V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(2\omega) B \text{cos}(2\omega t + \theta(2\omega)) given that H(\omega)e^{j\theta(\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))}

V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(\omega) B \text{cos}(2\omega t + \theta(\omega)) given that H(\omega)e^{j\theta(\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))}

V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(2\omega) B \text{cos}(2\omega t + \theta(2\omega)) given that H(\omega)e^{j\theta(\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))}

V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(\omega) B \text{cos}(2\omega t + \theta(\omega)) given that H(\omega)e^{j\theta(\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))}

V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(2\omega) B \text{cos}(2\omega t + \theta(2\omega)) given that H(\omega)e^{j\theta(\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))}