rc low pass filter

7/27/2019 RC Low Pass Filter

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RC Low pass filter

Transfer function

A low pass filter is designed to pass only frequencies from dc up to the cut off frequency. So as

the resistance increases the voltage becoming flatter.

1. Zero frequency (w = 0): The impedance of the capacitor is infinite, and the capacitor acts as anopen circuit. The input and output voltages are thus the same,

2. Frequencies increasing from zero The impedance of the capacitor decreases relative o the

impedance of the resistor , and the source voltage divides between the resistive impedance andthe capacitive impedance .Theo output voltage is thus smaller than the source voltage.

3. Infinite frequency (w=infinity): The impedance of the capacitor is zero, and the capacitor acts

as a short circuit. The output voltage is thus zero.

At 10 KOhms exactly same voltage patterns. The voltage drops when the capacitance and

resistance is increased.

Cutoff frequency

()= 1591.5Hz


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Effects of varying Impedance

The figures and the table show a decrease in output voltage as the impedance of the circuit is

varied.

Input

Frequency Hz

Resistance

(KOhms)

Capacitor

(Microfarads)

Peak-Peak Voltage

Output (Volts)

5 Hertz 1 KOhms

0.2 1.60 V

0.3 1.12 V

0.4 960mV

0.5 800mV

Input frequency(HZ)

Resistance(KOhms)

Capacitor(Microfarads)

Peak-Peak VoltageOutput

5 Hertz

1

0.1

2.72 V

2 1.60 V

3 1.12 V

4 960 mV

5 800 mV


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RC High Pass Filter Circuit

A high pass filter is designed to pass all frequencies above its cutoff frequency wc .

At w = 0, the capacitor behaves like an open circuit, so there is no current flowing in the resistor.

In this circuit .there is no voltage across the resistor and the circuit filters out the low-frequency

source voltage before it reaches the circuits output.

As the frequency of the voltages source increases the impedance of the capacitor decreasesrelative to the impedance of the resistor and the source voltage is now divided between the

capacitor and the resistor. The out output voltage magnitude thus begins to increase.When the frequency of the source is infinite (w=infinite), the capacitor behaves as a short circuit

and thus there is no voltage across the capacitor. In this circuit the input voltage and outputvoltage are the same.

The voltage increases when resistance is increased in the circuit. Therefore the Vc is inversely

proportional to the impedance of the resistor. The same relationship is observed when the

impedance of the capacitor is increased the Voltage output in increases simultaneously.

Cutoff frequency

()= 1591.5Hz


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As illustrated above the voltage remains fairly constant as the impedance of the circuit is varied.

Input frequency

(HZ)

Resistance

(KOhms)

Capacitor

(Microfarads)

Peak-Peak Voltage

Output

5 Hertz

1

0.1

7.83 V

2 8.32 V

3 8.48 V

4 8.48V

5 8.67 V


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Band Pass Filter Circuit

The 5 important Parameters of a Band pass Filter

cut-off frequencies

Center frequency ( ): the frequency at which the transfer function is entirely real.Bandwidth (): width of the pass band.Quality Factor (Q): ratio of the center frequency to the bandwidth

Unlike a low pass filterthat only pass signals of a low frequency range or a high passfilterwhich pass signals of a higher frequency range, a Band Pass Filters passes signals within a

certain "band" or "spread" of frequencies without distorting the input signal or introducing extra

noise. This band of frequencies can be any width and is commonly known as the

filters Bandwidth. Bandwidth is defined as the frequency range between two specified frequencycut-off points ( c ), that are 3dB below the maximum centre or resonant peak while attenuating

or weakening the others outside of these two points.

Then for widely spread frequencies, we can simply define the term "bandwidth", BW as being

the difference between the lower cut-off frequency ( cLOWER) and the higher cut-off frequency( cHIGHER) points. In other words, BW = H - L. Clearly for a pass band filter to function

correctly, the cut-off frequency of the low pass filter must be higher than the cut-off frequency

for the high pass filter.

The "ideal" Band Pass Filter can also be used to isolate or filter out certain frequencies that lie

within a particular band of frequencies, for example, noise cancellation. Band pass filters are

known generally as second-order filters, (two-pole) because they have "two" reactive component,the capacitors, within their circuit design. One capacitor in the low pass circuit and another

capacitor in the high pass circuit.

By varying the resistance and capacitance the value of the voltage output remains fairly constant.

Cutoff frequency

()

Lower/upper bands:

53051.6 Hz

22736.4 Hz
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Frequency LP HP OutputVoltage(resistor)(Volts)R(ohms) C

(microfarads)

R (ohms) C

(microfarads)

5 Hz 10 0.3 100 0.7 5.60

20 0.3 100 0.7 5.68

30 0.3 100 0.7 5.84

30 0.4 100 0.7 5.52

30 0.5 100 0.7 5.36

In this experiment the voltage remains fairly steady as various impedance contributing elements

are changed in the circuit.


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Band reject Filters

Series RLC Circuit

The output voltage is now defined across the inductor-capacitor pair.

Again, at 0 the capacitor acts as an open circuit the inductor acts as a short and at thecapacitor acts as a short circuit but the inductor acts as an open circuit. The voltage is across an

effective open circuit and the output equals the input.

Between =0 and = , the capacitor and inductor have finite impedance values reducing theoutput voltage and at a certain are equal and opposite resulting in no voltage output. (asillustrated below)

The magnitude frequency response plot compares the ideal Band reject filter to the actual

response seen from the RLC Circuit.

The effects of the phase shift due to the capacitor and inductor in the phase place. Starting fromzero the phase gets more negative till reaching -90 at which point it flips to +90 and goes

negative again towards zero.

Cutoff frequency

()()

5032.9 Hz for the band reject frequency.


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Capacitor(Micro

Farads)

Inductor(Mili

Henries)

Resitance (ohms) Output voltage

inductor (volts)

0.1 10 100 1.76

0.2 10 100 6.52

0.3 10 100 7.04

0.3 10 200 5.84

0.3 10 300 4.80

There is change in the voltage across the inductor as the impedance of the series circuit is

changed.

rc low pass filter

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