# .net barcode reader library Step-function response of a transmission line in Software Encoding DataMatrix in Software Step-function response of a transmission line

Step-function response of a transmission line
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Creating Data Matrix 2d Barcode In None
Using Barcode encoder for Software Control to generate, create Data Matrix 2d barcode image in Software applications.
Figure 3-3 shows a parallel transmission line with characteristic impedance Zo connected to a load impedance ZL The generator at the input of the line consists of a voltage source V in series with a source impedance Zs and a switch S1 Assume for the present that all impedances are pure resistances (ie, R + j0) Also, assume that Zs = Zo When the switch is closed at time To (Fig 3-4A), the voltage at the input of the line (Vin) jumps to V/2 In Fig 3-2, you may have noticed that the LC circuit resembles a delay line circuit As might be expected, therefore, the voltage wavefront propagates along the line at a velocity v of: v= where v is the velocity, in meters per second L is the inductance, in henrys C is the capacitance, in farads 1 LC 
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
DataMatrix Creation In C#
Using Barcode maker for Visual Studio .NET Control to generate, create ECC200 image in Visual Studio .NET applications.
Zs Zo V ZL
Data Matrix ECC200 Encoder In .NET Framework
Using Barcode creator for ASP.NET Control to generate, create DataMatrix image in ASP.NET applications.
Data Matrix 2d Barcode Creator In VS .NET
Using Barcode encoder for VS .NET Control to generate, create Data Matrix 2d barcode image in .NET applications.
Zs=ZL
Make Data Matrix 2d Barcode In VB.NET
Using Barcode encoder for .NET framework Control to generate, create ECC200 image in Visual Studio .NET applications.
Code-39 Maker In None
Using Barcode creator for Software Control to generate, create Code-39 image in Software applications.
3-3 Schematic example of transmission line
UPC Symbol Creation In None
Using Barcode generator for Software Control to generate, create UPC Code image in Software applications.
Encode European Article Number 13 In None
Using Barcode maker for Software Control to generate, create GS1 - 13 image in Software applications.
Transmission line responses 71
Generating Bar Code In None
Using Barcode generator for Software Control to generate, create barcode image in Software applications.
Make Code 128B In None
Using Barcode printer for Software Control to generate, create Code 128 image in Software applications.
T0 V
Encoding EAN-8 In None
Using Barcode generator for Software Control to generate, create EAN8 image in Software applications.
Drawing 1D Barcode In Visual Basic .NET
Using Barcode encoder for VS .NET Control to generate, create 1D Barcode image in .NET applications.
V/ 2 L/ 2
GTIN - 12 Recognizer In Visual Basic .NET
GS1 - 12 Creator In Objective-C
Using Barcode creation for iPad Control to generate, create UPC-A Supplement 2 image in iPad applications.
T1 V
Draw Barcode In Java
Using Barcode encoder for Android Control to generate, create barcode image in Android applications.
Draw Code 128 Code Set A In None
Using Barcode drawer for Online Control to generate, create Code 128 Code Set B image in Online applications.
3-4 Step-function propagation along transmission line at three points
Code-39 Scanner In Visual Basic .NET
Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in VS .NET applications.
Code 39 Extended Creator In None
Using Barcode generator for Excel Control to generate, create Code 39 Full ASCII image in Excel applications.
V/ L/
At time T1 (Fig 3-4B), the wavefront has propagated one-half the distance L, and by Td it has propagated the entire length of the cable (Fig 3-4C) If the load is perfectly matched (ie, ZL = Zo), then the load absorbs the wave and no component is reflected But in a mismatched system (ZL is not equal to Zo), a portion of the wave is reflected back down the line toward the generator Figure 3-5 shows the rope analogy for reflected pulses in a transmission line A taut rope (Fig 3-5A) is tied to a rigid wall that does not absorb any of the energy in the pulse propagated down the rope When the free end of the rope is given a vertical displacement (Fig 3-5B), a wave is propagated down the rope at velocity v (Fig 3-5C) When the pulse hits the wall (Fig 3-5D), it is reflected (Fig 3-5E) and propagates back down the rope toward the free end (Fig 3-5F) If a second pulse is propagated down the line before the first pulse dies out, then there will be two pulses on the line at the same time (Fig 3-6A) When the two pulses interfere, the resultant will be the algebraic sum of the two In the event that a pulse train is applied to the line, the interference pattern will set up standing waves, an example of which is shown in Fig 3-6B
Reflection coefficient
The reflection coefficient of a circuit containing a transmission line and load impedance is a measure of how well the system is matched The absolute value of the re-
72 Transmission lines
3-5 Rope analogy to transmission line
3-6A Interfering opposite waves
Transmission line responses 73
3-6B Standing waves
flection coefficient varies from 1 to +1, depending upon the magnitude of reflection; = 0 indicates a perfect match with no reflection, while 1 indicates a short-circuited load, and +1 indicates an open circuit To understand the reflection coefficient, let s start with a basic definition of the resistive load impedance Z = R + j0: ZL = where ZL is the load impedance R + j0 V is the voltage across the load I is the current flowing in the load Because there are both reflected and incident waves, we find that V and I are actually the sum of incident and reflected voltages and currents, respectively Therefore: ZL = ZL = where Vinc is the incident (ie, forward) voltage Vref is the reflected voltage Iinc is the incident current Iref is the reflected current V I Vinc + Vref Iinc + Iref [311A] [311B] V I 
74 Transmission lines Because of Ohm s law, you can define the currents in terms of voltage, current, and the characteristic impedance of the line: Vinc Iinc =  Zo and Iinc = Vref Zo 
(The minus sign in Eq 313 indicates that a direction reversal has taken place) The two expressions for current (Eqs 312 and 313) may be substituted into Eq 311 to yield ZL = Vinc + Vref Vinc Zo Vref Zo 
The reflection coefficient is defined as the ratio of reflected voltage to incident voltage: = Using this ratio in Eq 314 gives = ZL Zo ZL + Zo  Vref Vinc 
Example 3-3 A 50- transmission line is connected to a 30- resistive load Calculate the reflection coefficient Solution: ZL Zo ZL + Zo (50 ) (30 ) (50 ) + (30 ) 20 = 025 80
Transmission line responses 75 Example 3-4 In Example 3-3, the incident voltage is 3 V rms Calculate the reflected voltage Solution: If Vref = Vinc then Vref = Vinc = (025) (3 V) = 075 V The phase of the reflected signal is determined by the relationship of load impedance and transmission line characteristic impedance For resistive loads (Z = R + j0): if the ratio ZL/Zo is 10, then there is no reflection; if ZL/Zo is less than 10, then the reflected signal is 180 out of phase with the incident signal; if the ratio ZL/Zo is greater than 10 then the reflected signal is in phase with the incident signal In summary: Angle of reflection No reflection 180 0