Impedance Measurementand Relating it to Control Loop Stability

Part 1. Introduction

What you will (hopefully) learn -

Continuous performance improvement, shorter development cycle, lower cost target, smaller size, higher integration, lower voltage, higher current, faster switching

The multitude of problem(s) we face -

• How and why impedance measurement can help solve these problems• A variety of methods to acquire precise impedance test data• How control loop stability can be extracted from impedance• How impedance measurements aid in troubleshooting and optimizing performance

while also reducing cost

Housekeeping

I was recruited to work on the Space Shuttle project in 1978 and was immediately

mesmerized by space electronics. I’ve worked in the hi-rel community ever since. In 1995 I

founded AEi Systems, which today is a leading engineering services company specializing in

analysis, measurement, and troubleshooting of hi-rel systems. I’ve had the honor and privilege

of working on many projects including the International Space Station, GPS II and III, the Large

Hadron Collider at CERN and many other military and commercial projects. In 2010 I founded

Picotest, a company that provides low cost, high performance measurement solutions. My

experience is in RF, Analog, and Distributed Power Systems. I enjoy writing and lecturing as

much or more than anything else I do.

In our experience, we’ve found impedance to be the single most essential measurement for the

characterization, optimization, and troubleshooting of modern day distributed systems, both

large and small. We’ve developed a unique solution to obtain stability margins directly from an

impedance measurement. Not many people are using this powerful test. They either don’t

know about, or don’t have a full understanding of how it works. That’s about to change, at least

for you, over the next 4 hours.

Today, I’ll share our proven methods for measuring impedance, interpreting the results, and

transforming the results to stability margin. Much of this information is from my new book

“Power Integrity” from McGraw-Hill. For those interested you can find additional information at

https://www.picotest.com/Power-Integrity-Book.html

If You’re into Mind Maps – Here’s Today’s Journey

You are here

What is Impedance?

Measure of free space=120π=377Ω (until Oct 21 1983)

Under-appreciated figure of merit (FOM)

Foundation of target impedance

Fundamental principal of signal integrity

A way for audiophiles to talk for hours about the new speakers they just bought

Impedance vs. resistance

Our Definition of Impedance

Well it isn’t just electrical, but can be mechanical or even chemical

A good general definition might be - A measure of the opposition to a force acting on a system

𝑍(𝑓) =𝑉(𝑓)

𝐼(𝑓)

We’ll use something a bit moreSpecific for this lecture

Impedance vs. Resistance?

So resistance is a DC measure of the opposing force and impedance is the AC measure of the opposing force. One is a magnitude and the other is a vector

Not everyone would share this definition. In one lecture I asked if anyone could define resistance…..

I don’t ask that anymore…..

Relating Impedance to our Problems

Common Threads

Minimize/optimized decouplingFlatter, lower impedance PDNImprove control loop stabilityHigher level integrationFaster edges/switchingFewer iterations better choicesBetter simulation models

Reduced measurement accessDegraded measurement SNR

+

Impedance

Relating Impedance and Issues

Improved Performance at Lower CostBetter simulation models

Fewer design iterations

Better component selections

Passive components – L’s, C’s and Beads

Semiconductors – Diodes, BJT’s and MOSFETS

Active Circuits – Opamps, Voltage References and Regulators

Reduced EMI Locate and Characterize Resonant Planes and Circuits

Flatter, Lower Impedance PDN

Minimize/Optimized Decoupling

Improve Control Loop Stability

Stability Assessments – Minor Loop / Forbidden Region

Trace /Plane Impedance – SI and PI

Smaller signals and higher frequencies High Frequency Measurement CapabilityImproved SNR Require Narrow Band RBW

Higher Level Integration Generally Accessible Even in Limited Access Circuits

The Problem Impedance Data To the Rescue

Available Despite Reduced Access

2008 smartphone

Power supply

8.5mm

8.5mm

More power supplies72mm2

12mm2

Very dense, highly integrated circuits.

fortunately output capacitors are generally accessible to measure

6 output

2014 LDO

2013 eGaN

And shrinking

The MOST Useful Measurement

Magnitude (Metric?)

Optimization

Simulation support

Troubleshooting

Impedance is the MOST useful tool for the development and assessment of electrical systems

Part 2. Impedance Impacts (Symptoms)

Noise is Related to Impedance

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f/HzTR1: Mag(Impedance)

Memory 1 : Mag(Impedance)

~12dB 105kHz pk

~12dB105kHz pk

Voltage Reference Noise

Impedance Measurements

Noise Density Measurements

The additional noise from the voltagereference impacts the SNR of ADCs

The addition of noise suppressioncapacitors can INCREASE the noise

The noise and the impedance are directly related

This is an indication of the voltage reference being destabilized by the addition of the noise suppression capacitor

One More Direct from the MFR

Noise Impacts Can Be Far Reaching

Harmonic Comb

Vout

Here you can see the sensitivity of the voltage response to a current step

The result of the ringing is a noise comb with harmonics spaced at the repetition rate

The damped sine looks harmless, but it is quite a noise generator

The LOWER the repetition rate the BIGGER the problem!

Clock Jitter/Phase Noise

Low impedance linear regulator(data)

Moderate impedancePOL regulator (memory)

Power Supply Impedance

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TR1: |Mag(Gain)|

45mΩ

210mΩ

Low Z linear regulator

Moderate Z POL

Clock Sensitivity to Noise

6dB difference in sideband noise at 7MHz offset

6dB7MHz offset

Two different decoupling capacitors at the downstream voltage regulator(not at the clock)

Impedance at the clock

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f/HzCap 1 : Mag(Impedance)Memory 3 : Mag(Impedance)

6dB 7MHz peak

Interestingly, the lower impedance decoupling results in worse clock jitter.

Higher ESR=Lower peak

Lower ESR=Higher peak

Yet Another Form of Jitter

Impedance can also be used to predict frequency hops, like this one

In this case, there is a nearly 2% frequency jump which appears as jitter

EMI’s Relationship to Impedance

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Impedance at input cap near MOSFET

Resonant planes are often the Source of EMI

We can typically locate the general proximity of the source and then pinpoint with an impedance measurement

OPAMP Impedance vs. Capacitance

Vdd Droop (and Ground Bounce)

While FPGAs and CPUs typically have limited frequency content inthe current signal (due to die cap), high speed logic gates do not

This noise signal is due to a singleUHS7404 logic gate switching used as a 10MHz clock signal buffer

Note the voltage scale is 100mV/div

FPGA VDD Droop

While the VDD droop is alsoa function of impedance it isoften advantageous to measurethe voltage droop using a “spy hole”

This voltage must then be transformed to impedance in order to allow simulation and manipulation ofthe data

Sahar Sedeghi from AEi Systemsprovided this measurement of an RTAX2000 rad-had FPGA. The impedance was extracted using SEPIA, a program from Picotest for extracting R,L,C parameters from this measurement

Rogue Waves

A rogue wave is a wave that is much bigger than most waves in the same location at a given time. This typically relates to oceanography, but recently there has been a lot of discussion about whether rogue waves can exist in electronic circuits

In this case, the rogue wave response is an order of magnitude larger than the natural response

Natural response

Rogue wave

AC COUPLED VRM OUTPUT

Impedance and Rogue Waves

As of this time we’ve successfully simulated rogue waves using impedance models

We haven’t yet successfully created or measured one, primarily because the generation of a current loading profile that would cause a VRM to have such a problem is challenging to replicate

I hope we’ll demonstrate the measurement of a rogue wave at DesignCon 2016.

Impedance measurements can identify conditions that can result in a rogue wave

Our Present Location

You are here

Part 3. Measurement

Measurement Domains and Instruments

Time or Frequency?

Some instruments contain one domain natively and the other as a transformation. For example the S5048, E5071C and ZNB20 are all swept VNA instruments with transformation to TDR/TDT. The DSA8300A and SPARQ are TDR/TDT instruments with transformations to S parameters.

Which is better?

Frequency vs. Time

Each has advantages and disadvantagesTDR/TDT

Pros:Can directly measure characteristic ZCan locate physical aberrationsNeeds minimal calibrationAre easily gated to remove fixture artifacts

Cons:Have linear time scalesAre a bit more complicated to interpretHave lower SNR/dynamic range than VNALimited low frequency capability

VNA

Pros:Measure log in both X and Y axesBetter dynamic range/SNR (RBW)Easier to interpret R,L,CRequires calibration, but simple to do

Cons:Can’t directly measure characteristic ZGenerally start at 9kHz to 100kHzCan’t locate physical aberrations

Another Frequency Domain

VNA/FRA can measure as low as 1Hz and as high as 40MHz using the FRA function. This class of instrument can measure 50Ω (most common) S-parameters and can also measure frequency response.

What’s the difference?

The VNA has 2-ports (or more) that measure in pairs. Each port is 50Ω and the instrument measures S-parameters up to 10’s of GHz.

FRA

Keysight Technology E5061B

OMICRON Lab Bode 100

VNA

1Hz-40MHz 1Hz-40MHz

5Hz-30MHz 5Hz-3GHz

FRAs have 3 ports – an oscillator and two high impedance tracking receivers. The FRA measures transfer functions CH2/CH1 (magnitude and phase) as required for a Bode or Nyquist plot. Later we’ll see how to use this for impedance measurement.

DynamicRange

>100dB

>120dB

The OTHER Time Domain (Oscilloscope)

As we’ll see later today we can transform THIS time to impedance, but the domain has some limitations and the transformation is complex

Oscilloscope

Pros:Most engineers have oneMay offer spectrum functions

Cons:linear x and y scalesRequires significant transformationRequires external excitation in casesVery low SNR and dynamic rangeCan ifficult to interpret

Oscilloscope Spectrum

Pros:Significantly improved SNRLog y display improves dynamic range

Cons:Cannot calibrate the measurementNot as good as stand alone spectrumRequires external excitation in casesAn external preamp can improve usability

Instruments?

One or two slides are reserved here in order to show the various instruments available for impedance measurement if we elect to invite the vendors to include their wares

Impedance Measurement Tools

Measurement Methods

1. 1-port reflection 0.5Ω-2.5kΩ2. 2-port shunt thru 25uΩ-25Ω3. 2-port series thru 25Ω-1MΩ4. 3-port voltage/current 1mΩ-2kΩ5. Impedance adapters 0.1 Ω-400kΩ6. 1-port TDR 10mΩ-1kΩ7. 2-port TDT 10mΩ-100Ω8. Transient extraction mΩ*-1kΩ

APPROXIMATE measurement range

Method is chosen in large part by the impedance magnitude required

We’ll look at the connection diagrams when we get to the case studies

* Often limited by stimulus amplitude

Allocating the Tools

MethodImpedance

ProbesCurrent Injector

Preamplifier DC BlockCurrent Probe

Common Mode Xfmr

Impedance Fixture

1-port reflection X X

2-port shunt thru X X X X

2-port series thru X X

3-port voltage/current X X X X X X

Impedance adapters X

1-port TDR X X

2-port TDT X X X

Transient extraction X X X X X

Need a Break?

Measurement Philosophy

Direct vs Indirect

In-Situ vs Test Fixture

Invasive or non-invasive

We can measure impedance directly (Direct measurement) or we can measure the result or impact of the impedance impedance (Indirect measurement)

It is generally advantageous to measure In-Situ (in-circuit), so that the circuit is operating under typical condition (input voltage, load current, interconnect impedances, etc.)

An invasive measurement is one in which we are required to cut traces or wires or lift comments. An invasive measurement can also be one that distorts the measurement due to the test equipment.

Indirect Measurement

This clock spectrum sensitivity shows the result of an impedance peak near 7MHz. This is an indirect measurement of the localpower supply impedance.

7MHz offset

In some cases, the indirect measurement is more helpful as it is a DIRECT measurement of the TARGET function. In other cases, it may be for corroboration or because it is more accessible than a direct measurement.

Direct Measurement

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f/HzS301-2 : Mag(Impedance)

This impedance measurement is a direct measurement of the 7MHz peak seen in the previous indirect measurement.

In-Situ or Fixture testing

It’s possible for the test fixture to influence the results. In this example, the use of an electronic load alters theimpedance measurement of this DC-DC converter. Use of a low capacitance current injector does not.

Sensitive circuits, such as opampbuffers can be destabilized by PCB capacitance and so it is betterto assess these buffers In-Situ

Non-invasive Impedance testing is a means for assessing overall health

Non-Invasive is Common

Invasive Measurement

Invasive methods require cutting traces or lifting components

Invasive methods could also mean measurement methods that interfere with or distort the measurement result

Non-Invasive and Invasive

Metal/treasure detectorsUltrasonic Pipe thicknessX-ray solder inspectionRadar TDR testers locate cable damage

And many more…….

Non-invasive gas line detection

Invasive gas line detection

And ANOTHER Non-Invasive

A common example of an invasive measurement is measuring the switching frequencyOf a pulse width modulator timing ramp. The scope probe capacitance may alter the frequency and with potentially disastrous results.

Part 4. Extracting Stability

Applications for NISM

• Op-amps• Voltage Regulators – including LDOs, POLs, VRM’s…. • Voltage References• Audio Amplifiers – including switching types• Input Filter Stability• System Level Box-to-Box Stability• Current Regulator Stability (electronic load, LED, etc)• Almost any control loop

We’ll show a range of these applications in the case studies

Minor Loop Gain FoundationNathan Sokal published “System Oscillations Caused by Negative Input Resistance at the Power Input Port of a Switching Mode Regulator, Amplifier” in 1973, but the topic was popularized by Dr. R.D. Middlebrook in 1976 with his article “Input filter considerations in design and application of switching regulators”

Dr. Fred C. Lee (VPEC) has published many including “A Method of Defining the Load Impedance Specification for A Stable Distributed Power System” and “Stability Margin Monitoring for DC Distributed Power Systems via Perturbation Approaches”

The minor loop gain method was also used to analyze the stability of the ISS and the method was published in “Analysis of the Stability Margins of the Space Station Freedom Electrical Power System”. In fact it is quite commonly used in large systems

Today this is a highly researched university topic and many papers will be found using the search term “Minor Loop Gain”.

Albert Hull Sokal MiddleBrook Dr. Lee Steve Sandler1920’s 1973 1976 1976 2010

Minor Loop Gain

The minor loop gain assessment is interpreted from a Nyquist plot

𝑇𝑚 =𝑍𝑠𝑍𝐿

The non-invasive methodmeasures Zs and ZL while they are connected, thenMathematically separatesthem into two parts and computes Tm

System

SOURCE LOAD

Zs ZL

Phase margin is determined by setting 𝑇𝑀 = 1on the Nyquist plot and calculating the phase angle

Cursor Based Realization

Lab comparisons of 7 regulators/capacitorsBode plot and the NISM methods were within +0.9 degrees.

Noise free simulation results were within +0.3 degrees, attributable to cursor resolution.

The #1 Question – Accuracy?

The method is extremely accurate from 0 - 60 degrees(ish)

Active vs Passive

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𝐶𝑙𝑜𝑠𝑒𝑑_𝐿𝑜𝑜𝑝 =𝑂𝑝𝑒𝑛_𝐿𝑜𝑜𝑝

1 + 𝑇As |T| falls below unity Open is equal to Closed

Power off

Power on

passive

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Passive resonances Closed = Open

Active resonanceClosed > Open

Ideal stability Closed < Open

Below 1-portlimit

Non-Invasive FAQ

• Can you give us the math so we can use it in our own instruments?[ANSWER] Currently our math is included in the OMICRON Lab Bode 100 and as a an app for the Keysight E5061B and CMT S5048. Others are planned.

• Why do I get the wrong answer when I use the math from the Fundamentals Of Power Electronics?

[ANSWER] There are two reasons. The Q used in Fundamentals of Power Electronics is the open loop Q calculated from the voltage reference to the output and the non-invasive method uses the closed loop Q from the output impedance. The Fundamentals of Power Electronics derivation also does not include the capacitor ESR, which is a major stability term

• I don’t see a peak in the group delay, what am I doing wrong?[ANSWER] Likely you did everything RIGHT!

• I measured the bode plot and the phase margin is good, but the non-invasive measurement says it is bad. Why, and which is correct?

[ANSWER] We have several articles on this subject. Five Things Every Engineer Should Know About Bode Plots and When Bode Plots Fail Us. In these instances, the non-invasive measurement is generally more correct

Part 4. Case Studies/Demonstrations