# The explanation about why do we define the formula of Characteristic impedance,propagation constant and Velocity propagation

There is a long transmission line

1.Characteristic impedance $$\Z_C=\sqrt{\frac{z}{y}}=\sqrt{\frac{impedance}{admittance}}\$$,and in the lossless line,$$\Z_C=\sqrt{\frac{L}{C}}\$$

2.propagation constant $$\r=\sqrt{yz}=\sqrt{admittance \times impedance}\$$

3.Velocity propagation $$\v=\frac{1}{\sqrt{LC}}\$$

We will learn these formula above when we are learning the long transmission line,and i have three questions about these three formula.

Q1:

The definition of Characteristic impedance:the ratio of the amplitudes of voltage and current of a single wave propagating along the line,i know the ratio between $$\A\$$ and $$\B\$$ means $$\\frac{A}{B}\$$ ,but i still don't understand why can we define the Characteristic impedance $$\Z_C=\sqrt{\frac{z}{y}}\$$ according to its definition,can anyone tell me why?

Q2:

propagation constant $$\r=\sqrt{yz}=\sqrt{admittance \times impedance}\$$,why can we define that?because i don't think that there is any relation between "propagation" and " admittance and impedance" ,i think it is unreasonable when $$\r=\sqrt{admittance \times impedance}\$$ when there is no any relation between "propagation" and "admittance and impedance",why don't we just define $$\r=\sqrt{y+z}\$$ ,so can anyone know why can we define propagation constant like that?

Q3:

Why can we define Velocity propagation $$\v=\frac{1}{\sqrt{LC}}\$$?what is the relation between "Velocity or propagation" and "LC",L is inductance ,and C is capacitance.

• Derivation of characteristic impedance Commented Mar 28, 2020 at 9:53
• m.eet.com/media/1072731/C0466pt3.pdf Commented Mar 28, 2020 at 11:48
• @Andyaka why is $Z_0 = R + jwL + Z_o//\dfrac{1}{G + jwC}$? Commented Mar 29, 2020 at 0:59
• Which bit of that formula don't you understand? Commented Mar 29, 2020 at 8:16
• $Z_0||\dfrac{1}{G + jwC}$ Commented Mar 29, 2020 at 8:44