Design Calculation for Practical Op-Amp Integrator

An operational amplifier (op-amp) integrator circuit is essential in analog signal processing applications such as waveform generation, analog computation, and filtering. In this post, we will walk through the design calculation of a practical op-amp integrator using the LM358 op-amp, with a specified integration time of 25 ms. Additionally, we will include a compensation resistor calculation to ensure the stability and accuracy of the circuit.

Design Summary and Calculations

We will base the design on the following given parameters and calculate the necessary components:

• Amplification Factor (A): Given as $A=10$
• Input Resistor (R1): Given as $R1=10\text{k}\mathrm{\Omega }$
• Feedback Resistor (Rf): Calculated as $Rf=A\times R1=10\times 10\text{k}\mathrm{\Omega }=100\text{k}\mathrm{\Omega }$
• Input Frequency (f): Given as $f=400\text{Hz}$
• Break Frequency (fb): Chosen as $fb=\frac{f}{10}=\frac{400\text{Hz}}{10}=40\text{Hz}$
• Feedback Capacitor (Cf): To be calculated.

Step 1: Calculate the Feedback Capacitor (Cf)

We know that the break frequency $fb$ for an op-amp integrator is given by the equation:

$$fb = \frac{1}{2\pi Rf Cf}$$

Rearranging the equation to solve for $Cf$:

$$Cf = \frac{1}{2\pi Rf fb}$$

Substitute the given values:

$$Cf = \frac{1}{2\pi \times 100 \, \text{k}\Omega \times 40 \, \text{Hz}}$$

Solving for $Cf$:

$$Cf \approx 39.8 \, \text{nF}$$

Thus, the feedback capacitor $Cf$ is approximately 40 nF.

Compensation Resistor (Rcomp)

In practical op-amp circuits, a compensation resistor $R_{comp}$ is often used to improve the stability and performance of the integrator. The compensation resistor helps account for the small inaccuracies due to parasitic capacitances and ensures proper impedance matching in the circuit.

The compensation resistor $R_{comp}$ is typically calculated as the parallel combination of the input resistor $R$ and the feedback resistor $Rf$:

$$R_{comp} = R1 \parallel Rf = \frac{R1 \times Rf}{R1 + Rf}$$

Substituting the given values:

$$R_{comp} = \frac{10 \, \text{k}\Omega \times 100 \, \text{k}\Omega}{10 \, \text{k}\Omega + 100 \, \text{k}\Omega}$$ $$R_{comp} = \frac{1,000 \, \text{k}\Omega^2}{110 \, \text{k}\Omega} \approx 9.09 \, \text{k}\Omega$$

Thus, the compensation resistor $R_{comp}$ is approximately

An operational amplifier (op-amp) integrator circuit is essential in analog signal processing applications such as waveform generation, analog computation, and filtering. In this post, we will walk through the design calculation of a practical op-amp integrator using the LM358 op-amp, with a specified integration time of 25 ms. Additionally, we will include a compensation resistor calculation to ensure the stability and accuracy of the circuit.

Design Summary and Calculations

We will base the design on the following given parameters and calculate the necessary components:

• Amplification Factor (A): Given as $A = 10$
• Input Resistor (R1): Given as $R1 = 10 \, \text{k}\Omega$
• Feedback Resistor (Rf): Calculated as $Rf = A \times R1 = 10 \times 10 \, \text{k}\Omega = 100 \, \text{k}\Omega$
• Input Frequency (f): Given as $f = 400 \, \text{Hz}$
• Break Frequency (fb): Chosen as $fb = \frac{f}{10} = \frac{400 \, \text{Hz}}{10} = 40 \, \text{Hz}$
• Feedback Capacitor (Cf): To be calculated.

Step 1: Calculate the Feedback Capacitor (Cf)

We know that the break frequency $fb$ for an op-amp integrator is given by the equation:

$$fb = \frac{1}{2\pi Rf Cf}$$

Rearranging the equation to solve for $Cf$:

$$Cf = \frac{1}{2\pi Rf fb}$$

Substitute the given values:

$$Cf = \frac{1}{2\pi \times 100 \, \text{k}\Omega \times 40 \, \text{Hz}}$$

Solving for $Cf$:

$$Cf \approx 39.8 \, \text{nF}$$

Thus, the feedback capacitor $Cf$ is approximately 40 nF.

Compensation Resistor (Rcomp)

In practical op-amp circuits, a compensation resistor $R_{comp}$ is often used to improve the stability and performance of the integrator. The compensation resistor helps account for the small inaccuracies due to parasitic capacitances and ensures proper impedance matching in the circuit.

The compensation resistor $R_{comp}$ is typically calculated as the parallel combination of the input resistor $R1$ and the feedback resistor $Rf$:

$$R_{comp} = R1 \parallel Rf = \frac{R1 \times Rf}{R1 + Rf}$$

Substituting the given values:

$$R_{comp} = \frac{10 \, \text{k}\Omega \times 100 \, \text{k}\Omega}{10 \, \text{k}\Omega + 100 \, \text{k}\Omega}$$$$R_{comp} = \frac{1,000 \, \text{k}\Omega^2}{110 \, \text{k}\Omega} \approx 9.09 \, \text{k}\Omega$$

Thus, the compensation resistor $R_{comp}$ is approximately 9.09 kΩ.

Conclusion

The practical op-amp integrator circuit designed with the LM358 requires the following components for a 25 ms integration time and a 400 Hz input frequency:

• Amplification Factor (A): 10
• Input Resistor (R1): 10 kΩ
• Feedback Resistor (Rf): 100 kΩ
• Feedback Capacitor (Cf): 39.8 nF
• Compensation Resistor (Rcomp): 9.09 kΩ

This design ensures that the integrator operates effectively at the specified frequency and integration time while maintaining stability through the use of the compensation resistor.

Circuit Diagram

The following shows the circuit diagram of the designed practical op-amp with 25ms integration time.

For a detailed, hands-on approach, refer to the Practical Op-Amp Integrator Design Guide and learn more about the LM358 Op-Amp Integrator test with practical insights from our LM358 Op-Amp Integrator Test. For in-depth knowledge on building an LM358 op-amp integrator circuit, check out the Design LM358 Op-Amp Integrator.

Final Notes:

• The choice of components, especially the capacitor and resistors, can affect the frequency response and stability of the integrator.
• If you are designing for other frequencies or integration times, simply adjust the values of $R1$, $Rf$, and $Cf$ based on the calculations provided.

This design serves as a reliable starting point for building a practical LM358 op-amp integrator circuit for real-world applications.

or standard 10

Conclusion

The practical op-amp integrator circuit designed with the LM358 requires the following components for a 25 ms integration time and a 400 Hz input frequency:

• Amplification Factor (A): 10
• Input Resistor (R1): 10 kΩ
• Feedback Resistor (Rf): 100 kΩ
• Feedback Capacitor (Cf): 39.8 nF
• Compensation Resistor (Rcomp): 9.09 kΩ

This design ensures that the integrator operates effectively at the specified frequency and integration time while maintaining stability through the use of the compensation resistor.

For a detailed, hands-on approach, refer to the Practical Op-Amp Integrator Design Guide and learn more about the LM358 Op-Amp Integrator test with practical insights from our LM358 Op-Amp Integrator Test. For in-depth knowledge on building an LM358 op-amp integrator circuit, check out the Design LM358 Op-Amp Integrator.

Final Notes:

• The choice of components, especially the capacitor and resistors, can affect the frequency response and stability of the integrator.
• If you are designing for other frequencies or integration times, simply adjust the values of $R1$, $Rf$, and $Cf$based on the calculations provided.

This design serves as a reliable starting point for building a practical LM358 op-amp integrator circuit for real-world applications.