Answer Happy

+15V include National Semiconductor Models.lib U1: use opamp2, set SpiceModel and Value to LM741/NS .ac dec 1000 10 100k Using LTspice (linear.com) R3 C3 + V1 15V 22pF VO 1909.26 C1 C4 C2 V2 -15V 22uF 0.1 F 0.10F -15V R4 + +15V 53.05 2 U1 6 vi AC 1 U1 is a LM741 3 0 + VO -15V LM741/NS Figure 1. Active Bandpass Filter (values give a center frequency of fo = 5kHz and are for illustrative purposes only)
1. Conduct a theoretical analysis of the circuit response to the fo square wave. Proceed as follows. Express the input waveform as a Fourier series. Use the first three non-zero terms for your analysis, i.e. vi(t) = * (sin(2nfot) + sin(213fot) + Śsin(215fot)]. Find the circuit response to each of these three sinusoids by using your experimental gain and phase plots, i.e. 1T (jw) and ZT(jw) at fo, 3fo, and 5f0. Denote the gains as T1, T2, and Tz, respectively, and the angles as @1, O2, and 03, respectively. Thus the output voltage is approximately [T, sin(2nfot +0,) + Tzīsin(213fot + 02) + Təşsin(215fot+03)). vo(t) Plot both equations for vi(t) and v. (t) using a computer tool of your choice. Compare the results to those observed in the laboratory. Also plot each individual sinusoid in the equations for vi(t) and v. (t) to show the relative contribution of each to the waveforms. 2. Compare and contrast the active bandpass filter with the passive bandpass filter of the previous laboratory. What are the chief advantages and drawbacks of each circuit? Be specific and justify your conclusions based on engineering science.