What is the cutoff frequency of the capacitively loaded Transmission line

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circuitking

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Hi, I connected a circuit like shown below. Let mtlines have length l, per unit inductance Ltl and capacitance Ctl, and capacitance C, what should be the formula for cutoff frequency?

In various books it is given that the cutoff frequency should be fc=1/(pi*sqrt(Ltl(Ctl+C/l))) but I don't see the same when I simulated. Thanks in advance.
 

circuitslave said:
In various books it is given that the cutoff frequency should be fc=1/(pi*sqrt(Ltl(Ctl+C/l)))
Click to expand...
Generally wrong, although I don't know what book you read.

Your circuit is well-known capacitive discontinuity in uniform line.

circuitslave said:
but I don't see the same when I simulated.
Click to expand...
What value do you set for reference impedance of ports ?
 

circuitking said:
In various books it is given that the cutoff frequency should be fc=1/(pi*sqrt(Ltl(Ctl+C/l))) but I don't see the same when I simulated. Thanks in advance.
Click to expand...

That's probably for an infinite cascade of embedded capacitors. I'm not sure how well one capacitor would reproduce this result. I would recommend to try additional periods and see of anything changes.
 

If mtline is setup as an ideal 50 ohm transmission line, the answer is very simple and you should be able to derive it yourself. Just a first order low pass with tau = c*Z0/2.
 
FvM said:
If mtline is setup as an ideal 50 ohm transmission line, the answer is very simple and you should be able to derive it yourself. Just a first order low pass with tau = c*Z0/2.
Click to expand...
What happens if the Line is not 50 ohm. is the same equation applicable?
 

Surely not.You get reflections at the ports, the line length also matters, and the frequency characteristic is no longer monotone. Theres's no simple cutoff frequency formula applicable.
 

FvM said:
Theres's no simple cutoff frequency formula applicable.
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Then when to use this formula fc=1/(pi*sqrt(Ltl(Ctl+C/l)))? which scenarios, line with infinite length ?

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pancho_hideboo said:
You must not use S-parameter
Click to expand...
If the port impedances are 50 ohm (i.e, in matched condition) voltage gain is equal to power gain (S21). When the circuit is Linear, Pout(dBm)= S21(dB)+Pin(dBm). So it doesn't matter which one I am looking at, all should give same cut off frequency.
 

An example of Zline > Zport is shown below. How do you design cut-off frequency in this case?

 

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