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
Microcomputer A microprocessor is a  general purpose central processing  until of a digital  computer system. It has  arithmetic  logical unit  control circuits and a set of r

What is the difference between the shifts and rotate instructions? A rotate instruction is a closed loop instruction. That is, the data moved out at single end is put back in a

Q. Develop a schematic diagram of a system in which the D/A converter of Figure can be employed in a digital voltmeter.

Addressing Model As we have learned  already  that each instruction has two  parts  one is  op code and another  is operand. Op code  specified  the type  of operations to be

Q. For a JKFFwith JK = 11, the output changes on every clock pulse. The change will be coincident with the clock pulse trailing edge and the flip-flop is said to toggle, when T = 1

the plot of amper circuital law by using matlap?

Find the current through each resistor for the networking below using Superposition Theorem.

RST Restart Instructions Restart instructions  are one byte call instructions. Called location for each restart instruction is  predefined on page 0 ( read only memory). They

Define Sigma-Delta Analog to Digital Converters? Sigma-Delta ADCs have the benefit of being implemented almost totally in the digital domain.  They are extremely reliable, high

outline what three features you would add (choose the three that you feel would be most advantageous) to the 16 bit version of the processor in order to enhance its power.