Microstrip Inductor help

[odyseus]

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

 

[albbg]

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

 

[odyseus]

..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..

 

[albbg]

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