I am analyzing the integrator circuit and I can't get from which equation can I get the frequency where there is the intersection with x axis - 1/C*R1 ?


source  enter image description here

  • 1
    \$\begingroup\$ If \$2\pi f C R_2\$ is way larger than 1, you can take the 1 out of the denominator of the AC voltage gain expression. 0dB happens when gain is 1, so you end up (remembering that you're concerned with absolute values) with \$\frac{R_2}{R_1} \frac{1}{2 \pi f C R_2} = 1\$. Does this help? \$\endgroup\$ – TimWescott Sep 8 '19 at 19:41
  • 1
    \$\begingroup\$ Just a comment -- there are a number of inaccuracies in that. It looks like it's oversimplified, but poorly. You may want to find a different book to work from. \$\endgroup\$ – TimWescott Sep 8 '19 at 19:42
  • \$\begingroup\$ thanks a lot! s \$\endgroup\$ – tairit Sep 8 '19 at 19:43
  • \$\begingroup\$ This seems to be homework, but I think I understand the confusion. It depends on the type of frequency being used (angular frequency or regular frequency). The graph uses different type than the equations. \$\endgroup\$ – Huisman Sep 8 '19 at 19:51

Well, first of all we can look at the wiki-page of 'Operational amplifier applications' and look under 'Inverting amplifier', to find that your TF is given by:


In the complex analysis of this circuit we can write:


So, we get for the amplitude:


In dB's we get:

$$\left|\underline{\mathcal{H}}\left(\text{j}\omega\right)\right|_\text{dB}=20\log_{10}\left(\frac{\text{R}_2}{\text{R}_1}\cdot\frac{1}{\sqrt{1+\left(\text{CR}_2\omega\right)^2}}\right)=$$ $$20\log_{10}\left(\frac{\text{R}_2}{\text{R}_1}\right)-10\log_{10}\left(1+\left(\text{CR}_2\omega\right)^2\right)\tag4$$

Now, solve:



In order to provide feedback also at very low frequencies, they put \$\text{R}_2\$ in parallel over the capacitor. But they did not include it in the formula's, what they did:

  • For the amplitude: $$\left|\underline{\mathcal{H}}\left(\text{j}\omega\right)\right|_{\text{dB}\space\text{&}\space\text{R}_2\to\infty}=-20\log_{10}\left(\omega\text{CR}_1\right)\tag6$$
  • For the zero-crossing: $$\omega_{\text{R}_2\to\infty}=\lim_{\text{R}_2\to\infty}\frac{1}{\text{CR}_2}\cdot\sqrt{\left(\frac{\text{R}_2}{\text{R}_1}\right)^2-1}=\frac{1}{\text{CR}_1}\tag7$$
| improve this answer | |
  • \$\begingroup\$ I was interested to find how to calculate 1/C*R1 \$\endgroup\$ – tairit Sep 8 '19 at 23:04
  • \$\begingroup\$ @tairebit well according to my answer that is not the correct formula. \$\endgroup\$ – Jan Sep 8 '19 at 23:13
  • 1
    \$\begingroup\$ @tairebit in the calculation they did in your picture, they let \$\text{R}_2\to\infty\$. \$\endgroup\$ – Jan Sep 9 '19 at 18:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.