ANSI/AIM Code 128 Maker In .NET Framework
Using Barcode drawer for Visual Studio .NET Control to generate, create Code 128B image in Visual Studio .NET applications.
Code 128B Reader In VS .NET
Using Barcode reader for .NET Control to read, scan read, scan image in .NET applications.
Circuit Analysis Demysti ed
Bar Code Generation In VS .NET
Using Barcode encoder for VS .NET Control to generate, create barcode image in VS .NET applications.
Recognize Barcode In Visual Studio .NET
Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications.
The multiplicative constant, 10 in this example, gives us a way to compare the relative strength differences between two quantities That is, if the difference between IdB1 and IdB2 is 10 dB, then the intensity of I1 is ten times the strength of I2 Note that since the multiplicative factor in (151) is 20, a difference of 20 dB indicates that one signal has a magnitude 20 times as large as the other The log function is a useful measure of signal strength for two good reasons First, quantities can often vary quite a bit in strength sometimes over many orders of magnitude By using the logarithm we can rescale that variation down to a more manageable number One famous example where this behavior is apparent is the Richter scale used to characterize the strength of earthquakes The details of the Richter scale don t concern us; all that is important for our purposes is that this is a logarithmic quantity This means that each increment on the Richter scale describes an order-of-magnitude increase in strength An earthquake that is a 7 on the Richter scale is 10 times as strong as an earthquake that is a 6 In our case, using logarithms allows us to scale down a wide range of frequencies into a small scale that can be visualized and plotted more easily This works in a way similar to the Richter scale In our case, when the magnitude of the frequency increases by a factor of 10, then log increases by 1 The second reason that using logarithms is useful is that log(AB) = log A + log B (153)
Code 128 Code Set C Creator In Visual C#
Using Barcode generation for VS .NET Control to generate, create Code128 image in Visual Studio .NET applications.
Code 128 Code Set B Encoder In .NET Framework
Using Barcode creator for ASP.NET Control to generate, create USS Code 128 image in ASP.NET applications.
By turning multiplication into addition, the mathematics of a problem is simpli ed In engineering this can be useful when calculating the overall gain of a composite system, which could be an ampli er or lter By using logarithms, we can simply add together the gain at each stage (in dB) to arrive at the overall gain of the system We call each 10-to-1 change in frequency a decade That is, two frequencies A and B are separated by one decade if A = 10 B If one frequency is twice the other, we say they are an octave apart A = 2 B (155) (154)
ANSI/AIM Code 128 Generator In VB.NET
Using Barcode generator for .NET framework Control to generate, create Code 128 Code Set B image in VS .NET applications.
Generate Universal Product Code Version A In .NET Framework
Using Barcode generator for Visual Studio .NET Control to generate, create UPCA image in .NET framework applications.
Asymptotic Behavior of Functions
Make GS1 RSS In Visual Studio .NET
Using Barcode printer for VS .NET Control to generate, create GS1 RSS image in .NET applications.
Bar Code Drawer In .NET Framework
Using Barcode generator for .NET Control to generate, create bar code image in VS .NET applications.
When analyzing the transfer function for a given system, it is important to characterize its low- and high-frequency behavior Given a transfer function
Creating Barcode In Visual Studio .NET
Using Barcode generation for Visual Studio .NET Control to generate, create barcode image in .NET framework applications.
Drawing ITF In Visual Studio .NET
Using Barcode encoder for Visual Studio .NET Control to generate, create I-2/5 image in .NET framework applications.
Bode Plots and Butterworth Filters
Paint ECC200 In Java
Using Barcode drawer for Android Control to generate, create DataMatrix image in Android applications.
Data Matrix ECC200 Generator In None
Using Barcode printer for Online Control to generate, create Data Matrix image in Online applications.
H (s), we characterize the low-frequency behavior by considering the limit
Printing GS1 - 13 In None
Using Barcode printer for Software Control to generate, create EAN13 image in Software applications.
Paint UCC-128 In Java
Using Barcode creator for BIRT reports Control to generate, create USS-128 image in Eclipse BIRT applications.
lim H (s)
Barcode Reader In Java
Using Barcode reader for Java Control to read, scan read, scan image in Java applications.
Painting UPC Code In VS .NET
Using Barcode encoder for Reporting Service Control to generate, create UPC Code image in Reporting Service applications.
(156)
DataMatrix Encoder In .NET Framework
Using Barcode encoder for ASP.NET Control to generate, create Data Matrix 2d barcode image in ASP.NET applications.
Make UPC-A Supplement 2 In Visual C#
Using Barcode generation for .NET Control to generate, create UPC-A Supplement 2 image in .NET framework applications.
When doing the analysis in terms of frequency, we let s j and then examine the limit
lim |H ( j )|
(157)
In the high-frequency case, in the s domain we consider the limit
lim H (s)
(158)
Or we let s j and examine
lim |H ( j )|
(159)
EXAMPLE 15-1 Determine the asymptotic behavior of the transfer function H (s) = 2s + 6 s 12
SOLUTION First we do a bit of algebraic manipulation H (s) = 2s + 6 s+3 s+3 2 = H (s) = 2 2 =2 = s 12 s s 12 (s + 3)(s 4) s 4
At low frequencies 1 2 = s 0 s 4 2 lim To examine the function directly in frequency, we set s j and multiply top and bottom of H ( j ) by the complex conjugate H ( j ) = 2 2 = 4 + j 4 + j 4 j 4 j = 8 j2 2 + 16
The low-frequency behavior is lim H ( j ) = lim
Circuit Analysis Demysti ed
8 j2 8 1 = = 2 + 16 0 16 2
Now let s examine high-frequency behavior We have lim H (s) = lim 2 =0 s s 4
And similarly for What about the behavior of the phase angle First let s calculate it by using H ( j ) = We nd = tan 1 At high frequencies = lim tan 1
8 j2 2 + 16
2 8
= tan 1
= 90 4
On the other hand, at low frequencies we have = lim tan 1
= tan 1 0 = 0 4
Once we understand how to characterize the low- and high-frequency behavior of the transfer function and its phase angle, we are ready to create Bode plots
Creating Bode Plots
A Bode plot is a log linear plot The axes are de ned in the following way:
The horizontal axis is the logarithm of frequency (log10 ) The vertical axis is the frequency response in decibels