# Laplace transform and analysis in s-domain

Laplace Transform and Analysis in S-Domain

This week’s lab is based on the application of circuit analysis techniques to a capacitive circuit with Multisim. You will learn to utilize Multisim to perform the mesh analysis.

1.    Design a Wein bridge Oscillator in Figure 15.39 in Multisim to generate a sinusoidal signal at frequency of 300Hz. Consider a capacitor of 1uF, resistor R = 5950Ω, R1 = 3Ω, Rf = 6.05Ω for the oscillator circuit.

a.    Determine output voltage ‘Vo’ and run the simulation to plot the output of the oscillations at frequency of 300 Hz using an oscilloscope.

b.    Increase the frequency to 500Hz, 800Hz and 1000Hz and plot the output of the oscillator at these multiple frequencies.

c.    Take the screen capture of the oscilloscope readings for all the frequencies.

a.    What is the requirement to generate oscillation in the circuit? Is the circuit stable or unstable?

b.    What do you observe in the oscillations when the frequency is increased?

c.    With increased frequency, did you observe the oscillations? If not what did you adjust to observe the oscillations?

d.    Explore different practical applications of oscillator circuits and explain.

Fourier Series

Analyze the circuit and determine the output voltage ‘Vout’ of an Op Amp circuit, use a frequency of 150Hz.

1.    Construct Figure 18.15 in Multisim and perform the Fourier analysis.

a.    Run simulation to measure the frequency and the voltage gain of the amplifier.

b.    Change the input voltage magnitude to the values from the table and run the Fourier analysis again.

c.    Record the frequencies visible in the frequency spectrum in the table.

d.    Take the screen capture for the measurements for ‘Vout’.

 Vin Calculated ‘Vout’ (pk –pk) Measured ‘Vout’ (pk –pk) Identified frequencies in the spectrum 1V 1.5V 2V 3V

a.    Explain the effect of input voltage on the output voltage of the Op Amp.

b.    Express the voltage gain of an amplifier in terms of R1 and R2 and then compute it.

c.    From your measurements, what happens to the output when the magnitude of input voltage is increased?

d.    What is the effect of input voltage on the frequency spectrum? Explain with the help of measurement results and screenshots.