الأسبوع الثالث

1. الأسبوع الثالث Transmission Line Theory 1

3. Objectives • Understand the relation between voltage and current that move (propagate) through TL, the characteristics of TL relative to the propagation constant ϒ . • Understand the physical significance of ϒ which is complex in nature, and know How to solve problems with apply this parameter. • Complete the solution of differential Eqn. to get the final form of voltage and current fortransmission line.

4. Forward direction of propagation β is phase constant i.e. β is related to the wavelength

5. By definition • The wavelength is function of TL parameters (R,L,G,C) and frequency • Also phase constant βis a function of TL parameters • As the line parameters change; the wave propagation is change, wavelength change and phase change

7. Data sheets that talking about current and voltage uses Neper not dB

8. In general the propagation constant ϒ is a combination (function) of phase and attenuation ( β and α),and function on basic parameters of TL (R,L,G,C) . • As the frequency increase the attenuation parameter will increase too. • And at the same structure TL becomes more and more lossy at higher frequencies

9. EX. TL have the next basic parameters with Freq.=1GHz Find the attenuation and phase constants for that line

10. Solution f =1GHz ω=109*2πrad/sec Propagation constant Attenuation constant phase constants

11. Voltage expression of TL At some instant of time and some other point along TL Voltage traveling directions (forward)

12. In general the voltage V+ is complex , it has phase and magnitude i.E the maximum value of the voltage (Iv+I)=10 volt (at t=0,x=0) where Фis the initial phase

13. Note: The peak voltage at x=1m is The peak value =10 e-2.231*1 = 1.075 v If we know the initial values, we can calculate the voltage (max, peak, instantaneous ) at any time and any point at the TL

14. For back word traveling wave

15. Report Calculate the instantaneous value v(t); at t =100 ns, and x=1m.. For forward and backward wave propagation v(t)F= -0.88 v v(t)B= -83.77 v

17. Now we go to complete the solving of the wave differential equations so we take into consideration the original differential equations The original differential equations + General relation between voltage and current (F & B )

19. So we can get the direct relation between current and voltage

20. F + B - This parameters has a dimension of impedance

21. Its represent the characteristic impedance of TL Its known as Z0

22. Notes: The relation between current and voltage is fixed based on the parameter which is called the characteristic impedance Z0 -Ve resistance means that the energy is not supplied but the energy is received (from the load) The forward wave Always see (Z0) But the backward wave Always see (-Z0) The propagation constant (ϒ) and the characteristic impedance (Z0) completely characterize the TL and its energy flow

23. Finally:

24. Define the origin of TL For l increased in the direction of (-x) i.e the propagation from the load to the generator

25. Define the reflection coefficient This tell how much energy reflected from the load to the source through TL