Numbers are fascinating things, and the way they are presented can influence our thinking far more than we would like to admit, with $15.99 seeming like a much better deal than $16.00 (though it depends which side of the transaction you sit on!) When looking for a new job, you may prefer to round your existing salary up to the nearest thousand dollars, not down, when speaking with a potential employer. Likewise, a salary of $60,000 sounds better than one of $0.061 million, even though the latter is a larger number. Our brain has been programmed to suppress the importance of numbers to the right of the decimal point.
Such is the case with the loss tangent of materials. It is a tiny number and so to our minds looks insignificant, but it has a directly proportional effect on the energy loss suffered by a dielectric. I am always curious that engineers seem to obsess over dielectric constant, the ability of a substrate to store energy and its effect on impedance, which is a one over root effect, so this is a second order impact on Z0.
Yet engineers go to great lengths to attempt to find the exact value of Er despite its second-order effect on the circuit characteristic impedance. But the loss tangent? Well, it’s a small number, isn’t it? So, why not round it off to a few decimal places? Logical thought is suspended just because it is a small number, but when you are modeling insertion loss, the loss is directly proportional to the loss tangent.
A Practical Example
Because loss tangent is a small number, it is perhaps easy to forgive people who round it off to fewer decimal places. Our minds are wired to dismiss numbers far to the right of the decimal point. However, this can lead to unintended miscalculations when rounding small value parameters such as loss tangent which has a directly proportional effect on the insertion loss. A rounding to 2 decimal places of a TanD say, from 0.015 to 0.02 (quite legitimate, you may think) would actually lead to the modeling of insertion loss being overpredicted by a massive 33%.
You can see the effect when using a PCB field solver’s frequency-dependent calculation feature to model loss in an offset stripline 1B1A controlled impedance structure.
To read this entire column, which appeared in the October 2017 issue of The PCB Design Magazine, click here.