Smith Chart
Lumped Element Z-Matching
K5TRA
T.Apel
1
Origin of the Smith Chart
+j
REFLECTION COEFFICIENT:
ρ
ρ
|ρ |
-1
•
•
•
•
θ
+1
-j
IS RATIO OF REFLECTED TO FORWARD VOLTAGE AT LOAD
ρ
ρ IS COMPLEX NUMBER: (REAL, IMAGINARY) or (MAGNITUDE, ANGLE)
|ρ| =1.0 IS MAXIMUM POSSIBLE WITH PASSIVE LOAD (TOTAL REFLECTION)
|ρ| =1.0 CIRCLE IS OUTER BOUNDARY OF STANDARD SMITH CHART
K5TRA
T.Apel
2
(INDUCTIVE)
+ REACTIVE
Impedance View – Constant Resistance
RECTANGULAR CHART
SMITH CHART
CONSTANT
RESISTANCE
CIRCLE
0
50

0
K5TRA
(CAPACITIVE)
- REACTIVE
+ RESISTIVE
•
•
•
•
50
+ RESISTIVE

Z=R+jX
IMPEDANCE HAS A REAL PART AND AN IMAGINARY PART
IMPEDANCE REPRESENTS A SERIES CONNECTION
CONSTANT REAL LINES BECOME CIRCLES ON SMITH CHART
T.Apel
3
(INDUCTIVE)
+ REACTIVE
Impedance View – Constant Reactance
RECTANGULAR CHART
SMITH CHART
+j 50
+j 50
0
50

0
50

+ RESISTIVE
K5TRA
(CAPACITIVE)
- REACTIVE
-j 50
-j 50
•
•
•
•
CONSTANT REACTANCE LINES BECOME ARCS ON SMITH CHART
UPPER HALF IS INDUCTIVE
LOWER HALF IS CAPACITIVE
POSITIVE REAL IS INSIDE THE SMITH UNIT CIRCLE
T.Apel
4
(INDUCTIVE)
+ REACTIVE
Impedance View
RECTANGULAR CHART
SMITH CHART
+j 50
25
50
+j 25
+j 50
+j 25

0
0
25
50

+ RESISTIVE
-j 25
K5TRA
(CAPACITIVE)
- REACTIVE
-j 50
-j 25
-j 50
•
•
•
•
IMPEDANCE REPRESENTATION OF THE SMITH CHART
USUALLY IN RED
LOWER HALF IS CAPACITIVE
POSITIVE REAL IS INSIDE THE SMITH UNIT CIRCLE
T.Apel
5
Admittance View
-j 20 mS
•
•
•
Y = 1/Z = G + j B
ADMITANCE IS RECIPROCAL IMPEDANCE
ADMITANCE REPRESENTS A PARALLEL
CONNECTION

-j 10 mS
20 mS
10 mS
0 mS
+j 10 mS
+j 20 mS
•
•
•
K5TRA
ADMITANCE HAS A REAL PART (CONDUCTANCE) AND AN
IMAGINARY PART (SUSCEPTANCE)
CONSTANT CONDUCTANCE IS A CIRCLE ON SMITH CHART
CONSTANT SUSCEPTANCE IS AN ARC ON SMITH CHART
T.Apel
6
OVERLAY SMITH CHART
+j 50
-j 20 mS
•
BOTH IMPEDANCE AND
ADMITANCE VIEWS OF SAME POINT
•
SIMULTANEOUS VIEW OF SERIES
IMPEDANCE OR PARALLEL
ADMITTANCE
•
+j 25
0
25

THIS VIEW PROVIDES A
CONVENIENT WAY TO DESIGN
LUMPED ELEMENT MATCHING
NETWORKS
-j 10 mS

50
20 mS
-j 25
0 mS
+j 10 mS
+j 20 mS
-j 50
K5TRA
T.Apel
7
Lumped Element Z-Matching
•
A SIMPLE EXAMPLE IS TO MATCH
BETWEEN 25 Ω AND 50 Ω
•
FROM THE 25 Ω POINT WE FIRST USE
THE IMPEDANCE VIEW TO MOVE TO
EITHER POINT B OR C
•
B
THE (+) REACTIVE SHIFT FROM A TO B
REPRESENTS A SERIES INDUCTOR
25
A
50
20 mS
C
•
THE (-) REACTIVE SHIFT FROM A TO C
REPRESENTS A SERIES CAPACITOR
•
NOTE THAT BOTH B and C ARE ON THE
20 mS CIRCLE. THIS ALLOWS US TO
REACH 50 Ω WITH A SHUNT ELEMENT
K5TRA
T.Apel
 THROUGH B REQUIRES
SERIES INDUCTOR AND
SHUNT CAPACITOR
 THROUGH C REQUIRES
SERIES CAPACITOR AND
SHUNT INDUCTOR
8
Examples: LP
•
5 Ω to 50 Ω MATCH
•
N=2 :
•
LOWPASS ELEMENTS
SERIES L SHUNT C
5
50
Freq = 1296 MHz
K5TRA
T.Apel
9
Examples : HP
•
5 Ω to 50 Ω MATCH
•
N=2 :
•
HIGHPASS ELEMENTS
SERIES C SHUNT L
5
50
Freq = 1296 MHz
K5TRA
T.Apel
10
Examples : LPLP
•
5 Ω to 50 Ω MATCH
•
N=4 : SERIES L SHUNT C
SERIES L SHUNT C
•
LOWPASS ELEMENTS
5
50
Freq = 1296 MHz
K5TRA
T.Apel
11
Examples : HPHP
•
5 Ω to 50 Ω MATCH
•
N=4 : SERIES C SHUNT L
SERIES C SHUNT L
•
HIGHPASS ELEMENTS
5
50
Freq = 1296 MHz
K5TRA
T.Apel
12
Examples : LPHP
•
5 Ω to 50 Ω MATCH
•
N=4 : SERIES L SHUNT C
SERIES C SHUNT L
•
BANDPASS ELEMENTS
50
5
Freq = 1296 MHz
K5TRA
T.Apel
13
Examples : HPLP
•
5 Ω to 50 Ω MATCH
•
N=4 : SERIES C SHUNT L
SERIES L SHUNT C
•
BANDPASS ELEMENTS
5
50
Freq = 1296 MHz
K5TRA
T.Apel
14
Different Internal Z
5
50
5
Freq = 1296 MHz
K5TRA
50
Freq = 1296 MHz
T.Apel
15
LOSS CONSIDERATIONS
K5TRA
T.Apel
16
LOSS TRADE-OFFS
N=2
QU=20
N=6
QU=10
N=6
N=4
N=4
N=2
QU=5
N=4
N=6
QL=1
QL=2
QL=2.5
N=2
(1+QL2)
K5TRA
T.Apel
17
Software Tools: WINSMITH
K5TRA
T.Apel
18
Software Tools: SMITH
K5TRA
T.Apel
19