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    Lab 8 Experiment Report

    Uploaded by

    Caleb Swisher
    This lab report summarizes Caleb Swisher's work on basic filters in Lab 8. [1] A low pass filter was built and tested, with a theoretical cutoff frequency of 15.915 kHz but a measured cutoff of 14 kHz due to non-ideal components. [2] A high pass filter was designed, built, and tested with a theoretical cutoff of 48.228 kHz matching closely with measured results. [3] A band pass filter was designed and tested to have cutoff frequencies of 34 kHz and 280 Hz, with some variation likely due to non-ideal components and signal interactions within the circuit.

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    Lab 8 Experiment Report

    Uploaded by

    Caleb Swisher
    6 views8 pages
    This lab report summarizes Caleb Swisher's work on basic filters in Lab 8. [1] A low pass filter was built and tested, with a theoretical cutoff frequency of 15.915 kHz but a measured cutoff of 14 kHz due to non-ideal components. [2] A high pass filter was designed, built, and tested with a theoretical cutoff of 48.228 kHz matching closely with measured results. [3] A band pass filter was designed and tested to have cutoff frequencies of 34 kHz and 280 Hz, with some variation likely due to non-ideal components and signal interactions within the circuit.

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    This lab report summarizes Caleb Swisher's work on basic filters in Lab 8. [1] A low pass filter was built and tested, with a theoretical cutoff frequency of 15.915 kHz but a measured cutoff of 14 kHz due to non-ideal components. [2] A high pass filter was designed, built, and tested with a theoretical cutoff of 48.228 kHz matching closely with measured results. [3] A band pass filter was designed and tested to have cutoff frequencies of 34 kHz and 280 Hz, with some variation likely due to non-ideal components and signal interactions within the circuit.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    6 views8 pages

    Lab 8 Experiment Report

    Uploaded by

    Caleb Swisher
    This lab report summarizes Caleb Swisher's work on basic filters in Lab 8. [1] A low pass filter was built and tested, with a theoretical cutoff frequency of 15.915 kHz but a measured cutoff of 14 kHz due to non-ideal components. [2] A high pass filter was designed, built, and tested with a theoretical cutoff of 48.228 kHz matching closely with measured results. [3] A band pass filter was designed and tested to have cutoff frequencies of 34 kHz and 280 Hz, with some variation likely due to non-ideal components and signal interactions within the circuit.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 8

    Lab 8: Basic Filters

    Lab Report
    Name: Caleb Swisher Date: 10/28/23

    Part 1: Low Pass Filter

    Question: What is the theoretically calculated cutoff frequency for this filter (show
    calculations)?

    1/(2piRC) = Cutoff Frequency

    1/(2pi * 10,000 * .000000001) = 15915.49 Hz or 15.915 kHz

    Table 1 – Input and output amplitudes of the RC low pass filter at different frequencies
    along with the calculated gain in decibels.

    Frequency vin Peak-to-Peak Amplitude vout Peak-to-Peak Amplitude Gain (dB)


    10 Hz 1V 1V 0dB
    100Hz 1V 1V 0dB
    500Hz 1V 1V 0dB
    1kHz 1V 1V 0dB
    5kHz 1V 1V 0dB
    10kHz 985mV 782mV -2dB
    15kHz 979mV 650mV -3.5dB
    17kHz 980mV 600mV -4.2dB
    20kHz 941mV 501mV -5.5dB
    50kHz 995mV 258mV -11.7dB
    100kHz 998mV 132mV -17.57dB
    200kHz 942mV 65mV -23.2dB

    Question: What is the measured cutoff frequency of this filter? How does it compare to
    the theoretically calculated value? Please explain any variations.

    1
    The measured cutoff-frequency would be around 14kHz since that's where a 3dB rolloff would
    most likely occur. This is lower than the cutoff-frequency we calculated due to the fact that
    we're using a non-ideal voltage source that provides less voltage than we expected, altering the
    Vin to Vout ratio and ultimately altering our final measurement.

    Paste the measured Bode plot for the circuit below.

    Paste the screenshot of the oscilloscope output recording the noisy input and filtered
    output.

    2
    Sorry for the poor quality here!

    Question: How does the noise at the output compare to the noise on the input signal?
    Why are they the same/different?

    The output signal has much less noise compared to the input signal. They are different due to
    our circuit filtering frequencies around 14 kHz, improving the "quality" of the signal.

    Question: Paste the screenshot of the 10kHz waveforms, and show your calculations for
    gain/phase delay at 10kHz. Be sure to include the oscilloscope cursors in the figure.

    3
    Gain Reduction:

    20Log(782mV/985mV) = -3.5dB

    Delay Difference:

    -35.456nS - (-23.810nS) = -11.646 nano Seconds

    Part 2: High Pass Filter

    Question: What is the theoretically calculated cutoff frequency for this filter (show
    calculations)?

    Cutoff Frequency = R/(2piL)

    1000/(2pi*3.3mH) = 48.228 kHz

    Part 2b: Network analyzer

    ⦁ Include a screenshot of the measured AC response of your filter.

    4
    ⦁ Note the f3dB frequency and phase

    Cutoff Frequency = 51.12 kHz

    Phase = -316.45 Degrees

    Question: How do the measured values compare to the theoretical and simulated values?
    Why are they the same/different? Please explain the cause of any variations.

    Our measured values are slightly above our calculated values, which is most likely due to our
    non-ideal resistor having a slightly higher impedence, resulting in a greater measured cutoff
    frequency. This difference is within an acceptable range.

    5
    Part 3: Design of a Band Pass Filter

    Question: What are your two cutoff frequencies?

    fL = 34kHz fH = 280Hz

    Question: What are your high pass R and C values?

    RHP = 568.41 Ω CHP = .000001 F or 1 micro F

    Question: What are your low pass R and C values?

    RHP = 4681.02 Ω CHP = .000000001F or 1 nano F

    Question: Show the calculation of the resistor values from the cutoff frequencies.

    1/(2piRC) = Cutoff Frequency (Fc)

    1/(2piCFc) = R

    1/(2pi*.00001*280) = 568.41 Ohms

    1/(2pi*.000000001*34000) = 4681.02 Ohms

    ⦁ Include a screenshot of the measured AC response of your filter.

    ⦁ Note the f3dB frequencies and phases

    6
    Cutoff Frequency L = 33.52 kHz

    Cutoff Frequency R = 316.85 kHz

    Phase = -320.36 Degrees

    Question: How do the measured values compare to the theoretical and simulated values?
    Why are they the same/different? Please explain any variations. (Hint: Think about the
    discharge paths that the two capacitors have and the assumptions made during the
    resistance calculations.)

    7
    Our measured cutoff frequencies are relatively close to the values given, but they may be
    slightly different due to non-ideal resistors as was the case before, or the fact that the second
    capacitor in the circuit is discharging into the first capacitor, essentially going through the first
    filter again, possibly effecting our measurements

    Question: We characterize filters by their 3dB cutoff frequency which is where the power
    is halved. This occurs when the voltage is decreased to a factor of 0.707 times the input
    voltage. This comes from the fact that voltage and power gain have two different decibel
    definitions:

    Why do you think there is this factor of 2 difference between the 2 formulae? (hint: Think
    about the relationship between voltage and power and how exponents are handled in the
    argument of a logarithm.)

    P = V^2/R

    Log(x^2) = 2Log(x)

    Ap = 10Log((V^2/Rout)(R/V^2in))

    The factor of 2 is due to the V^2 in the logorithm that then gets pushed out to the front due to
    log rules

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