SBAA767 January   2026 OPA206

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
  5. 2General Transfer Function of the Second Order System
    1. 2.1 Damping Ratio
      1. 2.1.1 Underdamped (0 < ζ < 1)
      2. 2.1.2 Critically Damped (ζ = 1)
      3. 2.1.3 Overdamped (ζ>1)
  6. 3Modeling Op-Amp as a Second Order System
  7. 4Phase Margin vs Percent Overshoot
    1. 4.1 Phase Margin
    2. 4.2 Represent AOLβ as ΦPM
    3. 4.3 Represent ΦPM as Damping ratio
    4. 4.4 Phase Margin Represented by Percent Overshoot
    5. 4.5 Phase Margin Represented by Gain Peaking
  8. 5Simulation of Ideal Second Order System
    1. 5.1 Phase Margin: 30 Degrees
    2. 5.2 Phase Margin: 45 Degrees
    3. 5.3 Phase Margin: 60 Degrees
    4. 5.4 Phase Margin: 75 Degrees
    5. 5.5 Step Response with Different Phase Margin (Damping Ratio)
    6. 5.6 Gain Peaking with Different Phase Margin (Damping Ratio)
  9. 6Simulation Example Using an Op-Amp
    1. 6.1 OPA392 With Non-Inverting Amp Configuration
      1. 6.1.1 Step Response Simulation
      2. 6.1.2 Gain Peaking Simulation
      3. 6.1.3 Loop Gain Simulation
    2. 6.2 TLV9052 with Unity Gain Buffer Configuration
      1. 6.2.1 Step Response Simulation
      2. 6.2.2 Gain Peaking Simulation
      3. 6.2.3 Loop Gain Simulation
    3. 6.3 OPA206 with Unity Gain Buffer Configuration
      1. 6.3.1 Step Response Simulation
      2. 6.3.2 Gain Peaking Simulation
      3. 6.3.3 Loop Gain Simulation
  10. 7Causes of the Mismatch of Phase Margin Between Step Response and AC Analysis
    1. 7.1 The Transfer Function is not a Second Order System
    2. 7.2 Amplifier Showing Large-Signal Behavior
    3. 7.3 Noise Gain is Not Flat Within Crossover Frequency
  11. 8Summary
  12. 9References

3 Modeling Op-Amp as a Second Order System

In general, an op-amp can be approximately modeled as a second order transfer function, shown in Equation 9.

Equation 9. A s = A O L 1 + s ω p 1 1 + s ω p 2

Where:

AOL = DC gain

ωp1 = first pole

ωp2 = second pole

Figure 3-1 shows gain and phase response of Equation 9.

窓, グリーン, 建物, 座る が含まれている画像 AI 生成コンテンツは誤りを含む可能性があります。 Figure 3-1 Gain and Phase Plot of a Second Order System

Figure 3-2 shows an op-amp with negative feedback, where β is the feedback factor.

図形 AI 生成コンテンツは誤りを含む可能性があります。 Figure 3-2 Negative Feedback

Closed loop gain, ACL is given by

Equation 10. A C L s = V o u t s V i n s = A s 1 + A s β
Equation 11. = 1 1 A s + β

Substituting Equation 9 into Equation 11 :

Equation 12. = 1 1 ω p 1 ω p 2 s 2 + 1 ω p 1 + 1 ω p 2 s + 1 A O L + β
Equation 13. = A O L ω p 1 ω p 2 s 2 + ω p 1 + ω p 2 s + ω p 1 ω p 2 1 + A O L β

By comparing Equation 1 and Equation 13 ,we can derive each key parameter.

Equation 14. ω n = ω p 1 ω p 2 1 + A O L β
Equation 15. K = A O L 1 + A O L β
Equation 16. ζ = ω p 1 + ω p 2 2 ω n
Equation 17. = ω p 2 ω p 1 + ω p 1 ω p 2 2 1 + A O L β

To simplify Equation 17, damping ratio ζ, the ratio of ωP2/ωP1 is represented as h.

Equation 18. h = ω p 2 ω p 1
Equation 19. ζ = h + 1 h 2 1 + A O L β