# Optimal line length for TRL standard

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#### maria fernanda

##### Newbie level 5 trl line length

I am trying to create a TRL standard, but I am not sure what line lenght is correct to use.
According to "Network analysis appliyng the 8510TRL calibration for non-coaxial measurements", (pg 16) the optimal line length is chosen by

Electrical length(cm)=15/(f1(GHZ)+f2(GHz))

But I do not know if this length is the one that I fabricate "physically" or if I need to divide electrical length by the root square of dielectric constant of the substrate.

Also in delay offset I am not considering the dielectric constant...Is this correct?
All this is for on-wafer calibration..

Thanks!!!

##### Full Member level 6 The electrical length of the line should be greater than 20 degrees at your lowest frequency of measurement, but not more than 160 degrees at the highest frequency. In order to cover very wide bandwidths you need multiple lines.

Again, this is the electrical length however it's not sqrt(Er), it's sqrt(Eeff) where Eeff is the effective dielectric constant sicne your transmission line is probably in inhomogeneous dielectric (microstrip, CPWG).

Also use STEPPED sweep in the VNA instaed of SWEPT.

This is a good resource:

### maria fernanda

Points: 2

#### maria fernanda

##### Newbie level 5 e_eff ?

Ok, I understand the importance of the effective dielectric constant, but what are the relationship between electrical length (cm) as appears in "Network analysis appliyng the 8510TRL calibration for non-coaxial measurements", (pg 16) and physical length? I suppose the physical length is which I need to use in order to make the line “physically” on the substrate together with the DUT?

Please, let me explain you my experiment. I wish to use CPW structures for the calibrations. I found that I need two lines for covering the frequency span 1GHz-10GHz, and I found that the optimal break frequency was: 3.16GHz.
For this result I use:

Electrical length (cm)=15/(1GHz+3.16GHz)=3.605cm……for first line (1GHz-3.16GHz)
Electrical length (cm)=15/(3.16GHz+10GHz)=1.140cm…for the second line (3.16GHz-10GHz).

If these results were correct, I found the delay:

Delay(ps)=electrical length(cm)/light velocity(cm/s)

I do not know if this delay is the one that I enter to the NVA in order to modify the standards definitions or I need to affect it by the Eff?

I found that Eeff=6.9 for the CPW that I am using which uses a GaAs (h=400um) substrate and was designed with S=32um , W=22um for 50ohms.

Thanks so much! I appreciate you help! ##### Full Member level 6 multiline trl

You want to go from 1 GHz to 10 GHz so the break frequency is the geometric mean between the two; sqrt(1*10)=3.16 GHz.

So now you have a line to be used from 1 GHz to 3.16 GHz, and another from 3.16 GHz to 10 GHz.

The length of the line cannot be less than 20 degrees at the lowest frequency FL, and not more than 160 degrees at the highest frequency FH.

However the greatest accuracy is achieved at frequencies where the length is approximately 90 degrees, what I call the middle frequency FM.

So for the first line choose the midpoint FM=(1+3.16)/2=2.08 GHz.

Now use the equation to calculate a 90 degree long line:

length = 90/360 * c/(FM*sqrt(E_eff))

c=3E8 m/sec
FM=frequency in Hz
E_eff=effective permittivity of the transmission line

So plugging in the numbers you get 90/360*3E8/(2.08E9*sqrt(6.9))=1.37 cm

Now with this 1.37 cm line how low and high in frequency can you go?

Re-arrange that above equation to solve for both frequencies:

FL = 20/360 * c/(length*sqrt(E_eff))
FH = 160/360 * c/(length*sqrt(E_eff))

Solving for the two above yields FL=463 MHz and FH=3.7 GHz.

You can also just solve for the lowest frequency and the upper frequency is always 8 times that. This sets the useable bandwidth of the TRL LINE.

We also need to know the time delay which is:

D=length/C*sqrt(E_eff)
or
D=1/(4*FM)

So, to summarize so far we have LINE1:

FM=2.08 GHz
length=1.37 cm
FL=463 MHz : this is programmed in the VNA
FH=3.7 GHz : this is programmed in the VNA
D=120 ps : this is programmed in the VNA

Now repeating for the LINE2:

FM=6.58 GHz
length=0.43 cm
FL=1.5 GHz : this is programmed in the VNA
FH=12 GHz : this is programmed in the VNA
D=38 ps : this is programmed in the VNA

Now you should do a quick check of your calculations in a circuit simulator (see attached graphic).

So now you create two LINE standards in the VNA and you can actually run your cal from 463 MHz to 12 GHz. However, if you program in the frequencies as calculated the VNA will use LINE1 from 463 MHz to 1.5 GHz, and LINE2 from 1.5 GHz to 12 GHz. The higher frequency lines take precedence (I believe) or it may be the order in which you perform the cal. This may results in a little data bump at either 1.5 GHz or 3.76 GHz as the VNA transitions to new cal coefficients.

You have two lines that share a band from 1.5 GHz to 3.76 GHz but the VNA uses only one LINE standard. However if you use the NIST Multi-Line TRL algorithm you use both lines to get a better calibration. The Mult-Line algorithm computes a weighted average over frequency for both lines, eliminating any bump and giving you a more accurate calibration. You can even have multiple overlapping LINE standards and the algorithm will use all of them. If you buy the WinCal software it has the NIST algorithm included. You can get the algorithm for free from NIST but it runs under HTBasic and it very dated.

I like to build up a spreadsheet where I enter E_eff and length, and it calculates FL, FM, FH, and delay. Add a new row for each line and you can tweak the lengths to optimize the overlap.

Focus Microwaves claims you can go down below 20 degrees line length for you lower frequencies when using stepepd mode. Agilent disagrees with this. I don't know what NIST says. However you should always use stepped mode in TRL. I use it for all VNA measurements. You only need swept mode in a production environment for high throughput.

• Majid Rafei, mgberry, modjii and 4 others

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