modeling of capacitance microstrip line

How can I get the capacitance of transmission line in lower frequency ?
as what I know , in lower frequency , the capacitance effect is little , almost can be neglected.
How about this concept ? It it right ?

thanks

You may simulate your line with RF simulator and get impedance from which it is easy to see capacitance or inductance.

what impedance parameter should I use ?
I have S-parameter of microstrip line, how to calculate it into capacitance ?

thanks

imag(Y11)=2*PI*f*c

For <1GHz, just do hand calculation using the parallel plate formula.

I have used this formula imag(Y11)=2*PI*f*c
But the capacitance is negative.
My structure is only one trace , then add port in the terminal.

Which means you are high enough in frequency for inductance to effect your measurement. As the previous poster said, us the parallel plate formula for an estimate.

To myem,

In any RF simulator you may find 2 port black-box. If your S-parameter file is in s2p format just put two ports and this black-box in between. Assign your S-parameter file to the black-box and simulate for required frequency range. Then use reactive part of impedance to calculate capacitance (if X is negative) as C=1/w*X or inductance (if X is positive) as L=x/w for each of the frequencies of interest.

If you have s1p file use one port and terminate opposite end of the TL with required by S-parameter file resistance.

OK, now I see the problem. I need to think about this some more. Obviously it does not work at high frequencies since Z0=sqrt(L/C) and the distributed L and C cancel perfectly. It can't be measured by the Y parameter method at 0 Hz due to divide by zero. If you replace the microstrip with an ideal TLINE element you get zero L and C, which makes sense too. So what's going on here? Need to think about the math some more. Is it just a problem with a microstrip model (frequency domain model ill defined at DC), or something more fundamental as f approaches zero (that's kind of obvious trying to measure Xc=1/(2*PI*f*C).

C and L are essentially defined at DC, but we measure it with AC since that's easy. However when measuring at AC you can't have one without the other. So with structures where they are in balance we have a dilemma. This is a brain teaser. It probably can't be done with AC measurements without some knowledge of the structure, or maybe not possible at all (to get an accurate answer).

Well. I include here the first page of my MathCAD worksheet that was created for analysis of how PCB trace will affect the circuit performance. There is simple case when varactor with C=7.5pF and R=1 Ohm is connected to resonant tank through two traces 5 mm each. Total trace length was considered 2x5=10 mm. This is numerical calculations that show what tank will see at the opposite end of the line. 7.5 pF become 19.8 pF! Hard to believe, but this is the true. There is also verification for this calculation with RF simulator (LINC2). I hope it can help to understand how trace can change the impedance of one side termination.

The attachef file is microstrip line struture.
Below is the s2p content in 100MHz.
I want to see the 100MHz capacitance of this microstip line.
But don't know to calulate.

thanks



! symbol freq-unit parameter-type data-format keyword impedance-ohms
# MHz S RI R 50.000000

!BEGIN EXCITATION_MAPS
! Excitation 1 -> P1M1
! Excitation 2 -> P2M1
!END EXCITATION_MAPS

100 -0.056048 -0.223758 0.943486 -0.237151 0.943486 -0.237151
-0.056056 -0.223754

The RF simulators usually cannot work with single line S-parameter file, so I did a kind of surgery on your file and duplicate your line three times in order to "fool" the simulator. Results in attached file. If you measured S-parameter file right, then reactance X is equal to -19.2 Ohm. Therefore, it is capacitive and the capacitance for 100MHz is roughly 82.9 pF. Probably in your case it was better to submit the geometry and substrate data and I could model your line, but I hope that I answer your question.

You guys need to think about what you doing when asking for capacitance at a frequency. Xc=2*PI*F*C; C is generally not a function of frequency unless it's dielectric is. Capacitance is a DC term; how much charge (electric flux) is stored with an applied voltage. Same for inductance; how much magnetic flux for an applied current. So there are two things you could be asking for:

1) What is the total capacitance of the transmission line? It has a distributed capacitance which should sum up to the total capacitance; how much charge is stored up if I apply a DC voltage? This capacitance can be calculated by one of Maxwell's static equations (Gauss' law) and is straight forward for parallel plates.

2) What is the equivalent capacitance of the reactance that I measure at a certain frequency; C=1/(2*PI*Xc).

Take a look at the example simulation:

If I terminate a transmission line with Z0 and try to measure it's inherent capacitance at a certain frequency it's a futile exercise since I can't even get a signal back. It's capacitance measures 0 but it must have a capacitance since it's a conductor. This is shown by port 3 of the example. I can change the Z0 of the line or the termination and then I get a reflection to measure reactance, however I can tweak this to achieve any capacitor value I want.

Port 1 shows what happens when there is no termination. As frequency decreases the distributed capacitance looks more lumped. Port 2 measures a parallel plate capacitor of equivalent dimensions; this is the inherent capacitance. You can never truly measure the capacitance with an AC signal since you have inductance too. However by lowering frequency you can get get close.

To madengr,
You showed three typical cases: open stab, shorted stab and transmission line. The initial question was about transmission line and I provided the answer. Your port 3 schematic corresponds to this case.
Stabs are totally different story. These are the cases when we use transmission line as capacitor or inductor. Your schematics for port 1 and 2 may correspond to these cases if you replace capacitor in port 2 schematic with stab. Otherwise this simulation is meaningless for this topic discussion.
The initial question was as I think dictated by the interest what is the effect on the circuit from transmission line or PCB trace. This is why I posted such an example. This is practical question and analysis and it is not require Maxwell?s equations. I believe it answers your sentence ?You guys need to think about what you doing when asking for capacitance at a frequency?. Reactance of TL or trace is extremely important for RF design and it is function of frequency.

to RF-OM
As what I know about black_box simulation , the terminal should be ground in order to calculate reactance.
The attached file is procedure about my simulation.
result is the Z11 is positive and capacitance is negative.

thanks

I think that this is big mistake. When you use two port black box with three pins only the third ground pins must be grounded. Look on your s2p file. It has S22 parameter numbers and you are shorting this port! S-parameters are measured when ports are terminated with characteristic impedance which is usually 50 Ohm, but nor zero. You may ground an opposite end of the piece of transmission line for such measurements. In this case you will get shorted sub and will measure its impedance. The latter will be inductive for lengths below 1/4 wave, very high purely resistive at the 1/4 wave and capacitive for the next quoter of wavelength. You may see all from the Smith chart.

to RF-OM
thanks for you feedback very much.
But I don't know right or wrong about simulaion result.
Now let's do a simple case of microstrip line together.
the property is as shown below
(1)substrate
Alumina
thickness=200um , Er=9.8
(2)conductor
Copper
conductivity=5.8E+7 s/m , thickness=10um
length=10000um ; width=50um

to osbserve the 100MHz capacitance & inductance
My answer:
capacitanc=0.9971pF
inductance=6.793nH

I included three jpg files with three different simulations. One for microstrip as a transmission line, one for microstrip as a shorted stab and one for microstrip as an open stab. All simulations were done with LINC2 RF simulator for physical model of microstrip line. This is the most accurate simulator, I checked it accuracy for many times. Results are on pictures. Please note that only microstrip as a transmission line case may be simulated with S-parameter file as I mentioned earlier.