Analog Filtering Demo

This webpage describes a S/N enhancement demonstration using electronic circuitry. A simple RC filter is used to isolate a low-frequency signal from high-frequency noise. Instructors have the flexibility of demonstrating to the students how noise frequencies can be electronically isolated from signal frequencies to improve the signal-to-noise ratio.

Demonstration Equipment and Setup

Figure 1. Layout of the RC Filter Demonstration Setup

• Equipment needed for this demonstration, shown in Figure 1 above:
  • Two audio frequency function generators. Ours are Heathkit Sine-Square Generators, Model EUW-27.
  • Coax cable with BNC male connector ends
  • Two BNC female double stacking banana plug connectors (Pomona Electronics, Model 1269)
  • BNC “T”, female-male-female (Pomona Electronics, Model 3285)
  • Phono jack – BNC male adapter (Pomona Electronics, Model 4054)
  • Two phono plug-to-lugs speaker cables (Radio Shack, Cat. # 42-2449)
  • An RC Filter. The schematic and picture of the circuit used in this demonstration as a low pass filter is shown in Figure 2:

    

    Figure 2. The schematic of the RC filter (left) and a picture of the RC filter mounted in the demonstration setup (right).

    • The RC filter was mounted on a 4-position, dual row barrier strip (Radio Shack, Cat. # 274-658), which was then secured on a piece of scrap wood with two small wood screws. The electronic components were mounted on one side of the barrier strip (capacitor on screws 1 and 2, resistor on screws 2 and 4), and the lug ends of the speaker cables (for V_in and V_out) are mounted on the other side.
  • Y-adapter, phono jacks – stereo 1/8” plug (Radio Shack, Cat. # 274-369)
  • Computer equipped with a 16-bit sound card. My computer is a Compaq Presario 1685 laptop (1999 vintage).
• Equipment hookup
  • A double stacking BNC-banana plug connector was connected to the banana plug posts onto the sinewave output of each function generator
  • The male end of the BNC “T” was connected to the double stacking BNC-banana plug connector on the upper function generator.
  • One end of the coax cable was connected to one side of the BNC “T”. The other end was connected to the double stacking BNC-banana plug connector on the lower function generator.
  • The phono jack – BNC male adapter was connected to the other side of the BNC “T”. One of the speaker cables is connected to this phono jack and serves as V_in for the RC filter. The lugs are connected to screw 1 (bottom position on barrier strip as seen in the photo above) and screw 4 (top position on barrier strip)
  • The lug end of the other speaker cable for V_out is also connected to the RC filter:
    • If lugs are connected to screws 1 and 2, the circuit will behave as a low-pass filter
    • If lugs are connected to screws 2 and 4, the circuit will behave as a high-pass filter
  • The phono plug for the V_out cable is plugged into one of the phono jacks on the Y-adapter, and the Y-adapter is connected to the microphone input of the computer sound card.
• Getting Started
  • Once everything is connected, set the output range of each function generator to 1V (p-p) or less and the output of each function generator at a minimum level. If the output range is too large, you risk overloading the sound card microphone input at higher output levels. If the output is not at a minimum level, it is possible to have a startling noise come out of your computer speakers while the computer boots up.
  • Turn on the power to each function generator and allow the computer to boot up.

Sound Card Oscilloscope Software

While there is no substitute for a benchtop oscilloscope, there are a few freeware programs that allow your computer card to act as an oscilloscope in the audio frequency range. I decided upon the program Visual Analyser 8.10 (Homepage: http://www.sillanumsoft.org/) although similar software may be obtained here. After booting the computer and loading the Visual Analyser software, I perform my demonstration in the following manner:

Figure 3. This is a snapshot of the Visual Analyser software. By default, an oscilloscope display and a spectrum analyzer display appears. In the Settings menu, the number of points on the FFT were set at 8192 and the sampling frequency was set at 11025 Hz. No signal smoothing was performed. The “signal” function generator frequency was set at ~100 Hz and the function generator output was adjusted until a usable signal was obtained. The small peaks at higher frequencies seem to be overtones from the function generator itself. Students should notice a “clean” signal on the scope display with a peak-to-peak intensity of ±1 division.

Figure 4. The signal from the “noise” frequency generator was set at ~5000 Hz and the intensity of the noise was adjusted until a S/N of ~10 was obtained. Students should notice the noisy signal and that the amplitude of the signal has increased as a result of the added noise.

• Why S/N~10?
  • In Figure 4, the signal amplitude (S) is twice the noise amplitude (V_N).
  • But the noise amplitude is equal to ±2.58 times the standard deviation of the noise at the 99% confidence level.
    • ±zσ=V_N
    • σ=V_N/±z = V_N/±2.58 ~V_N/5
    • So if S/V_N = 2, then S/σ = 10

Figure 5. This is the filtered signal across the capacitor. After directing the noisy signal through the RC low-pass filter, the filtered signal magnitude is almost as large as the original signal, but the higher frequency noise decreased in magnitude by ~2.5X after filtering. This results in proportional improvement in the signal-to-noise ratio, and although the signal is not completely free of noise, it is much improved.

Figure 6. If the soundcard input is placed across the resistor in the RC filter, one can see that the majority of the higher frequency noise is accessed from the voltage drop across the resistor. Although the signal is mainly located across the voltage drop of the capacitor, there is a small contribution from the signal to the voltage drop across the resistor.