Low and high pass filters - calculate the cutoff frequencies, Electrical Engineering

At the completion of this unit, you will be able to determine the cutoff frequencies and attenuations of RC and RL low- and high-pass filters by using test circuits.

UNIT FUNDAMENTALS

A filter is a frequency-selective circuit that permits signals of certain frequencies to pass while it rejects signals at other frequencies.

1231_Low and High Pass Filters 1.png

A low-pass filter, as its name implies, passes low frequencies but rejects high frequencies.

1982_Low and High Pass Filters 2.png

The dividing line between the passing of low frequencies and the rejecting of high frequencies is the cutoff frequency (fc), or -3 dB point. In a low-pass filter, signals lower than the cutoff frequency pass essentially unmodified. Frequencies higher than the cutoff frequency are greatly attenuated, or reduced.

1595_Low and High Pass Filters 3.png

In a high-pass filter, signals higher than the cutoff frequency pass essentially unmodified. Signals lower than the cutoff frequency is greatly attenuated, or reduced.

The cutoff frequency (fc) is the point where the output voltage (Vo) drops to 70.7% of, or 3 dB down from, the input voltage.

1668_Low and High Pass Filters 4.png

Frequency response data may be expressed in terms of output voltage but is usually expressed in decibels (dB). Decibels are units that express or measure the gain or loss (attenuation) in a circuit. The decibel can be based on the ratio of the output voltage (Vo) to the input voltage (Vi).

2117_Low and High Pass Filters 5.png

NOTE: In the type of filters studied in this volume, the output voltage (Vo) is always less than the input voltage (Vi).

1191_Low and High Pass Filters 6.png

The rate of attenuation, or loss, beyond the cutoff frequency (fc) is highly predictable. This attenuation is 6 dB per octave or 20 dB per decade. An attenuation rate of 6 dB per octave is the same rate as 20 dB per decade.

NEW TERMS AND WORDS

band - a range of frequencies.

dB per octave - decibels per octave (dB/octave); a 1 dB increase or decrease over a two-to-one frequency range.

dB per decade - decibels per decade (dB/decade); a 1 dB increase or decrease over a ten-to-one frequency range.

octave - a two-to-one or one-to-two ratio; a frequency factor of two. One octave is the doubling or halving of a frequency.

decade - a ten-to-one or one-to-ten ratio; a frequency factor of ten.

rolled off - gradually attenuated, or decreased. A filter attenuates when its rejected frequencies are rolled off.

EQUIPMENT REQUIRED

F.A.C.E.T. base unit

AC 2 FUNDAMENTALS circuit board

Oscilloscope, dual trace

Generator, sine wave

Exercise 1 - Low-Pass Filters  

EXERCISE OBJECTIVE

When you have completed this exercise, you will be able to calculate the cutoff frequencies and attenuations of RC and RL low-pass filters. You will verify your results with an oscilloscope.

DISCUSSION

  • Several ways exist for the implementation of low-pass filters, each of which consist of a voltage-divider network containing a resistor and a frequency-varying component (inductor or capacitor).
  • Output voltage from the filters is "tapped off" the voltage divider.
  • Changes in the frequency of the supply voltage cause changes in the circuit reactance, resulting in output voltage variations.
  • In RC filters, the capacitive reactance is high at low frequencies compared to the resistance, causing most of the input voltage to appear across the output capacitor.
  • Capacitive reactance decreases as the generator frequency increases, causing larger voltage drops across the R and decreasing the voltage across the output capacitor.
  • Low-pass filters are designed so that frequencies below the cut-off frequency are passed while higher frequencies are attenuated.
  • In low-pass RL filters, the inductive reactance is small at low frequencies compared to the resistance, and most of the input voltage falls across the output resistor.
  • Inductive reactance increases as the generator frequency increases; therefore, more and more voltage is dropped across the inductor and less across the output resistor.
  • Cutoff frequency is defined as the frequency where the output signal is 3 dB down, or 0.707 x Vo.
  • For RC circuits: fc = 1/2πRC
  • For RL circuits: fc = R/2πL

 

 

 

 

 

 

Posted Date: 3/5/2013 4:44:57 AM | Location : United States







Related Discussions:- Low and high pass filters - calculate the cutoff frequencies, Assignment Help, Ask Question on Low and high pass filters - calculate the cutoff frequencies, Get Answer, Expert's Help, Low and high pass filters - calculate the cutoff frequencies Discussions

Write discussion on Low and high pass filters - calculate the cutoff frequencies
Your posts are moderated
Related Questions
Consider the circuit shown in Figure in the t -domain as well as in the s-domain. Formulate the s-domain nodal equations and use MATLAB to solve for V A (s) and V B (s).

Q. The power gain of an antenna is 10,000. If its input power is 1 kW, calculate the maximum radiation intensity that it can generate.

Q. A three-phase, 50-Hz induction motor has a full load speed of 700 r/min and a no-load speed of 740 r/min. (a) How many poles does the machine have? (b) Find the slip and t

Q. Define wireless communications? The latest wireless communications technology is the personal satellite phone. The coverage is planetary and one can reach anywhere on earth.

Solenoids find application in a variety of electrically controlled valves. The magnetic structure shown in Figure is a simplified representation of a solenoid in which the flux in

A 3-phase, wye-connected, 11.8 kV, 100 MVA turbo- generator of 0.8 power factor lagging has a synchronous reactance of 2.0 p.u. on rating. The generator is driven by a steam turbin

why we rotate the armature of dc motor in anticlockwise direction

TRANSISTOR CONFIGURATIONS: Transistor circuits may be categorized into three configurations based on which terminal is common to both of the input and output of circuit. Th

Difference between linear and non-linear resistors

Q. Three waveforms seen on an oscilloscope are shown in Figure. If the horizontal scale is set to 50 ms per division (500 ms for the entire screen width), and the vertical scale is