Module 2 : Transmission Lines
Lecture 16 : Impedance Matching using Transmission Line continues
Objectives
In this course you will learn about the following
Principle of double stub matching techniques and its step by step procedure.
Limitation of double stub matching technique.
Use of triple stubs to overcome limitations of the double stub matching technique.
Module 2 : Transmission Lines
Lecture 16 : Impedance Matching using Transmission Line continues
Double-Stub Matching Technique
To overcome the drawbacks of the single-stub matching technique, the double-stub matching technique is employed.
The technique uses two stubs with fixed locations. As the load changes only the lengths of the stubs are adjusted to
achieve matching.
Let us assume that a normalized admittance
is to be matched using the double stub matching technique. The first
stub is located at a convenient distance from the load say
the first stub.
(Figure). The second stub is located at a distance of
from
Module 2 : Transmission Lines
Lecture 16 : Impedance Matching using Transmission Line continues
Double-Stub Matching Technique (contd.)
We can note the steps involved in the double stub matching as follows:
(a)
Mark the admittance
(b)
Move on constant VSWR circle passing through A by a distance
(c)
Move along the constant-conductance (constant-
on the Smith chart (Point A).
to reach
) circle to reach
.
( a point on the rotated
circle). Note that a
stub at B will change only the reactive part and therefore we move on a circle which keeps the real part of
while going from
(d)
to
.
Transform admittance
. The point
at
to
by moving a distance of
must be lying to the
(e)
Add a stub to give susceptance
(f)
To calculate the length of the first stub
on a constant VSWR circle passing through
circle. Let the transformed admittance at point
at location C so as to move the point
between the susceptances at
susceptance
same
and
to
be
.
which is the matched point.
we note that this stub must provide a susceptance which is the difference
. That is, the stub susceptance
on the chart to get point
. Distance from
to
is equal to
. Mark the
in the anticlockwise direction gives the length
of the first stub.
(g)
The second stub should have a susceptance of
that used in the single stub matching. That is, mark
anti-clockwise direction to give
. To get the length
of the second stub the procedure is same as
on the Smith chart to get point
. Measure distance
in
.
Limitation
The whole matching process relies on the fact that by moving along a constant conductance circle one can go from point
to
. (
unrealizable.
lies on the rotated
circle). If this step is not realizable then the whole matching process is
If point
lies in the hatched region, moving along constant-g circle can never bring a point on rotated g=1 circle. Hence
that admittance cannot be matched by the Double Stub method.
Module 2 : Transmission Lines
Lecture 16 : Impedance Matching using Transmission Line continues
Triple-Stub Matching
Inorder to overcome the drawback of double-stub mathching technique one can use three stubs seperated by
distance, instead of the two stubs (see Figure). One still uses only two adjacent stubs (B, C or C, D) at a time for matching
purpose. For those loads which have
outside the forbidden region we use stub B and C as used earlier and stub D
is disconnected. The disconnection is not physical and is achieved by simply adjusting the length of the stub to
. The
-stub appears open at the junction point D.
If the admittance at B happens to lie in the forbidden region, disconnect stub B by adjusting its length to
, and use stubs
by
and the admittance
C and D for double-stub matching. Disconnection of stub B effectively increases
now corresponds to location C. So if the admittance at B is in the forbidden region, the admittance at C would definitely be
out of it.
A three-stub matching technique therefore is the final destination in the impedance matching, as it can match all
impedance/admittance without changing the stub locations.
Module 2 : Transmission Lines
Lecture 16 : Impedance Matching using Transmission Line continues
Recap
In this course you have learnt the following
Principle of double stub matching techniques and its step by step procedure.
Limitation of double stub matching technique.
Use of triple stubs to overcome limitations of the double stub matching technique.