Klofenstein taper design 101

Hi everyone,

I am an absolute newbie here and want to design a Klofenstein taper using a microstrip fabrication

Z1=15,

Z2=50Ohm,

starting frequency is 1.5GHz assuming until 20GHz

S11<-15dB

These are the specifications of the design.
Now I have found a very useful website which has been alot of
help
Klopfenstein Taper - Microwave Encyclopedia - Microwaves101.com

However what I want to know is how to use this frequency in my design I mean the impedance transformer will only work at the specified frequency band, but how to use the frequency to calculate the lenght?

Please any help will be greatly appreciated.

From the Microwave101 article:
"If you want to work down to 2 GHz the length has to be half wave at 2 GHz. If you want the taper to work down to 1 GHz it has to be twice as long."

Since your lowest freq of interest is 1.5GHz, the taper length needs to be lambda/2 @ 1.5 GHz on your substrate.

To find the wavelength in your dielectric, try this to get you started.
TEM Wavelength Calculator - Microwaves101