Synthesize X [Ω] : [f] [A] Analyze X [mm] : [f] [B] s→Zdiff X [mm] : [f] [D]
r7 : εr ‐ relative permittivity r8 : h ‐ dielectric height [mm] r9 : t ‐ conductor thickness [mm] x : Z ‐ charactoristic impedance [Ω] (Synthesize) | w ‐ microstrip line width [mm] (Analyze) | s ‐ side gap [mm] (s→Zdiff)
Output
r i : 1 / √εreff ‐ velocity of propagation
r 0 : Z ‐ charactoristic impedance [&Omega]
r 1 : w ‐ microstrip line width [mm]
y : 1 / √εreff - velocity of propagation (Synthesized, Analized)
| s ‐ side gap [mm] (Z →Zdiff)
x : w ‐ microstrip line width [mm] (Synthesized)
| Z ‐ Characteristic impedance [Ω] (Analyzed)
| Zd ‐ Differential impedance [Ω] (Zo→Zdiff)
Resources used
LBL A : Synthesize
LBL B : Analyze
LBL D : Z →Zdiff
LBL .0 : Subroutine .0
LBL .1 : Subroutine .1
r i : 1 / √εreff ‐ velocity of propagation
r 0 : Z ‐ charactoristic impedance [&Omega]
r 1 : w ‐ microstrip line width [mm]
r 7 : εr ‐ relative permittivity
r 8 : h ‐ dielectric height [mm]
r 9 : t ‐ conductor thickness [mm]
Program list
uZW ‐ Rev.1.78 : Nov. 29, 2012
- Copyright(c) 1998-2012 Takayuki HOSODA, All rights reserved.
Synthesize
Analyze
Effective width
Characteristic impedance
error ≤ 2% [1]
velocity of propagation
Differential impedance
000-
001-42,21,11
002- 44 0
003- 1
004- 0
005-45,20, 8
006- 48
007- 6
008-45,40, 7
009- 11
010-45,20, 0
011- 6
012- 9
013- 10
014- 12
015- 10
016- 36
017-45,30, 9
018-42,10,.0
019- 44 1
020- 32 .1
021- 45 1
022- 43 32
LBL A
STO 0
10
RCL× 8
.6
RCL+ 7
√x
RCL× 0
69
÷
e↑x
÷
ENTER
RCL- 9
SOLVE .0
STO 1
GSB .1
RCL 1
RTN
023-42,21,12
024- 32 .0
025-44,40, 0
026- 32 .1
027- 45 0
028- 43 32
LBL B
GSB .0
STO+ 0
GSB .1
RCL 0
RTN
029-42,21,.0
030- 44 1
031- 4
032-45,20, 8
033- 45 8
034- 1
035- 48
036- 1
037-45,20, 9
038-45,40, 1
039- 43 26
040- 20
041- 10
042- 43 11
043- 1
044- 40
045- 11
046-45,20, 9
047- 10
048- 43 12
049- 1
050- 40
051-45,20, 9
052- 43 26
053- 10
054- 45 7
055- 36
056- 40
057- 15
058- 48
059- 5
060- 40
061- 20
062- 43 36
063- 43 26
064- 43 11
065- 4
066- 43 33
067-45,40, 1
LBL .0
STO 1
4
RCL× 8
RCL 8
1.1
RCL× 9
RCL+ 1
π
×
÷
x²
1
+
√x
RCL× 9
÷
LN
1
+
RCL× 9
π
÷
RCL 7
ENTER
+
1/x
.5
+
×
LSTx
π
x²
4
R↑
RCL+ 1
068- 10
069-45,20, 8
070- 36
071- 33
072- 33
073- 20
074- 8
075-45,10, 7
076- 1
077- 4
078- 40
079- 1
080- 1
081- 10
082- 44 33
083- 20
084- 36
085- 33
086- 43 11
087- 40
088- 11
089- 43 33
090- 40
091- 20
092- 1
093- 40
094- 43 12
095- 4
096- 2
097- 48
098- 3
099- 9
100- 7
101- 0
102- 5
103- 6
104- 36
105- 1
106-45,40, 7
107- 11
108- 10
109- 20
110-45,30, 0
111- 43 32
÷
RCL× 8
ENTER
R↓
R↓
×
8
RCL÷ 7
14
+
11
÷
R↑
×
ENTER
R↓
x²
+
√x
R↑
+
×
1
+
LN
42.397056
ENTER
1
RCL+ 7
√x
÷
×
RCL- 0
RTN
112-42,21,.1
113- 1
114-42, 4, 7
115- 44 25
116- 45 1
117- 32 .0
118-45,40, 0
119-45,10, 0
120- 15
121-42, 4,25
122- 44 7
123- 45 25
124- 43 32
LBL .1
1
x<> 7
STO i
RCL 1
GSB .0
RCL+ 0
RCL÷ 0
1/x
x<> i
STO 7
RCL i
RTN
125-42,21,14
126- 36
127-45,10, 8
128- 48
129- 9
130- 6
131- 16
132- 20
133- 12
134- 48
135- 4
136- 8
137- 16
138- 20
139- 1
140- 40
141-45,20, 0
142- 36
143- 40
144- 43 32
LBL D
ENTER
RCL÷ 8
.96
CHS
×
e↑x
.48
CHS
×
1
+
RCL× 0
ENTER
+
RTN
Formulas used
Microstrip charactoristic impedance [1]

where,

Initial guess of the microstrip line width

Example
Synthesize
Input
R7 = 4.5 εr
R8 = 0.2 height [mm]
R9 = 0.018 thickness [mm]
x = 50 Z [Ω]
Output
R 1: 0.3583608 width [mm]
R i: 0.553140 1/√εeff
y : 0.5531403 1/√εeff
x : 0.3583608 width [mm]
REFERENCES
- H. A. Wheeler, "Transmission-line properties of a strip on a dielectric sheet on a plane",
IEEE Trans. Microwave Theory Tech., vol. MTT-25, pp.631-647, Aug. 1977.
- R. J. Douville and D. S. James, "Experimental study of symmetric microstrip bends and their compensation",
IEEE Trans. Microwave Theory Tech., vol. MTT-26, pp. 175-182, Mar. 1978
- James A. Mears, "Transmission Line RAPIDESIGNER Operation and Applications Guide",
National Semiconductor Application Note, AN-905, May.1996
SEE ALSO
for the HP 42S - Synthesize/Analyze microstrip transmission line
for the HP 32sII - Synthesize/Analyze microstrip transmission line
Online calculator - Synthesize/Analyze microstrip transmission line
Ostrowski's method



© 2000 Takayuki HOSODA.
Powered by