Microstrip Inductor help

Microstrip Inductors..

I'm probably being a bit think here, but I'm trying to find out how to make larger inductors out of microstrip for a low pass filter.

Eg When I design a 2GHz low pass-filter 9 section, the g values (ripple 0.05dB) for the 5th inductive element comes to

2.085 which equates to an inductance of 8.3nH.

However, using the formula's

lamdaD = c/ (freq x SQRT(Er))

Microstrip length = (lamdaD/2PI)x Arcsin((omega*L)/ZOL)

Where ZOL = 100ohms, ER = 4.5, freq = 2GHz.

If you try to enter 8.3nH, then the arsin section comes up with an error because it is greater than 1 (1.04).

How can I realise larger inductor (& capacitor values) in microstrip?

Cheers

Ody

You formula is referred to inductor having floating ends (i.e. not connected to ground). ZOL is the impedance of your microstrip. You must choose this impedance higher than XL (i.e.: omega*L); furthermore have to be satisfied:

arcsin((omega*L)/ZOL) < 45 degrees --> omega*L/ZOL < 0.7 --> ZOL > omega*L/0.7

In your example ZOL > 149 ohm

..trouble is 100 ohms is the practical limit at a width of approx 0.2mm. i can change the filter ripple value to lower the required inductors/capacitors. Of course all the examples i have found only use 3 elements with realisable component values..

You could move to a substrate having lower Er or change the layer thickness.