HFSS RF IC transformer issues

ic transformer

I want to use HFSS to simulate a RF-IC spiral transformer.

I have succeeded in simulating a single coil spiral inductor, and get the right inductance using the following formula: L=-1/2/pi/Freq/im(Y11)

Based on this, I want to use the following formula for mutual inductance: M=-1/2/pi/Freq/im(Y12)

But the results seem not quite right. The M values I get are negative, and worse, they have a larger magnitude than the L values! That should be impossible since M=k*sqrt(L1*L2) and 0<k<1, right?

Any ideas about what’s going on? Thanks!

My file is attached

hfss port transformer

Use im(Y12)/2/pi/freq instead!

Added after 8 minutes:

Are you sure the equation to caculate mutual inductance is correct?
In the addition,the transformer has four ports ,is it proper to simulate it with two ports?

mutual inductance hfss

Here is an update, now that I have figured out the issues a little better.

I used the formula: L=-1/2/pi/Freq/im(Y11)

This came from the following considerations: Impedance Z=jwL so Admittance Y=1/(jwL)=-j/w/L

Y11 means the ratio I1/V1 with V2=0.

I thought that was correct, but since then I have had doubts: Is it the right assumption that V2=0? Perhaps it is better to use the Z-parameter Z11, which assumes that I2=0! After all, a changing current in coil 2 will induce voltage in coil 1 which will change the ratio between V1 and I1. Forcing I2 to be zero should eliminate that effect, right?

So I started using L=im(Z11)/2/pi/Freq instead. And similarly, M=im(Z12)/2/pi/Freq to get the mutual inductance. (Note: these formulas are from memory and it's remotely possible I wrote them wrong.) With this formula, the M values were perfectly reasonable.

The L values were almost identical whether using Y or Z parameters, though the self-resonant frequency did change somewhat. All in all I see more reason to trust the Z parameters. I did a separate calculation based on the ABCD parameters (lots of complicated formulas which I got from somewhere), and the results were exactly the same as with Z parameters.

There seems to be a sort of chicken-and-egg relation between voltage and current which I don't quite understand (anyone want to explain?), but when using Z11 and Z12 the results seem to be correct.

I also decided that the minus sign issues were trivial. I think I fixed them by changing the direction of the integration line on the lumped port (between the two terminals of each inductor)

Re: mutual inductance hfss

Hi,

I happen to be working on the same project now on a 90nm process. I am also using HFSS to create a step up transformer. I used the formulas above for computing L and M and the values I am getting are perfectly reasonable.

My problem now is, I don't now how to compute for the amount of voltage gain created by my step up transformer. I understand that it must be reflected from the s-parameters I have but it is in terms of power and will always be less than '1' (in magnitude). Or is it possible that I will be getting an s-parameter greater than '1' in HFSS since I have a step up transformer?

Thank you!

You only have an exact voltage ratio if the transformer is absolutely ideal. In a non-ideal transformer, some energy will be dissipated and some reflected back to the source, so the destination voltage will be lower than expected. If energy goes through the transformer in the opposite direction, voltage will be lowered at the OTHER terminal. Thus there is no constant voltage ratio.

If you want an approximation for voltage ratio, assuming perfect coupling and no dissipation, you can calculate as follows:

Z1/Z2=L1/L2
Z1/Z2=(V1/V2)/(I1/I2)=(V1/V2)^2
V1/V2=sqrt(L1/L2)

Re: ic transformer

shlomo22 said:

I want to use HFSS to simulate a RF-IC spiral transformer.

I have succeeded in simulating a single coil spiral inductor, and get the right inductance using the following formula: L=-1/2/pi/Freq/im(Y11)

Based on this, I want to use the following formula for mutual inductance: M=-1/2/pi/Freq/im(Y12)

But the results seem not quite right. The M values I get are negative, and worse, they have a larger magnitude than the L values! That should be impossible since M=k*sqrt(L1*L2) and 0<k<1, right?

Any ideas about what’s going on? Thanks!

My file is attached

Click to expand...

can you send me the project about the single coil spiral inductor? email:820267612@qq.com
thanks!

Re: ic transformer

mustangyhz said:

can you send me the project about the single coil spiral inductor? email:820267612@qq.com
thanks!

Click to expand...

Unfortunately, I have moved on to a different project and field... Ask on the forum for examples of a single coil spiral inductor, or HFSS examples in general, somebody should have.