Transfer function of amplifier

operational-amplifiertransfer function


I would like to find transfer function between input signal \$U_1\$ and output signal \$U_2\$. So, I know how to find the transfer function of each op-amp, for example,

1 transfer function: $$\frac{v_o}{v_i} = -\frac{R_3}{R_1}\frac{1}{1+R_3C_3 s}$$
2 transfer function: $$\frac{v_o}{v_i} = -\frac{1}{C_4 s R_4}$$
3 transfer function: $$\frac{v_o}{v_i} = \frac{R_2}{2R}$$

Is that correct way to find $$G(s)=\frac{U_2}{U_1}$$? How can I do it?

Best Answer

For my opinion, the simplest solution makes use of the classical feedback formula from H. Black:

$$\frac{V_2}{V_1}=\frac{H(s)}{1-LG}$$

with:

  • \$H(s)=H_1(s)H_2(s)\$=Forward transfer function for an open loop (in our case: \$H_1=V_3/V_1\$ for \$R_2\$>>infinite and \$H_2=V_2/V_3\$.)
  • Loop gain \$LG\$=Product of all three transfer functions within the loop (with \$V_1=0\$ or \$R_1\$>>infinite).

Note that \$H(s)\$ is positive and the loop gain \$LG\$ must be negative (three inverting stages in series). The transfer functions of the three blocks are basic (inverting lowpass, inverting integrator, inverting amplifier).