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Lab 4 - Passive Filters

Objective

  1. Construct passive low-pass, high-pass, and band-pass filters with resistor, capacitor, and inductor.
  2. Find the gain, phase, cut-off frequency and the central frequency of the filters.
  3. Observe the difference between the OrCAD-simulated bode diagram and the plot generated by actual experimental data.
  4. Observe the changes in the output waveforms on the oscilloscope as we change the frequency.

Passive Filters

Low-Pass Filter

Figure31

High-Pass Filter

Figure32

Band-Pass Filter

Figure33

Equipment

Simulation

  • Cadence OrCAD for simulation

Real-World Measurement

  • Breadboard
  • Circuit Components from the schematics
  • Oscilloscope
  • Power Supply
  • Signal Generator

OrCAD Simulation

Figure34

High and Low-Pass Filter

|H(jω)| φ (Degrees)
Low-Pass Filter 0.708 -45.1
High-Pass Filter 0.708 44.99

Band-Pass Filter

Frequency |H(jω)| φ (Degrees)
$\omega_0$ 1 0
$\omega_{c1}$ $\frac{1}{\sqrt{2}} ≈ 0.707$ 45
$\omega_{c2}$ $\frac{1}{\sqrt{2}} ≈ 0.707$ -45

Low-Pass Filter Bode Plot

Figure35

High-Pass Filter Bode Plot

Figure36

Band-Pass Filter Bode Plot

Figure37

Real-World Measurement

  • Ain = peak to peak value of the input voltage
  • Aout = peak to peak value of the output voltage
  • $|H(j\omega)|$ = $\frac{A_{out}}{A_{in}}$
  • $|H(j\omega)|(dB) =20log(|H(j\omega)|)$
  • td = Channel 1 (Ain) Time - Channel 2 (Aout) Time
  • Degrees = td * Frequency (Hz) * 360 (Degrees)

Low-Pass Filter

Figure38

Frequency (Hz) Aout (Vpp) Ain (Vpp) |H(jω)| |H(jω)| (dB) td(s) φ (Degrees)
10 2.05 2.07 0.990 -0.08 -1.08E-03 -3.89
50 1.95 2.03 0.961 -0.35 -9.98E-04 -17.96
100 1.67 1.99 0.839 -1.52 -9.00E-04 -32.40
160 1.38 1.95 0.708 -3.00 -7.80E-04 -44.93
200 1.20 1.95 0.615 -4.22 -7.12E-04 -51.26
400 0.70 1.91 0.366 -8.72 -4.60E-04 -66.24
800 0.40 1.87 0.214 -13.40 -2.60E-04 -74.88
1600 0.18 1.87 0.098 -20.19 -1.33E-04 -76.61

Figure39 Figure40

High-Pass Filter

Figure41

Frequency (Hz) Aout (Vpp) Ain (Vpp) |H(jω)| |H(jω)| (dB) td(s) φ (Degrees)
10 0.127 2.05 0.062 -24.16 2.38E-02 85.68
50 0.599 2.03 0.295 -10.60 4.04E-03 72.72
100 1.05 1.99 0.528 -5.55 1.60E-03 57.60
160 1.37 1.95 0.703 -3.07 7.80E-04 44.93
200 1.51 1.95 0.774 -2.22 5.40E-04 38.88
400 1.73 1.89 0.915 -0.77 1.52E-04 21.89
800 1.83 1.87 0.979 -0.19 3.92E-05 11.29
1600 1.87 1.87 1.000 0.00 9.60E-06 5.53

Figure42 Figure43

Band-Pass Filter

Figure44

Frequency (KHz) Aout (Vpp) Ain (Vpp) |H(jω)| |H(jω)| (dB) td(s) φ (Degrees)
1 1.05 2.03 0.517 -5.73 1.58E-04 56.88
1.6 1.43 2.01 0.711 -2.96 7.60E-05 43.78
2.5 1.67 2.05 0.815 -1.78 3.70E-05 33.30
5 1.89 2.01 0.940 -0.53 9.20E-06 16.56
16 1.97 1.95 1.010 0.09 0.00E+00 0.00
40 1.93 1.95 0.990 -0.09 8.20E-07 -11.81
100 1.73 1.97 0.878 -1.13 9.20E-07 -33.12
160 1.47 1.97 0.746 -2.54 8.30E-07 -47.81
200 1.31 1.97 0.665 -3.54 7.90E-07 -56.88
300 0.98 1.99 0.492 -6.15 6.70E-07 -72.36

Figure45 Figure46

Low-Pass Filter at 200 Hz

The yellow wave is the input, and the green wave is the output

Figure47 Figure48

High-Pass Filter at 200 Hz

The yellow wave is the input, and the green wave is the output

Figure49 Figure50

Band-Pass Filter at 16 kHz

The yellow wave is the input, and the green wave is the output

Figure51 Figure52

Summary

$%difference = \frac{|Experimental \space Data - Simulation \space Data|}{Experimental \space Data}$

|H(jω)| simulated φ (Degrees) simulated |H(jω)| measured φ (Degrees) measured |H(jω)| Difference (%) φ Difference (%)
Low-Pass Filter 0.708 -45.1 0.708 -44.93 0.14 0.22
High-Pass Filter 0.708 44.99 0.703 44.99 0.14 0.02
$\omega_0$ 1 0 1.01 0 1 0
$\omega_{c1}$ 0.707 45 0.711 43.8 0.57 2.67
$\omega_{c2}$ 0.707 -45 0.746 -47.8 5.5 6.22