# How to Solve 8 of 10 Design Issues

Steve Sandler finds that eight out of 10 design issues are due to a single problem that is easy to solve.

**Unclear how to interpret the stability**

Engineers may not recognize control loop stability issues from closed loop performance (or the ramifications). For example, the impedance plot below shows the output impedance of an LM4050 voltage reference with a 1uF capacitor. (No additional details about the cap are provided.) This device also shows a typical phase margin of approximately 12 degrees. The inexperienced or untrained engineer will not recognize the looming stability issue, the ramifications for circuit performance (including degraded PSRR, crosstalk, noise, reverse transfer, and voltage excursion), or the possible consequences for downstream circuits that connect to this device -- an ADC, for example.

This assessment is supported by the fact that I find so many circuits with control loop stability issues.

**Different operating conditions than the datasheet**

The datasheet example also shows that different reference voltages produce different stability results. This is also true of different reference bias currents (or output currents in the case of the linear regulator) and different capacitor values. The graph is for a bias current of 100uA. The published data is often not shown for the operating conditions applied in the circuit being assessed.

**Contradictory or dated information**

Many device datasheets tell us to use tantalum capacitors on the outputs of our linear regulators. One issue is that the ESR of these capacitors has been continually dropping as technology has advanced. Unfortunately, this degrades the control loop stability.

There is also frequently contradictory or conflicting information reaching the design engineers. The linear regulator might state that moderate ESR capacitors are recommended, but then the datasheets for the digital circuits and op-amp connected to the device (often from the same manufacturer) recommend ceramic capacitor decoupling for every chip. As circuits become more complex and use less power, we are connecting ceramic decoupling capacitors, negating the benefit of the moderate ESR recommendation. It is not unusual for me to see more than 50 ceramic capacitors connected to a single voltage regulator.

**Multilayer PCBs**

High-speed op-amps and multilayer circuits don't always get along well together. The high-speed or high-bandwidth op-amp -- especially when used in a unity-gain or low-gain configuration -- is sensitive to much lower values of capacitance than either a voltage reference or a linear regulator. There are two sensitive nodes: the op-amp output and the op-amp inverting input. Large pads on multiple-layer PCBs can result in significant capacitance, especially when using wider traces and larger device solder pads, as well as signal and grounds on adjacent layers.

**Solving the issue**

First, it is important to get data at the operating bias conditions of the intended circuit. The simplest data to obtain is the output impedance measurement. There are many application notes on the Picotest website about making this measurement and assessing non-invasive stability.

With the impedance information in hand, we might now recognize that the device impedance appears as a series resistor and inductor (as identified by the +6dB/octave slope of the impedance curve). Converting this impedance measurement to an inductance,

For example, the plot at the top of this page shows that the 2.5V reference configuration has an impedance of approximately two Ohms at 1kHz or 318uH.

The inductance can also be calculated from the resonant frequency and output capacitance, as in

In this case, the plot shows that the 2.5V reference configuration has a resonant frequency of about 1kHz with a 1uF capacitor.

With both the inductance and capacitance defined, the value of the desired ESR can be estimated by setting the resonant Q to 0.5.

This ESR value is not realistic, but it is possible to add 36 Ohms in series with the capacitor to produce stable performance. The resistor can also be placed between the active device and the capacitor or (optimally) equally split between the two locations, with half the resistance connected to the active device and the other half connected in series with the capacitor. Of course, the non-invasive measurement is simple and inexpensive and provides the data required to achieve an ideal solution or to assess the stability in circuit quickly.

Have you seen evidence of stability issues in your circuits? It could be the reason for unexpectedly high clock jitter, circuit noise, or excessive EMI. Do you think device manufacturers could do a better job of providing stability relationships for their devices?

Author

Steve.Picotest 9/2/2013 3:05:43 PM

You are mostly, but not entirely correct. The stability definition you presented is reasonable, the question is the metric for quantifying the margin of stability, which in most cases is the closest proximity of the gain vector to the singular unstable point (1,0).

The ringing is not quite preditcable, as it has much to do with the degree and Q of the open loop, which is often unknown. The issue is particularly troublesome in circuits where the loop is not accessible for measurement. This is often the case with class D monolithic audio amps, voltage references and fixed voltage regulators to name a few. So for example if you look at a LDO datasheet and it says stable for capacitors from 1uF to 100uF what exactly does this mean? Will the circuit ring? If so, how much and do we care?

I'm currently writing a new book for McGraw-Hill on high fidelity measurement and it will address some of these issues and how they propagate through systems. The book should be submitted to the publisher in early 2014.

The point of this article is that we should be concerned about even a little bit of ringing (especially in a high performance system) might rwreak havoc on the performance.

Author

felixk1 9/2/2013 5:41:30 AM

I was taught (and I have read in many books on control system theory), that the definition of a fully-stable system is one in which one or more bounded inputs to the control system (i.e. The transfer function), results in one or more bounded outputs (for SISO and MIMO systems). Put another way if a finite input results in a finite output; put yet another way (in terms of the impulse response of said system), if the impulse response of the system tends to zero after "some" time.

You can have marginally stable systems where the impulse response tends to some finite non-zero value but never goes to zero. Hence a system is unstable (in terms of the impulse response), if the impulse response reaches infinity after a certain time. [Ref: "Electronic Devices and Amplifier Circuits with MATLAB computing", Second Edition by Steven T. Karris, Orchad Publications 2008 [ISBN-13: 978-1-934404-14-0, ISB-10: 1-934494-14-4].

Sidenote: The impulse response in the digital domain is simply a vector (of necessary length (n)), that contains a 1 followed by n-1 zeros.

With respect to the ringing due to the output capacitor, this is entirely predictable I thought. Without the capacitor (in combination with the output impedance), you have all frequencies passing through (due to the input of Dirac-delta function equivalents at the start and end of the square wave pulse), resulting in an approximation of a theoretical impulse (we are in the analog (or analogue) world now :)). With the capacitor much of the high-frequency components have been filtered (passed-through to ground) but some low-pass signals have passed through. In any case the system (or more commonly subsystem) still appears fully-stable in theory as the output voltage is tending to zero; the problem comes when this is inputted into the next stage. This is all undergraduate stuff so I must be missing something!?!?

With regards to not being able to measure something in one's design; if you can't measure it you can't test it and if you can't test it then you may be in trouble. One would have to go back and think how do I know the existence of something that can't be measured? In general it is because some [acceptable number of] mathematician/physicist says it has to be there in theory. One may have to look at what the unmeasurable object affects, with a view to being able to measure the effects and work backwards with theory (math).

Regards,

William Knox

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Steve.Picotest 8/29/2013 7:01:01 PM

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David Ashton 8/29/2013 4:10:20 PM

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Steve.Picotest 8/29/2013 3:43:04 PM

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bcarso 8/29/2013 3:35:16 PM

Sometimes the bast way to proceed is local fast shunt regulation, although it entails substantially higher quiescent current. But it can render local current fluctuations small enough to allow grounds to be shared, which is helpful at very high frequencies.

Brad

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elucches 8/28/2013 2:36:39 PM

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Steve.Picotest 8/27/2013 3:00:29 PM

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Niso 8/27/2013 2:53:29 PM