RL Filters

High pass filter[edit]

When the inductor is in parallel with the load while the resistor is in series with the inductor and load, this creates a high pass filter.

High pass filter has a transfer function

${\displaystyle H(j\omega )={\frac {v_{o}}{v_{i}}}={\frac {j\omega T}{1+j\omega T}}}$

${\displaystyle T={\frac {L}{R}}}$

Frequency response of High pass filter

${\displaystyle \omega =0.v_{o}=0}$

${\displaystyle \omega =\omega _{o}.v_{o}={\frac {v_{i}}{2}}}$

${\displaystyle \omega =00.v_{o}=v_{i}}$

Cut off frequency, ${\displaystyle \omega _{o}}$ , frequency at which ${\displaystyle v_{o}={\frac {1}{2}}v_{i}}$

${\displaystyle \omega _{o}={\frac {1}{T}}}$

Low pass filter[edit]

When the resistor is in parallel with the load while the inductor is in series with the resistor and load, a low pass filter is created.

Low pass filter has a transfer function

${\displaystyle H(j\omega )={\frac {v_{o}}{v_{i}}}={\frac {1}{1+j\omega T}}}$

${\displaystyle T={\frac {L}{R}}=RC}$

Frequency response of Low pass filter

${\displaystyle \omega =0.v_{o}=0}$

${\displaystyle \omega =\omega _{o}.v_{o}={\frac {v_{i}}{2}}}$

${\displaystyle \omega =00.v_{o}=v_{i}}$

Cut off frequency, ${\displaystyle \omega _{o}}$ , frequency at which ${\displaystyle v_{o}={\frac {1}{2}}v_{i}}$

${\displaystyle \omega _{o}={\frac {1}{T}}}$

A single RL circuit creates a filter with a 20.0 dB/decade, or 6.02 dB/octave, slope.

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Filters and its Types-Electronics

A Low Pass Filter is a circuit that can be designed to modify, reshape or reject all unwanted high frequencies of an electrical signal and accept or pass only those signals wanted by the circuits designer.
In other words they “filter-out” unwanted signals and an ideal filter will separate and pass sinusoidal input signals based upon their frequency. In low frequency applications (up to 100kHz), passive filters are generally constructed using simple RC (Resistor-Capacitor) networks, while higher frequency filters (above 100kHz) are usually made from RLC (Resistor-Inductor-Capacitor) components.

Passive filters are made up of passive components such as resistors, capacitors and inductors and have no amplifying elements (transistors, op-amps, etc) so have no signal gain, therefore their output level is always less than the input.

Filters are so named according to the frequency range of signals that they allow to pass through them, while blocking or “attenuating” the rest. The most commonly used filter designs are the:

• The Low Pass Filter – the low pass filter only allows low frequency signals from 0Hz to its cut-off frequency, ƒc point to pass while blocking those any higher.
• The High Pass Filter – the high pass filter only allows high frequency signals from its cut-off frequency, ƒc point and higher to infinity to pass through while blocking those any lower.
• The Band Pass Filter – the band pass filter allows signals falling within a certain frequency band setup between two points to pass through while blocking both the lower and higher frequencies either side of this frequency band.

Simple First-order passive filters (1st order) can be made by connecting together a single resistor and a single capacitor in series across an input signal, ( VIN ) with the output of the filter, ( VOUT ) taken from the junction of these two components.

Depending on which way around we connect the resistor and the capacitor with regards to the output signal determines the type of filter construction resulting in either a Low Pass Filter or a High Pass Filter.

As the function of any filter is to allow signals of a given band of frequencies to pass unaltered while attenuating or weakening all others that are not wanted, we can define the amplitude response characteristics of an ideal filter by using an ideal frequency response curve of the four basic filter types as shown.

Ideal Filter Response Curves

Filters can be divided into two distinct types: active filters and passive filters. Active filters contain amplifying devices to increase signal strength while passive do not contain amplifying devices to strengthen the signal. As there are two passive components within a passive filter design the output signal has a smaller amplitude than its corresponding input signal, therefore passive RC filters attenuate the signal and have a gain of less than one, (unity).

A Low Pass Filter can be a combination of capacitance, inductance or resistance intended to produce high attenuation above a specified frequency and little or no attenuation below that frequency. The frequency at which the transition occurs is called the “cut-off” or “corner” frequency.

The simplest low pass filters consist of a resistor and capacitor but more sophisticated low pass filters have a combination of series inductors and parallel capacitors. In this tutorial we will look at the simplest type, a passive two component RC low pass filter.

The Low Pass Filter

A simple passive RC Low Pass Filter or LPF, can be easily made by connecting together in series a single Resistor with a single Capacitor as shown below. In this type of filter arrangement the input signal ( VIN ) is applied to the series combination (both the Resistor and Capacitor together) but the output signal ( VOUT ) is taken across the capacitor only.

This type of filter is known generally as a “first-order filter” or “one-pole filter”, why first-order or single-pole?, because it has only “one” reactive component, the capacitor, in the circuit.

RC Low Pass Filter Circuit

As mentioned previously in the Capacitive Reactance tutorial, the reactance of a capacitor varies inversely with frequency, while the value of the resistor remains constant as the frequency changes. At low frequencies the capacitive reactance, ( XC ) of the capacitor will be very large compared to the resistive value of the resistor, R.

This means that the voltage potential, VC across the capacitor will be much larger than the voltage drop, VR developed across the resistor. At high frequencies the reverse is true with VC being small and VR being large due to the change in the capacitive reactance value.

While the circuit above is that of an RC Low Pass Filter circuit, it can also be thought of as a frequency dependant variable potential divider circuit similar to the one we looked at in the Resistors tutorial. In that tutorial we used the following equation to calculate the output voltage for two single resistors connected in series.

We also know that the capacitive reactance of a capacitor in an AC circuit is given as:

Opposition to current flow in an AC circuit is called impedance, symbol Zand for a series circuit consisting of a single resistor in series with a single capacitor, the circuit impedance is calculated as:

Then by substituting our equation for impedance above into the resistive potential divider equation gives us:

RC Potential Divider Equation

So, by using the potential divider equation of two resistors in series and substituting for impedance we can calculate the output voltage of an RC Filter for any given frequency.

Low Pass Filter Example No1

A Low Pass Filter circuit consisting of a resistor of 4k7Ω in series with a capacitor of 47nF is connected across a 10v sinusoidal supply. Calculate the output voltage ( VOUT ) at a frequency of 100Hz and again at frequency of 10,000Hz or 10kHz.

Voltage Output at a Frequency of 100Hz.

Voltage Output at a Frequency of 10,000Hz (10kHz).

Frequency Response

We can see from the results above, that as the frequency applied to the RC network increases from 100Hz to 10kHz, the voltage dropped across the capacitor and therefore the output voltage ( VOUT ) from the circuit decreases from 9.9v to 0.718v.

By plotting the networks output voltage against different values of input frequency, the Frequency Response Curve or Bode Plot function of the low pass filter circuit can be found, as shown below.

Frequency Response of a 1st-order Low Pass Filter

The Bode Plot shows the Frequency Response of the filter to be nearly flat for low frequencies and all of the input signal is passed directly to the output, resulting in a gain of nearly 1, called unity, until it reaches its Cut-off Frequency point ( ƒc ). This is because the reactance of the capacitor is high at low frequencies and blocks any current flow through the capacitor.

After this cut-off frequency point the response of the circuit decreases to zero at a slope of -20dB/ Decade or (-6dB/Octave) “roll-off”. Note that the angle of the slope, this -20dB/ Decade roll-off will always be the same for any RC combination.

Any high frequency signals applied to the low pass filter circuit above this cut-off frequency point will become greatly attenuated, that is they rapidly decrease. This happens because at very high frequencies the reactance of the capacitor becomes so low that it gives the effect of a short circuit condition on the output terminals resulting in zero output.

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Green Computing

I. Introduction

Green Computing has become an innovative way on how technology and ecology converge together. With the recent years many industries and companies have turned their attention in realizing how going 'green' can benefit public relations, reduced costs, and lowering global emissions from industrial manufacturing. Though the term green computing covers a vast range of methods, from energy saving techniques, to the study of materials used in our lives, it all fundamentally breaks down to finding ways to not damage or consume all of earth's natural resources.Ultimately green computing focuses on ways in reducing overall environmental impact, its main purpose is to find and promote new ways of reducing pollution, discovering alternative technologies, and creating more recyclable products (Gingichashvili, 2007).

II. Background

The idea of green computing has been around a good time, the government themselves play a role in it. For example the Environmental Protection Agency (EPA) launched the 'energy star' program in the 90s, to promote energy efficient methods. The EPA today still plays an active role by providing not only energy effective methods, but also cost effective methods for the consumers. In 2006 the EPA established a way to save U.S. households and businesses money; "With an eye to saving U.S. households and businesses more than $1.8 billion in energy costs over the next 5 years, today EPA announced new Energy Star specifications for computers and related equipment.These new modifications are also expected to prevent greenhouse gas emissions equal to the annual emissions of 2.7 million cars."(Jones, 2006) Though the EPA is a recognizable agency, they are not the only ones who promoting new ways of going green in the technological aspect. Organizations such as European Union and TCO Certification are one of the leading groups in green computing.

III. How it is beneficial for Human Beings and Environement?

The ever rapid growth of technologies and innovations brings forth many ways on how green computing will have a positive impact, along with great benefits. The benefits of green computing is large, not only from just the consumer, or business, or country's standpoint, but a global benefit. Green computing helps reduce energy demands, waste, and money of how we use technology which positively effects the environment, and our costs.Though the method of green computing can also benefit in simple ways, methods such as turning off your computers during the night. For example, a computer left on for "24 hours will cost you between $115-160 in annual electric costs and also produce 1,500 pounds of CO2 in the atmosphere" (Schneider, 2008). By simply turning off your computer during the nights, you ultimately can save up to" 67 percent annually in your electric bill"(Schneider, 2008), along with reducing greenhouse gases. Overall the benefits of green computing will result in saving money, reducing costs, and conserving energy, along with helping the environment.

IV. Ethical Issues

Going green is not only a fashion statement, it is a real movement that begun back in 1992 with "The Energy Star Program" (Brandrick, 2009). It has become a way of life for many big corporations to try and reduce the amount of energy waste that they would normally excrete and nowadays it is not only expected to be done by such corporations but also by small businesses and individuals alike who have a moral responsibility to their community.Due to the widely known need to save energy and natural resources of our ever dyeing planet many manufacturers have come out with ideas on how to make your device energy efficient, the problem is that with good inventions come the useless ones and those are made to assume a purpose that it is not properly attributed. Some manufacturers will label a product as energy efficient just so it can be sold but sadly it will not work.

Consumers can easily be deceived to buy such products that end up causing more harm to the environment "considering the materials and energy used to manufacture it"(Brandrick, 2009) such products are truly a waste.Like the "Eco Button that promised its consumers that they would save energy and money" (Brandrick, 2009) on their PC but there was a downloadable content available on the internet that would provide the same results. It is not moral or ethical for such manufacturers to lie on the efficiency of their product but it's not illegal to say that the product was misinterpreted by the consumer.

V. Security Concerns & Social Problems

Many belief that being eco-friendly is a get rich idea from big corporations that know that if the consumer is unhappy then they will not buy their product. Even though this is somewhat true and the consumer does look bad at companies believed to be unjust, it is also true that such companies care for the environment. We all remember the "Gulf of Mexico Oil Spill" (Mufson, 2010) and how things like that can "seriously burn their reputation" (Wharton, 2007), this is why such big companies care for the environment and how they affect it. We all remember the oil spill on the gulf of Mexico in 2010 and how that dilemma hurt the BP company and still is hurting it even after a year, if they had followed all the right protocols maybe this tragedy could have been averted.

VI. Further Required Research

Advancements in green computing have become vast. There are so many new ways of combining ecology with technology, that we practically are trying a bit of everything. Such as using solar technology, solar technology now is being used on keyboards and mice now to reduce energy costs. Another green computing method is eliminating certain materials that are hazardous to the environment, and replacing them with cleaner and efficient materials which are biodegradable and eco-friendly. Even now certain computer components such as processor units have reduced heat emissions, and monitors as well with their advancement of flat screens.

Not only is green computing effecting components and other various hardware, it has changed in ways businesses use technology such as cloud computing. Cloud computing essentially is a method of a user connecting to a network or server, through the internet. Ultimately this reduces the need of businesses to have purchase more computers, which can emit greenhouse gases when left on.

The practice of green computing has essentially branched off to every form of technology out there. Cars being a great example, now with hybrids becoming mainstream, people are able to save on gas, money, and also cutting on carbon monoxide, and other various dangerous gases to the atmosphere.

Green computing has also grasped how industries market themselves, and many realize how going green in their technologies can aid them. One great example of green computing corporation is Apple. "Apple has been criticized by some environmental organizations for not being a leader in removing toxic chemicals from its new products, and for not aggressively or properly recycling its old products" (Jobs, 2009) but that has changed, when looking now upon Apple's computers, their unibody designs material is a great source to dissipate heat, along with their products being able to conserve energy very well. Not only have they implemented ways in being more eco-friendly by removing hazardous materials in their computers and products, but their manufacturing and delivering their goods has also been altered to help the environment.

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