Question on transmission line equation

Hi,

I am new to RF. After some time thinking, I still cannot get the answer. For 2-port device, port-2 is open. Z_in is given below. My question is how I can get the numerator and denumerator? i.e. I don't know where the fraction part is from.

Thanks,

Z_0 is the characteristic impedance of the TL, whereas Z_L is the load (Z_2). This is infinite for an open circuit.

To solve, the standard technique is to divide through by Z_L.

Thank you for your reply. I did not express my question clearly in my first post. I mainly don't understand the right part of the first equal sign, i.e. which had 'tan Bl' . I see an equation for Zin having (1+Lamda*exp(bl))/(1-Lamda*exp(bl)). The 'tan' part in the picture seems has used Lamda=+1, i.e. it is not a general equation to describe any load impedance condition. Is it right?

Regards,

You could refer to book named microwave engineering by david m. pozar. You can see where does the expression come from in chapter 2 section 3.

ruwan2 said:

Thank you for your reply. I did not express my question clearly in my first post. I mainly don't understand the right part of the first equal sign, i.e. which had 'tan Bl' . I see an equation for Zin having (1+Lamda*exp(bl))/(1-Lamda*exp(bl)). The 'tan' part in the picture seems has used Lamda=+1, i.e. it is not a general equation to describe any load impedance condition. Is it right?

Regards,

Click to expand...

Impedances can vary all over the place. An impedance might be inifite (open circuit), zero (short circuit), purely resistive, some combination of resistive and reactive. So a trasmission line with varying loads has to be able to show all those posibilities. The TAN function can go to infinity, zero, be real and imaginary, etc, so it is a good thing to model a transmission line with.

For example, a transmission line that is 88 degrees long and terminated with an short circuit might have a coulple hundred ohms of reactive impedance at the input. But change the frequency slightly so the line is now 90 dregrees long, and the input impedance is now infinite. That sudden jump for a small change in frequency is accurately predicted by the TAN BL function.

check this