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Questions and Answers

Why can't the voltage drop across the resistor and capacitor be measured simultaneously?

  • The oscilloscope has common ground among all channels. (correct)
  • It is unsafe to connect two probes at once.
  • The oscilloscope cannot display multiple waveforms at once.
  • The measurement would interfere with the circuit operation.

    • What should be the adjustment range for the 'Time/div' scale on the DSO when measuring a square waveform?

  • 1 to 2 cycles of the input signal should be displayed.
  • 5 to 6 cycles of the input signal should be displayed.
  • The time scale does not need to be adjusted.
  • 2 to 4 cycles of the input signal should be displayed. (correct)

    • What is the consequence of changing the trigger setting after synchronizing the square wave on the DSO screen?

  • It will improve the accuracy of the measurement.
  • The output waveforms will be amplified.
  • It will cause the synchronization to be lost. (correct)
  • It will automatically reset the DSO to factory settings.

    • Which method should be used to observe the output waveforms across the resistor and capacitor?

    <p>Use MATH function with Channel-1 and Channel-2.</p> Signup and view all the answers

    What is a precaution to take before applying the square waveform to the circuit?

    <p>Adjust the square waveform values using the DSO.</p> Signup and view all the answers

    What does the variable Vavg represent in the Fourier series of a square wave signal?

    <p>The average value of the waveform</p> Signup and view all the answers

    Which harmonic components are included in the calculation of the Fourier series for the square wave signal?

    <p>Only odd harmonics</p> Signup and view all the answers

    What is the formula for the peak value of the nth harmonic component (an)?

    <p>$\frac{2V_{pp}}{n\pi}$</p> Signup and view all the answers

    For what type of signal does the formula for the RMS value of 'nth' harmonic components apply?

    <p>For periodic signals</p> Signup and view all the answers

    What is the default output of the low-pass filter when there is no input signal?

    <p>Zero voltage</p> Signup and view all the answers

    In a low-pass RC filter, what role does the capacitor (C) play?

    <p>It smooths out rapid changes in voltage</p> Signup and view all the answers

    Which mathematical representation defines the frequency of the square wave in the Fourier series?

    <p>$\omega_0$</p> Signup and view all the answers

    Which component is not part of the block diagram of a low-pass filter circuit?

    <p>Inductor</p> Signup and view all the answers

    What is the general trend in the voltage across the capacitor (Vc) as the frequency (f) increases for a low-pass filter?

    <p>Vc decreases</p> Signup and view all the answers

    Which of the following best describes the attenuation factor for a low-pass filter with a square wave signal at a frequency of 11fs?

    <p>The attenuation factor is reduced from its previous values</p> Signup and view all the answers

    What is the relationship between the peak voltage (Vin(p)) and the RMS voltage (Vin(RMS)) as stated in the content?

    <p>Vin(RMS) = Vin(p)/√2</p> Signup and view all the answers

    For a sine wave signal, what happens to the capacitor voltage (Vc) as the input supply voltage (Vin) increases?

    <p>Vc increases proportionally</p> Signup and view all the answers

    In a low-pass filter, what is the significance of the attenuation factor noted as Vc/Vin?

    <p>It quantifies how much signal is reduced at the output</p> Signup and view all the answers

    What would be expected if a low-pass filter is tested with very high frequencies beyond the cut-off?

    <p>The output voltage will be significantly reduced</p> Signup and view all the answers

    What is the expected behavior of a low-pass filter when tested with a square wave signal at lower frequencies?

    <p>The filter passes the majority of the signal</p> Signup and view all the answers

    Which frequency has the highest attenuation factor based on the given observations for both square and sine wave signals?

    <p>11fs</p> Signup and view all the answers

    What is the transfer function of the R-C circuit?

    <p>$\frac{(1 + sCR)}{R + sC}$</p> Signup and view all the answers

    How is the cut-off frequency ($f_c$) for an R-C circuit calculated?

    <p>$\frac{1}{2\pi RC}$</p> Signup and view all the answers

    In the LC-R circuit, what is the effect of a very small inductance series resistance ($r$)?

    <p>It has no significant effect on the circuit.</p> Signup and view all the answers

    What type of filtering action does the voltage across the capacitor in the R-C circuit provide?

    <p>Low-pass filtering action</p> Signup and view all the answers

    What is the characteristic of the voltage across the resistor (R) in an R-C circuit?

    <p>It exhibits high-pass filtering action.</p> Signup and view all the answers

    Which mathematical expression describes the transfer function of the LC-R circuit?

    <p>$\frac{R}{(LCR)s^2 + (rRC + L)s + (R + r)}$</p> Signup and view all the answers

    What is necessary to observe the harmonic components in an LC-R circuit setup?

    <p>Use of a DSO and cursor settings</p> Signup and view all the answers

    Which scenario is most likely to cause deviation in computed and measured values of harmonic components?

    <p>Neglecting series resistance effects</p> Signup and view all the answers

    What is the range of resistance values specified for the parameters in the setup?

    <p>1.0 kΩ ~ 5.0 kΩ</p> Signup and view all the answers

    Which of the following is the frequency at which the square wave signal generator operates?

    <p>1000 Hz</p> Signup and view all the answers

    What is the peak-to-peak voltage specified for the square wave generator?

    <p>10 Volts</p> Signup and view all the answers

    What type of waveform is produced by the signal generator?

    <p>Square wave</p> Signup and view all the answers

    What is the capacitance range specified in the parameters?

    <p>100 nF ~ 220 nF</p> Signup and view all the answers

    What is the duty ratio of the square wave signal?

    <p>50%</p> Signup and view all the answers

    What is the relationship between frequency and the period of a square wave signal?

    <p>Period = 1/Frequency</p> Signup and view all the answers

    Which frequency is NOT listed in the parameters for the signal generator?

    <p>20 kHz</p> Signup and view all the answers

    Study Notes

    Low-Pass Filter Circuit

    • The circuit consists of a resistor (R), capacitor (C), and a voltage source (Vin).
    • The transfer function for the RC circuit is:
      • v0(s) / vin(s) = 1 / (1 + sCR)
    • The cut-off frequency is 1/(2πRC).
    • Measuring simultaneously the voltage drop across both R and C is not possible, as the oscilloscope uses a common ground for all channels.
    • The voltage across the capacitor (Vc) gives the low-pass filter response.
    • The voltage across the resistor (Vr) gives a high-pass filter response.

    Test-2: LC-R Low-pass Filter Circuit

    • This circuit adds an inductor (L) in series with the resistor in the previously described circuit.
    • The transfer function for the LC-R circuit is:
      • v0(s) /vin(s) = (R) / ((LCR)s^2 + (rRC + L)s +(R + r))
    • The inductance series resistance is assumed to be negligible ( r ≈ 0).
    • To analyze the circuit, you need to use the MATH feature of the oscilloscope.

    Experiment Setup for Analyzing the Filter Circuit

    • Use various frequencies for the square wave input signal.
    • Vary the values for the resistor (R) and capacitor (C) and record values.
    • Use different combinations of R and C to study and compare the filter responses.
    • Record experimental observations for both square and sine wave input signals and compare them to simulated results.
    • Compute the theoretical values of the signal's harmonic components using the formulas in the text.
    • Observe the resulting harmonic components with an oscilloscope set on the “MATH” mode.

    Harmonic Components

    • The harmonic components are various frequencies that comprise the square wave signal.
    • The RMS value of the nth harmonic component is An = (an/2) ^ 0.5

    Important Considerations

    • When setting up the experiment, adjust the DSO's time scale so that 2-4 cycles of the input signal are shown on the screen.
    • Stabilize and synchronize the square wave on the DSO screen before changing the time scale.
    • Avoid connecting two oscilloscope probes to measure voltage drop across R and C simultaneously. Use the MATH functionality instead.
    • The input square wave should be measured using the DSO and verified that it is within the desired parameters before applying to the circuit.

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    Experiment 6: RC, LC-R Low-pass Filters PDF

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