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Questions and Answers
Why can't the voltage drop across the resistor and capacitor be measured simultaneously?
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?
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?
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?
Which method should be used to observe the output waveforms across the resistor and capacitor?
What is a precaution to take before applying the square waveform to the circuit?
What is a precaution to take before applying the square waveform to the circuit?
What does the variable Vavg represent in the Fourier series of a square wave signal?
What does the variable Vavg represent in the Fourier series of a square wave signal?
Which harmonic components are included in the calculation of the Fourier series for the square wave signal?
Which harmonic components are included in the calculation of the Fourier series for the square wave signal?
What is the formula for the peak value of the nth harmonic component (an)?
What is the formula for the peak value of the nth harmonic component (an)?
For what type of signal does the formula for the RMS value of 'nth' harmonic components apply?
For what type of signal does the formula for the RMS value of 'nth' harmonic components apply?
What is the default output of the low-pass filter when there is no input signal?
What is the default output of the low-pass filter when there is no input signal?
In a low-pass RC filter, what role does the capacitor (C) play?
In a low-pass RC filter, what role does the capacitor (C) play?
Which mathematical representation defines the frequency of the square wave in the Fourier series?
Which mathematical representation defines the frequency of the square wave in the Fourier series?
Which component is not part of the block diagram of a low-pass filter circuit?
Which component is not part of the block diagram of a low-pass filter circuit?
What is the general trend in the voltage across the capacitor (Vc) as the frequency (f) increases for a low-pass filter?
What is the general trend in the voltage across the capacitor (Vc) as the frequency (f) increases for a low-pass filter?
Which of the following best describes the attenuation factor for a low-pass filter with a square wave signal at a frequency of 11fs?
Which of the following best describes the attenuation factor for a low-pass filter with a square wave signal at a frequency of 11fs?
What is the relationship between the peak voltage (Vin(p)) and the RMS voltage (Vin(RMS)) as stated in the content?
What is the relationship between the peak voltage (Vin(p)) and the RMS voltage (Vin(RMS)) as stated in the content?
For a sine wave signal, what happens to the capacitor voltage (Vc) as the input supply voltage (Vin) increases?
For a sine wave signal, what happens to the capacitor voltage (Vc) as the input supply voltage (Vin) increases?
In a low-pass filter, what is the significance of the attenuation factor noted as Vc/Vin?
In a low-pass filter, what is the significance of the attenuation factor noted as Vc/Vin?
What would be expected if a low-pass filter is tested with very high frequencies beyond the cut-off?
What would be expected if a low-pass filter is tested with very high frequencies beyond the cut-off?
What is the expected behavior of a low-pass filter when tested with a square wave signal at lower frequencies?
What is the expected behavior of a low-pass filter when tested with a square wave signal at lower frequencies?
Which frequency has the highest attenuation factor based on the given observations for both square and sine wave signals?
Which frequency has the highest attenuation factor based on the given observations for both square and sine wave signals?
What is the transfer function of the R-C circuit?
What is the transfer function of the R-C circuit?
How is the cut-off frequency ($f_c$) for an R-C circuit calculated?
How is the cut-off frequency ($f_c$) for an R-C circuit calculated?
In the LC-R circuit, what is the effect of a very small inductance series resistance ($r$)?
In the LC-R circuit, what is the effect of a very small inductance series resistance ($r$)?
What type of filtering action does the voltage across the capacitor in the R-C circuit provide?
What type of filtering action does the voltage across the capacitor in the R-C circuit provide?
What is the characteristic of the voltage across the resistor (R) in an R-C circuit?
What is the characteristic of the voltage across the resistor (R) in an R-C circuit?
Which mathematical expression describes the transfer function of the LC-R circuit?
Which mathematical expression describes the transfer function of the LC-R circuit?
What is necessary to observe the harmonic components in an LC-R circuit setup?
What is necessary to observe the harmonic components in an LC-R circuit setup?
Which scenario is most likely to cause deviation in computed and measured values of harmonic components?
Which scenario is most likely to cause deviation in computed and measured values of harmonic components?
What is the range of resistance values specified for the parameters in the setup?
What is the range of resistance values specified for the parameters in the setup?
Which of the following is the frequency at which the square wave signal generator operates?
Which of the following is the frequency at which the square wave signal generator operates?
What is the peak-to-peak voltage specified for the square wave generator?
What is the peak-to-peak voltage specified for the square wave generator?
What type of waveform is produced by the signal generator?
What type of waveform is produced by the signal generator?
What is the capacitance range specified in the parameters?
What is the capacitance range specified in the parameters?
What is the duty ratio of the square wave signal?
What is the duty ratio of the square wave signal?
What is the relationship between frequency and the period of a square wave signal?
What is the relationship between frequency and the period of a square wave signal?
Which frequency is NOT listed in the parameters for the signal generator?
Which frequency is NOT listed in the parameters for the signal generator?
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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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