Embedded Track Inductance

I'm trying to determine the inductance of a track embedded within a PCB to simulate its affect. The layer stack info is below as I've found plenty of tools to determine trace impedance:



The length of the track is 77 mm. How do I get from the stack info provided to an inductance that I could plug into LTSpice to simulate?

Better tools give you specific capacitance and inductance per length unit. Does the tool really display -17.7 ohm? Something's obviously wrong then.

I get 56 nH/m.

There are a few problems:

- The online calculator gives invalid results (negative ZL), most likely because the aspect ratio (line width / line thickness) is too extreme
- That very wide line has a lot of shunt capacitance, so treating it as a series inductance is inaccurate.

Line impedance of a lossless line is
ZL=sqrt(L'/C')

You can get the free Sonnet Lite EM solver and simulate the line as a flat (zero thickness) conductor, which is quite accurate at this width. Then, you can export a SPICE pi model (L + C).

I did a quick setup (model attached) and get ~ 7.6 Ohm line impedance.
Sonnet Lite model: View attachment sl.zip

A simple equivalent circuit with series L and shunt C is valid if the line length is less than 1/20 wavelength. For the line length of 10mm that I simulated, I get this equivalent circuit:

C_C1 1 0 3.991385pf
C_C2 2 0 3.993408pf
L_L1 1 2 0.590898nh

If the line is longer than 1/20 wavelength at your frequency of interest, you need to cascade multiple short segments (cascaded LC ladder network, optional R and G are conductor losses and dielectric losses).

Thanks for your replies FvM and Volker. Sonnet Lite looks really good, but the track I want to simulate isn't RF. It's the highlighted track below:



The gate of the SCR will be driven by a micro and the trigger coil is a Tokyo Photoflash. There is concern that a track that is too long from the SCR to capacitor TC will be too inductive and the interaction of the parasitics would cause problems, so I'm just trying to get a feel for a realistic value to plug into Spice.

HardwareChap said:

Sonnet Lite looks really good, but the track I want to simulate isn't RF.

Click to expand...

Fast signals are RF, too :grin:

In any case, include a PI model with both shunt C and series L for realistic results: 77mm*0,059nH/mm series L and 77mm*0.4pF/mm shunt C at both ends.

You can ignore trace capacitance an inductance in this circuit. The trigger transformer has primary referred leakage inductance in a µH order of magnitude, trigger circuit capacitance is tens to hundreds nF.