I have no issue finding a and b. However to find K, I would like to know if I'm taking the right approach. I found $$a = 1/24$$ and $$b = 4$$
So how I'm planning on calculating K is as followed:
$$2k/a = 8$$
since $$a = 1/24$$ then
$$k = 1/6$$
Am I right? if not, please explain why this approach is wrong.
Thank you.
Bode plot finding K
bode plottransfer function
Related Solutions
If you wish to redraw the circuit without the op-amp, try something like this:
simulate this circuit – Schematic created using CircuitLab
See the difference?
Any complex number \$Z\$ can be represented in rectangular coordinates or polar coordinates $$Z = x + jy = A\angle\phi$$ where, \$A = \sqrt{x^2+y^2}\$ and \$\phi = atan2(y,x)\$ where, \$atan2(y,x)\$ is defined as
As you can see your conversion formula is valid only if \$x>0\$.
Hence \$\phi\$ for \$a+jb\$ and \$\phi\$ for \$-a-jb\$ will be different.
I think this solves your problem.
Best Answer
Your calculations to find a and b looks good to me but I don't agree on K.
You are given only the "unity frequency" or better "unity pulsation" (hope that's correct in English). You should take your transfer function and approximate it appropriately, then fill in the informations you have, i.e. at pulsation 8 gain is 1. The TF you are looking for is the TF stripped of all its poles and zeroes except the "origin pole" (again, hope that's correct), i.e.: $$G(s)=\frac{2K}{s}$$ that's because you are assuming \$s\ll s_l\$ where \$s_l\$ is the lowest singularity. Solving the previou equation for k: $$K=\frac{s\cdot G(s)}{2}=\frac{8\cdot 1}{2} = 4$$ that's about 12dB.