3.2.2 Impedances

 represent the loss of the dielectric

Combination of the series and parallel parameters present an opposition to the current flowing through the line and is called an Impedance Z, where

�� =(�� ∓����)��ℎ��

A measure of how easily a circuit or device will allow a current to flow is called an admittance Y, where,

1 ��

Therefore, admittance can be calculated from given impedance Z and vice versa.

EXAMPLE 1:

(a) Determine the admittance Y1 for the given Z1= (100 + j50) Ω and

(b) Z2 for given Y2= (0.015 – j0.023) S

(a) Y1(S)= 1

Z1

1 100+j50 =⋯ … (��) ��2( )= 1 ��2

1 0.015−��0.023

3.2.2 Impedances

In high frequency transmision line, signal propagates inside the line using electromagnetic wave. The input signal will be referred as incident wave that will travel along the transmission line of length l. When the wave reaches the load at the end of the line, part of the wave will be reflected back as shown by Figure 3.1.3. The magnitude or the strength of the reflected wave will be determined by the characteristic of the load.

Figure 3.1.3: Propagation of signal or wave inside the transmission line where the incident wave is reflected back by the load at the end of the line.

3.2.2.1 Characteristic impedance Z0

In high frequency transmission line, the impedance Z, can be also represented by the ratio of E field to the H field of the wave or the ratio of Voltage to Current.

If the ratio of voltage amplitude to current amplitude is constant (that a wave travelling in one direction only with no reflection, then, it is called Characteristic Impedance Zo, and can be determine by the following according to type of transmission line ��+������LossyLine ��0 = √��+������

For lossless line G = R = 0, thus,

LosslessLine ��0 = √�� ��

From the above equations, Zo, is determined by the material of the conductor and the dielectric surrounding the conductor and length of transmission line does not effect the value of Zo

3.2.2.2 Input impedance Zin

Generally, the impedance at a position near the generator is not the same as the impedance of the load, because of the presence of the transmission line. It is called input impedance Zin. The input impedance is the impedance of the transmission line at an input position looking towards to the load.

The input impedance is determined according to type of transmission line as follows; For lossy line , ������ =��0 (���� ��0 + + �� �� ��0 ���� ������ℎ���� ������ℎ����) For lossless line , ������ =��0 (���� ��0 + + �� �� ��0 ���� ������ℎ���� ������ℎ����)

Where �� is the propagation constant

And is also stated in term of attenuation constant α and phase constant β,