I have some questions regarding the user's guide for Momentum in ADS2005A:

1. On page 3-5, there is a note at the bottom of the page under the "Defining an Interface Layer" heading, that says thick substrates should be less than 0.5 wavelength in thickness. An example is given, that a 10-mil substrate with a cover height of air of 300 mils is good up to 20 GHz (it's not listed in the example, but I calculate the free space wavelength as 590 mils at 20 GHz, so a half wavelength is 295 mils). I don't understand how this distance relates to the substrate--a 10 mil substrate is nowhere near 295 mils. Is this an error in the example?

2. On page 3-16, there is an equation for the high frequency equivalent sheet impedance, ZHF = (1+j)/(2*conductivity*skin_depth). Can you provide some information as to where this equation comes from? I find by looking in textbooks that the surface resistance is given by 1/(conductivity*skin_depth), but I cannot find where the remainder of the equation comes from. Also, why does this equation not contain a term for the conductor thickness? What if the conductor thickness is less than a skin depth?

3. On page 3-18, there is a sentence that says "Typically, when the height/thickness aspect ratio is smaller than a factor of 5, the effect of accounting for the finite thickness of the conductors will need to be allowed for in Momentum simulations." What is the "height" that this statement is referring to? I would think a thick conductor would be relative to the width/thickness ratio.

4. I'm trying to model rectangular spiral inductors on an IC that has many layers of metals. I'm looking for an accurate value for both inductance and Q. We've been using sheet metals and giving them "thickness" using vias within the substrate layers. As I've read through the Momentum manual, I'm wondering what benefit there is to this approach, and if it would be better for us to use the thick conductor model. Are the vias doing anything other than contributing to the loss/Q calculation? Or do they affect the inductance? In this case, the via has the same shape as the strip metal traces. I believe my question could be rephrased as, does Momentum compute current flow in the vias, or does it simply use the vias to determine the voltage/potential of the various layers that they connect?

Thanks.

1. On page 3-5, there is a note at the bottom of the page under the "Defining an Interface Layer" heading, that says thick substrates should be less than 0.5 wavelength in thickness. An example is given, that a 10-mil substrate with a cover height of air of 300 mils is good up to 20 GHz (it's not listed in the example, but I calculate the free space wavelength as 590 mils at 20 GHz, so a half wavelength is 295 mils). I don't understand how this distance relates to the substrate--a 10 mil substrate is nowhere near 295 mils. Is this an error in the example?

2. On page 3-16, there is an equation for the high frequency equivalent sheet impedance, ZHF = (1+j)/(2*conductivity*skin_depth). Can you provide some information as to where this equation comes from? I find by looking in textbooks that the surface resistance is given by 1/(conductivity*skin_depth), but I cannot find where the remainder of the equation comes from. Also, why does this equation not contain a term for the conductor thickness? What if the conductor thickness is less than a skin depth?

3. On page 3-18, there is a sentence that says "Typically, when the height/thickness aspect ratio is smaller than a factor of 5, the effect of accounting for the finite thickness of the conductors will need to be allowed for in Momentum simulations." What is the "height" that this statement is referring to? I would think a thick conductor would be relative to the width/thickness ratio.

4. I'm trying to model rectangular spiral inductors on an IC that has many layers of metals. I'm looking for an accurate value for both inductance and Q. We've been using sheet metals and giving them "thickness" using vias within the substrate layers. As I've read through the Momentum manual, I'm wondering what benefit there is to this approach, and if it would be better for us to use the thick conductor model. Are the vias doing anything other than contributing to the loss/Q calculation? Or do they affect the inductance? In this case, the via has the same shape as the strip metal traces. I believe my question could be rephrased as, does Momentum compute current flow in the vias, or does it simply use the vias to determine the voltage/potential of the various layers that they connect?

Thanks.

1. Since the Microstrip field is not confined to the substrate but extends into the air above, the air layer up to the cover is the thickest layer of interest. It's 300 mils are pretty close to the 295 mils you calculated.

2. The cited equation basically results from the solution of the Helmholtz equation for plane waves in cartesian coordinates (i.e. layered media, as substrate stacks). Wave propagation is defined by a generally complex epsilon, the imaginary part of which also accounts for the conduction current density induced by an electric field, depending on bulk conductivity. Ideal vacuum and ideal metal are the extreme cases of such a general "dielectric".

Practical dielectrics possess an epsilon_r (affecting the epsilon's real part, slowing down wave propagation) and on top a certain conductivity (affecting the imaginary part, causing freq. dependent losses, specified as tan_delta). For practical metals in contrast the epsilon's real part is usually neglected, it's imaginary part dominates by far (or is infinite in perfect metal). This remaining "purely" imaginary epsilon in conjunction with a purely real mju produces a characteristic wave impedance (Z=sqrt(mju/epsilon)) in metal with equal real an imaginary parts, as suggested by the formula on page 3-16.

But: Where the factor 2 comes from, is not clear to me. ??? According to my books it should read (1+j)/(conductivity*skin_depth). Identical current flow on upper and lower surface of the strip assumed??

Only for metal thick as compared with the skin depth, the "sheet impedance" is equal to the "characteristic wave impedance". (Sheet impedance is only a model, assuming all current flow on the surface, current density in fact decays exponentially). For thinner metal a higher sheet impedance results!

Your formula for surface resistance, at last, marks in fact the real part of the sheet impedance. This is the important one for calculating the copper loss. The imaginary part is often omitted, it corresponds to the less interesting inner inductance and converges towards zero as frequency approaches infinity.

3. I assume, "height" actually is supposed to mean "width".

4. Earlier versions did not have real thick conductor modelling capability, the only way to account for these effects was using sheet conductors connected by vias. Only from ADS2003C on this was improved step by step ( http://eesof.tm.agilent.com/products/ad ... ew_13.html ). Using "thick conductor" sure is the better choice. Probably you could refer to documentation of the older versions available online for detailed implications of the via approach.

Best Regards, eltz