# STB Analysis Improves Op-Amp Feedback

### Key Takeaways

• STB analysis is a rough grouping of qualitative and quantitative techniques that measure feedback stability.

• Calculations may indicate the presence or lack of stability; a measurement approach is generally more applicable.

• There are multiple methods to compensate for poor stability in the design, depending on which amplifier characteristics are most/least vital.

STB analysis improves op-amp performance by stabilizing feedback response.

One of the difficulties of working with electronics is establishing both current and future parameters of the circuit, i.e., where values “are” and where they’re “going.” Operational amplifier networks compound this issue due to the defining feedback loop found in most topologies. Although leveraging the amplifier’s high gain is essential to the operation, linking input and output can lead to a new host of errors if the network lacks calibration. Arguably, the most crucial factor for performance is system stability or the conditions that allow a system to react predictably. Stability, or STB analysis, is the set of tools and methods to diagnose the presence and quality of feedback reliability.

Stability Analysis for Linear and Nonlinear Systems

 Linear Nonlinear A linear system is stable if all zeros lie in the left-hand plane, provided no individual terms have poles in the right-hand plane.From the determinant equation, divide by the second determinant (all right-hand plane zeroes removed) to generate the normalized determinant.The system is unstable if any right-hand plane zeroes are present in the normalized determinant (the converse is also true). Nonlinear systems use a similar methodology but a different approach: the normalized determinant systematically measures the response of a group of perturbation frequencies, with each successive perturbation shorting out the suspected nodes that came before it.The second determinant uses the same process but replaces all the suspected elements with passives.

## STB Analysis: Quantitative or Qualitative?

Formally, a circuit can exhibit stability based on a few categorizations:

1. Bounded input, bounded output (BIBO)

2. The Dirac delta function (ẟ(t)) decays to 0

3. Excitation frequencies map uniquely to their response frequency

The presence of just one of these conditions is enough to indicate stability.  However, real-world circuitry has a noise floor and distortion ceiling on signal outputs that undermine this simple characterization, as the former ensures output even in the absence of input, and the latter creates attenuation at the output. A more quantitative method devises stability factors based on impedance or admittance while treating the amplifier as a two-port network:

where K is either the admittance or impedance of the circuit. The drawback of this approach is that it only indicates the possibility of instability and remains applicable only in cases where no additional feedback is present at the input. The latter condition was critical to refining instability to a more general form that expands to hybrid (h) and inverse-hybrid (g) parameter matrices:

where the real component of the 1,1 and 2,2 matrix parameters (either impedance, admittance, hybrid, or inverse-hybrid) are positive. The value of this model is the importance of measurement, as circuit stability is easily measurable but more challenging to demonstrate solely from calculations. These equations intend to present a simple stability estimation from measured values, but even then, stability can behave unexpectedly compared to calculated results. Generally speaking, a K-value greater than one indicates strong stability, while a value less than 1 is likely (but not necessarily) to experience some instability. The true benefit of the model is that stability is a prerequisite for evaluating the steady-state signals necessary for calculation – measuring values alone indicates stability, given the state of the circuit.

A better method for measuring stability is probing in simulator tools to determine the Bode plot of the circuit. Here, engineers can rapidly see the gain and phase output as a function of frequency and even quantify more minimal changes like transient responses to small and large steps. Understanding the circuit response across its bandwidth will help guide compensation efforts at the test and prototype stages of design.

## How Designers Can Compensate to Improve Stability

The component or circuit stability response will affect certain operations; compensation efforts will focus on mitigating or balancing these effects to strengthen feedback stability. These compensation styles will vary according to the level of design integration and how they address instability factors:

• Intenal compensation - For general ease of use, compactness of design complexity, and the ability to quickly integrate the feedback system with minimal additional calibration, most discrete op-amp components will trade bandwidth for a larger apparent single-pole (i.e., seemingly unconditional) stability. However, internally compensated op-amps are vulnerable to ringing, especially when external interfacing options provide a considerable electrical load.
• External compensation - Designers can reference datasheets to counteract certain performance constraints and better target individual aspects of op-amp performance for a more robust stability response. Like internal compensation, external compensation sacrifices some bandwidth to achieve the desired behavior, but this compensation is more easily accessible and modular.
• Gain compensation - Voltage feedback op-amps can use the gain of the amplifier to stabilize the circuit output by decreasing the accuracy and bandwidth of the response. However, circuits that can withstand the increase in the gain experience few side effects, making this a preferred option for stabilizing amplifiers.
• Lead compensation - Parasitic capacitance arising from the intersection of the board, component, and solder joint (or wire for test boards). This capacitive effect can greatly undermine circuit performance (especially in the case of high-frequency applications); it also provides a stabilizing impact that reduces noise, making its inclusion in the circuit a little less straightforward.
• Compensation attenuator - Stray capacitance on the inverting input of an op-amp depresses the circuit's frequency response. Designers can effectively cancel out this capacitance similarly to lead compensation, making the loop gain independent of any contributions from the capacitors.
• Lead-lag compensation - Offers stabilization with a minimal effect on the closed-loop characteristics, making it well-suited for circuits using or built around amplifier networks without internal compensation.

Designers need to understand that no compensation technique can ever improve upon the baseline characteristics of the amplifier. For example, while compensation can improve specific performance metrics, it can not provide a bandwidth that exceeds the amplifier's. Ensure component selection meets the design intent of the circuit.

## Cadence Solutions Stabilize and Optimize Circuit Performance

STB analysis is a broad class of techniques for determining and analyzing the presence of instability. Instead of a hard-and-fast equation, engineers should lean on sophisticated modeling and measurement tools that provide a more thorough treatment of system stability. Engineers can even revise circuit simulations to incorporate the equivalent compensation, greatly reducing the time and cost compared to a physical prototype model. Cadence’s PCB Design and Analysis Software suite is a comprehensive package of cutting-edge ECAD tools that give designers everything they need to plan and optimize circuit design. Alongside the powerful and easy-to-use OrCAD PCB Designer, circuit design has never been more robust.

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