in Figure 14.

Summary

I found the MXO3 oscilloscope is very useful for general EMC debugging and troubleshooting. The ability to observe both the time domain and frequency domain with its fast capture is a real advantage. Up to eight waveforms may be stored for comparison to the measured waveform. This will greatly help in comparing “before and after” measurements as various mitigations are tried.

Part 2 of this series will discuss how to measure high-frequency currents on cables. Because cables are the most frequent contributor to radiated emissions, characterizing these harmonic currents is really one of the most important steps in mitigating emissions. We’ll also demonstrate how to connect a simple antenna to the scope to measure the relative strength of the actual emissions.

References

[1] Rohde & Schwarz, https://www.rohde-schwarz.com/us/home_48230.html
[2] Wyatt, EMC Troubleshooting Trilogy, https://www.amazon.com/stores/Kenneth-Wyatt/author/B00SNQ1LJ2
[3] Sensepeek, https://sensepeek.com
[4] Wyatt, Review: PCBite circuit board holder and probe kit, https://www.testandmeasurementtips.com/review-pcbite-circuit-board-holder-and-probe-kit/
[5] Wyatt, Characterize EMI from DC-DC converter ringing, https://www.eeworldonline.com/characterize-emi-from-dc-dc-converter-ringing/

The post R&S MXO3 Oscilloscope for EMC measurements: part 1 appeared first on Test & Measurement Tips.

In part 3 of this series, we used Kirchhoff’s voltage law to derive the branch currents and node voltages for an unbalanced Wheatstone bridge with five known, fixed resistors (Figure 1). Now, we propose to replace R5 with a digital multimeter (DMM) to directly measure V_V – V_X and use that measurement to determine the value of an unknown resistor in the position of R₄.

Q: Could we backtrack first? Last time, we solved three loop equations. I was trying to use Kirchhoff’s current law to write six-node equations and got lost. Could you elaborate?

How far did you get?
I_IN = I₁ + I₂, I₁ = I₃ + I₅, I2 = I₄ + I₅, I₃ = I₁ – I₅…

Stop there. Your first three are good, but the last one is just a restatement of the second one. We need an independent equation for I₃.

We know I₃ = V_V/R₃, but we don’t know V_V.
Right, but we can express V_V in terms of one of our original six unknowns, namely I₁. V_V is V_IN minus the voltage drop across R₁, which is I₁ times R₁. Substituting our component values, we can write:

Similarly, we can derive V_X as a function of I₂ and solve for I₄:

And finally, I₅ is V_V minus V_X divided by R₅:

Table 1 shows all six node equations in the format required for the online solver^[1] I’m using, and the solutions are shown in red. With this approach, the solver generates the branch currents directly; we don’t have to derive them from the loop currents. I’ve also included our results from part 3 based on the loop method, with the loop values in blue, and the results agree within a third of a percent.

Table 1. Node equations and solutions.

Now, let’s look at the situation where we have an unknown resistor but a known voltage.
Right. Keep in mind that in the 19th century, galvanometers were good at indicating zero current, but not good at quantifying nonzero levels. Consequently, accurate measurements were made under zero-current conditions. We no longer face that limitation, and we can use a measurement setup in Figure 2, which shows a way to make strain-gauge measurements. Here, a DMM, data logger, or data-acquisition instrument replaces the galvanometer from part 2, and R₅ from Figure 1 becomes essentially infinite. R_X, which takes the place of R₄, is a strain-gauge element that has a resistance of 120 Ω when not subjected to strain. To optimize measurement resolution, we assign resistors R₁, R₂, and R₃ the same 120-Ω value.

So, we basically have two voltage dividers.
Right:

and

We can now write an equation for what our DMM would read for a resistance value R_X:

Now we can solve for R_X:

Figure 3 plots this transfer function. Note that for strain-gauge measurements, resistance changes are often less than 1%, and sometimes much less.

Figure 4 shows a simulation result.

Q: Why use the bridge—why not just measure the resistance of R_X directly?
A: Temperature compensation is one reason. In Figure 2, R₂ is often a strain-gauge element identical to R_X maintained at the ambient temperature of R_X, but that never undergoes strain. If both R₂ and R_X increase by 0.1% because of a rise in ambient temperature, but R_X continues to be unstrained, the DMM will continue to read zero.

Q: What is strain anyway, and what are its units?
A: Good question. That’s beyond the scope of this series on Kirchhoff’s laws, but we can consider strain measurement in depth in a future series.

Reference

[1] Simultaneous Linear Equations Solver for Six Variables, handymath.com.

Related EEWorld Online content

Sorting out PC-based instrumentation
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Wheatstone bridge, Part 2: Additional considerations
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What’s a half digit and are they all the same?

The post Making sense of test circuits with Kirchhoff’s laws: part 4 appeared first on Test & Measurement Tips.

Connecting electronic devices to test equipment can be daunting, especially when building an automated test system and connecting several test instruments to devices under test. You probably start with a spreadsheet that lists connector types, cables, connector pins, signal names, and termination points. Things can get hairy very quickly. Is there a better way?

The people at Pickering Interfaces think so. Pickering specializes in PXI switching modules, so they’ve seen firsthand how messy designing cables can be. To help you design test cables, Pickering has developed Test System Architect, a free online design tool. Sign up and give it a try.

“All too often, engineers designing automated test systems don’t consider the signal path,” Pickering’s Kyle Voosen told me when I met him at Pickering’s Boston office. “Errors in spreadsheets only become apparent once you build the cable.” Voosen gave me a demonstration where he specified a cable to connect four devices to a multimeter through a switch matrix.

With Test System Architect, you specify the connector type, cable length (with or without accounting for connector size), and then you add the connections. You can also pull in specifications for Pickering’s PXI switching modules to complete the design. Test System Architect will show you the cable design and its schematic. When designing a cable, you can select from PXI switch modules that include matrix, mux, RF mux, and general-purpose switches. You can also add PXI, PXIe hybrid, and LXI/USB chassis into your overall design.

Through your online account, Test System Architect will let you save your design documentation. You can then export it as a data file, SVG file, PNG graphic, datasheet, or BOM CSV file.

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We concluded part 2 of this series by starting to write node and loop equations for a five-resistor Wheatstone bridge circuit, to calculate the currents through each resistor. Figure 1 repeats Figure 3 from part 2, but I’ve assigned component values so we can calculate a numerical result. Note that I’ve retained the V_V and V_X labels, which denote the nodes connecting to the variable and unknown resistors in our version of the bridge with a galvanometer.

Q: How do we know which directions of the currents, for example, through R₅?
A: We don’t. The current direction through R₅ will depend on the resistor values. If our arrow direction is “wrong,” we will get a negative value of I₅.

Q: So, how do we solve this circuit?
A: We’ll need six equations to compute the six unknown branch currents (red arrows) or three equations to compute the three unknown loop currents. The latter approach looks easier, so we’ll start there, beginning with the loop on the left. Starting at the top and moving clockwise, we note that the current through R₁ is I_A–I_B, so the drop across R1 is (I_A–I_B)R₁. Next, the current through R₃ is I_A–I_C, so R₃ contributes a drop of (I_A–I_C)R₃. Finally, continuing clockwise, we start with our source, which, from our perspective, adds a negative voltage drop. So, we can write our first loop equation summing the voltage drops:

We continue this process for the top right and bottom right loops to get the additional loop equations:

We will probably want to use a program like MATLAB or an online tool to solve these equations, so we’ll put them in the following form, where each variable is preceded by a constant and the right-hand term is a constant:

With some algebra, we come up with these versions of the three equations:

Next, we insert the numerical values:

I used an online solver^[1] to get the results shown in Table 1. Since I entered values in kilohms, the results are in milliamps.

Table 1. Kirchhoff Loop equations and solutions:

Q: How do we use these results to get our branch currents and node voltages?
A: We quickly notice that I_IN equals I_A, or 0.393 mA, and we can calculate the equivalent impedance of our resistor network as 1.5 V divided by 0.393 mA, or about 3.82 kΩ. We also see that I₄ equals I_C, which equals 0.139 mA, so V_X equals 0.139 mA times 6.8 kΩ, or 947 mV. Similarly, I₂ equals I_B, which equals 0.251 mA, and the drop across R₂ equals 0.251 mA times 2.2 kΩ, or 553 mV.

For the other resistor currents, we’ll need to subtract loop currents. The R₅ current is I_C minus I_B, or -0.112 mA, so the actual current flow is in the opposite direction from the I₅ arrow, and the voltage across R₅ is -112 mV. We can continue with R₁ (for which I₁=I_A–I_B) and R₃ (I₃=I_A–I_C), with the complete results shown in Figure 2.

Q: Now we’ll have to build this circuit to see if the calculations are correct.
A: My thought was to simulate it in LTspice^[2] as shown in Figure 3. The traces on the left for V_V and V_X are a bit difficult to see, so I have added some notation. The simulation confirms our calculated result.

And then I breadboarded the circuit with 1% resistors and confirmed the equivalent resistance, as shown in Figure 4, and the node voltages.

Q: Why so many resistors?
A: I didn’t seem to have a 6.8-kΩ version in my collection, so, alluding back to the rat’s nest in part 1, I had to build one out of parts I did have.

Q: What do we look at next?
A: We previously commented on the downside of using a balanced bridge and galvanometer to determine the value of an unknown resistor (in the R₄ position). In part 4, we’ll look at using an unbalanced bridge and a high-impedance voltmeter to make that measurement, a technique useful in strain-gauge and other sensor applications.

References

[1] Simultaneous Linear Equations Solver for Three Variables, handymath.com.
[2] LTspice, Analog Devices

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The post Making sense of test circuits with Kirchhoff’s laws: part 3 appeared first on Test & Measurement Tips.

As powering circuits and systems get more complex, you often need to source, sink, and measure DC power for more than just DC levels. After all, DC isn’t really DC. Loads vary in real-time, which adds AC components to power rails. Furthermore, today’s boards and systems often have multiple power rails, and you need to see how they interact. The IT2705 mainframe and modules from ITECH provide eight channels of sources, loads, and source-measure units (SMUs).

DC power modules support:

• 20 V, 3 A, 20 W
• 30 V, 15 A, 200 W and 30 A, 500 W
• 60 V, 10 A, 200 W and 20 A, 500 W
• 150 V, 5 A, 200 W and 10 A, 500 W

The system can sample up to 200 ksamples/s. You can operate the system in oscilloscope or datalogger modes through the graphical display, front-panel controls, or with software running on a PC. That’s in addition to having digital voltage and current displayed on the screen. Communications links include USB and LAN.

You can operate the sources and loads in either a list mode to get precise steps or in arb mode to simulate transients such as surges and drops. A sequence mode lets you combine output waveforms to consistently simulate usage conditions. The system lets you use loads to simulate batteries for testing chargers under consistent conditions. Electronic loads let you test your power sources under constant voltage, constant current, and constant resistance conditions. A dynamic mode switches between two preset test conditions.

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In part 1 of this series, we looked at ways to simplify resistor networks by identifying series and parallel combinations of resistors. We closed with a look at a version of the Wheatstone bridge, such as the one in Figure 1. Although it has only five resistors, not one of them is in series or parallel with another, so the simple equations we used in part 1 won’t work here. There is a workaround, called a delta-to-wye conversion.^[1] But that just gives you three more equations to memorize, and unless you do the conversion often (if you work with three-phase power, for example), those equations aren’t likely to become second nature, the way the series and parallel resistor equations are for most electrical engineers.

Q: Wait, what about the version of the Wheatstone bridge with a galvanometer taking the place of R₅?
A: That version, shown in Figure 2, is easier to analyze. Here, R₃ becomes a variable resistor R_V, and R₄ becomes an unknown resistor R_X, whose value we are trying to find.

In the classic Wheatstone bridge application, we manually adjust R_V until the galvanometer or multimeter voltage V_G is 0, at which point we have what we call a balanced bridge. It consists of two simple voltage dividers, and R5 from Figure 1 is essentially infinite. R₁ and R_V make up the first divider, and the voltage across R_V is:

R₂ and R_X make up the second divider, and the voltage across R_X is:

Since the galvanometer reads zero, we can determine R_X as follows:

Q: What’s the drawback to this balanced bridge?
A: If we are trying to measure a parameter such as strain in real time, it’s not practical to manually adjust R_v until V_G is zero, then record the value of R_V, and calculate R_X. We could probably kludge together something based on a voltage-controlled or digitally controlled resistor to replace the manual adjustment, but Kirchhoff’s and Ohm’s laws offer a simpler way for us to derive R_X from the voltages and currents in a fixed-resistor bridge.

Q: How does that work?
A: Let’s go back to our original Figure 1 bridge with five fixed resistors. In Figure 3, I’ve rearranged Figure 1 to make more room for notations showing branch (red arrows) and loop (blue arrows) currents. Kirchhoff gives us two laws that we can apply to solving such a problem. The current law states that the net sum of currents into any node is 0. In Figure 3, for example, that law implies the following:

The second law, Kirchhoff’s voltage law, states that the voltage drops around any closed loop must equal zero. For the loop on the left of Figure 3, this law results in the following equation:

For a given circuit, each law will give us multiple equations on multiple unknowns. Which law or combination of the two laws is easiest for us to use will depend on exactly what we are trying to determine. In our case, we have two goals. First, following up on our work from part 1, what is the equivalent impedance of the bridge if all resistors are fixed and we know their individual values? In other words, what is V_IN/I_IN? And second, of particular interest from a test-and measurement-perspective, is this question: If R₁, R₂, R₃, and R₅ are fixed and known and R₄ is unknown (it might be a strain-gauge element or temperature sensor, for instance), can we calculate R₄ based on the voltage V_V – V_X across R₅? We’ll take a closer look in part 3.

References

[1] Delta-to-Wye Equivalent Circuits, Utah State University.

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The post Making sense of test circuits with Kirchhoff’s laws: part 2 appeared first on Test & Measurement Tips.

Low-cost spectrum analyzers often lack tracking generators, preventing you from having a signal source that tracks the analyzer’s frequency sweep. Not having a tracking generator can make some measurements difficult. You can, however, use a low-cost noise generator to characterize filters, amplifiers, and coax cable loss. In effect, they serve as a scalar network analyzer (no phase information).

In this article, I’ll describe how to use a noise source as a substitute for a tracking generator.

Figure 1 shows a typical broadband noise source. Available from Amazon^[1], the broadband noise source will produce a wide range of RF signals from near DC to 2 GHz. This board is designed to run on 12 V, but I found it also operated well at 5 V. I did notice the amplifiers get quite hot.

The noise is generated by biasing a Zener or Schottky diode, which creates low-level broadband noise. The board then runs this noise voltage through three broadband amplifiers and terminates it into a 50 Ω matching network. In Figure 1, the noise diode is in the board’s lower-left corner, and the three amplifier stages lie between that and the RF output port on the right.

Noise voltage is difficult to capture on an oscilloscope because of randomness. I was, however, able to trigger on one cycle that appeared to have about 500 ps of rise time. I was using a R&S MXO38 (8-channel, 12-bit, 1 GHz bandwidth) oscilloscope and the spectrum plot showed usable broadband emission all the way past 1 GHz (Figure 2).

Noise generator applications

I switched over to using my Siglent SSA3032X spectrum analyzer so I could capture multiple spectral plots. We’ll measure cavity resonance and a couple of filter responses.

Cavity Resonance: We’ll use the “cookie tin” cavity resonance demo (Figure 3) we used to demonstrate ferrite absorber performance earlier^[2] to demonstrate how the noise source can identify structural resonances. Recall the cookie tin lid had two BNC connectors attached with short (1 cm) stubs soldered to the center conductors. The position of these is not important. We’ll drive one with the noise source and connect the other to the analyzer input port.

The resonance equation was covered in^[2], and for a circular cavity, the fundamental resonant frequency was 1.275 GHz. Figure 4 shows the resulting screen capture with the marker at the peak of 1.23 GHz. The yellow trace was the baseline measurement with the noise source off.

Scanner filter: The radio scanner filter is designed to allow VHF Low Band (30 to 50 MHz), VHF High Band (140 MHz to 174 MHz and UHF Band (420 MHz to 512 MHz) to be heard and to block other strong ambient signals such as AM/FM broadcast, TV, and other high-powered signals. Figure 5 shows the general test setup using a noise generator to drive the filter, which is connected to the analyzer input port.

Figure 6 shows the two bands being blocked with markers at the band edges of the VHF Low Band and VHF High Band. The notches are about 20 dB down. The yellow trace indicates the noise floor of the measurement.

FM Broadcast Notch Filter: This will be a similar measurement to that above, except we’ll use a Mini-Circuits ZX75BS-88108-S+ FM Broadcast Band Stop Filter^[3]. This would be a good filter to use when operating a spectrum analyzer near high-powered FM stations to prevent overload of the front end. Figure 7 shows the test setup.

In Figure 8, you can clearly observe the band-stop filter edges at 81 MHz and 108 MHz. The yellow trace is the measurement noise floor.

Summary

For spectrum analyzers lacking a tracking generator, this broadband RF noise source is affordable and will help measure a host of RF applications, including filter and amplifier responses. While missing the dynamic range of a vector network analyzer, it can serve in a pinch to help identify or confirm RF characteristics of many devices.

References

1. Noise Source (Amazon, $17)
2. Wyatt, Kenneth, How to compare EMI absorption materials with a cookie tin
3. Mini-Circuits FM Band Stop Filter

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When you buy test instruments, you hope they’ll have the flexibility to provide the necessary stimulus to the device under test (DUT) and acquire and process the response. Occasionally, however, you’ll need to design an external network to get exactly what you want, or perhaps worse, you’ll have to deal with a custom interface network that somebody else built.

Q: You mean like an external network of resistors?
A: Yes, something such as the rats’ nest in Figure 1. The result is similar to what you might get if you gave a handful of random components to an engineer and asked for an interface between a test system and DUT without using a circuit board.

Q: So basically, is it just a combination of resistors in parallel and series to get the necessary values?
A: Right. Figure 2 shows a specific schematic, but with fewer resistors than Figure 1.

Q: How can we analyze this?
A: If you have the actual circuit and a multimeter, you can disconnect the voltage source and measure the equivalent impedance. If you have a schematic such as Figure 2 or can derive one, you can use Ohm’s law and Kirchhoff’s current or voltage law and write node or loop equations, respectively, allowing you to calculate currents through each resistor and the voltages at each node. But we can avoid solving simultaneous equations in multiple unknowns if we can identify series and parallel combinations of resistors, as shown in Figure 3.

We know that for two resistors in series, we simply add the resistances, and for two resistors R₁ and R₂ in parallel, the resistance is the product over the sum:

For N resistors in parallel, you can take them two at a time, computing the successive products over sums, or you might find it more convenient to compute the inverse of the sum of the reciprocals:

For the three parallel resistors in the light blue box on the right, we can determine that 820 Ω in parallel with 360 Ω equals 250 Ω, which in turn is in parallel with 1 kΩ and equals 200 Ω. Or, we can simply calculate the inverse of 1/1,000 Ω plus 1/820 Ω plus 1/360 Ω, which also equals 200 Ω. That 200 Ω is in series with 1.8 kΩ, so in the dark blue block on the right, we have a total of 2 kΩ.

You can perform similar calculations on resistors in the other blocks shown in Figure 3, and get the voltage-divider network shown in Figure 4. This divider could be useful for a DUT that requires a supply voltage V, and that also has two high-impedance inputs requiring voltages of 50% and 20% of V. The resistor approach costs less than buying two additional programmable power supplies to generate the 50% and 20% levels. It can be faster than a multiplexer-based approach, where you would use a single supply to sequentially apply the required 100%, 50%, and 20% levels. And if your DUT requires that all three voltages be present simultaneously, the multiplexer won’t work at all. Just remember that the voltages must go to high-impedance loads to prevent loading down the circuit.

Q: Can all resistor networks be simplified into series and parallel combinations?
A: No. Consider the circuit on the left of Figure 5. Although it’s simple, consisting of just five resistors, none are in series or parallel with any of the others (unless R₅ is either zero or infinite). This particular circuit is very important in test and measurement. If I redraw it as shown on the right, you might recognize it.

Q: It looks like the Wheatstone bridge, but isn’t R₂ variable, and isn’t a galvanometer used in place of R₅?
A: Yes, it’s the Wheatstone bridge, and in the original Wheatstone bridges, you’re right about R₂ and the galvanometer. In addition, R₄ was the unknown value that the bridge was designed to measure. Next time, we’ll comment on why the variable resistor and galvanometer are not often used in modern applications. In part 2, we’ll see how we can analyze voltages and currents in this circuit using Ohm’s law and Kirchhoff’s current law, and we’ll see why this configuration is useful in strain gauges and other sensitive measurement devices.

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