A microstripline design of a 50 mHz power amplifier
by Louis LeeGrande Barrett
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Electrical Engineering
Montana State University
© Copyright by Louis LeeGrande Barrett (1977)
Abstract:
Microstripline is a name given to the use of double-sided, copper-clad, circuit board for construction of
very-high-frequency (VHF), ultra-high-frequency (UHF) and microwave transmission lines, inductors
and capacitors. Microstripline differs from stripline construction in that stripline uses two
ground-planes with a smaller main conductor sandwiched between them. Microstripline employs a
single ground-plane. Microstripline is constructed by etching one side of the double-clad circuit board
to a width corresponding to a desired characteristic impedance while the opposite, wider side acts as a
ground-plane. If the width is narrow, the series inductance characteristic of the transmission line will
dominate. Conversely, a wide width would cause the shunt capacitance of the line to dominate. By
cascading microstripline sections of the proper widths, networks may be synthesized. This type of
construction lends itself well for the application of VHF radio frequency amplifiers, where tab type
transistors are used. Advantages of microstripline construction as contrasted with the use of all discrete
components are improvements in amplifier performance, plus ease in design and fabrication of the
amplifier. An amplifier for the 50 mHz region was designed, built, and tested using microstripline
techniques and is described here. Methods of measuring circuit board parameters, criteria for amplifier
network design, and results are given. The amplifier performed admirably. Results are discussed and
analyzed and suggestions made for further study. STATEMENT OF PERMISSION TO COPY
In p re s e n tin g t h i s th e s is in p a r t i a l
f u l f i l l m e n t o f th e
re q u ire m e n ts f o r an advanced degree a t Montana S ta te U n iv e r s it y ,
I
I a g ree t h a t th e L ib r a r y s h a ll make i t f r e e l y a v a ila b le f o r
in s p e c tio n .
o f th is
I f u r t h e r agree t h a t p e rm issio n f o r e x te n s iv e copying
th e s is f o r s c h o la r ly purposes may be g ra n te d by my m ajor
p r o fe s s o r , o r , in h is absence, by th e D ir e c t o r o f L i b r a r i e s .
It
is understood t h a t any copying o r p u b lic a tio n o f t h i s th e s is f o r
f i n a n c ia l
gain s h a ll n o t be a llo w e d w ith o u t my w r it t e n
S ig n a tu re
Date
2 S
M rM J
p e rm is s io n .
/ /
A MICROSTRIPLINE DESIGN OF A 50 MHZ POWER AMPLIFIER
by
Louis LeeGrande B a r r e t t
A th e s is s u b m itte d in p a r t i a l f u l f i l l m e n t
o f th e re q u ire m e n ts f o r th e degree
of
MASTER OF SCIENCE
in
E l e c t r i c a l E n g in e e rin g
A pproved:
C h a irp e rs o n , G raduate Committee
le a d . M a jo r Departm ent
G raduate Dean
MONTANA STATE UNIVERSITY
Bozeman, Montana
Ju n e, 1977
iii
ACKNOWLEDGMENT
The a u th o r w ishes to acknowledge th e g u id a n ce , p a tie n c e , tim e ,
and s u p p o rt of. P ro fe s s o r R obert E. Leo d u rin g t h is p r o je c t .
c ia t i o n
Appre­
is a ls o expressed to D r. Dan March and D r i Norm Shyne f o r
t h e i r h e lp in p re p a rin g t h i s m a n u s c rip t.
The a u th o r is g r a t e f u l to
th e E l e c t r i c a l E n g in e e rin g Departm ent o f Montana S ta te U n iv e r s ity f o r
th e f i n a n c ia l s u p p o rt ren d ered as a G raduate A s s is ta n ts h ip .
A v e ry
s p e c ia l thanks is g iv en to th e a u th o r 's w i f e , Judy, f o r h e r encour­
agem ent, p a tie n c e , and s k i l l f u l
ty p in g .
TABLE OF CONTENTS
Page
V I T A .........................
ii
ACKNOWLEDGMENT ..................
iii
LIS T OF TABLES ................... ......................................... ..........................
LIST OF FIGURES ............................................... ........................... '......................
ABSTRACT .................................................
vi
v ii
ix
INTRODUCTION .........................
I
PROBLEM ANALYSIS .....................................
3
PRELIMINARY DATA ..........................................
9
Phase V e lo c it y Measurements ...........................................................
9
C h a r a c t e r is t ic Impedance Measurements ...................................
14
D ata E v a lu a tio n
16
................................
AMPLIFIER DESIGN METHODS ..............................
33
Ampli f i e r D e s ign ............................................
33
Network Design ■.........................................................................................
38
S t a b i l i t y .............. ..........................
49
Power D is s ip a tio n
51
..............................
A m p lif ie r C i r c u i t D e s c rip tio n
— ..............................
52
RESULTS ................................
54
CONCLUSION .................................................................
63
' LITERATURE CITED .........................
67
V
TABLE OF CONTENTS
(C o n tin u e d )
Page
APPENDICES ............................................................................. ........... ..
Appendix I
Appendix I I
\
........................................................................... ............. ....
.......................................... ...................................................
68
69
73
. -I
vi
LIS T OF TABLES .
Table
1.
2.
Page
E xp e rim en tal Measurement R e s u lts f o r MSL Phase
V e lo c it y as a F u n ctio n o f Main Conductor Width ..............
12
E xp e rim en tal Measurement R e s u lts f o r MSL
C h a r a c t e r is t ic Impedance as a F u n c tio n o f
Main Conductor W idth ................................. ! .......................................
17
/
3.
MSL"Tee" F i l t e r T e s t R e s u lts
4.
Measurement Data f o r th e D i e l e c t r i c C onstant o f
G -IO E poxy-g lass P rin te d C i r c u i t Board o f I mm
Thickness by use o f P a r a l l e l P la te C a p a c ito rs
a t I kHz .........................................................................................................
5.
6.
7.
............................................
26
31
Comparison o f C a lc u la te d C h a r a c t e r is t ic Impedance
to Measured C h a r a c t e r is t ic Impedance f o r S e v e ra l
MSLW idths .................................................................................
31
A m p lif ie r Network Component V alues C a lc u la te d to '
Match a 50 Ohm T e rm in a tin g Impedance f o r a
Loaded Q o f 10 .............. ....................................................... i ................
40
A m p lif ie r C a p a c ito r Measurements Compared to th e
C a lc u la te d V alues ....... ............................................................
46
v ii
2
LIS T OF FIGURES
F ig u re
Page
1.
T ransm ission L in e S e c tio n M o d e l s ....... ......................................
4
2.
Geometry o f an MSL S e c tio n
6
3.
C o a x ia l I n t e r f a c i n g to an MSL Conductor Using a
BNC C onnector ............................................................................................ 10
4.
An A lt e r n a t e Method o f M easuring MSL Phase
V e lo c it y ........................................................................................
13
Schem atic Diagram o f "Tee" F i l t e r Used to T e s t
E xp e rim en tal Data and Design E quations .................................
18
Dim ensional I l l u s t r a t i o n and Photograph o f th e
T ested MSL "Tee" F i l t e r ....................................................................
23
5.
6.
........................................................
7.
Method f o r T e s tin g th e MSL "Tee" F i l t e r ............................... 25
8.
R e s u lts o f th e MSL "Tee" F i l t e r T e sts Compared to
S e v e ra l S t r i p l i n e and an Id e a l Low Pass F i l t e r
C h a r a c te r is tic s ..........................................................................
28
Photograph o f th e BM70-12 T r a n s is to r Used in a
52 mHz A m p lif ie r ....................................................................................
35
G eneral and Maximum S p e c ific a t io n s o f th e BM70-12
T r a n s is to r ..................................................................................................
36
A m p lific a tio n C h a r a c te r is tic s o f th e BM70-12
T r a n s is to r .................................................
37
9.
10.
11.
1 2.
P o s s ib le T r a n s is to r C o lle c t o r M atching Network
Designs f o r th e 52 mHz A m p l i f i e r ....... .......................................... 41
13.
Schem atic Diagram o f th e 52 mHz A m p lif ie r ............................. 42
14.
Photograph o f th e 52 mHz A m p lif ie r w ith Heat
S in k Removed .................................................................................................47
15.
Completed Schem atic Diagram o f th e 52 mHz A m p lif ie r . . 52
v iii
LIS T OF FIGURES
(C o n tin u e d )
Figure
Page
16.
I n i t i a l T e s tin g Method f o r th e 52 mHz
A m p lif ie r ................................................................................................... 55
17.
F in a l T e s tin g Method f o r th e 52 mHzA m p lif ie r ....................
57
18.
Photograph o f th e 52 mHz A m p lif ie r w ith Heat
S in k in P lace .........................................................................................
60
Harmonics Measured a t th e O utput o f th e 52 mHz
A m p lif ie r ...................................
61
20.
H eat S in k Power Model
69
2 1.
H eat S in k Thermal R e s is ta n c e and Area
.22,
E xp e rim en tal Phase V e lo c it y and C h a r a c t e r is t ic
Impedance Data P lo tte d f o r th e R e c ip ro c a l o f
V a rio u s MSL S e c tio n W idths Using th e G -IO
E poxy-g lass P r in te d C i r c u i t Board o f I mm
Thickness ................................................................................................... 74
19.
......................................................................
Graph .....................
72
ABSTRACT
M i c r o s t r i p l in e is a name g iven to the. use o f d o u b le -s id e d ,
c o p p e r-c la d , c i r c u i t board f o r c o n s tru c tio n o f v e ry -h ig h -fre q u e n c y
(V H F ), u lt r a -h ig h -f r e q u e n c y (UHF) and microwave tra n s m is s io n l i n e s ,
in d u c to rs and c a p a c ito r s .
M i c r o s t r ip l i n e d i f f e r s from s t r i p l i n e
c o n s tru c tio n in t h a t s t r i p ! in e uses two gro u n d -p lan es w ith a s m a lle r
main co nductor sandwiched between them.
M i c r o s t r ip l i n e employs a
s in g le g ro u n d -p la n e .
M i c r o s t r ip l i n e is c o n s tru c te d by e tc h in g one
s id e o f th e d o u b le -c la d c i r c u i t board to a w id th c o rresp o n d in g to a
d e s ire d c h a r a c t e r is t i c impedance w h ile th e o p p o s ite , w id e r s id e a cts
as a g ro u n d -p la n e .
I f th e w id th is n a rro w , th e s e r ie s inductance
c h a r a c t e r is t i c o f th e tra n s m is s io n l i n e w i l l dom inate.
C o n v e rs e ly ,
a w ide w id th would cause th e shunt c a p a c ita n c e Of th e l i n e to dom­
in a te .
By cascading m i c r o s t r ip lin e s e c tio n s o f th e p ro p e r w id th s ,
netw orks may be s y n th e s iz e d .
T h is ty p e o f c o n s tru c tio n lends i t s e l f
w e ll f o r th e a p p lic a t io n o f VHF ra d io fre q u e n cy a m p li f ie r s , where
ta b ty p e t r a n s is t o r s a re used. Advantages o f m ic r o s t r ip I.in e con­
s t r u c t io n as c o n tra s te d w ith th e use o f a l l d is c r e te components are
improvements in a m p li f ie r p e rfo rm a n ce , plus ease in design and
f a b r i c a t i o n o f th e a m p li f ie r .
An a m p li f ie r f o r th e 50 mHz re g io n
was d e s ig n e d , b u i l t , and te s te d using m ic r o s t r ip lin e tec h n iq u es and
is d e s c rib e d h e re .
Methods o f m easuring c i r c u i t board p a ra m e te rs ,
c r i t e r i a f o r a m p li f ie r netw ork d e s ig n , and r e s u lts a re g iv e n .
The
a m p l i f i e r perform ed a d m ira b ly .
R e s u lts a re discussed and an aly ze d
and su g g estio n s made f o r f u r t h e r s tu d y ..
INTRODUCTION
M ic r o s t r ip l i n e
(MSL) is a.m ethod o f r e a l i z i n g LC netw orks by
c ascad in g tra n s m is s io n l i n e le n g th s o f d i f f e r e n t c h a r a c t e r is t i c
impedance.
The tra n s m is s io n l i n e s e c tio n s a re made by e tc h in g a
narrow c o n d u c tin g w id th on one s id e o f a p ie c e o f d o u b le -s id e d ,
c o p p e r-c la d , p r in te d c i r c u i t board w h ile th e f o i l
on th e s id e
d i r e c t l y o p p o s ite is e i t h e r etched s e v e ra l tim es l a r g e r in w id th
o r l e f t unetched.
The w id e r s id e a c ts as a g ro u n d -p la n e f o r , t h e
o th e r co n d u c to r.
MSL is a s im p lif ie d .v e r s io n o f " s t r i p l i n e " netw ork s y n th e s is .
\
In s t r i p l i n e methods, two gro u n d -p lan es a re used w ith th e n a rro w ly
e tc h ed c e n te r conductor sandwiched between them.
MSL is m o s tly a p p lie d in th e microwave and u ltr a -h ig h -f r e q u e n c y
(UHF) re g io n s (450 mHz and above) in e i t h e r a com plete netw ork o r
commonly as p a r t o f a h y b rid netw ork a ls o in v o lv in g d is c r e te com­
p onents.
The purpose o f th e fo llo w in g s tu d y was to a p p ly MSL to th e
design o f a 50 mHz r e g io n , v e ry -h ig h -fre q u e n c y (VHF) a m p l i f i e r .
The
s tu d y was done to e x p lo re th e f e a s i b i l i t y o f MSL a t VHF and p e r fe c t
design methods f o r use by e x p e rim e n te rs who do n o t have expensive
la b equipm ent.
7
'
'
'
2
The f i r s t p a r t o f t h i s paper d e a ls w ith methods used and d a ta
ta k e n on s e v e ra l MSL w id th s .
Once, c h a r a c t e r is t i c impedance and
v e l o c i t y d a ta had been ta k e n , i t was te s te d f o r v a l i d i t y by b u ild in g
a low pass netw ork a ls o d e s c rib e d .
The second p a r t e x p la in s procedures used in th e design and
t e s t in g o f a 52 mHz a m p l i f i e r .
T h is fre q u e n cy was chosen because
o f a v a i l a b i l i t y o f equipm ent to make measurements and t e s t th e
a m p li f ie r .
G -IO e p o x y -g la s s c i r c u i t board was used th ro u g h o u t w ith a
d i e l e c t r i c th ic k n e s s o f I mm.
The methods d e s c rib e d in t h i s study
may be used to a ls o e s t a b lis h l i n e c h a r a c t e r is t ic s and design
netw orks using o th e r d i e l e c t r i c s and th ic k n e s s e s .
An advantage to MSL is ease in c o n s tru c tin g tuned networks
using c o n v e n tio n a l p r in te d c i r c u i t board methods.
Once an a c c u ra te
p ro to ty p e is d e ve lo p e d , i t may be e a s i l y d u p lic a te d w ith no f u r t h e r
tu n in g needed.
PROBLEM ANALYSIS
I f MSL s e c tio n s were to be used to s y n th e s iz e n e tw o rk s , design
e q u a tio n s had to be e s t a b lis h e d .
The lo g ic a l p la c e to begin was=with
th e tra n s m is s io n l i n e e q u a tio n s .
R e la tio n s h ip s were sought which
would r e l a t e c a p a c ita n c e o r in d u c ta n c e p e r u n it le n g th to m easurable
p a ra m e te rs .
Such r e la tio n s h ip s would then le a d to th e design
e q u a tio n s f o r th e r e a l i z a t i o n
o f netw o rks.
MSL is s i m i l a r to c o a x ia l l i n e
in t h a t th e c o nductor s u rfa c e
is p u rp o s e ly s m a lle r in w id th than i t s
a s s o c ia te d g ro u n d -p la n e .
W ith
t h a t in m ind, th e c o a x ia l tra n s m is s io n l i n e model was used to begin
th e d e r iv a t io n o f design e q u a tio n s .
F ig u re la shows th e g en eral
model f o r a p a r a l l e l , balanced tra n m is s io n l i n e
1 9 6 3 ).
( P o t t e r and Fich
The model is m o d ifie d in F ig u re lb to t h a t o f a c o a x ia l,
unbalanced l i n e .
r e s is ta n c e
The model c o n s is ts o f s e r ie s in d u c ta n ce (L ) and ac
(R ) shunted by c a p a c ita n c e
(C ) and lea k ag e conductance ( G ) .
I f th e l i n e may be assumed lo s s le s s , th e model may be s im p lif ie d to
t h a t shown in F ig u re Tc.
Only th e s e r ie s in d u c ta n ce and shunt
c a p a c ita n c e com prise th e l i n e c h a r a c t e r is t i c s .
I t was assumed th e l i n e was lo s s le s s i n i t i a l l y .
The lo s s le s s
tra n s m is s io n l i n e e q u a tio n s a re then given by P o tte r and Fich (1 9 6 3 ):
(Ohms).
(I)
4
(a)
P arallel conductor transmission line with losses
R
U
R
L
t i> )
Coaxial transmission line with losses
L
L
z m -------------
ZYTX
c
o
c
(c)
Lossless coaxial transmission line
F ig u re I
Transm ission Line S e c tio n Models
I
and
I
(m e te rs /s e c o n d )
y r r
w here:
L
In d u c ta n ce p e r le n g th
(H e n rie s /m e te r)
C
C a p acitan ce per le n g th
(F a ra d s /m e te r)
I
q
V
=
C h a r a c t e r is t ic l i n e
impedance (Ohms)
=
Phase v e lo c it y through th e l i n e
S o lv in g f o r L and then C from e q u a tio n
L
=
Z 2C
(m e te rs /s e c o n d )
(1 ):
(H e n rie s /m e te r)
(:
and
(F a ra d s /m e te r)
I f e q u a tio n
(3 )
is s u b s titu te d in t o e q u a tio n
( 2 ) , the
c a p a c ita n c e p e r u n it le n g th becomes:
c
S im ila r ly ,
=
(F a ra d s /m e te r)
O
i f e q u a tic n
( 4 ) is s u b s t itu te d in t o e q u a tio n
(2 ),
th e in d u c ta n ce p e r u n it le n g th i s :
L
=
-rr-
(H e n rie s /m e te r)
As seen from e q u a tio n s (5 ) and ( 6 ) ,
impedance (Z q ) and th e phase v e l o c i t y
(6 )
i f th e c h a r a c t e r is t i c
(V ) could be e s ta b lis h e d by
e x p e rim e n ta l means, netw orks using s e r ie s indu ctan ces and shunt
c a p a c ita n c e s c o u ld by s y n th e s iz e d by using th e r e s p e c tiv e MSL le n g th s .
6
The n e x t problem encountered was how to make th e in d u c ta n ce in
th e tra n s m is s io n l i n e dom inate o v e r th e c a p a c ita n c e o r v ic e -v e r s a .
S in ce th e c a p a c ita n c e p e r u n it le n g th on th e tra n s m is s io n l i n e
s t a t i c c a p a c ita n c e
th e p a r a l l e l
is
(Sams 1 9 6 8 ), perhaps a c lu e could be found from
p la te c a p a c ito r e q u a tio n .
F ig u re 2 i l l u s t r a t e s
th e p h y s ic a l p r o p e r tie s o f an MSL s e c tio n .
The narrow main conductor o f th e l i n e
forms a p a r a l l e l p la t e c a p a c ito r
MAIN CONDUCTING STR IP
C IR C U lTB O A R D DIELECTRIC
GROUND PLANE CONDUCTOR
F ig u re 2
Geometry o f an MSL S e c tio n
w ith th e ground p la n e using th e c i r c u i t board m a te ria l as the
d ie le c tr ic
between th e p la t e s .
If
f r in g in g o f th e e l e c t r i c
fie ld
7
between th e p la te s is n e g le c te d , th e t o t a l c a p a c ita n c e is given by
Kraus and C a rv e r (1 9 7 3 ):
a
C
w here:
(F a ra d s )
C1 =
C a p a cita n c e (F a ra d s )
e
=
D i e l e c t r i c c o n s ta n t o f th e in s u la t in g medium (F a ra d s /
m e te r)
A
=
S u rfa c e a re a o f th e s m a lle s t p la te
d
=
P la te s e p a ra tio n
(s q u a re m e te rs )
(m e te rs )
The s u rfa c e a re a (A ) o f th e s m a lle s t p la t e is t h a t o f th e main
c o n d u c to r.
The a r e a . i s g iv en by:
A
\
=
£W
(s q u a re m ete rs )
S u b s titu tin g e q u a tio n (8 ) in t o e q u a tio n
eSLYI
C
(7 ):
(F a ra d s )
D iv id in g through by i th e main conductor le n g th :
C
eW
d
S in ce e q u a tio n
( 10)
(F a ra d s /m e te r)
(1 0 ) shows u n its o f F a ra d s /m e te r, t h i s is an
e x p re s s io n f o r th e c a p a c ita n c e p e r u n i t le n g th .
Then e q u a tio n (1 0 )
becomes:
C
=
E xam ination o f e q u a tio n
(F a ra d s /m e te r)
(1 1 ) re v e a ls t h a t i f
(1 1 )
e and d a re
c o n s ta n ts , th e c a p a c ita n c e p e r u n it le n g th is p r o p o r tio n a l to th e
8
w id th o f th e c o n d u c to r.
T h e r e fo r e , i f th e w id th is s m a ll, th e
c a p a c ita n c e p e r u n i t le n g th w i l l be a ls o and th e s e r ie s in d u ctan ce
p e r u n i t le n g th w i l l
begin to dom inate th e MSL c h a r a c t e r is t i c s .
A t t h i s p o in t , th e netw ork s y n th e s is appeared s i m p l i f i e d .
A
method o f a r r i v i n g a t th e c h a r a c t e r is t i c impedance and th e phase
v e l o c i t y through th e l i n e
f o r a given w id th needed to be e s ta b lis h e d
I f th e s e two param eters were known, a d i r e c t c o n versio n could be
made u sing th e p r e v io u s ly d e riv e d e q u a tio n s f o r c a p a c ita n c e and
in d u c ta n ce p e r u n it le n g th .
I f shunt c a p a c ita n c e was re q u ire d to
d o m in a te , th e w id th was made s i g n i f i c a n t l y w id e r th a n when s e r ie s
in d u c ta n ce was re q u ire d .
In th e above a n a ly s is , f r i n g i n g was n e g le c te d f o r ease in
c a lc u la t io n s .
n e g le c te d .
I t was found t h a t f r i n g i n g could n o t be g e n e r a lly
More d is c u s s io n is given l a t e r on t h i s p o in t .
• PRELIMINARY DATA
Phase V e lo c it y Measurements
The e a s ie s t p a ram e te r to measure was th e phase v e l o c i t y through
th e l i n e .
The e x p e rim e n t design began w ith th e e x p re s s io n f o r
v e l o c i t y in terms o f w avelength (R adio S o c ie ty o f G re a t B r i t a i n
V
w here:
=
fx
(m e te rs /s e c o n d )
V
=
Phase v e lo c it y
f
=
Frequency ( H e r tz )
X
=
W avelength (m e te rs )
1969)
(1 2 )
(m e te rs /s e c o n d )
When w o rkin g in fr e e sp ace, V would be n e a r ly th e speed o f l i g h t
O
(3x10 m e te rs /s e c o n d ) (Kraus and C a rv e r 1 9 7 3 ).
In a d i e l e c t r i c
m a te r ia l such as e p o x y -g la s s c i r c u i t b o a rd , th e v e l o c i t y would be
exp ected to be somewhat s lo w e r.
e x p re s s io n f o r v e l o c i t y , e q u a tio n
The e xp e rim en t design used both th e
(1 2 ) above, and th e f a c t t h a t a
q u a rte r-w a v e le n g th tra n s m is s io n l i n e a c ts as an impedance i n v e r t e r
(A tw a te r 1 9 6 2 ).
S e c tio n s o f s e v e ra l conductor w id th s w ere etched
using common c i r c u i t board e tc h in g te c h n iq u e s and c u t to le n g th s o f
a p p ro x im a te ly .4 5 7 m e te r.
The lin e s were fe d using a fe m a le BNC
c o a x ia l c o n n e cto r as shown in F ig u re 3.
A f t e r an in v e s t ig a t io n o f fe e d in g o r "la u n c h in g " methods from
c o a x ia l
lin e s to MSL a t microwave fre q u e n c ie s
(F a r r e ll
1 9 6 3 ), the
BNC CONNECTOR
/W V W A
C IR C U IT BOARD
iZ ^ X .
WVAAyN/
J
COPPER S T R A P
A
3
GROUND PLANE
F ig u re 3
C o axial
In t e r f a c in g to an MSL Conductor
Using a BNC Connector
n
la u n c h in g method used was assumed n e a r ly .lo s s le s s .
T h is was due to
th e low fre q u e n c y used (5 0 mHz r e g io n ) .
As p r e v io u s ly s t a t e d , a q u a rte r-w a v e le n g th tra n s m is s io n l i n e
s e c tio n a c ts as an impedance i n v e r t e r .
T h is p ro p e rty a ls o holds f o r
odd m u ltip le s o f^ a q u a rte r-w a v e le n g th .
I f th e o u tp u t o f a tr a n s ­
m issio n l i n e s e c tio n was te rm in a te d in an open c i r c u i t , s e v e ra l
fre q u e n c ie s could be found where th e in p u t o f th e l i n e would appear
n e a r ly s h o rte d .
True in p u t s h o rts would occur i f an id e a l tr a n s ­
m issio n l i n e were used in t h i s
c o n fig u r a tio n .
The le n g th o f th e
l i n e s e c tio n would be equal to one q u a rte r-w a v e le n g th o f th e lo w est
fre q u e n c y a t w hich t h i s
impedance in v e rs io n o c c u rre d .
T h is lo w est
fre q u e n cy was term ed the. q u a rte r-w a v e le n g th re so n a n t fre q u e n c y ( f 0 ) .
The c o n n e cto r end o f th e open c ir c u i t e d MSL was connected to a
H e w le tt-P a c k a rd Model 4815A v e c to r impedance m eter and th e freq u en cy
ranges were swept w ith in c re a s in g fre q u e n c y from 500 kHz u n t i l th e
f i r s t impedance minimum was o b served.
The fre q u e n cy where th e
impedance was a minimum and th e impedance phase a n g le was ze ro
degrees was noted as th e q u a rte r-w a v e le n g th re so n a n t fre q u e n c y .
A
fre q u e n c y c o u n te r connected to th e o s c i l l a t o r o f th e v e c to r impedance
was used to make th e fre q u e n c y measurements.
Once a c c u ra te le n g th measurements were made o f th e tra n s m is s io n
l i n e s e c tio n s , e q u a tio n (1 2 ) was m o d ifie d as shown below :
12
I
w here:
I
=
=
x_
4
Conductor le n g th (m e te rs )
X
=
4&
V
=
4f&
and
(m e te rs /s e c o n d )
(1 3 )
T a b le I p re s e n ts th e d a ta taken by t h i s method.
T a b le I
E xp e rim en tal Measurement R e s u lts f o r MSL Phase V e lo c it y
as a F u n ctio n o f Main Conductor W idth
fo N
(mHz)
%
(m e te rs )
X
(m e te rs )
V
(m e te rs /s e c o n d )
.381
9 6 .0 7
.42 1 6
1 .6 8 7
I . 62x1O8
.76 2
8 7 .1 5
.45 8 0
1 .8 3 2
I . 59x1O8
1 .5 8 0
8 3 .4 3 .
.4580
1 .8 3 2
I . 53x1O8
2 .5 4 0
8 0.2 1
.45 8 0
1 .8 3 2
1 .4 7 x l0 8
3 .8 1 0
7 6 .8 5
.45 8 0
1 .8 3 2
I .4 1 XlO8
6 .3 5 0
7 1 .8 0
.4 5 7 0
1 .8 2 9
I S lx lO 8
1 2 .7 0 0
6 5 .4 9
.4320
1 .7 2 7
I . IS x lO 8
2 5 .4 0 0
5 3 .6 2
.43 1 0
1 .72 3
9 .2 4 x 1 O7
W idth
V (mm)
.
An a lt e r n a t e method where a v e c to r impedance m eter is not
a v a ila b le is shown in F ig u re 4 .
The r e s u lt s o f t h i s method were
.\
OSCILLOSCOPE
FREQUENCY
CO UNTER
F ig u re 4
An A lte r n a te Method o f M easuring MSL Phase V e lo c ity
.1 4
in c lo s e agreem ent w ith those ta k en w ith th e v e c to r impedance m e te r.
A sweep o s c i l l a t o r o r s ig n a l g e n e r a to r , m onitored by a fre q u e n cy
c o u n te r , fe d a 10 dB a tte n u a to r f o r is o la t i o n purposes.
The O utput
o f th e a tte n u a to r was " te e -e d " w ith th e c o a x ia l in p u t end o f th e
open c ir c u i t e d MSL s e c tio n and a second i s o la t i o n
10 dB a tte n u a to r .
The o u tp u t o f th e second a tte n u a to r drove th e v e r t i c a l
a m p li f ie r o f an o s c illo s c o p e .
in p u t
The s ig n a l source was c a r e f u l l y
tuned in fre q u e n c y u n t i l th e f i r s t and lo w e s t in fre q u e n c y minimum
v o lta g e p o in t was found as observed on th e o s c illo s c o p e .
At
q u a rte r-w a v e le n g th reso n a n c e, th e open c ir c u i t e d MSL e x h ib ite d a
s h o r t a t th e c o a x i a ll y connected end o f th e MSL s e c tio n .
r e s u l t , th e v o lta g e was a t a minimum in th e c o a x ia l
As a
lin e .
A fte r
n o tin g th e g e n e ra to r fre q u e n c y and a c c u r a te ly m easuring th e MSL
co n d u ctor le n g th , e q u a tio n
v e lo c ity
(1 3 ) was used to d e term in e th e phase
(V ) a lo n g th e l i n e .
The system te s te d in t h i s method
used 50 Ohms as a c h a r a c t e r is t i c impedance- f o r c o n ven ien ce.
was ta k en to keep c o a x ia l
Care
in te rc o n n e c tio n lin e s s h o rt to p re v e n t
in a c c u ra c ie s due to p o s s ib le c o a x ia l l i n e resonance.
C h a r a c t e r is t ic Impedance Measurements
Once th e phase v e l o c i t y was e s ta b lis h e d by th e methods d e s c rib e d
p r e v io u s ly , o n ly c h a r a c t e r is t i c impedance (Z q) d a ta was needed b e fo re
netw ork s y n th e s is c o u ld ta k e p la c e .
I
15
The method used to determ in e l i n e c h a r a c t e r is t i c impedance was
t h a t o f d e te rm in in g th e g e o m etric mean o f th e open c i r c u i t and s h o rt
c i r c u i t impedances ( P o t t e r and Fich 1 9 6 9 ).
C h a r a c t e r is t ic impedance
is g iv en by:
zo
w here:
=
(0 h " s )
<14)
Zq
=
Z
=
L in e in p u t impedance w ith o p p o s ite end te rm in a te d in
an open c i r c u i t (Ohms)
=
L in e in p u t impedance w ith o p p o s ite end te rm in a te d in
a s h o rt c i r c u i t (Ohms)
oc
Z
sc
C h a r a c t e r is t ic impedance (Ohms)
The v e c to r impedance m eter was used a g ain f o r th ese measurements.
Care had to be taken to o b ta in a c c u ra te d a ta .
c i r c u i t i n g th e l i n e
When s h o rt
s e c tio n f o r s h o rt c ir c u i t e d impedance measure­
m ents, th e e n t i r e w id th o f th e main conductor was connected to the
g ro u n d -p la n e s id e .
I f a na rro w e r c o n n e ctio n were made, i t
could
have appeared as a te r m in a tin g in d u c ta n c e .
Data p o in ts were ta k en a t th re e d i f f e r e n t fre q u e n c ie s to v e r i f y
r e s u lts .
I t was noted t h a t th e s e p o in ts had to be s e v e ra l m egahertz
away from th e q u a rte r-w a v e le n g th resonance fre q u e n cy to a vo id
resonance e f f e c t s and, hence, e r r o r .
For t h i s re a s o n , some h ig h e r
fre q u e n cy d a ta p o in ts were thrown o u t because o f th e obvious e f f e c t s
o f resonance.
16
The r e s u lt s o f th e s e measurements a re p re s e n te d in T a b le 2 .
/
.
An average o f th e d a ta was ta k en and used as th e c h a r a c t e r is t i c
impedance f o r each w id th .
I t was noted t h a t th e impedance phase
a n g les were v e ry c lo s e to z e ro d e g ree s .
T h a t co n firm ed th e
p re v io u s assum ption t h a t such lin e s a re n e a r ly lo s s le s s .
A n other method t r i e d was to te rm in a te th e MSL s e c tio n in
a c tu a l carbon r e s i s t o r s .
I f th e r e s i s t o r used was n e a r th e
c h a r a c t e r is t i c im pedance, th e v e c to r impedance m e te r c o u ld be
swept o v e r s e v e ra l decades o f fre q u e n c y w ith l i t t l e
th e l i n e
in p u t impedance phase from ze ro degrees.
change o f
A sm all
d e p a rtu re from an impedance phase a n g le o f ze ro degrees w ith
la r g e fre q u e n c y changes meant th e carbon r e s i s t o r v a lu e was
c lo s e to th e v a lu e o f th e c h a r a c t e r is t i c impedance.
was tim e consuming and cumbersome.
T h is method
A ls o , a c c u ra te r e s u lt s were
o n ly o b ta in e d f o r la rg e main c o nductor w id th s .
As a r e s u l t , t h is
method o f impedance d e te rm in a tio n was abandoned.
Data E v a lu a tio n
A f t e r th e c h a r a c t e r is t i c impedances and v e l o c i t i e s p e r w id th
were e s t a b lis h e d , a method was d e vis e d to t e s t th e e q u a tio n s f o r
in d u c ta n ce and c a p a c ita n c e p e r u n it le n g th
(e q u a tio n s
(5 ) and ( 6 ) ) .
The method used was to b u ild a low pass f i l t e r by im plem enting th e
measurement d a ta through e q u a tio n s (5 ) and ( 6 ) .
I f a low pass
17
Table 2
E xp e rim en tal Measurement R e s u lts f o r MSL C h a r a c t e r is t ic Impedance
as a F u n ctio n o f Main Conductor Width
Width (mm)
f(mHz)
Zoc(Ohms)
Zs c (Ohms)
.381
Z0 (Ohms)
20
298
i-9 0 °
40
£ 90°
30
190
£-90°
64
£ 90°
110.3 £ 0°
40
134
£-90°
95
£ 90°
112.8 £ 0°
20
235
£-90°
36
£ 90°
40
102
£-90°
85
£ 90°
93.1 £ 0°
60
48
£-90°
190
£ 90°
95.5 £ 0°
63
£ 90°
68.1 £ 0°
109.2 £ 0°
Zo Ave.762
= 110.1 Ohms
91.8 £ 0 °
Z0 Ave. =
1.580
■ 40
73.5 £-90° '
60
32
£-90°
140
L 90°
67.2 £ 0°
108
32
£ 90°
151
£-90°
69.5 £ 0°
•
2.540
£-90° '
Zo Ave- =
22.5 £ 90°
20
135
56
£-90°
52
£ 90°
55.1 £ 0°
54.0 £ 0°
50
37
£-90°
74
£ 90°
52.3 £ 0°
20
105
£-90°
40
44
£-90°
18.5 £ 90°
44
£ 90°
Zo Ave- =
6.350
44
£ 0°
44
£ 0°
44.0 Ohms
£-90°
14
£ 90°
29.5 £-90°
34
£ 90°
31.7 £ 0°
50
17.5 £-88°
46
£ 90°
28.4 £ 1°
74
M)°
15
20
30
61
‘
32.2 £ 0°
=
15
20
30
30.8 Ohms
£-90°
6.8 £ 90°
20.4 £ 0°
44
£-90°
9.2 £ 90°
20.1 £ 0°
26
£-90°
14
£ 90°
Z0 Ave. =
25.400
53.8 Ohms
40
20
i
12.700
68.3 Ohms
40
Zo Ave- =
3.810
93.5 Ohms
. 31.5 £-90°
4 .6 £ 90°
£-90°
6.2 £ 90°
11.7 £-88°
9.5 £ 90°
22
Zo Ave- =
19
£ 0°
19.8 Ohms
12
£ 0°
11.7 £ 0°
10.6 £ 1°
11.4 Ohms
18
f i l t e r could be s y n th e s iz e d using th e s e param eters and th e c o rn e r
fre q u e n c y be a c c u r a te ly p r e d ic te d , then th e design e q u a tio n s could
be assumed c o r r e c t .
The c o rn e r fre q u e n c y o f a low pass f i l t e r , which is a ls o
known as th e h a lf-p o w e r fre q u e n c y , is th e fre q u e n cy where th e
o u tp u t v o lta g e is 7 0 .7 p e rc e n t th e in p u t d r iv e v o lta g e .
A low pass "Tee" f i l t e r was b u i l t to t e s t th e design eq u atio n s
and d a ta .
The schem atic diagram o f th e f i l t e r
d /2
L'/2
O
nm —
O--------------n m -
Z in = 5 0 OHMS
O
is shown in F ig u re 5.
C'
O
SOOHMS
O-
= Z
out
O
F ig u re 5
Schem atic Diagram o f "Tee" F i l t e r Used to T e s t
E xp e rim en tal Data and Design Equations
The in d u c ta n ce and c a p a c ita n c e s e c tio n s in MSL a re s e t a p a rt
o n ly by a b ru p t t r a n s it io n s
The la r g e r th e t r a n s it io n
in s e c tio n c h a r a c t e r is t i c
impedances.
in c h a r a c t e r is t i c impedance is between
19
cascaded l i n e s e c tio n s , th e b e t t e r each s e c tio n w i l l e x h i b i t th e
d e s ire d c h a r a c t e r is t ic s w h eth er in d u c tiv e o r c a p a c it iv e .
There a re l i m it a t io n s to th e r a t i o o f impedances between
s e c tio n s , however.
One c o n s id e ra tio n is t h a t o f p h y s ic a l s iz e o f
th e MSL main c o n d u c to r.
I f th e main c onductor is to be narrow to
p e rfo rm as a high impedance in d u c tiv e s e c tio n , th e re is a l i m i t a t i o n
on how narrow a c i r c u i t board f o i l may be e tc h e d .
I f th e main
co n d u ctor is to be w ide and a c t as a low impedance c a p a c itiv e
s e c t io n , th e s iz e could be to o la r g e and cumbersome to be p r a c t ic a l .
In summary, f o r p ro p e r perform ance o f th e in d u c tiv e and
c a p a c itiv e MSL s e c tio n s , th e r a t i o o f c h a r a c t e r is t i c impedances
between cascaded MSL s e c tio n s must be k e p t to a maximum w ith in
s iz e and m a n u fa c tu rin g to le ra n c e s
(Howe 1 9 7 4 ).
Though th e impedance o f MSL s e c tio n s in c re a s e s as th e main
co n d u ctor w id th n a rro w s , t h i s
discussed l a t e r .
is n o t a l i n e a r fu n c tio n as w i l l
be
As a r e s u l t , th e r a t i o o f impedances between
s e c tio n s should n o t be confused w ith th e main c onductor w id th r a t i o .
For th e low pass "Tee" f i l t e r t e s t e d , two 9 3 .5 Ohm (.7 6 2 mm
w id th ) s e c tio n s were chosen as in d u c to rs and a 3 0 .8 Ohm (6 .3 5 mm
w id th ) s e c tio n was chosen f o r th e c a p a c ito r .
between s e c tio n s was 3 .
The impedance r a t i o
20
S o lv in g f o r th e in d u c ta n ce p e r u n it le n g th o f th e
.7 6 2 mm
l i n e u sing e q u a tio n ( 6 ) :
L
=
(H e n rie s /m e te r)
(1 5 )
9 3 .5 Ohms
>8
1 .6 x 1 0 m/sec
=
.5 8 4 yH /m eter
L ik e w is e , f o r th e 6 .3 5 mm l i n e , th e c a p a c ita n c e p e r u n it
le n g th using e q u a tio n
(5 ) was:
I
(F a ra d s /m e te r)
(1 6 )
y
I
(3 0 .8 Ohms)( I . S lx lO 8 m /sec)
=
248 p F /m e te r
/
Fo r a low pass "Tee" f i l t e r as shown in F ig u re 5 , th e design
e q u a tio n s a re given by P o tte r and Fich (1 9 6 9 ):
\
R1.
L'
(H e n rie s )
07)
(F a ra d s )
(1 8 )
and
” f cRk
w here:
L'
In d u c ta n ce (H e n rie s )
C
C a p acitan ce (F a ra d s )
f
C orner fre q u e n cy o f th e f i l t e r
, •i ^
'X ■■ V
(H e r tz )
C h a r a c t e r is t ic impedance o f th e f i l t e r
(Ohms)
/
21
•
was chosen as 50 Ohms f o r convenience in t e s t in g as a l l
th e t e s t equipm ent a v a ila b le was 50 Ohms.
\
The c o rn e r fre q u e n c y was chosen a t 60 mHz because th e f i l t e r
pass-band covered th e fre q u e n cy range o f i n t e r e s t .
Using e q u a tio n s
(1 7 ) and (1 8 ) and n o tin g each in d u c ta n c e s e c tio n
LI
is -Tj-, th e re q u ire d in d u c ta n ce and c a p a c ita n c e was found as shown:
LJ
2
2 ir f
(H e n rie s )
(1 9 )
(F a ra d s )
(20)
50 Ohms
2 ir ( 6 x l0 7 Hz)
=
.1 3 3 wH
=
.... A
-irV k
=
-
and .
C*
—
H
—
—
irtG xlO 7 H z ) (50 Ohms)
=
106 pF
A t t h i s p o in t , th e le n g th s o f th e low pass s e c tio n s were c a l ­
c u la te d by d iv id in g th e r e s u lt s o f e q u a tio n (1 9 ) by th e r e s u lts o f
e q u a tio n
(1 5 ) and th e r e s u lt s o f e q u a tio n
e q u a tio n
(1 6 ).
F o r in d u c ta n c e :
LJ
_2
L
I
(2 0 ) by th e r e s u lt s o f
22
=
=
.1 3 3 yH
.5 8 4 p H /m eter
.2 2 8 m eter
Fo r c a p a c ita n c e :
*c = >
=
106 pF
. 248 p F /m e te r
=
.4 2 7 m eter
The low pass f i l t e r was c o n s tru c te d using s ta n d a rd p h o to g rap h ic
r e d u c tio n , p r in te d c i r c u i t board e tc h in g 'm e th o d s .
dim ensions a re i l l u s t r a t e d
fin is h e d f i l t e r
in F ig u re 6 a .
The f i l t e r
A photograph o f th e
is shown in F ig u re 6b.
As noted from F ig u re s 6a and b , th e f i l t e r was. to o long to
e tc h in a s t r a ig h t l i n e .
For t h i s
re a s o n , th e MSL s e c tio n was
an g led a t 90 degrees to form a "U" shape to f a c i l i t a t e
c o n s tr u c tio n .
ease o f
When r i g h t an g le co rn ers a re made, th e c o rn ers must
be m ite re d a t 45 degrees to decrease s ta n d in g waves caused by
boundary c o n d itio n s a t th e c o rn ers
(Howe 1 9 7 4 ).
Many re fe re n c e s
show o n ly th e o u ts id e co rn ers m ite re d as shown in F ig u re 6 a.
Curved co rn ers may be used b u t ta k e up more a rea on th e p r in te d
c i r c u i t board.
Howe (1 9 7 4 ) p re s e n ts more d a ta on t h i s s u b je c t o f
m ite re d co rn ers and s ta n d in g waves a t c o rn e rs .
w ill
No more d is c u s s io n
.
be g iv e n h e re .
/
23
,y
.LlTt M E T t a
}
I
Z HMC
COAXIAL
CO NN EC TTk
OPPOSITE SIDE
IC SOLID FOIL
. Z li
(a ) Dim ensional
N K T ii
f
illu s tr a tio n
(b ) Photograph
F ig u re 6
Dim ensional I l l u s t r a t i o n and Photograph
o f th e Tested MSL "Tee" F i l t e r
24
The f i l t e r was tap ed tw ic e s iz e on a p ie c e o f m y la r.
By using
t h i s method and re d u c in g th e ta p in g , to an a c tu a l s iz e n e g a tiv e by
p h o to g ra p h ic methods, any e r r o r made a t tw ic e s iz e is a ls o reduced
in h a l f .
A l a r g e r la y o u t would have been d e s ir a b le to use due to
t h i s e r r o r re d u c tio n c h a r a c t e r i s t i c .
However, th e p h y s ic a l s iz e
o f th e 50 mHz f i l t e r would have made a la r g e r la y o u t to o la rg e to
fit
in th e g ra p h ic s camera a v a i l a b l e .
Once th e p r in te d c i r c u i t board was e tc h e d , th e f i l t e r was te s te d
by th e method i l l u s t r a t e d
in F ig u re 7 .
Connections were made through
fe m a le BNC coax connecto rs as p r e v io u s ly shown in F ig u re 3 .
\
A H e w le tt-P a c k a rd Model '85541 spectrum a n a ly z e r was used as a
m easuring d e v ic e .
The spectrum a n a ly z e r was used because i t
is
s e n s i t i v e , has a broadband fre q u e n cy resp o n se, and p ro v id e s a 50 Ohm
te r m in a tio n to o u ts id e c o n n e c tio n s .
The 10 dB, 50 Ohm a tte n u a to rs were used as i s o la t i o n to p re v e n t
lo a d in g o f th e g e n e ra to r and to p ro v id e p ro p e r f i l t e r te r m in a tio n .
Care was ta k en to keep coax le n g th s s h o rt to p re v e n t any e f f e c t s o f
coax resonance from a f f e c t i n g th e f i l t e r d a ta .
R e s u lts o f th e measurements a re g iv e n in T a b le 3 .
The a c tu a l
c o rn e r fre q u e n c y o c cu rre d a t 67 mHz r a t h e r than 60 mHz as exp e c te d .
T h a t was an e r r o r o f 12 p e rc e n t across th re e elem ents in th e f i l t e r .
Upon remeasurement o f th e p h y s ic a l le n g th s o f each MSL s e c t io n , i t
=.5HMTWtS
W
I OJ h
------Q------- ATTENUATOR
SVlBBP
50
'T E E '
FILTER
OHM
I Odb
a ttenuato r
50
DHM
GENERATOR
©
SPECTRUM
AI MA YZ ER
F R E Q U E N CY
COUNTER
F ig u re 7
Method f o r T e s tin g th e MSL "Tee" F i l t e r
26
T a b le 3
MSL, "Tee" F i l t e r T e s t R e s u lts
Frequency (mHz)
A tte n u a tio n
10*
0
20
0
40
LO
O
I
60
-2 .6
6 0 .5
-2 .6
62
-2 .6
64
CO
CM
I
O
CO
67
70
-3 .2
100
-7 .0
150
-7 .5
200
-4 .0
250
-9 .0
500
-8 .0
^ fre q u e n c ie s le s s than 10 mHz showed 0 dB a t te n u a tio n .
(dB)
27
was observed t h a t th e c a p a c ito r c o nductor had l o s t some le n g th and
a sm all amount o f s u rfa c e a re a due to c o rn e r m it e r in g .
Both a s h o r te r
le n g th and a lo s s o f p la t e a re a r e s u lte d in le s s c a p a c ita n c e than
exp ected causing a r i s e in th e c o rn e r fre q u e n c y .
The in d u c to r
le n g th s had been c o n s tru c te d a c c u r a te ly .
The graph in F ig u re 8 i l l u s t r a t e s
th e perform ance o f th e MSL
"Tee" f i l t e r compared to a t h e o r e t ic a l s t r i p l i n e and s e v e ra l a c tu a l
s tr ip lin e f i l t e r s
1 9 7 4 ).
b u i l t and te s te d a t microwave fre q u e n c ie s
(Howe
The MSL f i l t e r response was p lo t t e d w ith th e dashed l i n e .
The s t r i p l i n e f i l t e r responses and t h e o r e t ic a l
p lo t t e d w ith s o lid l i n e s .
and th e s t r i p l i n e
MSL f i l t e r
filte r s
response.w ere
The MSL f i l t e r was a t h i r d o rd e r f i l t e r
were f i f t h
o rd e r.
For t h i s re a s o n , the
d id n o t p ro v id e th e a tte n u a tio n in th e s to p -b a n d as d id
th e o th e r s t r i p l i n e f i l t e r s .
The r i p p l e e f f e c t in th e responses was due to using tra n s m is s io n
l i n e s e c tio n s f o r s y n th e s is .
The a b ru p t impedance changes d e s c rib e d
e a r l i e r between th e in d u c ta n ce and c a p a c ita n c e s e c tio n s caused
s ta n d in g waves a lo n g th e tra n s m is s io n l i n e s e c tio n s .
As th e d r iv e
fre q u e n c y changed, th e v o lta g e maximas and minimas moved as a fu n c tio n
o f w a v e le n g th .
As t h i s o c cu rre d th e o u tp u t v o lta g e c o rre s p o n d in g ly
peaked and n u lle d .
I t was a ls o noted t h a t th e r i p p l e became les s
s ev e re as th e impedance r a t io s between l i n e s e c tio n s in c re a s e d .
THEORETICAL AND ACTUAL PERFORMANCE OF
SEVERAL PRINTED "HIGH Z - LOW Z" LOW PASS
TESTED MICROSTRIP FILTER
(N:3)-dashed line
THEORETICAL
zH = non
zL - 30 n
Z h = 150 rz
zL= 2 0 n
NORMALIZED FREQUENCY
F ig u re 8
R e s u lts o f th e MSL "Tee" F i l t e r Tests Compared to S ev e ral S t r i p l i n e
and an Id e a l Low Pass F i l t e r C h a r a c te r is tic s
29
An in c re a s e in impedance r a t i o s between l i n e s e c tio n s in a
g iv en f i l t e r a ls o caused th e o u tp u t response o f t h a t f i l t e r to
b e t t e r app ro xim ate th e t h e o r e t ic a l
response.
T h is a s p e c t o f
impedance r a t i o s between cascaded s e c tio n s o f l i n e was noted to
a id in f u r t h e r netw ork s y n th e s is ,
The l a s t t e s t was to te rm in a te th e f i l t e r
measure th e in p u t impedance o f th e f i l t e r .
impedance o f th e f i l t e r
in 50 Ohms and
I f th e c h a r a c t e r is t i c
(R^) was n e a r 50 Ohms, th e in p u t impedance
would be 50 Ohms a ls o in th e pass-band.
The v e c to r impedance
m eter was used to make th e measurement and was swept from .5 mHz .
through 70 mHz.
The pass-band impedance was 48 Ohms ± s ix degrees,
o v e r th e range from .5 mHz to 50 mHz.
Above 50 mHz th e impedance
began to r i s e and th e phase a n g le in d ic a te d th e f i l t e r was
becoming la r g e ly in d u c tiv e on th e in p u t.
B efo re le a v in g th e s u b je c t o f p a ram e te r d e te r m in a tio n s , a
f i n a l e xa m in a tio n was made o f th e c h a r a c t e r is t i c impedance
R e fe r r in g to e q u a tio n
is tic
(5 ) e a r l i e r ,
Uq).
i t was noted t h a t th e c h a r a c te r ­
impedance c o u ld be d e riv e d in term s o f th e c a p a c ita n c e p e r
u n i t le n g th
(C) and th e phase v e l o c i t y
Zq
=
(Ohms)
(V ) through th e l i n e .
. .
(2 1 )
By s u b s t it u t in g th e e xp re s s io n f o r c a p a c ita n c e p e r u n it le n g th
from e q u a tio n
(1 1 ) i n t o e q u a tio n
(2 1 ) above, th e c h a r a c t e r is t i c
30
impedance is d e s c rib e d as:
Zo
w h e re :
"
~ ^ r
. (Ohms)
<2 2 >
Zq =
C h a r a c t e r is t ic impedance (Ohms)
e
=
D i e l e c t r i c c o n s ta n t o f th e c i r c u i t board in s u la t in g
m a te r ia l (F a ra d s /m e te r)
V
=
Phase v e l o c i t y o f th e wave through th e l i n e
second)
w
=
W idth o f th e main c o nductor (m e te rs )
A l l o f th e v a r ia b le s
in e q u a tio n
d e te rm in e e , s e v e ra l p a r a l l e l
(m e te rs /
(2 2 ) were known e x c e p t e .
To
p la t e c a p a c ito rs were made by c u ttin g
s e v e ra l s iz e s o f re c ta n g le s from d o u b le -s id e d unetched p r in te d
c i r c u i t board and m easuring t h e i r c a p a c ita n c e s on a H e w le tt-P a c k a rd
Model
4260A u n iv e rs a l RLC b rid g e .
I f th e a re a o f th e p la te s was
la r g e w ith re s p e c t to th e spacing o f th e p la te s
(th e th ic k n e s s o f
th e p r in te d c i r c u i t board d i e l e c t r i c ) , then i t was assumed fr in g in g
co u ld be n e g le c te d in th e measurements.
E quation (7 ) was used to
c a lc u la t e th e d a ta p re se n te d in T a b le 4 .
The r e l a t i v e d i e l e c t r i c c o n s ta n t (e ^ ) f o r t h is p r in te d c i r c u i t
board m a te ria l
is g iven as:
e
=
r
w here:
(d im e n s io n le s s )
eo
er =
R e la t iv e d i e l e c t r i c c o n s ta n t
e
D i e l e c t r i c c o n s ta n t o f th e m a te ria l
=
Eq =
(F a ra d s /m e te r)
D i e l e c t r i c c o n s ta n t o f fr e e space (F a ra d s /m e te r)
31
T a b le 4
Measurement Data f o r th e D i e l e c t r i c C onstant o f G -IO E poxy-glass
P r in te d C i r c u i t Board o f I mm Thickness by use o f
P a r a l l e l P la te C a p a c ito rs a t I kHz
P la te Area
(s q . m e te rs )
C a p acitan ce
(F a ra d s )
D i e l e c t r i c C onstant
(F a ra d s /m e te r)
.0 4 7 4
I . 29x1O"9
2 .7 1 X 1 0 " 11
.01 4 6
4.25X10™10
2 .9 1 X 1 0 '11
.0161
4 .5 5 X 1 0 " 10
2 .8 3 x 1 0 " 11
.0 0 9 4
2 .6 9 x l0 ™ 10
2 .8 6 x 1 0 " 11
.0 0 5 4
l . 6 3 x l 0 ~ 10
3 .0 3 X 1 0 '11
Average
=
2 .8 7 x 1 0 " ^
T a b le 5
Comparison o f C a lc u la te d C h a r a c t e r is t ic Impedance
t o Measured C h a r a c t e r is t ic Impedance
f o r S ev e ral MSL Widths
Wi dth
(mm)
Measured C h a r a c t e r is t ic
Impedance (Ohms) .
C a lc u la te d C h a r a c t e r is t ic
Impedance (Ohms)
E rro r
(%)
.7 6 2
92
.. 2 5 8 .0
180
2 .5 4 0
55
8 4 .0
53
6 .3 5 0
32
3 7 .5
16
32
Then:
2 .8 7 x 1 0 “ ^
r
F a ra d s /m e te r
8 .8 5 x l0 ~ ^ 2 F a ra d s /m e te r
3 .2 4
The p re v io u s measurements on th e unetched r e c ta n g u la r p r in te d
c i r c u i t board c a p a c ito rs were made a t one k il o H e r t z .
F u rth e r
measurements made a t microwave fre q u e n c ie s confirm ed th e r e l a t i v e
d ie le c tr ic
c o n s ta n t as in th e neighborhood o f th re e and one h a l f .
M a n u fa c tu re r s p e c if ic a t io n s on th e same c i r c u i t board d i e l e c t r i c ,
how ever, c laim ed an Eyi o f f i v e a t one m egaH ertz.
Because th e
measured d a ta a t both one k ilo H e r t z and a t microwave fre q u e n c y
agreed c lo s e l y , th e measured r e l a t i v e d i e l e c t r i c c a lc u la t e d above
was used.
Once e was d e te rm in e d , e q u a tio n (2 2 ) was used to f i n d th e
c h a r a c t e r is t i c impedance o f MSL s e c tio n s w ith w id th s o f .7 6 2 ,
2 .5 4 , and 6 .3 5 mm.
These c a lc u la t e d r e s u lt s a re shown in T a b le 5
w ith th e measured MSL s e c tio n impedances f o r com parison.
The
e r r o r in c a lc u la t io n became la r g e r as th e w id th o f th e MSL main
c o n d u ctor decreased .
From t h i s d a ta th e c o n clu s io n was drawn t h a t
f r in g in g may n o t be g e n e r a lly n e g le c te d .
As th e main conductor
becomes n a rro w , f r i n g i n g has more o f an e f f e c t .
made to m odify e q u a tio n
No a tte m p t was
(2 2 ) to compensate f o r f r i n g i n g .
AMPLIFIER DESIGN METHODS
A m p lif ie r Design
The o r i g i n a l g o a l .o f th e p r o je c t was to c o n s tru c t a power
a m p li f ie r f o r th e 50 mHz re g io n using MSL s e c tio n s to s y n th e s iz e
th e in p u t and o u tp u t n e tw o rks .
Up to t h i s p o in t , th e s tu d y had
been d ir e c te d tow ard d e r iv a t io n o f design e q u a tio n s f o r MSL n e t­
works and t e s t in g t h e i r v a l i d i t y through e x p e rim e n ta l means.
S ince th e measured d a ta r e s u lt in g from th e p re v io u s ly d e s c rib e d
"Tee" f i l t e r e x p e rim e n t in d ic a te d th e design e q u a tio n s to be
u s e f u l, th e design and c o n s tru c tio n o f th e power a m p l i f i e r began.
The a m p li f ie r was used as th e power o u tp u t s ta g e f o r an
am ateur r a d io t r a n s m it t e r o p e ra tin g on 5 2 .5 2 5 mHz.
The d r iv e
source f o r th e a m p li f ie r was a c o m m erc ially made tr a n s c e iv e r
which d e liv e r e d 10 w a tts o u tp u t as d r iv e f o r th e power a m p li f ie r .
The mode used was narrowband FM.
The a m p li f ie r was designed to o p e ra te as a c la s s C (non­
l i n e a r ) a m p li f ie r f o r th r e e reaso n s.
F i r s t , th e a m p lif ic a t io n
o f FM r e q u ire s no p re s e rv a tio n o f l i n e a r i t i e s
v a r ia t io n s as do AM ty p e s ig n a ls .
in a m p litu d e
Second, c la s s C o p e ra tio n
would p ro v id e a g r e a t e r t h e o r e t ic a l c o l le c t o r e f f i c ie n c y than
l i n e a r typ es o f a m p li f ie r s .
T h ir d , c la s s C is b ia se d such t h a t
th e q u ie s c e n t o p e ra tin g p o in t is below t r a n s is t o r c u t o f f .
34
The a s p e c t o f th e q u ie s c e n t p o in t b e in g below c u t o f f a llo w e d
th e t r a n s i s t o r base to e m it t e r ju n c tio n diode to be used as a .
method o f b ia s g e n e ra tio n .
The t r a n s i s t o r would rem ain c u t o f f
u n t i l enough s ig n a l v o lta g e appeared across t h i s ju n c tio n diode to
fo rw a rd b ia s i t .
For a s i l i c o n t r a n s i s t o r , th e fo rw a rd b ia s v o lta g e
would be about .6 v o l t .
Once fo rw a rd b ia s e d , th e ju n c tio n diode
would c o n tin u e to r e c t i f y th e in p u t s ig n a l to p ro v id e base d r iv e
f o r th e t r a n s i s t o r .
The t r a n s i s t o r to be used was a s i l i c o n BM70-12 m anufactured
by Communication T r a n s is t o r C o rp o ra tio n (C T C ).
T h is t r a n s is t o r was
chosen because i t c o n ta in e d in t e r n a l m atching f o r e a s ie r i n t e r ­
fa c in g w ith n e tw o rk s , i t was c o n s tru c te d f o r use in MSL c i r c u i t s
in th e VHF r e g io n , and i t was im m e d ia te ly a v a i l a b l e .
o f th e BM70-12 is shown in F ig u re 9 .
A photograph
The BM70-12 was designed to
o p e ra te from a 12 v o l t power source as a la r g e s ig n a l a m p li f ie r
w ith an o u tp u t power o f 70 w a tts .
A lthough i t was designed to
o p e ra te in th e 200 mHz r e g io n , no problems could be fo re s e e n in
u sin g i t
a t 52 mHz.
Complete s p e c if ic a t io n s f o r th e t r a n s is t o r
a re g iv en in F ig u re s 10 and 11.
The common e m it t e r mode was chosen
f o r o p e ra tio n o f th e t r a n s is t o r .
C o n s id e ra tio n was g iven to th r e e main areas d u rin g th e design
p ro c e d u re .
Discussed in th e fo llo w in g s e c tio n s a re th e methods
F ig u re 9
Photograph o f th e BM70-12 T r a n s is to r
Used in a 52 mHz A m p lifie r
36
COMMUNICATIONS TRANSISTOR CORPORATION
BM70-12 • 70 w a t t
175 MHz • 12 VOLT RF POWER TRANSISTOR WITH INTERNAL MATCHING
MATCHED 1/2" FLANGE
GENERAL DESCRIPTION -Specifically designed to meet rugged mobile
c r portable radio requirements, internal matching sim plifies circu it de­
sign and gives excellent broadband performance.
—
-1 7 0 -1 9 0
FEATURES
• MAXIMUM RELIABILITY DUE TO SINGLE CHIP CONSTRUCTION.
• GUARANTEED TO WITHSTAND ~ VSWR AT A L L PHASE ANGLES
WHEN OPERATED AT RATED POWER WITH A 16V DC SUPPLY.
• EXCELLENT HERMETIC SEAL FOR EXTENDED LIFE IN HOSTILE
ENVIRONMENTS.
• LOIV THERMAL RESISTANCE--0 .8 ° C/W.
• HIGH POWER GAIN.
• INTERNAL MATCHING FOR HIGHER IN P U T
IMPEDANCE AND
INCHES
A L L LEADS 5 M iLS ♦
THICK
LOWER Q.
T
m
T
1
!
ELECTRICAL CHARACTERISTICS
ABSOLUTE MAXIMUM RATINGS
MAXIMUM TEMPERATURES
Storage Temperatures
Operating Junction Temperatures
Lead Temperature (Soldering 8 seconds time lim it)
S 1 /3 2 " frbm Ceramic
-6 5% to + 2000C
200°C
260%
MAXIMUM POWER DISSIPATION (Note I)
Total Power D issipation at 2 5 % Case Temperature
220 W
MAXIMUM VOLTAGES AND CURRENT
36
4
18
20
BVCES Collector to Emitter Voltage
BV EBO Emitter to Base Voltage
LV CEO Co1 lector to Emitter Voltage
Iq
Collector Current
F ig u re 10
G eneral and Maximum S p e c ific a t io n s o f th e BM70-12 T r a n s is to r
V
V
V
A
37
COMMUNICATION TRANSISTOR
( a
outwt k h s u s
BM70-12
( 5 J W W H CAM VHSUS HEOUHCV
w w H w in
«
S
i
a°
Pc w f TOW
130
Pin -
(C )
pow er
150
60
170
60
190
l-FREOUENCY-MHi
INPUT- w a t t s
£ j
SERIES INPUT IMPEDANCE VERSUS FREQUENCY
^SERIES LOAD IMPEDANCE VERSUS FREQUENCY
I FREOUENCY-MHi
• -FREQUE NOY-MHi
(e /
140
OWER DERATING CURVE
(f)
ft VERSUS Ic
Ic - COLLECTOR CURRENT-AMPS
TEMPERATURE -
F ig u re 11
A m p lific a tio n C h a r a c te r is tic s o f th e BM70-12 T r a n s is to r
38
and re as o n in g used in d e a lin g w ith th e areas o f netw ork d e s ig n ,
power d is s i p a t i o n , and s t a b i l i t y o f th e a m p l i f i e r .
Network Design
R a th e r than go through th e step s o f netw ork s y n th e s is f o r th e
t r a n s i s t o r in p u t and o u tp u t n e tw o rk s , a M o to ro la a p p lic a t io n note
(D a v is A N -267) was used which gave computer s o lu tio n s to s e v e ra l
n e tw o rks .
p a r a lle l
These s o lu tio n s were f o r m atching a known s e r ie s o r
impedance through one o f s ix netw orks to a n o n -r e a c t iv e ,
50 Ohm load w ith a s p e c ifie d loaded c i r c u i t "Q" (Q|_).
Ql
w here:
=
Q[ 15 given by:
(d im e n s io n le s s )
Q. =
L
Q o f th e tuned netw ork w ith a l l
(d im e n s io n le s s )
f
Resonant fre q u e n c y o f th e tuned netw ork ( H e r tz )
=
BW =
loads connected
H a lf-p o w e r bandwidth o f th e tuned netw ork (H e r tz )
B e fo re use could be made o f th e computer s o lu t io n s , th e
t r a n s i s t o r base in p u t impedance and th e t r a n s is t o r c o l l e c t o r o u t­
p u t impedance had to be known.
The in p u t and o u tp u t impedances o f
a la r g e s ig n a l , c la s s C a m p l i f i e r , how ever, were hard to e s t a b lis h .
The g e n e ra l recommendation o f th e re fe re n c e s c o n s u lte d on t h is
p o in t was to a p p ly power to th e d e v ic e and measure th e f u l l
d r iv e c u r r e n t and v o lta g e to th e t r a n s i s t o r base.
th e f u l l
in p u t
S i m i l a r l y , w ith
d r iv e power a p p lie d to th e t r a n s i s t o r base c i r c u i t s , th e
39
c o lle c t o r , o u tp u t v o lta g e and c u r r e n t in t o a known lo a d re s is ta n c e
would be m easuredi
Once th e r e s p e c tiv e v o lta g e and c u rre n ts were
known, th e base in p u t and c o l le c t o r o u tp u t impedances c o u ld be
c a lc u la t e d .
however.
Such measurements re q u ire d s p e c ia liz e d equipm ent,
A ra d io fre q u e n c y s ig n a l g e n e ra to r w ith enough d r iv e
pow er, a known source im pedance, and c a p a b i l it y o f tu n in g 52 mHz
was needed.
In a d d i t i o n , ra d io fre q u e n c y c u r r e n t m eters w ith
dependable accuracy in th e 52 mHz range were r e q u ire d .
Because
such t e s t d e vic e s were n o t r e a d ily a v a i l a b l e , t h i s method o f
impedance d e te rm in a tio n was n o t used.
The o n ly o th e r impedance d a ta a v a ila b le was t h a t shown in
F ig u re s l i e
and l i d .
A lthough th e pa ram e te r curves shown were n o t
extended, below 130 mHz in th e fig u r e s
and were perhaps c la s s A
( l i n e a r ) p a ra m e te rs , i t was decided to t r y and make use o f them.
The r e a c t iv e p a rts o f th e impedance curves in th e s e f ig u r e s dropped
s l i g h t l y w ith d e c re a s in g fre q u e n cy as d id th e r e a l p a r t s .
The
r e a l p a rts were assumed as one Ohm a t 50 mHz, how ever, in both
in p u t and o u tp u t cases f o r ease in l a t e r c a lc u la t io n s .
The
r e a c t iv e p a rts were p ro je c te d from th e curves to 50 mHz.
r e s u l t , a t r a n s is t o r base in p u t impedance o f I + j . 2 5
As a
Ohms and
a t r a n s i s t o r c o l le c t o r o u tp u t impedance o f I - j . 2 5 Ohms were
assumed.
40
Three o f th e p r e v io u s ly m entioned s ix netw orks ta k e n from th e
M o to ro la a p p lic a t io n n o te were e lim in a te d because th e y were designed
t o match i n t o a p a r a l l e l source impedance.
The t r a n s i s t o r impedances
d e te rm in e d above were s e r ie s source impedances.
F ig u re 12 i l l u s t r a t e s
th e th r e e re m ain in g netw orks and component v alu e s c a lc u la t e d f u r th e
t r a n s i s t o r c o l le c t o r o u tp u t impedance using procedures from th e
M o to ro la a p p lic a t io n n o te .
S i m i l a r l y , th e same netw orks (n o t shown)
were c a lc u la te d f o r th e t r a n s i s t o r base impedance.
S o lu tio n s o f
th e s e netw orks a re d e t a ile d in th e a p p lic a tio n note and w i l l
d e s c r ib e d .h e re .
n o t be
A summary o f netw ork component v alu e s is given in
T a b le 6 below .
T a b le 6
A m p lif ie r Network Component Values C a lc u la te d
to Match a 50 Ohm T e rm in a tin g Impedance
f o r a Loaded Q o f 10
C a lc u la te d Value
Component
. .0 3 2 yH
V
L2
=1
C2
C3
.
.
.0 3 0 uH
271 pF
271 pF
60 pF
I
41
303PT .OSZuH
o— It-T r n Z r -
ZZ 424PF > SOOHHS
(S)
O
/7 7
.OlZyuF
.0 3 CUH
60PF
wT----------- ' ' --- ------ it-----
b)
: z 271PF
<
)
transistor squivalbnt
.OlIyuH
.OISyM
o--------- m n _ ,__mn__
(0
i
3 30PF > sc OHns
O
/7 7
F ig u re 12
P o s s ib le T r a n s is to r C o lle c to r M atching Network Designs
f o r th e 52 mHz A m p lif ie r
42
R e fe r r in g to F ig u re 1 2 , netw orks a and b were th e b e s t choices
as th e y p re se n te d c a p a c itiv e o u tp u t lo a d in g and tu n in g .
T h is was
an advantage o v e r th e in d u c tiv e o u tp u t c i r c u i t in c because c a p a c ito r
e r r o r s could be compensated through a d d itio n o f d is c r e t e trim m er
c a p a c ito rs i f n e c e s s a ry .
C i r c u i t b was decided upon because th e
s e r ie s c a p a c ito r in c i r c u i t a was la r g e r than t h a t in b.
In the
lo n g ru n , th e s m a lle r c a p a c ito r in c i r c u i t b would c o n tr ib u te to a
s m a lle r p h y s ic a l p r in te d c i r c u i t board s iz e f o r th e com pleted
a m p lifie r .
The a m p l i f i e r schem atic diagram using networks p a tte rn e d a f t e r
c i r c u i t b in F ig u re 12 is
illu s tr a te d
in F ig u re 13.
+ 12v
I /
T
\
.0 5 u f
IOOv
1+ IOuf
T
16v
L S uh
BM7Q-12
F ig u re 13
Schem atic Diagram o f th e 52 mHz A m p lif ie r
'
■'!
43
The in p u t and o u tp u t netw orks were to be c o n s tru c te d as MSL
s y n th e s iz e d n e tw o rk s .
c a lc u la t e l i n e
E quations ( 5 ) and (6 ) were now used to
le n g th s f o r th e MSL s e c tio n s .
Only th e s e r ie s
in d u c to rs and shunt c a p a c ito rs could be c a lc u la te d by t h i s method.
The c a lc u la t io n s f o r th e s e r ie s c a p a c ito rs a re discussed l a t e r .
R e c a llin g th e e a r l i e r d is c u s s io n on c h a r a c t e r is t i c impedance
r a t io s between cascaded MSL s e c tio n s , i t was d is c o v e re d t h a t
impedance r a t io s from s e c tio n to s e c tio n produced th e b e s t netw ork
p erfo rm ances.
For t h i s re a s o n , th e netw orks f o r th e a m p li f ie r
were designed w ith a la r g e c h a r a c t e r is t i c impedance r a t i o between
s e c tio n s .
An MSL main conductor w id th o f .381 mm c o rresp o n d in g to
a l i n e c h a r a c t e r is t i c impedance o f 110.1 Qhms was chosen f o r
in d u c to r s e c tio n s w h ile an. MSL main conductor w id th o f 2 4 .5 mm
c o rresp o n d in g to a l i n e c h a r a c t e r is t i c impedance o f 1 1 .4 Ohms was
chosen f o r c a p a c ito r s e c tio n s .
An impedance r a t i o between th e
c a p a c itiv e and in d u c tiv e MSL s e c tio n s o f 6 6 .7 r e s u lte d from these
ch o ices o f MSL s e c tio n s .
Due to e x a m in a tio n o f e a r l i e r measurements
and r e fe re n c e d a ta , such an impedance r a t i o was exp ected to perform
w e ll.
U sing e q u a tio n s
(5 ) and (6 ) in a d d itio n to th e phase v e lo c it y
and impedance d a ta shown in T ab les I and 2 r e s p e c t iv e ly , th e c a p a c i­
ta n c e (C ) and th e in d u c ta n ce (L ) p e r u n i t le n g th were c a lc u la t e d :
44
H O . I Ohms
O
I .6 2 x 1 O m eters/seco n d
.6 8 0 yH /m eter
I
and
I
z Ov
I
( 1 1 .4 Ohms)(9 .2 4 x 1 0 ' m e te rs /s ec o n d )
=
949 p F /m e ter
T h is d a ta made th e s e r ie s in d u c ta n c e and shunt c a p a c ita n c e l i n e
le n g th s easy to c a lc u la t e :
■
t L1
=
h
L
.03 2 yH
.6 8 0 yH /m eter
=
.0 4 7 m eter
and
*1
2
=
L
.0 3 0 yH
.6 8 0 y H /m e te r
.0 4 4 m eter
45
and
C
I
C
n
y
271 pF
949 p F /m e te r
=
.2 8 6 m eter
The s e r ie s c a p a c ito rs were made by e tc h in g two area s o f f o i l on
o p p o s ite s id e s o f th e p r in te d c i r c u i t board to form p a r a l l e l p la t e
c a p a c ito r s .
S ince th e d i e l e c t r i c o f th e e p o x y -g la s s was determ ined
e a r l i e r , th e f o i l
e q u a tio n
(7),
s iz e s could be e a s i l y c a lc u la t e d .
R e fe r r in g to
th e p la t e spacing and d i e l e c t r i c o f each c a p a c ito r
were c o n s ta n ts im p ly in g th e c a p a c ita n c e would be d ete rm in e d by th e
p la t e a re a .
The p la t e a re a was c a lc u la t e d as shown below :
dC
e
(.0 0 1 m e t e r ) ( 6 x l0 ~ ^
F a rad s )
( 2 . 8 7 x l 0 -11 F a ra d s /m e te r)
=
«3
2 .0 9 x 1 0 " square m eter
The in p u t and o u tp u t c i r c u i t s were etched on a c i r c u i t board in
such a way t h a t a sm all p ie c e o f w ir e s o ld e re d through th e board was
used to connect th e main conductor o f
o f Cg and C^, r e s p e c t iv e ly .
and
to th e bottom p la te s
The in d u c ta n ce and c a p a c ita n c e s e c tio n s
were fo ld e d and m ite re d to conserve space in th e la y o u t .
Care was
ta k en to assure t h a t th e le n g th s were a c c u ra te through m ite r in g to
46
a v o id th e e r r o r en co u n tered in th e e a r l i e r MSL "Tee" f i l t e r e x p e r i­
m ent.
F ig u re 14 p re s e n ts a photograph o f th e etch ed a m p li f ie r
netw orks w ith th e t r a n s i s t o r in p la c e and th e h e a t s in k removed.
The o p p o s ite s id e is s o lid f o i l w ith th e e x c e p tio n o f th e areas
under Cg and
which a re th e c a p a c ito r areas connected to th e
in p u t and o u tp u t c o n n e c to rs , r e s p e c t iv e ly .
The f o i l
a re a around th e MSL s e c tio n s is grounded to th e f o i l
s id e beneath by means o f s e v e ra l sm all w ire s s o ld e re d through th e
board a t sm all le n g th i n t e r v a l s .
B e fo re th e t r a n s i s t o r was p la ce d in th e c i r c u i t , th e c a p a c ito r
v a lu e s were measured w ith a H e w le tt-P a c k a rd Model 4260A RLC b rid g e .
No easy method could be th o u g h t o f to measure th e in d u c ta n c e sec­
t io n s .
T a b le 7 d e p ic ts th e r e s u l t s .
T a b le 7
A m p lif ie r C a p a c ito r Measurements Compared
to th e C a lc u la te d Values
C a p a c ito r
C1
C2
C3
Measured C ap acitan ce
(p F )
C a lc u la te d C apacitance
(p F )
223
271
201
271
60
60
64
60
Photograph o f the 52 mHz A m p lifie r
w ith Heat Sink Removed
48
The r e s u lt s o f th e measurements in d ic a te d Cg as b e in g th e o n ly
c a p a c ito r to .b e a c c u ra te .
E rro rs in th e o th e r measured c a p a c ito r
v a lu e s compared to th o se c a lc u la te d were d is tu r b in g .
The d if f e r e n c e between th e m easured.and c a lc u la te d v alu e s o f
was th e e a s ie s t to e x p la in .
le n g th and s iz e e r r o r s ,
p la te a re a .
W h ile rem easuring f o r p h y s ic a l
was found to be s l i g h t l y to o la r g e in
N othing was done to change
th e a c tu a l o p e ra tio n o f th e a m p l i f i e r .
a t t h a t tim e pending
A t t h a t tim e some " f in e
tu n in g " was exp ected to be done.
The d is c re p a n c ie s found in th e MSL c a p a c ito r s ,
were n o t so e a s i l y e x p la in e d .
and C2 ,
A f t e r re c o n s u ltin g s e v e ra l
r e fe r e n c e s , a reason f o r th e problems became e v id e n t.
The c o rn e r
m ite r in g had been done i n c o r r e c t ly in both t h i s c i r c u i t and th e
p r e v io u s ly te s te d MSL "Tee" f i l t e r .
co rn ers in th e s e c i r c u i t s
Both in s id e and o u ts id e
had been m ite re d and no method had
been used to govern th e m ite r a n g les o r le n g th s .
O nly th e o u t­
s id e c o rn e rs should have.been m ite re d a cco rd in g to methods backed
by e x p e rim e n ta l d a ta g iv en by Howe (1 9 7 4 ).
As a r e s u l t o f t h is
o v e r s ig h t, th e tra n s m is s io n lin e s became mismatched a t th e corners
causing th e lin e s to change c h a r a c t e r is t i c s .
The r e s u l t was
perform ance o th e r th an expected in th e s e c a p a c ito r s e c tio n s .
These s e c tio n s were n o t a d ju s te d u n t i l th e a m p li f ie r was te s te d .
49
Some doubt was r a is e d a t t h i s p o in t as to th e accu racy o f
th e in d u c to r MSL s e c tio n s .
As p r e v io u s ly s t a t e d , no good method
o f m easuring th e in d u c to rs could be produced.
As a r e s u l t , i t
was d ecid ed to t e s t th e a m p li f ie r w ith o u t f u r t h e r in v e s t ig a t io n o f
th e s e s e c tio n s .
S ta b ility
Many papers and books were r e f e r r e d to f o r c lu es on how to
p re d e te rm in e th e s t a b i l i t y o f th e a m p l i f i e r .
S ince th e t r a n s is t o r
was a la r g e s ig n a l d e v ic e , s e v e ra l problems p resen ted th e m selves.
F i r s t , th e "S" p a ra m e te rs , which a r e commonly used in design
o f VHF c i r c u i t s , were e lim in a te d because th e y a re sm all s ig n a l
p a ra m e te rs .
Second, most methods o f c a lc u la t in g s t a b i l i t y
in L i n v i l l
such as d e sc rib e d
and Gibbons (1 9 6 1 ) used "Y" param eters w hich a re a ls o
sm all s ig n a l p a ra m e te rs .
T h ir d , th e a m p li f ie r was to o p e ra te in c la s s C which is
e x tre m e ly n o n lin e a r .
T h is a s p e c t added doubt to a l l
pa ram e te r
s e ts because t r a n s i s t o r param eters a re u s u a lly measured in the
l i n e a r o r a c t iv e re g io n o f o p e r a tio n .
W ith o u t any method o f p re d e te rm in in g s t a b i l i t y ,
i t was
d ecid ed to c o n s tru c t th e a m p li f ie r in such a way as to a v o id
e f f e c t s which would cause i n s t a b i l i t y .
These e f f e c t s c o u ld have
50
been f i e l d
c o u p lin g between in d u c to rs from o u tp u t to in p u t o r
feedback through th e re v e rs e p a ram e te r o f th e power t r a n s i s t o r .
As s ta te d p r e v io u s ly , la r g e s ig n a l param eters a re n o t r e a d ily
a v a ila b le f o r t r a n s is t o r s such as th e BM70-12 used in t h i s e x p e r i­
m ent.
For t h i s
re a s o n , feedback th ro u g h th e re v e rs e d ir e c t io n o f
th e a m p l i f i e r t r a n s i s t o r was assumed n o t to be a f a c t o r in th e
a m p lifie r s t a b i l i t y .
P ro v is io n s f o r th e a d d itio n o f n e u t r a liz in g
components to th e c i r c u i t board were p ro v id e d , how ever, in case
t h i s assum ption proved in a c c u ra te d u rin g a m p li f ie r t e s t i n g .
The rem ain d er o f th e s t a b i l i t y e f f o r t was spent in p re v e n tin g
netw ork c o u p lin g between in p u t and o u tp u t.
S p e c i f i c a l l y , L-j and
Lg posed th e g r e a t e s t problems in term s o f f i e l d c o u p lin g .
An e x p e rim e n t was conducted using two 10 cm le n g th s o f MSL
w ith c o nductor w id th s o f 1 .5 8 mm.
w ith 2 mm spacing between them.
The le n g th s were run p a r a l l e l
A 50 mHz s ig n a l source was
connected to one l i n e and an o s c illo s c o p e to th e o th e r l i n e .
The
o u tp u t v o lta g e to th e o s c illo s c o p e from th e second l i n e was 10 dB
below th e in p u t v o lta g e to th e f i r s t l i n e .
These r e s u lt s
illu s tr a te d
t h a t th e r e is poor c o u p lin g between p a r a l l e l MSL s e c tio n s .
The r e s u lt s o f t h i s p a r a l l e l
l i n e e x p e rim e n t seemed to in d ic a te
t h a t i f MSL lin e s would n o t c ro s s -c o u p le w e ll a t c lo s e s p a c in g , then
extrem e spacing o f lin e s would f u r t h e r reduce mutual c o u p lin g
■7
.
51
p o s s ib ilitie s .
W ith t h i s
in m ind, th e in p u t and o u tp u t networks
o f th e a m p l i f i e r were p la c e d o p p o s ite each o th e r w ith as much
sp acin g between th e in d u c to r s ,
and L g , as p o s s ib le .
To f u r t h e r c u t down on in d u c to r c o u p lin g a s h ie ld was con­
s tr u c te d .
S o ld ere d to th e to p ground f o i l was a d o u b le -c la d
c i r c u i t board w a ll th e h e ig h t o f th e t r a n s i s t o r which extended
th e e n t i r e w id th o f th e board.
T h is s t r i p
p ro v id ed s h ie ld in g o f
th e in p u t netw ork from th e o u tp u t netw ork to a id in s t a b i l i t y .
The t r a n s i s t o r s e p a ra te d one s e c tio n o f t h i s s h ie ld from th e
o th e r as may be seen from F ig u re 14.
Power D is s ip a tio n
S ince th e o u tp u t power o f th e t r a n s i s t o r was exp ected to be
fa ir ly
l a r g e , th e power d is s ip a tio n
be la r g e .
lik e w is e would be exp ected to
Some s o r t o f h e a t s in k had to be developed to t r a n s f e r
th e h e a t to am bient a i r and cool th e t r a n s i s t o r so ju n c t io n h e a t
damage would n o t be s u s ta in e d .
Am bient te m p e ra tu re o f th e a i r was
assumed a t 25°C .
C a lc u la tio n s were made using methods d e s c rib e d by A lle y and
Atwood (1 9 7 3 ) and a re p re se n te d in Appendix L
The fo rm u la tio n o f th e c o r r e c t h e a t s in k s iz e p re s e n te d a
problem .
The method used r e s u lte d in a re q u ire d h e a t s in k a re a
la r g e r in s iz e than th e e n t i r e a m p l i f i e r .
T h is seemed unreasonable
52
( .4 5 square m e te r ).
A h e a t s in k made from 3 .2 mm b r ig h t aluminum
a p p ro x im a te ly o n e -fo u rth th e s iz e c a lc u la te d
used in s te a d on a t r i a l
b a s is .
If
it
( .1
square m e te r) was
became to o h o t, a la r g e r
h e a t s in k would be t r i e d .
The h e a t s in k was a tta c h e d to th e t r a n s is t o r w ith a t h in
la y e r o f s il i c o n h e a t compound between them to a id h e a t t r a n s f e r .
A m p lif ie r C i r c u i t D e s c rip tio n
R e fe rrin g to th e com pleted schem atic diagram in F ig u re 1 5,
C-J1 C3 , and L-J match th e 50 Ohm in p u t d r iv e source to th e base o f
+12v
.0 5 u f
I
T
\
/
1+ IO u f
T
16v
LS uh
BM 70-12
/7 7
/7 7
F ig u re 15
Completed Schem atic Diagram o f th e 52 mHz A m p lif ie r
53
th e t r a n s i s t o r .
and
re s o n a te th e c i r c u i t w h ile Cg tunes o u t
any unwanted re a c ta n c e a t th e in p u t.
Cg, C^1 and Lg match th e 50 Ohm lo a d impedance t o th e c o l le c t o r
impedance o f th e t r a n s i s t o r .
Cg and Lg re s o n a te h ere w ith C^
m atching th e r e a c t iv e component a t th e o u tp u t te r m in a ls .
Because th e t r a n s i s t o r was to run in c la s s C s no b ia s was
a p p lie d to th e t r a n s i s t o r .
A dc r e tu r n f o r th e t r a n s i s t o r base was
p ro v id e d by a 1 0 .pH, c o m m e rc ia lly m a n u fa ctu red , ra d io fre q u e n c y
choke ( R F C g ) .
T h is r e tu r n was necessary due to th e dc component o f
th e c la s s C wave fo rm .
No ra d io fre q u e n c y s ig n a l was a llo w e d to
pass to ground due to th e choke a c t io n .
A n other ra d io fre q u e n c y choke (R F C y) was used to s u p p ly dc
v o lta g e to th e t r a n s is t o r c o l le c t o r .
from e n te r in g th e power s u p p ly .
I t p re ve n te d r a d io freq u en cy
Any unwanted ra d io fre q u e n c y
v o lta g e le a k in g th rough t h i s choke was s h o rte d to ground by the
bypass c a p a c ito rs on th e power s u p p ly end o f th e choke.
T h is
choke was c o n s tru c te d from 12 tu rn s o f #18 AWG magnet w ir e about
2 5 .4 mm long and 20 mm in d ia m e te r.
The re a c ta n c e o f t h i s choke
measured 480 Ohms a t 52 mHz o r about 1 .5 pH.
. RESULTS
The f i r s t t e s t o f th e a m p l i f i e r used a tu n a b le VHF s ig n a l
g e n e ra to r s u p p ly in g about .5 w a tt through a v a r ia b le 50 Ohm
a tte n u a to r as a d r iv e source to th e in p u t.
The fre q u e n c y o f th e
g e n e ra to r was m o nitored by a fre q u e n c y c o u n te r.
The a m p li f ie r o u tp u t was te rm in a te d by a 50 Ohm, 20 dB power
a tte n u a to r fe e d in g a H e w le tt-P a c k a rd Model 8554A spectrum a n a ly z e r.
The a t te n u a to r p ro v id e d a matched lo a d impedance to th e a m p li f ie r
o u tp u t t e r m in a l.
F ig u re 16 i l l u s t r a t e s
th e t e s t s et-u p ..
Tw elve v o lts was a p p lie d to th e a m p li f ie r and w ith a sm all
amount o f s ig n a l a p p lie d to th e in p u t , th e fre q u e n cy was swept in
th e neighborhood o f 52 mHz.
5 7 .3 2 8 mHz.
Only one resonance was observed a t
A h ig h e r fre q u e n cy was exp ected because th e c a p a c ito r
measured a b i t sm all as was shown in T a b le 7 .
The netw ork freq u en cy
e r r o r o v e r a ll was n in e p e rc e n t o v e r s ix MSL and p r in te d c i r c u i t
board components.
The loaded netw orks to g e th e r produced a h a lf-p o w e r bandwidth
o f 2 mHz o r a
The f i n a l
o f 2 8 .7 .
t e s t was made by r e p la c in g th e s ig n a l g e n e ra to r and
v a r ia b le a t te n u a to r by a 10 w a tt o u tp u t, Model IC -6 F , FM tr a n s c e iv e r
as a d r iv e s o u rc e .
The o u tp u t fre q u e n c y was a t 5 2 .5 2 5 mHz.
The
S VE E P
GENERflTOR
VARIABLE
ATTENUATOR
x . S V O lT
A M P L IF IE R
5 0 OHM
5 0 OHM
FREOUENCY
COUNTER
F ig u re 16
In itia l
T e s tin g Method f o r th e 52 mHz A m p lifie r
SPECTRUM
ANALYZER
7
.
■
56
20 dB 50 Ohm power a tte n u a to r and spectrum a n a ly z e r rem ained connected
to th e o u tp u t as b e fo re .
c o n n e c tio n s .
F ig u re 17 i l l u s t r a t e s
th e f i n a l
te s t
Two w a ttm e te rs were in s e r te d in s e r ie s w ith th e in p u t
and o u tp u t o f th e a m p l i f i e r so power g a in could be measured.
W ith o u t tu n in g th e n e tw o rk s , 12 v o lts dc was a p p lie d to th e
c o l le c t o r c i r c u i t r y .
W ith an in p u t d r iv e power o f 10 w a t t s , the
a m p li f ie r o u tp u t was 28 w a tts .
T h is was d e c id e d ly n o t optimum
p erfo rm ance.
A f t e r adding ARCO 461 compression trim m e r c a p a c ito r s , the
a m p li f ie r was f i n e tu n e d .
These c a p a c ito rs p a r a lle le d
and Cg
and were i n s t a l l e d from th e MSL s e c tio n ju n c tio n s o f L-j -C-j and
Lg-Cg to ground.
W ith 12 v o lts dc to th e c o l le c t o r and d r iv e
a p p lie d , th e trim m ers were tuned f o r maximum power o u tp u t.
This
r e s u lte d in 35 w a tts o f o u tp u t f o r 10 w a tts o f d r iv e .
The ARCO 461 trim m ers were removed and measured.
The c a p a c ito r
on th e in p u t measured 21 pF w h ile t h a t on th e c o l le c t o r measured
65 pF.
R e fe r r in g to T a b le
both th e sum o f th e ARCO 461 base
c a p a c ito r p lu s C^ and th e sum o f th e ARCO 461 c o l le c t o r c a p a c ito r
p lu s Cg came o u t s l i g h t l y le s s than th e c a lc u la te d 271 pF.
f a c t p o in te d to th e in d u c to r s iz e s being s l i g h t l y to o la r g e .
This
Any
in d u c to r e r r o r noted here was p ro b a b ly due to th e m ite r in g problems
d iscu ssed e a r l i e r .
©
WATTMETERS
F ig u re 17
F in a l T e s tin g Method f o r th e 52 mHz A m p lif ie r
SPECTRUM
AMLYZER
58
To f u r t h e r in c re a s e th e o u tp u t pow er, th e s ta n d in g wave r a t io s
on both in p u t and o u tp u t were te s te d using th e w a ttm e te rs .
There
i d e a l l y should have been no r e f l e c t e d power on e i t h e r th e in p u t o r
o u tp u t.
The o u tp u t had no power r e f l e c t e d .
The in p u t , how ever,
d is p la y e d n e a r ly two w a tts r e f l e c t e d w ith 10 w a tts in th e fo rw a rd
d ir e c tio n .
S ince Cg was th e m atching c a p a c it o r , a s m all ARCO 460
com pression trim m e r c a p a c ito r was p a r a l l e le d w ith i t .
The r e s u lt in g
r e f l e c t e d power a t th e in p u t was g r e a t e r even a t minimum c a p a c ita n c e .
T h is in d ic a te d t h a t th e c a p a c ita n c e o f C3 was to o la r g e to begin
w it h .
The ARCO 460 trim m e r was removed and a rea o f th e C3 f o i l
on
th e c i r c u i t board was decreased by c u t t in g d ia g o n a ls through th e
fo il.
As seen from e q u a tio n
( 7 ) , d e c re a s in g th e c a p a c ito r p la te
a re a d ecreased th e c a p a c ita n c e o f th e c a p a c ito r .
As C3 was d e c re a s e d , th e in p u t r e f l e c t e d power began to drop
as e x p e c te d .
The process o f d e c re a s in g th e p la te a re a was c o n tin u ed
u n t i l w ith 10 w a tts fo rw a rd , o n ly .1 w a t t was r e f l e c t e d .
W ith th e in p u t m atched, optimum perform ance was a c h ie v e d .
an in p u t o f 10 w a t t s , th e o u tp u t power was measured a t 65 w a tts
f o r a power g a in o f 8 .1 3 dB.
(E ).
) to th e a m p li f ie r was:
Pin
=
IE
(Po u t)
The in p u t c u rre n t was 9 .5 amperes ( I )
a t a c o l l e c t o r v o lta g e o f 12 v o lts
(P i
W ith
(w a tts )
The average in p u t power
( 9 . 5 A ) (12 V)
114 w a tts
E f f ic ie n c y o f th e a m p li f ie r is g iv en by:
100
x
P_
out
Pin
TOO
=
x
65 w a tts
114 w a tts
57 p e rc e n t
The exp ected e f f i c i e n c y o f a c la s s C a m p li f ie r is somewhat
h ig h e r than t h i s .
However, th e re was no r e a l a t t e n t io n g iven to
th e q u ie s c e n t b ia s p o in t o f th e t r a n s i s t o r which c o n trib u te d to
th e lo w e r e f f i c i e n c y .
F ig u re 18 p re se n ts , a photograph o f th e fin is h e d a m p li f ie r w ith
th e h e a t s in k in p la c e , th e ARCO 461 trim m ers across
shown, and th e c u ts in th e top f o i l
The f i n a l
a n a ly z e r .
and
o f Cg to tune th e in p u t v i s i b l e .
d a ta ta k en was harmonic d a ta from th e spectrum
The d a ta is p lo t t e d in F ig u re 19.
Good re d u c tio n in
a m p litu d e o f th e harmonics was n o te d .
The o n ly problem encountered was o v e rs ig h t in th e c o lle c t o r
c i r c u i t d e s ig n .
The in d u c to r s e c tio n , Lg, was p h y s ic a lly to o sm all
(.3 6 5 mm) to handle th e high power ra d io freq u en cy c u r r e n ts .
o v erh e a te d and broke j u s t a f t e r th e f i n a l
d a ta was ta k e n .
It
The
m e ltin g o f Lg was a case in p o in t on why c h a r a c t e r is t i c impedance
HEAT SINK
F ig u re 18
Photograph o f the 52 mHz A m p lifie r
w ith Heat Sink in Place
Normalized Frequency-nF0
F ig u re 19
Harmonics Measured a t th e O utput
o f the 52 mHz A m p lif ie r
r a t i o s between MSL s e c tio n s cannot exceed p r a c t ic a l s iz e c o n s id e ra ­
tio n s as discussed p r e v io u s ly .
I t was now obvious t h a t th e
impedance r a t i o o f 6 6 .7 used here was to p la r g e f o r p r a c t ic a l
c o n s tru c tio n a lth o u g h th e netw orks perform ed a d m ira b ly w h ile
la s t e d .
The h e a t s in k ch o ice made e a r l i e r tu rn e d o u t w e l l .
a f t e r s e v e ra l m inutes o f tra n s m is s io n a t f u l l
s in k became o n ly warm to th e to u c h .
Even
pow er, th e h e at
th e y
CONCLUSION
T h is p r o je c t was undertaken to e x p lo re th e f e a s i b i l i t y
o f MSL
a t VHF and to p e r f e c t design methods f o r use by e x p e rim e n te rs who
do n o t have e xp e n s ive la b equipm ent.
T h is was done through th e
desig n o f a 52 mHz a m p li f ie r .
O v e r a l l, th e p r o j e c t was a success.
I t was dem onstrated t h a t
MSL te c h n iq u es used in th e UHF and microwave re g io n s work e q u a lly
w e ll a t 52 mHz.
The main c o n s id e ra tio n proved to be th e p h y s ic a l
s iz e o f th e r e s u lt in g c i r c u i t s .
The fin is h e d a m p li f ie r measured
21 cm x 35 cm.
S iz e may be reduced by bending th e MSL s e c tio n s w ith p ro p e rly
m ite re d o u ts id e co rn ers as p re v io u s ly re fe re n c e d or. by c u rv in g th e
co rn ers w ith th e optimum curve ra d iu s being th re e MSL main conductor
w id th s
(Howe 1 9 7 4 ).
M ite r in g co rn ers ta k es le s s a re a than does
c u rv in g w ith e s s e n t i a l l y th e same r e s u lt s i f p ro p e r dim ensions are
used.
N e ith e r ty p e o f c o rn e r, when p ro p e rly made, has l i n e
c h a r a c t e r is t ic s d is tin g u is h a b le from a s t r a ig h t s e c tio n o f l i n e .
A
f u r t h e r s tu d y c o u ld be done in t h i s a re a to compare m ite re d co rners
w ith r a d ia l
c o rn e rs .
The a m p li f ie r r e s u lt s were good a lth o u g h problems in m ite rin g
were d is c o v e re d which made i t necessary to add d is c r e te trim m er
c a p a c ito rs to tune th e netw orks to resonance.
64
Cg had to be s e v e r e ly reduced in s iz e in o rd e r to reduce
r e f l e c t e d power a t th e in p u t.
A p p a re n tly th e assum ption o f
I + j . 2 5 Ohms f o r th e t r a n s is t o r base in p u t impedance was in c o r r e c t .
The assumed t r a n s i s t o r c o l le c t o r o u tp u t impedance o f I
- j . 2 5 Ohms
seemed c o r r e c t , how ever, as no r e f l e c t e d power was measured a t
th e a m p li f ie r o u tp u t.
The MSL methods used to design th e m atching netw orks f o r the
a m p li f ie r were based on e q u a tio n s d e riv e d from th e lo s s le s s c o a x ia l
tra n s m is s io n l i n e m odel.
I t was found t h a t th e lo s s le s s c o a x ia l
tra n s m is s io n l i n e model approxim ates MSL c h a r a c t e r is t ic s q u ite w e l l .
Once th e c h a r a c t e r is t i c impedance and phase v e lo c it y f o r a given
\
w id th o f main c o nductor in an. MSL s e c tio n
was known, s e r ie s
in d u ctan ces and shunt c a p a c ita n c e s were r e a d i l y s y n th e s iz e d .
Cascading o f th e s e MSL s e c tio n s may be used to s y n th e s iz e n etw orks.
The c h a r a c t e r is t i c impedance and phase v e lo c it y d a ta was
measured by methods d e s c rib e d e a r l i e r .
Once th e d a ta was accum ulated ,
i t was te s te d f o r v a l i d i t y by c o n s tru c tin g and t e s t in g a low pass
"Tee" f i l t e r o u t o f MSL s e c tio n s .
problem s in th e f i l t e r
Ig n o rin g m ite r in g and le n g th
i t s e l f , th e MSL d a ta proved a c c u ra te .
A
summary o f th e MSL desig n e q u a tio n s and a graph o f th e e x p e rim e n ta l
d a ta ta k en f o r phase v e l o c i t y and c h a r a c t e r is t i c impedance is given
in Appendix I I .
The d a ta given i s f o r G -IO e p o x y -g la s s p r in te d
c i r c u i t board o f I rran th ic k n e s s .
65
These e q u a tio n s and th e d a ta a re g iv en f o r re fe re n c e by th e .
e x p e rim e n te r.
A lthough a s im p le method f o r f in d in g phase v e lo c it y
w ith s im p le a p p ara tu s was g iv e n , c h a r a c t e r is t i c impedance is a much
h a rd e r p a ram e te r to m easure.
F rin g in g may n o t be n e g le c te d in MSL d e s ig n s .
th e main c o n d u c to r,
The na rro w e r
th e more f r in g in g e f f e c t s a re n o tic e d .
For
t h i s re a s o n , th e c h a r a c t e r is t i c impedance o f a l i n e s e c tio n may no t
be e a s i l y c a lc u la t e d .
im pedances.
The q u ic k e s t method is to measure these
I f a v e c to r impedance m eter is n o t a v a i l a b l e , a
re a c ta n c e b rid g e could be used.
The c h a r a c t e r is t i c impedance is
th e g e o m etric mean o f th e open and s h o rte d impedances o f th e l i n e .
Care must be ta k e n to keep lea d s s h o r t.
A ls o , th e fre q u e n c y o f
such measurements must be s e v e ra l m egahertz away from q u a r t e r w avelen gth measurements.
A suggested f u r t h e r s tu d y would be to
f in d an a c c u ra te m o d ifie d e q u a tio n f o r c h a r a c t e r is t i c impedance
which compensates f o r f r in g in g ..
An a d d it io n a l o b s e rv a tio n made concerns th e a c tu a l cascading
o f MSL s e c tio n s to s y n th e s iz e n e tw o rks .
t h a t th e c h a r a c t e r is t i c impedance r a t i o
The c o n c lu s io n here was
between cascaded MSL
s e c tio n s must be k e p t as high as p o s s ib le f o r p ro p e r in d u c tiv e o r
c a p a c itiv e o p e ra tio n o f th e l i n e s e c tio n s .
The g r e a t e r t h i s r a t i o ,
th e le s s tra n s m is s io n l i n e type v o lta g e r ip p l in g occurs in th e
■■'I
66
netw ork o v er a g iven fre q u e n c y ra n g e .
The p o in t was w e ll demon­
s t r a t e d by th e MSL "Tee" f i l t e r r e s u lt s and com parisons.
filte r ,
In t h is
th e impedance r a t i o between MSL s e c tio n s was 3 and p e r f o r ­
mance in th e s to p -b a n d was n o t v e ry im p re s s iv e .
There is a p r a c t ic a l
l i m i t to t h i s
impedance r a t i o , however.
T h is was dem onstrated in th e c o l le c t o r o u tp u t c i r c u i t o f th e
a m p l i f i e r when th e c o l le c t o r in d u c to r (Lg) m elted due to i t s
p h y s ic a l s iz e being to o sm all to handle th e o u tp u t c u r r e n t .
The c h a r a c t e r is t i c impedance r a t i o between th e MSL in d u c to r and
c a p a c ito r s e c tio n s was 6 6 .7 .
From th e s e f in d i n g s , a good
e s tim a te d v a lu e f o r th e impedance r a t i o o f cascaded s e c tio n s
would be 10.
As a r u l e , i f
la r g e r r a t i o s may be used w ith o u t
h in d ra n ce o f c i r c u i t p e rfo rm a n ce , th e netw ork w i l l
p e rfo rm
b e tte r.
F i n a l l y , MSL is n o t r e a d i l y a f f e c t e d by th e p r o x im ity o f
m e t a ll i c o b je c ts .
An aluminum s h e e t was used and p la c e d in t h e .
im m ediate a re a o f th e netw orks f o r th e 52 mHz a m p li f ie r .
No
\
e f f e c t s were n o tic e d in perform ance u nless th e p la t e was to u ch in g
one o f th e netw ork components.
67
LITERATURE CITED
A l l e y , C h a rles L. and Kenneth W. Atwood.
E le c tr o n ic E n g in e e rin g .
New Y ork: John W ile y & Sons, 1973. .838 pp.
A tw a te r , H. A.
In tr o d u c tio n to Microwave T h e o ry .
M c G ra w -H ill, 1962.
244 pp.
New Y ork:
D a v is , F ra n k.
"M atching Network Designs W ith Computer S o lu tio n s "
M o to ro la Sem iconductor Products A p p l. Note A N -267.
12 pp.
F a r r e l l , G. F.
"Low VSWR Coax to S t r i p l i n e T r a n s itio n "
General
^
E l e c t r i c Tech. In f o . S e rie s No. R63EMH4, January 1963.
19 pp.
Howe, H a r la n , J r .
S t r i p l i n e C i r c u i t D e s ig n . B u r lin g to n ,
M assachusetts: Microwave A s s o c ia te s , 1974.
344 pp.
K rau s, John D. and K e ith R. C a rv e r.
M c G r a w - H i l l , 1973.
828 pp.
E le c tro m a g n e tic s .
New York:
\
L i n v i l l , John G. and James F. Gibbons.
T r a n s is to rs and A c tiv e
C ir c u it s .
New Y ork: M c G ra w -H ill, 1961.
515 pp.
P o t t e r , James I . and S ylvan F ic h .. Theory o f Networks and L in e s ,
Englewood C l i f f s , New J e rs e y : P r e n t ic e - H a l l , 1963.
436 pp.
T e b b it , J . E. and A. D. W ile s , eds.
The Radio Communication
Handbook.
4 th ed .
Radio S o c ie ty o f G re a t B r i t a i n , J u ly
1969.
Westman, H. P . , ed .
R eference Data f o r Radio E n g in e e rs .
New Y ork: Howard W. Sams, 1968.
5 th ed.
1
APPENDICES
69
Appendix I
T h is s e c tio n p re s e n ts h e a t s in k c a lc u la t io n s made d u rin g the
a m p l i f i e r desig n s ta g e .
Using th e power model from A lle y and Atwood ( 1 9 7 3 ) , th e heat
s in k s iz e was d e te rm in e d .
T h is model is shown in F ig u re 2 0.
C ollector junction te m p e ra tu re
C ase te m p era tu re
Tj
Tc
H ea t sink te m p era tu re T
A m bient te m p era tu re T
1
0
Absolute zero
F ig u re 20
H eat S in k Power Model
By rearran g em en t o f th e e q u a tio n s g iv e n by A lle y and Atwood, the
h e a t s in k therm al r e s is ta n c e was g iv en by:
0sa
w here:
0
=
TmaX Pd ^
'
6Jc "
0 CS
( ° C /w a tt)
123)
=
Thermal r e s is ta n c e o f th e h e at s in k ( ° C /w a t t )
=
Thermal re s is ta n c e o f th e t r a n s is t o r - ju n c t i o n to
case ( ° C /w a t t )
Sd
6.
JC
9
=
T
v =
IuaX
Tamb
Thermal r e s is ta n c e between th e t r a n s i s t o r case and
h e a t s in k ( ° C /w a t t )
Maximum te m p e ra tu re o f th e t r a n s is t o r ju n c tio n
( 0C)
E nvironm ental am bient te m p e ra tu re ( 0C)
The maximum a llo w e d t r a n s i s t o r power d is s ip a tio n
(w a tts )
F ig u re 10 in th e t e x t shows th e maximum ju n c tio n te m p e ra tu re
(T max) as 2 0 0 °C .
Am bient te m p e ra tu re was chosen as room te m p e ra tu re
o r 25°C .
F ig u re 10 r a te s th e power o u tp u t o f th e t r a n s is t o r a t 70 w a tts .
Though a c la s s C a m p li f ie r should o p e ra te in th e range o f 75 p e rc e n t
e f f i c i e n c y , f o r c o n s e rv a tiv e reasons th e e f f i c i e n c y was assumed to
be 50 p e rc e n t.
As such, 70 w a tts would be d is s ip a te d
(P d) by the
t r a n s i s t o r a t 70 w a tts o u tp u t from th e a m p li f ie r .
The ju n c tio n to case therm al r e s is ta n c e ( e . ) was g iv en as
Jc
.8 ° C /w a t t in F ig u re 10.
The therm al r e s is ta n c e between th e h e at
s in k and t r a n s i s t o r case (Qc s ) was t h a t o f th e s i l i c o n h e a t s in k
compound used between them.
I t was e s tim a te d a t . l ° C / w a t t .
By s u b s t it u t in g th e above d a ta i n t o e q u a tio n ( 2 3 ) , thfe h e at
s in k th erm al r e s is ta n c e was c a lc u la t e d :
71
=
— Q-0-p~d - 5-°-C-
=
1 .6 ° C /w a tt
.8 ° C /w a t t
-
.l° C /w a tt
The o n ly h e a t s in k d a ta a v a ila b le a t th e tim e was t h a t shown in
F ig u re 21 ( A lle y and Atwood 1 9 7 3 ).
The l i n e shown is f o r 3 .2 mm
( .1 2 5 in c h ) t h ic k b r ig h t aluminum.
I f t h i s were u sed , . 4 5 , square
m eter (700 square in c h e s ) o f aluminum would have to be used.
72
I
M
l
Z iMm
li
i ;I i
ilLH
THERMAL RESISTANCE
F ig u re 21
Heat S in k Thermal R e s is ta n c e and Area Graph
73
Appendix I I
T h is s e c tio n c o n ta in s a summary o f MSL design e q u a tio n s and a
graph o f e x p e rim e n ta l d a ta measured using G -IO e p o x y -g la s s p r in te d
c i r c u i t board having a th ic k n e s s o f I mm.
The in d u c ta n c e p e r u n i t le n g th o f an MSL s e c tio n is g iven by:
L
w here:
L
=
Zq =
. V
=
=
■- y°- ■
(H e n rie s /m e te r)
In d u c ta n ce p e r u n i t le n g th
(H e n rie s /m e te r)
MSL s e c tio n c h a r a c t e r is t i c
impedance (Ohms)
MSL s e c tio n phase v e l o c i t y
(m e te rs /s e c o n d )
The c a p a c ita n c e p e r u n i t le n g th o f an MSL s e c tio n is given by
C
w h e re :
C
=
=
-g -y -o
(F a ra d s /m e te r)
C a p a cita n c e p e r u n it le n g th
(F a ra d s /m e te r)
Zq =
MSL s e c tio n c h a r a c t e r is t i c
impedance (Ohms)
V
MSL s e c tio n phase v e l o c i t y
(m e te rs /s e c o n d )
=
To f i n d th e MSL s e c tio n le n g th f o r a given component v a lu e ,
s im p ly d iv id e th e c a p a c ito r v alu e s by C and th e in d u c to r v alu e s
by L .
The r e s u lt in g u n its w i l l
be le n g th in both c ases.
I / Widtk
(■■" )
F ig u re 22
E xp erim en tal Phase V e lo c it y and C h a r a c t e r is t ic Impedance Data
P lo tte d f o r th e R e c ip ro c a l o f V ario u s MSL S e c tio n Widths
Using th e G-IO E poxy-glass P rin te d C i r c u it Board
o f I mm Thickness
X
t asr*reU X JV C n t^ .
3 1762
cop. 2
'O O ls ffJ
Barrett, Louis L
A microstripline
design of a 50 irHz
power amplifier