SBOA626 December   2025 OPA187 , OPA192 , OPA202 , OPA320

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
    1. 1.1 Simple Analogy Explaining Instability
    2. 1.2 Circuits With Possible Stability Issues
    3. 1.3 Simple Stability Correction Based on Datasheet Plots
    4. 1.4 Introducing Lab Tools and Measurements
  5. 2Stability Theory for Operational Amplifiers
    1. 2.1 Poles and Zeros
    2. 2.2 Operational Amplifier Model Requirements for Stability Verification
    3. 2.3 Stability Definitions Based on Control Loop Model
    4. 2.4 Graphing Loop-Gain Based on AOL and 1/β
    5. 2.5 Rate of Closure Stability Test
    6. 2.6 Indirect (Non-Invasive) Stability Tests
  6. 3Simulating Open-Loop Stability Tests
    1. 3.1 Breaking the Loop the Wrong Way
    2. 3.2 Breaking the Loop With LC Test Circuit
    3. 3.3 Differential Loop Break Test
  7. 4Stability Correction for Capacitive Load
    1. 4.1 Isolation Resistor (RISO) Method
    2. 4.2 Dual Feedback Method
      1. 4.2.1 RISO-Dual-Feedback With RL
      2. 4.2.2 Dual Feedback With RFX Method
    3. 4.3 Snubber Circuit for Compensating Power Amplifiers and Reference Drive
    4. 4.4 Noise Gain for Stability Compensation
    5. 4.5 Feedback Capacitor (CF) Compensation for Capacitive Load
  8. 5Stability Corrections for Capacitance on the Inverting Node
    1. 5.1 Input Capacitance Instability Due to Zero in 1/β
    2. 5.2 Feedback Capacitor Solves Stability Issue for Capacitance on the Inverting Node
    3. 5.3 Minimum, Balanced, and Maximum Feedback Capacitance
    4. 5.4 Transimpedance Case
  9. 6Complex Open-Loop and Closed-Loop Output Impedance
    1. 6.1 Converting Open-Loop Output Impedance to Closed-Loop Output Impedance
    2. 6.2 Open-Loop and Closed-Loop Model Test
    3. 6.3 Instability Due to Resonance From Complex Output Impedance
    4. 6.4 Impact of Internal Op Amp Topology on Output Impedance Versus Frequency
    5. 6.5 Other Factors Effecting Output Impedance
  10. 7AOL Impact on Stability
    1. 7.1 AOL Secondary Poles and Zeros
    2. 7.2 Modeling the AOL Secondary Poles and Zeros and Input Capacitance
    3. 7.3 Decompensated Op Amps and Stability
    4. 7.4 The Impact of Closed-Loop Gain on Stability
  11. 8Common Problems in Stability Analysis
  12. 9References

2.3 Stability Definitions Based on Control Loop Model

Figure 1-1 shows a simple non-inverting op amp circuit with a simple control-systems equivalent diagram. The control diagram models the op amp input as a summing block with the feedback path inverted. The open-loop gain across frequency is modeled as shown in Figure 2-3. The op amp feedback network forms the β factor in the control system. The feedback factor is the gain from the output to the inverting amplifier node (β = VFB / VOUT). For this example, β is a simple voltage divider, but in many cases, β can be a more complex relationship. The closed-loop gain equation can be derived by applying the input and output signals to the control system diagram and applying simple algebra (see Equation 10). The denominator of the closed-loop gain equation contains the term AOL × β. This term is critical to stability analysis and is called loop gain (see Equation 11). For very large values of loop gain, the closed-loop gain can be approximated as 1/β. The limit function in Equation 12 shows that when AOL × β is much greater than 1, the 1 in the denominator can be ignored and the AOL terms cancel out leaving ACL ≅ 1/β. Substituting Equation 9 into Equation 12 and applying algebra produces the familiar gain equation for a non-inverting amplifier (G = RF / RG + 1).

OPA187 OPA202 OPA320 OPA192 Op Amp Circuit and Equivalent Controls System Diagram Figure 2-7 Op Amp Circuit and Equivalent Controls System Diagram
Equation 8. A O L = O p e n   L o o p   G a i n   o v e r   f r e q u e n c y
Equation 9. β = F e e d b a c k   F a c t o r = V F B V O U T = R G R G + R F
Equation 10. A C L = C l o s e d   L o o p   G a i n = A O L 1 + A O L β
Equation 11. A O L β = L o o p   G a i n
Equation 12. A C L = lim A OL β → ∞ ⁡ A O L 1 + A O L β ≅ 1 β = 1 + R F R G

The closed-loop gain equation (Equation 10) can be used to determine amplifier stability. An amplifier is considered unstable when the denominator of ACL is zero. This happens when AOL × β = –1. Converting the linear value of loop gain to decibels (AOL × β= –1) means that the magnitude of AOL × β(dB) = 0dB, and the phase shift AOL × β(phase_shift) = –180°. If you remember the analogy in Section 1.1, the instability is due to a delay in the feedback. The –180° phase shift is the feedback delay that causes instability. The op amp thinks the output is going up when the output is actually going down. In any case, when loop gain in decibels is 0dB and the phase shift relative to the DC phase is 180°, the closed-loop gain becomes very large and the circuit is unstable. In Section 2.6, you can see that an indirect way of measuring circuit stability in the lab is to look for large gain peaking.

Note: Criteria for stability:
  • Instability happens when the denominator of ACL is zero
  • The denominator is zero when AOL × β = –1
  • AOLβ = –1 sets the denominator of ACL = 0
  • AOLβ = –1 when AOLβ(dB) = 0dB and AOLβ(phase_shift) = –180°
  • Phase shift is relative to the DC phase

Phase margin describes how close a circuit is to instability. Mathematically, this description is the amount of phase remaining when AOL × β(dB) = 0dB before the phase shift AOL × β(phase_shift) = –180°. For example, if the phase shift relative to DC is 170° when AOL × β(dB) = 0dB, then the phase margin is 10°. From a practical perspective, amplifiers with a very low phase margin are effectively nonfunctional. Poor phase margin leads to very large gain peaking, large overshoot, and oscillations. In some cases, the oscillations are continuous even when the input is a DC signal. Some engineers consider cases where the oscillations eventually settle out as an acceptable outcome. However, circuits that are marginally stable have large overshoot and oscillations for any change on the input, power supplies, or output loading.

Note: Definition of phase margin:
  • Phase margin describes how close a circuit is to instability
  • When AOL × β(dB) = 0dB the phase margin is the phase remaining before AOL × β(phase_shift) = –180° and the circuit is unstable
  • If the phase shift is 170° when AOL × β(dB) = 0dB, than the phase margin is 10°
  • On a bode plot, phase margin is the phase shift relative to DC phase when AOL intersects 1/β, or when AOL × β(dB) = 0dB (see Figure 2-8)
  • Most op amp circuits have a phase of 180° at DC, so the phase margin can be read directly on the graph where 0° is unstable (see Figure 2-8)

If the phase margin is zero, the circuit generally oscillates continuously. Circuits with a low, but non-zero, phase margin have high gain peaking, large overshoot, and very poor settling times. The recommendations for minimum phase margin differ depending on the engineering reference. TI recommends using a phase margin ≥ 45° for good stability. For some circuits, achieving a 45° phase margin is a challenge, so a phase margin as low as 35° is potentially acceptable. Keep in mind that the parameters impacting stability (such as open-loop output impedance, open-loop gain, and external component values) all have tolerance, so generally, having a phase margin above 45° is advisable so the design is robust across process corners.

Note: Phase margin general guidance:
  • TI recommends a phase margin ≥ 45° for stable circuits
  • 45° > Phase margin ≥ 35° is considered marginally stable, but can be acceptable in some cases
  • Phase margin < 35° is unstable and leads to large overshoot, gain peaking, and oscillations

When looking at open-loop gain and phase plots, engineers can find the phase margin by looking at the loop-gain phase at the frequency where 1/β intersects with AOL. Alternatively, the phase margin can also be found at the frequency where the loop-gain magnitude is 0dB (AOL × β(dB) = 0dB). For most amplifiers, the DC loop-gain phase is 180°, so the phase margin is directly read from the graph. In Figure 2-8, the phase starts at 180° and drops to 8° when AOL × β(dB) = 0dB, so the phase margin is 8°.

OPA187 OPA202 OPA320 OPA192 Phase Margin Definition Figure 2-8 Phase Margin Definition