# Calculating dimensions of a transformer on microstrip

1. May 12, 2016

### jendrix

1. The problem statement, all variables and given/known data

Using the graphs calculate lengths and widths of transformers (quarter wave) if they are realised as microstrip lines on a substrate that has Er=2 and height of 1.6mm at frequency 1.8GHz

Z1=22.5ohm

Z2=77.5ohm

2. Relevant equations

Guided wavelength = c/((Eef)^1/2)*f)

Graphs

http://i.imgur.com/GCVqNo1.jpg

3. The attempt at a solution

Using the top graph Z1 =22.5ohm for Er=2 gives an w/h ratio of 10 therefore with a height of 1.6mm width would equal 16mm

For length it would be 1/4 of a guided wavelengh.From the bottom graph using a w/h ratio of 10 then Eeff=2

(3*10^8) /( (4*1.8*10^9) * (2)^1/2 ) =29.5mm

For Z2 w/h ratio for 77.5ohm = 2

w/h of 2 from graph gives Eeff of 1.8

Width = 1.6*2 =3.2mm

length =(3*10^8) / (4*1.8*10^9*(1.8)^1/2 ) = 31mm

2. May 12, 2016

### Tom.G

Yup, I get the same answer using your Guided wavelength equation (which seems to be the one I remember.)

3. May 13, 2016

### jendrix

Thanks for you r help Tom :)