Filters





Study Objective:

(1) To study the operation of passive low- pass and high- pass filters.
(2) Understand the effect of the (R, L & C) on the cut-off frequency in low-pass and high- pass filter.
(3) Study the characteristics of passive filters by obtaining the frequency response of Low Pass RC filter and High Pass RL filter.
(4) Construct a Band Pass Filter by cascading a low pass filter and a high pass filter, and obtain the frequency response of the filter using the Bode plotter.

Introduction:

In electronic communication systems, it is often necessary to separate a specific range of frequencies from the total frequency spectrum. This is normally accomplished with filters. A filter is a circuit that passes a specific range of frequencies while rejecting other frequencies. A passive filter consists of passive circuit elements, such as capacitors, inductors, and resistors. There are four basic types of filters, low-pass, high-pass, band-pass, and band-stop.
A low-pass filter is designed to pass all frequencies below the cutoff frequency and reject all frequencies above the cutoff frequency. A high-pass filter is designed to pass all frequencies above the cutoff frequencies and reject all frequencies below the cutoff frequency. A band-pass filter passes all frequencies within a band of frequencies and reject all other frequencies outside the band. A band-stop filter rejects all frequencies within a band of frequencies and passes all other frequencies outside the band.
In this experiment, you will study low-pass and high-pass filters only. The most common way to describe the frequency response characteristics of a filter is to plot the filter voltage gain (Vo/Vin) in dB as a function of frequency (f). The frequency at which the output power gain drops to 50% of the maximum value is called the cutoff frequency (fC). When the output power gain drops to 50%, the voltage gain drops -3 dB (0.707 of the maximum value). When the filter dB voltage gain is plotted as a function of frequency on a semilog graph using straight lines to approximate the actual frequency response, it is called a Bode plot. A Bode plot is an ideal plot of filter frequency response because it assumes that the voltage gain remains constant in the band pass until the cutoff frequency is reached, and then drops in a straight line.
The filter network voltage gain in dB is calculated from the actual voltage gain (Av) using the equation:
Av(dB) = 20 log Av.
where Av =Vo/Vin.
When the frequency at the input of a low-pass filter increases above the cutoff frequency, the filter output voltage drops at a constant rate. The constant drop in filter output voltage per decade increase (10), or decrease (/10), in frequency is called roll-off. An ideal low-pass or high-pass filter would have instantaneous drop at the cutoff frequency (fC), with full signal level on one side of the cutoff frequency and no signal level on the other side of the cutoff frequency.
A first order filter has one RC circuit tuned to the cutoff frequency and rolls off at -20 dB/decade. A two pole filter has two RC circuits tuned to the same cutoff frequency and rolls off at -40dB/decade. Each additional pole (RC circuit) will cause the filter to roll off an additional -20dB/decade. Therefore, An RC filter with more poles (2nd and above RC circuits) more closely approaches an ideal filter.
In the first order filter, shown in Fig. 1 and Fig. 3, the phase (θ) between the input and the output will change by 90o over the frequency range and be 45o at the cutoff frequency. In a two poll filter, the phase (θ) will change by 180o over the frequency range and be 90o at the cutoff frequency.


Low Pass Filter
A low-pass RC filter is shown in Fig 1. At frequencies well below the cutoff frequency, the capacitive reactance of capacitor C is much higher than the resistance of resistor R, causing the output voltage to be practically equal to the input voltage (Av=l) and constant with variation in frequency. At frequencies well above the cutoff frequency, the capacitive reactance of capacitor C is much lower than the resistance of resistor R and causing the output voltage to decrease as the frequency increase.


Fig. 1 First -order Low-Pass Filter.

At the cutoff frequency, the capacitive reactance of capacitor C is equal to the resistance of resistor R, causing the output voltage to be 0.707 times the input voltage (-3dB). The expected cutoff frequency (fC) of the low-pass filter in Fig 1, based on the circuit component values, can be calculated from:

For RC filters: Xc=R

If sine wave is applied as shown in Fig. 1(a), output waveform will not be changed, but its amplitude will be less than input voltage, and will lag behind input waveform for θo. According to voltage dividing rule, we can derive:

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Frequency Response: It is a graph of magnitude of the output voltage of the filter as a function of the frequency. It is generally used to characterize the range of frequencies in which the filter is designed to operate within.




Fig. 2 Bode Diagram of Low-Pass Filter with a cut-off frequency fc.

High Pass Filter

A high-pass Rc filter is shown in Fig. 3. At frequencies well above the cutoff frequency, the capacitive reactance of capacitor C is much lower than the resistance of resistor R, causing the output voltage to be practically equal to the input voltage (A=1) and constant with variations in frequency.





Fig. 3 First -order High-Pass RC and RL Filter.

At frequencies well below the cutoff frequency, the capacitive reactance of capacitor C is much higher than the resistance of resistor R, causing the output voltage to decrease as the frequency decrease as the cut off frequency. At the cut off frequency the capacitive reactance of capacitor C is equal to the resistance of resistor R, causing the output voltage to be 0.707 times the input voltage (-3 dB). The expected cutoff frequency (fC) of the high pass filter shown in Fig.3, is calculated from;
For RC filters: XC=R
For RL filters: XL=R

Fig. 4 Bode Diagram of high-Pass Filter

If sine wave is applied as shown in Fig. 3(a), output waveform will not be changed, but its amplitude will be less than input voltage, and will lead input waveform for θo. In accordance with voltage dividing rule, we can derive:

Band Pass Filter

A Band Pass Filter allows a specific frequency range to pass, while blocking lower and higher frequencies. It allows frequencies between two cut-off frequencies while attenuating frequencies outside the cut-off frequencies.
A good application of a band pass filter is in Audio Signal Processing, where a specific range of frequencies of sound are required while eliminating the rest. Another application is in the selection of a specific signal from a range of signals in communication systems.
A band pass filter may be constructed by cascading a High Pass RL filter with a roll-off frequency fL and a Low Pass RC filter with a roll-off frequency fH, such that:
fL < fH
The Lower cut-off frequency is given as:

The higher cut-off frequency is given as:


The Band Width of frequencies passed is given by: BW = fH - fL


Fig. 5 Circuit Diagram of Band-Pass Filter.



Fig. 6 Bode Diagram of Band-Pass Filter

Experiment Equipment:
Using Multisim software you need:
(1) One function generator.
(2) One Bode Plotter.
(3) Capacitor: 0.02μF, 0.04μF and Inductor: 20mH, 200mH.
(4) Resistor: 1kΩ, 2kΩ.
Experiment items:

Item one (1): Low-pass filter.

1 -1 Experiment Procedures:
Gain – frequency response :
Connect the circuit shown in Fig. 7, Apply 10kHz/ l0Vp-p sine wave to the input terminal (Vin), with the following Bode plotter setting, Magnitude, Vertical axis (Log, I= -50dB, F=0dB), Horizontal axis (Log, I= 1Hz, F=1MHz) .
Run the simulation. Notice that the voltage gain in dB has been plotted between the frequencies of 1Hz and 1MHz by the Bode plotter. Sketch the curve plot.
Move the cursor (red line) to a flat part of the curve at a frequency of approximately 1Hz. Record the voltage gain in dB on the curve plot.
Calculate the actual voltage gain (A) from the dB voltage gain (AdB).
Move the cursor as close as possible to a point on the curve that is -3dB down from the maximum dB gain at 1Hz. Record the frequency value which represents the cutoff frequency.
Calculate the cutoff frequency (fc) based on the circuit component values in Fig. 7
Move the cursor to a point on the curve that is as close as possible to a frequency of f2=1MHz. Record the dB gain on the curve plot and Calculate the actual voltage gain (A) from the dB voltage gain (AdB), and tabulate your results in Table -1.



Fig. 7 Low-Pass Filter.

Phase frequency response

Click "phase" on the Bode plotter to plot the phase curve. Change the vertical axis initial value (I) to(-90o) and the final value (F) to (0o). Keep Horizontal scale.
Run the simulation again.
Move the cursor to approximately 1Hz, 1 MHz and fc, record the phase (θ) in degrees on the curve plot for each frequency (f), Tabulate your results in Table -1.
Change the value of resistor R to 2kΩ in Fig 7. Click "Magnitude" on the Bode plotter. Run the simulation .Sketch the curve plot. Measure the cutoff frequency (fc) and record your answer. Click "Phase on the Bode plotter" Run simulation. Sketch the curve plot, Tabulate your results in Table -1.
Change the value of capacitor C to 0.04F in Fig 7. Click "Magnitude" on the Bode plotter. Run the simulation .Sketch the curve plot. Measure the cutoff frequency (fc) and record your answer. Click "Phase on the Bode plotter" Run simulation. Sketch the curve plot. Tabulate your results in Table -1.

Table -1

Frequency
AV (dB)
θ (Degree)

f1= 1Hz

fC=
-3

f2= 1MHz

Item Two (2): Experiment for High-pass filter.
2 -1 Experiment Procedures:
Gain frequency response :
Connect the circuit shown in Fig. 8, Apply 10kHz/ l0Vp-p sine wave to the input terminal (Vin), with the following Bode plotter setting, Magnitude, Vertical axis (Log, I= -50dB, F= 0 dB), Horizontal axis (Log, I= 1Hz, F=1MHz) .
Run the simulation. Notice that the gain in dB has been plotted between the frequencies of 1Hz and l MHz by the Bode plotter. Sketch the curve plot in the space provided.
Move the cursor to a flat part of the curve at a frequency of approximately 1MHz. record the voltage gain in dB on the curve plot.
Calculate the actual voltage gain (A) from the dB voltage gain (A dB).
Move the cursor as close as possible to a point on the curve that is -3 dB down from the dB gain at 1MHz. Record the frequency (cutoff frequency, fC) on the curve plot.
Calculate the expected cutoff frequency (fC) theoretically based on the circuit component values in Fig 8.
Move the cursor to a point on the curve that is as possible to near that f2=1MHz. Record the dB gain on the curve plot, and tabulate your results in Table -1.
Repeat steps (1, 2, 3, 4, 5, 6 and 7) for the circuit shown in Fig. 9.


Fig. 8 High-Pass RC Filter





Fig. 9 High-Pass RL Filter

b) Phase frequency response
Click "phase" on the Bode plotter to plot the phase curve. Change the vertical axis initial value (I) to (0o) and the final value (F) to (90o). Keep Horizontal scale.
Run the simulation again.
Move the cursor to approximately 1Hz, 1 MHz and fc, record the phase (θ) in degrees on the curve plot for each frequency (f), and tabulate your results in Table -1.
Change the value of resistor R to 2kΩ in Fig 8. Click "Magnitude" on the Bode plotter. Run the simulation .Sketch the curve plot. Measure the cutoff frequency (fc) and record your answer. Click "Phase on the Bode plotter" Run simulation. Sketch the curve plot, and tabulate your results in Table -1.
Change the value of capacitor C to 0.04F in Fig 8. Click "Magnitude" on the Bode plotter. Run the simulation .Sketch the curve plot. Measure the cutoff frequency (fc) and record your answer. Click "Phase on the Bode plotter" Run simulation. Sketch the curve plot, and tabulate your results in Table -1.
Repeat steps (1, 2 and 3) for the circuit shown in Fig. 9.


Item Three (3): Experiment for Band-pass filter.
2 -1 Experiment Procedures:
Gain frequency response:
Repeat steps (1, 2, 3, 4, 5, 6 and 7) for the circuit shown in Fig 5, with the component values R=1 kΩ, C=0.1 μF and L=200mH. Sketch the curve plot, and tabulate your results in Table -2.
Repeat steps (1, 2, 3, 4, 5, 6 and 7) for the circuit shown in Fig 10, with the component values R=1 kΩ, C=0.1 μF and L=200mH. Sketch the curve plot, and tabulate your results in Table -2.

Fig. 10 Band-Pass RCL Filter

Phase – frequency response:
Repeat steps (1, 2 and 3) for the circuit shown in Fig 5, with the component values R=1 kΩ, C=0.1 μF and L=200mH. Sketch the curve plot, and tabulate your results in Table -2.
Repeat steps (1, 2 and 3) for the circuit shown in Fig 10, with the component values R=1 kΩ, C=0.1 μF and L=200mH. Sketch the curve plot, and tabulate your results in Table -2.

Table -2

Frequency
AV (dB)
θ (Degree)

f1= 1Hz

fCL= fCH=-3fo=0f2= 1MHz
Discussions:
1. Discuss the shape of the frequency curve of a low-pass filter and high-pass filter?
2. What is the voltage gain on the flat part of the frequency response curve for low-pass filter and high-pass filter? Explain why?
3. How much did the dB gain decrease for a one-decade increase (l0) in frequency for single-pole (single Rc) first order low-pass filter?
4. How much did the dB gain decrease for a one-decade decrease (/10) in frequency for a single-pole (single RC) first order high-pass filter?
5. For the signal that transmitted by phone used filter of fC =4 kHz. Design a filter which makes a nice sound for music system? (Note: the human ear response to frequency up to 20 kHz).
6. What are the most common applications of the low pass filter?
7. From the results why the angle (Ө) is sign (-) in the low pass filter and sign (+) in the high pass filter?
8. Explain the differences between the circuit in Fig. 5 and the circuit in Fig. 10.


Experiment (2): Passive Low-pass, High-pass and Band-pass filter circuits

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Experiment No. (2)
Passive Low-Pass, High-Pass & Band- Pass Filter Circuits

0.02F

0.02F

1 kΩ

20 mH

vin

vo


2016/2017