Q2. Find the output waveform
If the input to the op-amp circuit below is A ext{sin}(\omega t) + B ext{cos}(2 \omega t) where A and B are constants, and \omega is the angular frequency, what is the output waveform? Assume that the op-amp input impedance is infinite but it has a frequency dependent differential gain given by \frac{G\omega_0}{(\omega_0+j \omega)} , where G is a constant and \omega_0 is a constant.

Question

Q2. Find the output waveform 
 If the input to the op-amp circuit below is   A	ext{sin}(\omega t) + B	ext{cos}(2 \omega t)  where   A  and   B  are constants, and   \omega  is the angular frequency, what is the output waveform? Assume that the op-amp input impedance is infinite but it has a frequency dependent differential gain given by   \frac{G\omega_0}{(\omega_0+j \omega)}  , where   G  is a constant and   \omega_0  is a constant.

Answer

V_{out}(t) = H(\omega) A	ext{sin}(\omega t + 	heta(\omega) )+ H(2\omega) B 	ext{cos}(2\omega t + 	heta(2\omega))  given that    H(\omega)e^{j	heta(\omega)} = -\frac{GR_2\omega_0}{R_2(j\omega + (1+G)\omega_0) + R_1(j\omega + \omega_0 + j\omega C_1 R_2 (j \omega + (1+G)\omega_0))}

Answer

V_{out}(t) = H(\omega) A	ext{sin}(\omega t + 	heta(\omega) )+ H(\omega) B 	ext{cos}(2\omega t + 	heta(\omega))  given that    H(\omega)e^{j	heta(\omega)} = \frac{GR_2\omega_0}{R_2(j\omega + (1+G)\omega_0) + R_1(j\omega + \omega_0 + j\omega C_1 R_2 (j \omega + (1+G)\omega_0))}

Answer

V_{out}(t) = H(\omega) A	ext{sin}(\omega t + 	heta(\omega) )+ H(2\omega) B 	ext{cos}(2\omega t + 	heta(2\omega))  given that    H(\omega)e^{j	heta(\omega)} = -\frac{GR_1\omega_0}{R_2(j\omega + (1+G)\omega_0) + R_1(j\omega + \omega_0 + j\omega C_1 R_2 (j \omega + (1+G)\omega_0))}

Answer

V_{out}(t) = H(\omega) A	ext{sin}(\omega t + 	heta(\omega) )+ H(\omega) B 	ext{cos}(2\omega t + 	heta(\omega))  given that    H(\omega)e^{j	heta(\omega)} = \frac{GR_1\omega_0}{R_2(j\omega + (1+G)\omega_0) + R_1(j\omega + \omega_0 + j\omega C_1 R_2 (j \omega + (1+G)\omega_0))}

Answer

V_{out}(t) = H(\omega) A	ext{sin}(\omega t + 	heta(\omega) )+ H(2\omega) B 	ext{cos}(2\omega t + 	heta(2\omega))  given that    H(\omega)e^{j	heta(\omega)} = -\frac{GR_1R_2\omega_0}{R_2(j\omega + (1+G)\omega_0) + R_1(j\omega + \omega_0 + j\omega C_1 R_2 (j \omega + (1+G)\omega_0))}

Crowdly

Q2. Find the output waveform If the input to the op-amp circuit below is A\t...

Want instant access to all verified answers on learning.monash.edu?