13: HIGH /L /LOW PASS FILTER
A. Introduction Filter plays important role in achieving sound quality. Filters can also be used to synthesize complex sounds. This lab is to do experiments on a low pass and high pass filter.
B. Low/High Pass Filter The impedance of a capacitor and an inductor can be used to construct Low and High pass filter. The impedance of an inductor is proportional to frequency, and the impedance of a capacitor is inversely proportional to frequency. These characteristics can be used to select or reject certain frequencies of an input signal. This selection and rejection of frequencies is called filtering, and a circuit which does this is called a filter . If a filter passes high frequencies and rejects low frequencies, then it is a high-pass filter. Conversely, if it passes low frequencies and rejects high ones, it is a low-pass filter.
Filters, like most things, aren’t perfect. They don’t absolutely pass some frequencies and absolutely reject others. A frequency is considered passed if its magnitude (voltage amplitude) is within 71% (or 1/ √2) of the maximum amplitude passed and rejected otherwise. The 71% frequency is called corner frequency, roll-off frequency or half-power frequency. The roll off frequency of low pass filter is f H=1/(2πRC), and high pass filter f L=R/(2πL).
13: 13: High/Low pass Filters - 1
1. Low pass filter with RC circuit a.
Set up circuit shown in Fig. 1 with R=3.9 k Ω and C = 0.01μF. Switch on the Power Supply. Select the Function Generator from the Sinusoidal wave as input voltage to the circuit and keep the input voltage at 1 V peak to peak. Use the Oscilloscope to measure the voltage across the capacitor.
b.
Calculate the roll-off frequency of your setup, and choose function generator to cover the entire range of the roll-off frequency. The calculated roll off frequency: f roll-off =
Hz.
c.
Vary the frequency and record the measured voltage in the Table below.
d.
Plot the measured voltage vs frequency. Find the cut-off (roll-off) frequency of your Low Pass RC filter. (Make sure that the input voltage is maintained at a peak-to-peak value of 1 V)
frequency (Hz)
Input voltage (V)
Output voltage (V)
Vout/Vin
500 1,000 2,000 3,000 4,000 5,000 8,000 10,000 20,000 50,000 100,000
The left photo shows the breadboard configuration of the low pass filter, and right photo shows signals from the function generator (bottom trace), and that from across the capacitor (top trace).
13: High/Low pass Filters - 2
2. High pass filter characteristics a.
Set up the circuit of Fig.2 with R=1 k Ω, and L = 20 mH. Switch on the sinusoidal wave from the Power Supply of breadboard and keep the input voltage at 1 V peak to peak . Measure the voltage across the inductor by using the Oscilloscope. Use the Oscilloscope function to measure the voltage across the inductor.
b.
Calculate the roll-off frequency of your setup, and choose function generator to cover the entire range of the roll-off frequency. The calculated roll off frequency: f roll-off =
Hz.
c.
Vary the frequency and record the measured voltage in the Table below.
d.
Plot the measured Vout/Vin vs frequency. Find the cut-off (roll-off) frequency of your High Pass RL filter. (Make sure that input voltage is 1V peak to peak).
frequency (Hz)
Input voltage (V)
Output voltage (V)
Vout/Vin
500 1,000 2,000 3,000 4,000 5,000 8,000 10,000 20,000 50,000 100,000
The left photo shows the breadboard configuration of the high pass filter, and right photo shows signals from the function generator (bottom trace), and that from across the inductor (top trace).
13: High/Low pass Filters - 3
100
1,000
13: High/Low pass Filters - 4
10,000
100,000
