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.net barcode reader library Stepfunction response of a transmission line in Software
Stepfunction response of a transmission line Reading ECC200 In None 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 33 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 34A), the voltage at the input of the line (Vin) jumps to V/2 In Fig 32, 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 [39] Reading ECC200 In None 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
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Code39 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 34B), the wavefront has propagated onehalf the distance L, and by Td it has propagated the entire length of the cable (Fig 34C) 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 35 shows the rope analogy for reflected pulses in a transmission line A taut rope (Fig 35A) 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 35B), a wave is propagated down the rope at velocity v (Fig 35C) When the pulse hits the wall (Fig 35D), it is reflected (Fig 35E) and propagates back down the rope toward the free end (Fig 35F) 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 36A) 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 36B 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
35 Rope analogy to transmission line
36A Interfering opposite waves
Transmission line responses 73
36B 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 shortcircuited 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 [310] 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 = [312] Zo and Iinc = Vref Zo [313] (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 [314] 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 [316] Vref Vinc [315] Example 33 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 34 In Example 33, 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

