Quality factor of an inductor (Sonnet)

[omarelmorsy]

When I create a series (floating) 2-port inductor in sonnet I know it is equivalent to a pi model where we have a series R and series L and shunt components at the 2 ports.

after eming the inductor using sonnet, I knew that inductance 2 represents the series inductance and same for resistance 2 also represents series resistance.

1) I wanted to know what is the quality factor of that (series/floating) inductor, as Q represents quality factor if port 2 is grounded and Q3 represents quality factor for differential inductor, but how to calculate quality factor for the floating inductor ?

2) After I emmed an inductor I found that resistance 2 has negative value at some frequencies is that even possible or did I do something wrong ?

 

[omarelmorsy]

2) After I emmed an inductor I found that resistance 2 has negative value at some frequencies is that even possible or did I do something wrong ?

I have added a photo at which resistance 2 has a negative value with frequency, and would it be in that case the quality factor (w*L2/R2) even if R2 has a negative value ? or what should be the quality factor of a 2 port floating inductor ?

 

[volker@muehlhaus]

From what I remember, inductance2 and resistance2 are the series elements of the pi model, excluding the effect of shunt elements. I also see negative resistance2 for inductors on silicon substrates when using resistance2 equation.

I would recommend to use equation "Untapped Rdiff" which is the total effective resistance between ports 1 and 2. The corresponding inductance is "Untapped Ldiff". Both these results include the effect of series and shunt path when port 1 and port 2 are floating.

 

[omarelmorsy]

I also see negative resistance2 for inductors on silicon substrates when using resistance2 equation.

From this, it is normal to have a -ve resistance when using resistance 2 equation ? and does this physically have a meaning or just an empirical representation ?

I would recommend to use equation "Untapped Rdiff" which is the total effective resistance between ports 1 and 2. The corresponding inductance is "Untapped Ldiff". Both these results include the effect of series and shunt path when port 1 and port 2 are floating.

In this case a untapped Qdiff will represent the quality factor of the inductor in this case and the whole representation is approximately equivalent (disregarding shunt caps) to that of the pi network if both are floating ?

 

[volker@muehlhaus]

When working for Sonnet, I verified that negative resistance2 is caused by shunt branches by using an equivalent circuit pi model for silicon inductors. So it is correct in a formal way - but be aware that resistance2 not the total (effective) resistance that you measure between the terminals!

Yes, untapped Qdiff is the Q for an inductor where both terminals are floating. It is larger than Q for an inductor where one terminal is grounded.

I had created an appnote for ADS that is partially covering the topic of single ended Q vs differential Q, the pictures of grounded vs. floating shunt elements might help to understand why shunt elements have an impact on effective series impedance.

Dr. Mühlhaus Consulting & Software GmbH » Inductor EM simulation: 1-port or 2-port?

Your RF EDA solution partner since 1993

muehlhaus.com

 

[omarelmorsy]

Thanks this really helped, but from what I know that the untapped diff notation is used if the inductor used as inductor which means a differential signal is across its 2 ports, is same is valid if the inductor is used as a floating inductor for single ended circuits like Lg in image 1 where one port has input signal with maybe source resistance and other terminal connected to another device ?

One additional thing, would the same Rdiff and Ldiff would be valid if I added port 3 and port 4 as ports for ground shield ?

 

[volker@muehlhaus]

You are correct that Ldiff and Rdiff are EXACT if the inductor feed is symmetric. In your case, it is not exact but by far the best method to extract these values. The inductance2 and resistance2 values are NOT applicable for your case.

Regarding inductors with more than 2 ports: Sonnet provides another set of equations for center tapped inductors. For my own general inductors cases, I wire up everything at schematic level and then extract values for the impedance between terminals (=differential values as discussed above).