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A first-order lowpass filter has the frequency response

H L P ( j Ω ) = 1 1 + j Ω Ω c

The frequency at which the frequency response magnitude has dropped to 1 / 2 is called the corner frequency This term most likely originates from it's role in Bode plots, a shortcut method for sketching the graph of a frequency response. . The frequency response magnitude and phase are plotted in [link] . It is common to express the frequency response magnitude in units of decibels (dB) using the formula

20 l o g 10 H ( j Ω )

At the corner frequency for a first order lowpass filter, the frequency response magnitude is 1 / 2 or roughly -3 dB. From [link] , it can easily be seen that the impulse response for the first-order lowpass filter is given by

h L P ( t ) = Ω c e - Ω c t u ( t )

A first-order highpass filter is given by

H H P ( j Ω ) = j Ω Ω c 1 + j Ω Ω c

Notice that

H H P ( j Ω ) = 1 - 1 1 + j Ω Ω c

This makes sense since a highpass filter can be constructed by taking the filter input x ( t ) and subtracting from it a lowpass filtered version of x ( t ) . The impulse response of the first-order highpass filter therefore becomes:

h H P ( t ) = δ ( t ) - Ω c e - Ω c t u ( t )
Frequency response magnitude and phase for a first-order lowpass filter ( Ω c = 1 rad/sec).
Frequency response magnitude and phase for a first-order highpass filter ( Ω c = 1 rad/sec).

First order filters can be easily implemented using linear circuit elements like resistors, capacitors, and inductors. [link] shows a first order filter based on a resistor and a capacitor. Since the impedance for a resistor and capacitor are R and 1 / j Ω C , respectively, voltage division leads to a frequency response of

H L P ( j Ω ) = 1 1 + j Ω R 1 C 1

Therefore the corner frequency for this filter is Ω c = 1 R 1 C 1 . Similarly, a first-order highpass filter can be implemented using a resistor and capacitor as shown in [link] . This filter has a frequency response of

H H P ( j Ω ) = j Ω R 2 C 2 1 + j Ω R 2 C 2

The corner frequency for the highpass filter is seen to be Ω c = 1 R 2 C 2 .

Circuit implementation of a first-order lowpass filter having Ω c = 1 / R 1 C 1 .
Circuit implementation of a first-order highpass filter having Ω c = 1 / R 2 C 2 .

Now one might be tempted to apply the results of [link] to build a bandpass filter by cascading the lowhpass and highpass circuits in Figures [link] and [link] , respectively. Theory would predict that the equivalent frequency response of this circuit is given by

H e q ( j Ω ) = H L P ( j Ω ) H H P ( j Ω )

Unfortunately, this is not possible since the circuit elements in the lowpass and highpass filters interact with one another and therefore affect the overall behavior of the circuit. This interaction between the two circuits is called loading will be studied in greater detail in the exercises. To get theoretical behavior, it is necessary to use a voltage follower circuit, between the lowpass filter from the highpass circuits. The voltage follower circuit is usually an active circuit (requires external power supply) that has very high input impedance and very low output impedance. This eliminates any loading effects which would normally occur between the lowpass and highpass filter circuits.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
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Source:  OpenStax, Signals, systems, and society. OpenStax CNX. Oct 07, 2012 Download for free at http://cnx.org/content/col10965/1.15
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