Simple RL and RC circuits serve as high-pass and low-pass audio frequency filters.
What it shows:
Simple RL and RC circuits act as a passive high-pass and low-pass audio frequency filters. Their effect is clearly evident when listening to music (or white noise).
How it works:
The high-pass filter consists of a resistor and inductor wired as shown. The reactance of the inductor is low at low frequencies and it basically shunts low frequency signals from the higher impedance speaker.
One may think of the circuit as a voltage divider. Since XL = ωL and Z = √ (R2+XL2), Vin/Vout = 0.31 at 100 Hz and 0.95 at 1000 Hz. The following figures show Vout as a function of frequency up to about 780 Hz. (Vin was white noise.) The spectrum on the left is without the speaker connected. The cursor is at 180 Hz. The spectrum on the right shows the effect of adding the 8 Ω speaker load.
The low-pass filter consists of a resistor and capacitor wired as shown. The reactance of the capacitor is low at high frequencies and thus it shunts high frequency signals from the speaker.
Again, one may think of the circuit as a voltage divider. Since XC = 1/ωC and Z = √ (R2+XC2), Vin/Vout = 0.85 at 100 Hz and 0.16 at 1000 Hz. The following figures show Vout as a function of frequency up to about 780 Hz. (Vin was white noise.) The spectrum on the left is without the speaker connected. The spectrum on the right shows the effect of adding the 8 Ω speaker load. The cursor is at 180 Hz.
To calculate the "cross-over" frequency for the two filters, set the output voltages to be equal and solve for ω. Using the values of the components in the circuits, f = 225 Hz. The actual spectra shown above are consistent with that calculation.
Setting it up:
The components of the filters are permanently mounted on a white acrylic board as shown in the photograph.
Dual banana jacks provide input and output connections. A CD player and power amplifier connect to the input. The output goes to an 8 Ω loudspeaker. A rotary switch selects either high-pass, low-pass, or no filter. The circuit board may be placed on a small easel. Choose a piece of music which is rich in bass as well as high tones ("The Way You Make Me Feel" by Michael Jackson fits the bill).
For the power amplifier, choose one with a flat frequency response. The Samson Servo 120 Stereo Power Amp (in bridge mode) is excellent. Compare its frequency response to that of an RCA SA-155 Integrated Stereo Amp (on the right):
The RCA amp output looks very much like the low-pass filter output! Cheap and weak power amps tend to boost the bass to make them sound a little less tinny, so check the frequency response specs of the amp you want to use. Otherwise you may be puzzeled by the results. BTW, all the spectra were recorded with a model SRS 785 Dynamic Signal Analyzer. The white noise source was a Gen Rad 1383 20Hz-20MHz Random Noise Generator.
It's a simple but effective demonstration of an application of RL and RC circuits often talked about in lectures. Well worth the time doing....