Examcrazy Logo
HOME  SITEMAP CONTACT US LOGIN
HOME Engineering AIEEE GATE IES DRDO-SET BSNL-JTO
MBA in India CAT How to Prepare for Exams Technical Freshers Jobs
  Follow us|  twitter  Orkut  facebook
Electronics II Tutorials
   Overview Analog Wireless Communcation
   Resistors, Capacitors, RC Networks
   Diodes, Amplitute Modulation, Diode Detection
   RL Circuits, Inductive Kicks, Diode Snubbers
   RC filters. Series resonance and quality factor, Matching, Soldering
   Ladder filters Butterworth and Chebyshev filters Filter tables ADS
   Bandpass ladder filters Quartz crystals
   Impedance inverter
   Ideal Transformers
   Transformer shunt inductance
   BJT-Large signal models
   Transistor switches. Voltage regulators
   Transistor switches. Voltage regulators
   Common emitter amplifier. Max. efficiency of class A amps. Transformer coupled loads
   Available power. Distortion. Emitter degeneration. Miller effect
   Emitter follower and differential amplifiers
   JFET Source follower amplifier
   Oscillators. Clapp oscillator. VFO startup
   Variable frequency oscillator. Gain limiting
   Receiver incremental tuning. Crystal oscillators
   Mixers. Gilbert cell
   Superheterodyne receivers. Spurious responses of mixers
   Decreasing channel bandwidth by using CW
   Audio amplifiers
   JFETs as variable resistors
   Automatic gain control
   Noise, SNR, MDS, noise power density and NEP
   Nyquist noise formula. Cascading noisy components. Noise figure
   Receiver intermodulation and dynamic range
Other Electronics 1 Tutorials
   Diode Tutorials
   BJT Tutorials
   MOSFET Tutorials
   Applied Electromagnetics Tutorials
Free Electronics Tutorials
   Diode Tutorials
   BJT Tutorials
   MOSFET Tutorials
   Electronics II Tutorials
   Applied Electromagnetics Tutorials
   Microwave Tutorials
GATE preparation tips
   GATE Books & How to prepare
   Objective Solving Tricks
   Other GATE links
   IES exam preparation
   All about DRDO-SET
More Engineering Links
   Directory of coaching Institutes
   Govt engg college rankings
   Private engg college rankings
   Admission notifications for Mtech/PhD
   All Engineering Colleges in India
Ladder Filters. Butterworth and Chebyshev Filters

Ladder Filters. Butterworth and Chebyshev Filters. Filter Tables. ADS.
Ladder filters are networks that are composed of alternating series and shunt elements.


Notice that the same source and load resistances are assumed. This is called “doubly terminated” filters. All of our filters will be doubly terminated.
Ladder filters are actually one of the oldest types of filters. They have been around since the mid-1800’s. A circuit designer can achieve a sharper (or steeper) frequency roll off with ladder filters than with simple RC or RL circuits. Consequently, one can obtain more ideal low, high or band pass filter responses and with little resistive loss. Additionally, doubly terminated ladder filters have a low sensitivity to component variation. That is a good characteristic.
There are four basic types of ladder filters:
1. Maximally flat, also called Butterworth filters,
2. Equal ripple, also called Chebyshev filters,
3. Elliptic, also called Cauer filters,
4. Linear phase filters.
We will consider the first two in this course. The circuits in Figs. 1 and 2 can be either Butterworth or Chebyshev filters. The topology is the same for both. Only the values for L and C vary between the two types of filters. We will characterize these two filter types by the response of the loss factor L( f ) magnitude versus frequency. [The loss factor is
sometimes referred to as the insertion loss = IL = 10 log10(L).]
Maximum Available Power
Before further discussion of ladder filters, we must first define maximum available power, P+. This is the maximum time average power that can be provided by a source, or by the previous stage in the circuit, to a matched load. Consider that a source or previous circuit stage has been modeled by this Thévenin equivalent circuit:

As you determined in homework prob. 1, a dc source delivers maximum power when a resistive load Rs is connected to the output, similar to that shown above. For the ac circuit shown here, the maximum power delivered to the load Rs is

In summary, P+ is the maximum available power from an ac source (or a Thévenin equivalent) with internal resistance Rs. It is the maximum time-average power that can be delivered to a matched source. Very important formula. (Note that Vs is the amplitude, not p-to-p.)
1. Maximally Flat, or Butterworth, Low Pass Filter
For this filter, the values of the inductors and capacitors are somehow chosen so that

Where LB is the loss factor as a function of f. In this expression:
• Pi = maximum available power from the source (see Lecture 10),
• P = delivered power to the load,
• fc = cutoff frequency of the filter,
• n = order of the filter (number of L’s and C’s in high and low pass filter; number of L-C pairs in bandpass filters).
For the Butterworth (maximally flat) low pass filter

2. Equal Ripple, or Chebyshev Low Pass Filter
The values of the inductors and capacitors in this type of filter are somehow chosen so that

In this expression:
• ? = ripple size,
• Cnn)) Chebyshev polynomial of order n
Chebyshev filters might be more susceptible to variations in component values than Butterworth filters. This is due to the large coefficients of the polynomials listed

Comments
• Whether to use Butterworth, Chebyshev or another filter type depends on the specifications/requirements of the circuit (required rejection, roll off, phase variation, etc.), the available components, component value variations and so on. • Once you have the specifications, then you can synthesize the filter. The required filter specifications are:

• With these specifications, you can calculate the specific inductor and capacitor values needed to realize the filter (i.e., “synthesize” it). It is a complicated procedure to derive the formulas for these component values. There are entire books devoted to this topic. (See the attachment at the end of this lecture for a simple example.)
• Instead of deriving these formulas, designers often simply use filter tables. These are tabulated values for normalized susceptance and reactance (collectively called immittance, a). To un-normalize values from filter tables for low pass filters, Use

RN and ?N are the normalization values used in the tables (often both = 1), while R and ?c are the actual circuit values. An example will help explain this procedure.
Example
Design a fifth-order, Butterworth, low-pass filter (see Fig. 1 above) with a cutoff frequency of 8 MHz, a rejection of at least 23 dB at 14 MHz and an impedance level of 50 ?. With a fifth order filter, n = 5. From (5.1) and f/fc = 14/8 then

which meets the 23 dB spec. (Note that there is also loss in the passband. At 7 MHz, for example, IL = 10 log10[1+(7/8)10]=1.0 dB. Where does this “lost” energy go?) Now, for this fifth-order Butterworth filter we read the immittance coefficients from Table 5.1 to be a1 = 0.618, a2 =1.618, a3 = 2, a 4=1.618 and a5 = 0.618.
For a low pass filter, these immittance coefficients are the normalized susceptances of the shunt elements at fc and the normalized reactances of the series elements at fc.

For R = 50 ? and W3=2 ? Fc=5.027 10 ×107 rad/s (at 8 MHz), then

All of these values are “in the ballpark” for the Harmonic Filter. Of course, one generally needs to use standard values of components for the filter, unless you build your own inductors and/or capacitors. Consequently, the circuit may need to be “tweaked” after completing this synthesis step.
Advanced Design System (ADS)
This tweaking process can be performed using analysis software such as SPICE, Puff or Advanced Design System (ADS). Your text uses the passive microwave circuit simulator called Puff, which comes with your text. It is DOS-based and requires the use of “scattering parameters” to characterize the behavior of circuits, including filters. (S parameters are discussed extensively in EE 481 Microwave Engineering.) For these, and other, reasons we will NOT be using Puff in this course. Instead, we will be using Advanced Design System (ADS) from Agilent Technologies. Consequently, all of the text problems that refer to Puff have been rewritten to use ADS. These can be found on the course web site. The manual “Getting Started with ADS” has been written to help you get going with ADS. It can also be found on the course web site. ADS has just a couple of nuances. Other than that, it is very straightforward to use. To illustrate the use of ADS, we will verify the proper operation of the low-pass filter designed previously.
ADS Simulation of a Low-Pass Ladder Filter
ADS Startup Window:

To get going with ADS, you must first create a “project”:

ADS example with Rs = 50 ?:

Here is a plot of Pout/Pin in dB:

This doesn’t look like the response of a maximally flat low pass filter. What’s wrong? Here’s a plot of |Vout| Vin| in dB:

This plot has the general shape of a maximally flat filter, but there is an extra 6 dB of attenuation at the design frequency of 7 MHz. What’s going on here? Lastly, here’s a plot of Pout/P+ in dB where P+ is the maximum available power from the source:

Alas, this is the plot we’ve been looking for. Why? Because by definition, insertion loss is the ratio of the output power to the maximum avaliable source power. See (5.1) as an example. From this last plot, we can see that ADS predicts an insertion loss of –1.017 dB at 7.000 MHz. This is very close to our design prediction of –1.0 dB at 7 MHz.
ADS example with Rs = 100 ?:


Changing the impedance “level” (from 50 ? to 100 ?) has a dramatic effect on the performance of the filter. Can you explain why?


Discuss about MOSFET here
   START NEW THREADS
Discussion Board for MOSFET
You can discuss all your issues on MOSFET here
Thread / Thread Starter Last Post Replies Views
fourier transform
sir,
plz send me the notes for fourier transforms its very urgent.


Posted By :-
 shruthi.s
Aug 31, 12:14:03 PM 0 52449
Fourier Transform
Sir I want tutorial on Fourier Transform.........


Posted By :-
 jainpooja.1989@yahoo.com
Jul 15, 3:24:49 PM 0 55478
fourier transform
sir i want tutorial on fourier transform


Posted By :-
 apseng2005
Jul 11, 10:08:19 AM 0 51807
match filter
heloo sir ,i want a tutorial for match filter.plz send it as soon as possible it is very urgent.


Posted By :-
 richa
Jun 4, 2:25:18 AM 0 72794
Electic circuits
I want lecture notes for single phase ac & 3phase ac circuits


Posted By :-
 kalaivanisudhagar
May 21, 11:32:46 AM 1 87236
electro statics
what is the work done to move a charge? derive an expression for assembling a configuration of point charges


Posted By :-
 harismhkt
May 12, 8:28:18 AM 0 51140
electromagnetic waves
i want lcr circiut teorems derivations


Posted By :-
 harismhkt
May 12, 8:23:58 AM 0 50819
oscillators
i want oscillator frequency derivations for all. plz let me know from where i can get that


Posted By :-
 shruthi.s
May 4, 5:21:01 PM 0 51623
Equivalent circuit Models
I've got a question in one of my revision papers,

Explain the advantages of representing a transistor by means of an equivalent circuit circuit model

The only thing i can remember is that you can take complex circuits and break them down into simpler circuits which are easier to understand,

Is this the only advantage or do you have any more?

Please help!


Posted By :-
 ally79
Apr 12, 6:33:57 PM 2 109640
temperature Vs reverse satuation current
I want to know the variation of reverse saturation current with the increase in temperature for both germanium and silicon diodes


Posted By :-
 bhrahma@yahoo.co.in
Jan 28, 7:17:23 PM 0 57762
communication system
analog and digital communication system, fiber optic communication, telecommunication technique and application, mobile communication


Posted By :-
 hirakec@gmail.com
Dec 17, 10:38:27 AM 0 64136
CMOS TRANSISTOR
I WANT A TUTORIAL FOR CMOS TRANSISTORS.


Posted By :-
 maroofalamkhan
Dec 14, 3:29:22 PM 0 63184
coaching in ies in indore
what about coaching


Posted By :-
 satish21
Dec 7, 5:27:52 PM 0 67758

To start your new thread you must login here.
New user signup at ExamCrazy.com Exam Crazy
To reply/post a comment you need to login, Use your user name and password to login if you are already registered else register here

EXISTING USER LOGIN
(Members Login)
Username:
Password:
NEW USER REGISTERATION FORM
Login-Id
Email-ID
Password
Confirm-Password
Full-Name

  About us | Privacy Policy | Terms and Conditions | Contact us | Email: support@Examcrazy.com  
Copyright © 2014 Extreme Testing House, India. All rights reserved.  2947