Why is Capacitance Effect Modeled as Admittance Branch and Not as Series Impedance in Transmission Line Circuits?

Question

I am reading the very basics of the transmission lines circuits. I am asking this question to know more about the fundamentals and to reason out the basics.

I have two questions:

(1)

The basic circuit of a transmission line circuit consists of the elements that cause losses of the transmitted voltage and current. I always see: cable resistance, inductance and capacitance. Why do I see the inductance and resistance modeled as just series impedance (which makes things so smooth and easy in circuit analysis... just a voltage drop by an impedance) but the capacitor element is modeled as an admittance and not like them?

What I know is this:

Inductance is modeled as a XL = jωL in the frequency domain. Capacitance is modeled as Xc= -j/(ωC) in the frequency domain.

Mathematically, I can add up these two as one impedance but why do I see the transmission line circuits "insist" in putting the Xc as an admittance branch and not as series impedance? Why do they confuse us?

Is it:

• Conventional thing?
• Physical reasoning behind it? See this question what is shunt charging in power systems? I mean just to show off that it is a capacitor between the line and ground?
• Mathematical Easiness? Y as an admittance is 1/Z. Okay? Would this cause the series Z to be flipped vertically in the circuit diagram? is this the reason?

Also, (2)

As I was reading the basics, there is a Line to Line C and there is a Line to Neutral C. Are both of these two modeled in the circuit diagram in the same way..an admittance thing?

Answer 1

Because the capacitance models electric field between the signal and return conductors.

And the electric field in a capacitor is directed from one plate to the other. Therefore in our model, one plate of the capacitor must be connected to the signal wire and the other to the return wire.

An obvious way to think about why the capacitor isn't in series with the signal wire: What is the behavior of a capacitor at low frequency? What is the behavior of a transmission line at low frequency?

Answer 2

It depends on ease of math to choose Admittance or Impedance.

^{simulate this circuit – Schematic created using CircuitLab}

These are equivalent circuits with distributed LRC per unit length (m,km)

The use of Admittance or Impedance depends on the math being used for power transfer, Loading factors , impedance matching etc. There is no one right or wrong way to express it. Smith Charts and Admittance Charts in RF are very useful.