AIM: EXPERIMENT TO DEMONSTRATE ACTIVE FILTERS OBJECTIVES To determine the input/output characteristics of a low pass filter To Explain the polarity of the capacitors To calculate cut off frequency of a lowpass filter. APPARATUS DC power supply Signal generator Resistors R1 = 1k, R2 = 10k and 100k, R3 = R4 = 330 Ω Capacitors C1 = 2.2 µF ,C2=47 µF Op- amp UA 741 THEORY A filter is a device that passes electric signals at certain frequencies or frequency ranges while preventing the passage of others. A filter is a circuit that is designed to pass a specified band of frequencies while attenuating all signals outside this band. Filter networks may be either active or passive. Passive filter networks contain only resistors, inductors, and capacitors. Active filters, employ operational amplifiers (op-amps) as well as resistors and capacitors The passband of a filter is the range of frequencies that are allowed to pass through the filter with minimum attenuation. (Usually defined as less than – 3 dB of attenuation). The most common kinds of frequency selective filters are: Low pass filter – passes signals with a frequency lower than certain cut off frequency High pass filters – passes signals with a frequency higher than certain cut off frequency Band pass filters – passes signals with a frequency within certain band or vice versa. The critical frequency, fc ,(also called the cutoff frequency) is defined as the end of the passband and is normally specified at the point where the response drops – 3 dB (70.7%) from the passband response. Following the passband is a region called the transition region that leads into a region called the stopband. There is no precise point between the transition region and the stopband. Fig 1. Frequency response of a band pass filter Fig 2. Frequency response of a high pass filter Fig 3. Frequency response of a low pass filter. The frequency response of a filter is the graph of its voltage gain versus frequency. Frequency response of an operational amplifier refers to how the amplifier responds to different input frequencies. In order to measure the frequency response we use input signals with a range of frequencies . The input signal can be a sinusoidal waveform, a square wave, a triangular wave or another type of a periodic wave. The output signal will also be a periodic waveform but the amplitude and the phase of the output may be different from the input depending on the character of the amplifier. Gain is given by; 𝑜𝑢𝑡𝑝𝑢𝑡 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 Gain = 𝑖𝑛𝑝𝑢𝑡 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 to convert gain to dB we use the following formula gain in dB=20log|gain| A graph of the magnitude of gain versus frequency in dB on a logarithmic scale can be plotted. The frequency of an op amp is important because it is used to determine the amplifier’s performance at different frequencies. The frequency response of an op amp can affected by different factors such as the gain-band width product, the input and output impendences and the type of feedback used in the amplifier circuit. THE LOW PASS FILTER A low-pass filter is one that passes frequencies from dc to fc , and significantly attenuates all other frequencies. This RC circuit will provide a low frequency path to the input of the amplifier. The amplifier acts as a buffer circuit providing unity gain output. This circuit has more input impedance value. Even though the input impedance of the op-amps high below the cut-off frequency, this input impedance is limited by the series impedance which is equal to R+ 1⁄jωC. The output impedance of the op-amp which is connected in the circuit is always low. This circuit will provide high stability to filter. The main drawback of this configuration is voltage gain is unity. Even for this circuit also the output power is high since the input impedance is low. Fig 5. An active RC circuit PROCEDURE The circuit is arranged as shown below. The output of the op amp is biased under no signal conditions at half supply volts. This is achieved by using the potential divider R3 and R4 and helps to have a maximum output undistorted signal swing. The frequencies are varied from the signal generator from 100Hz to 1MHz as we obtain the output and the results are tabulated. TABLE OF RESULTS WHEN R2=10KΩ FREQUENCY 100 200 300 500 1000 2000 5000 8000 10000 20000 30000 50000 70000 100000 200000 300000 600000 900000 1000000 INPUT 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 OUTPUT 22.4 22.4 22.4 22.4 22.4 22.4 22.4 22.4 22.4 18.0 12.0 5.20 3.60 1.60 1.20 800m 800m 800m 800m GAIN 18.06 18.06 18.06 18.06 18.06 18.06 18.06 18.06 18.06 14.52 9.68 4.19 2.90 1.29 0.97 0.65 0.65 0.65 0.65 Gain(dB) 25.13 25.13 25.13 25.13 25.13 25.13 25.13 25.13 25.13 23.24 19.18 12.44 9.25 2.21 -0.26 -3.74 -3.74 -3.74 -3.74 Note and explain the polarity of the capacitor C1 and C2 C1 Terminal connected to the 10k resister is negative and the other to the Vin positive. C2 The negative terminal is connected to the op amp and the positive is connected to the output. Explanation; For C1 the terminal that is connected to the input is the positive terminal and the terminal connected to the other connected to the 10k resister is the negative. For C2 the output voltage is measured with respect to the ground therefore it is the negative and the other is the negative. TABLE OF RESULTS WHEN R2=1MΩ Frequency 100 200 300 500 1000 2000 5000 8000 10000 20000 30000 50000 70000 100000 200000 300000 600000 900000 1000000 Input 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.21 Output 24.0 23.6 23.6 23.6 23.2 23.2 23.2 23.2 23.2 18.4 13.2 5.20 3.60 1.60 1.20 800m 800m 800m 800m Gain 19.83 19.50 19.50 19.50 19.17 19.17 19.17 19.17 19.17 15.21 10.91 4.30 3.00 1.32 0.99 0.66 0.66 0.66 0.66 Gain(dB) 25.95 25.80 25.80 25.80 25.65 25.65 25.65 25.65 25.65 23.64 20.76 12.67 9.54 2.41 -0.09 -3.61 -3.61 -3.61 -3.61 OBSERVATION At the input, one terminal is connected to the Vin therefore that side of the capacitor is positive and the side connected to the 10KΩresistor is negative. Also at the output, voltage is measured with respect to the ground implying that the right side of the capacitor,C2 is positive and the one connected to the ground is negative. CONCLUSION The polarity of the capacitors was determined. REFERENCES ACTIVE_FILTERS_Theory_and_Design.pdf https://www.electronicshub.org/active-low-pass-filter/