See too: Special cases of the quarter wavelength impedance conversion.

Impedance of transmission line A is Z1, impedance of line B is Z3.
The aim is to connect these two lines without affecting standing wave reflections..

The resolution is a piece of  line which impedance is Z2. The length of the line must be equal a quarter wavelength.
Calculation equation is above.

The Microstrip method is suitable to almost all impedances to convert.
Microstrip is a transmission line which is fabricated by etching traces on a printed circuit board. Usually it is made from two layer pc material. The bottom layer is left solid while the upper is etched to form traces. The impedance of the trace depends of the width of it. For example a trace of 50 ohm ipedance is 2.8 mm wide in typical 1.5 mm thick fiberglass board.

Wavelength calculation :  L/mm = k x 300 / (f / GHz)

k is velocity factor, which is 0,47 - 0,57 in fiberglass circuit boards a little depending in the width of the strip.

For example: The length of 2.45 GHz 50 ohm quarter wavelength strip is 0.52 x 300 / 2.45 / 4  mm = 15.9 mm.
 

Microstrip values in 1.5 mm fiberglass circuit board (@ 1 GHz)
(varies not very much in other frequencies)
 

Impedance / ohm	width of trace / mm	Velocity factor
5	41.2	0.47
10	19.9	0.48
15	12.7	0.49
20	9.2	0.50
25	7.0	0.50
30	5.6	0.51
35	4.6	0.51
40	3.8	0.52
45	3.2	0.52
50	2.8	0.52
55	2.4	0.53
60	2.1	0.53
65	1.8	0.53
70	1.6	0.54
75	1.4	0.54
80	1.2	0.54
85	1.0	0.54
90	0.9	0.55
95	0.8	0.55
100	0.6	0.55
105	0.5	0.55
110	0.4	0.56
115	0.4	0.56
120	0.3	0.56
125	0.2	0.57
130	0.1	0.57
135	0.1	0.57

 

Other pages:

Wlan-antenna Do-It-Yourself

11.10.2003
Martti Palomäki