Presentation is loading. Please wait.

Presentation is loading. Please wait.

Figure 11.1 Figure 11.1 Basic transmission line circuit, showing voltage and current waves initiated by closing switch S 1.

Similar presentations


Presentation on theme: "Figure 11.1 Figure 11.1 Basic transmission line circuit, showing voltage and current waves initiated by closing switch S 1."— Presentation transcript:

1 Figure 11.1 Figure 11.1 Basic transmission line circuit, showing voltage and current waves initiated by closing switch S 1.

2 Figure 11.2 Figure 11.2 Lumped-element model of a transmission line. All inductance values are equal, as are all capacitance values.

3 Figure 11.3 Figure 11.3 Lumped-element model of a short transmission line section with losses. The length of the section is Δz. Analysis involves applying Kirchoff’s voltage and current laws (KVL and KCL) to the indicated loop and node respectively.

4 Figure 11.3-1 Figure 11.3-1 Propagation Animation of electric Field in transmission line.

5 Figure 11.4 Figure 11.4 Current directions in waves having positive voltage polarity.

6 Figure 11.5 Figure 11.5 Voltage wave reflection from a complex load impedance.

7 Figure 11.6 Figure 11.6 Plot of the magnitude of V sT as found from Eq.(85) as a function of position, z, in front of the load (at z=0). The reflection coefficient phase is Φ, which leads to the indicated locations of maximum and minimum voltage amplitude, as found from Eqs. (86) and (89).

8 Figure 11.7 Figure 11.7 Finite-length transmission line configuration and its equivalent circuit.

9 Figure 11.8 Figure 11.8 A transmission line that is matched at both ends produces no reflections, and thus delivers maximum power to the load.

10 Figure 11.9 Figure 11.9 The polar coordinates of the Smith chart are the magnitude and phase angle of the reflection coefficient; the rectangular coordinates are the real and imaginary parts of the reflection coefficient. The entire chart lies within the circle |Γ|=1.

11 Figure 11.10 Figure 11.10 Constant-r circles are shown on the Γ r, Γ i plane. The radius of any circle is 1/(1+r).

12 Figure 11.11 Figure 11.11 The portion of the circles of constant x lying within |Γ| = 1 are shown on the Γ r, Γ i axes. The radius of a given circle is 1/|x|.

13 Figure 11.12 Figure 11.12 The Smith chart contains the constant-r circles and constant-x circles, an auxiliary radial scale to determine |Γ|, and an angular scale on the circumference for measuring Φ.

14 Figure 11.13 Figure 11.13 A normalized Smith Chart.

15 Figure 11.14 Figure 11.14 The normalized input impedance produced by a normalized load impedance z L = 0.5 + j1 on a line 0.3 λ long is z in = 0.28 - j0.40.

16 Figure 11.15 Figure 11.15 A sketch of a coaxial slotted line. The distance scale is on the slotted line. With the load in place, s=2.5, and the minimum occurs at a scale reading of 47 cm. For a short circuit, the minimum is located at a scale reading of 26 cm. The wavelength is 75 cm.

17 Figure 11.16 Figure 11.16 If z in = 2.5 + j0 on a line 0.3 wavelengths long, then z L = 2.1 + j0.8.

18 Figure 11.17 Figure 11.14 A short-circuited stub of length d 1, located at a distance d from a load Z L, is used to provide a matched load to the left of the stub.

19 Figure 11.18 Figure 11.14 A normalized load, z L = 2.1 + j1.8, is matched by placing a 0.129-wavelength short-circuited stub 0.19 wavelengths from the load.

20 Figure 11.19 Figure 11.19 (a) Closing the switch at time t = 0 initiates voltage and current waves V + and I +. The leading edge of both waves is indicated by the dash line, which propagates in the lossless line toward the load at velocity v. In this case, V + =V 0 ; the line voltage is V + everywhere to the left of the leading edge, where current is I + =V + /Z 0. To the right of the leading edge, voltage and current are both zero. (b) Voltage across the load resistor as a function of time, showing the one- way transit time delay, I/v.

21 Figure 11.20 Figure 11.20 With the series resistance at the battery location, voltage division occurs when the switch is closed, such that V 0 =V rg +V 1 +. Shown is the first reflected wave, which leaves voltage V 1 + +V 1 - behind its leading edge. Associated with the wave is current I 1 -, which is –V 1 - /Z 0. Counter- clockwise current is treated as negative and will occur when V 1 - is positive.

22 Figure 11.21 Figure 11.21 (a) Voltage reflection diagram for the line of Figure 11.20. (b) The line voltage at z=3l /4 as determined from the reflection diagram of (a). Note that the voltage approaches the expected V 0 R L /(R g +R L ) as time approaches infinitely.

23 Figure 11.22 Figure 11.22 (a) Current reflection diagram for the line of Figure 11.20 as obtained from the voltage diagram of Figure 11.21a. (b) The current at z=3l /4. Note that the current approaches the expected steady-state value V 0 /(R g +R L ) as time approaches infinitely.

24 Figure 11.23 Figure 11.23 Reflection diagram for example 11.11. (a) Voltage (b) Current

25 Figure 11.24 Figure 11.24 Voltage across the load (a) and current in the battery (b) as determined from the reflection diagrams of Figure 11.23 (Example 11.11).

26 Figure 11.25 Figure 11.25 In an initially charged line, closing the switch as shown initiates a voltage wave of opposite polarity to that of the initial Voltage. The wave thus depletes the line voltage and will fully discharge the line in one round trip if R g =Z 0.

27 Figure 11.26 Figure 11.26 Voltage reflection diagram for the charged line of Figure 11.25, showing the initial condition of V 0 everywhere on the line at t=0.

28 Figure 11.27 Figure 11.27 Voltage across the resistor as a function of time, as determined from the reflection diagram of Figure 11.26, in which R g = Z 0 (Γ=0 ).

29 Figure 11.28 Figure 11.28 Resistor voltage (a) and current (b) as function of time for the line of Figure 11.25, with values as specified in Example 11.12.


Download ppt "Figure 11.1 Figure 11.1 Basic transmission line circuit, showing voltage and current waves initiated by closing switch S 1."

Similar presentations


Ads by Google