A double stub tuner is an impedance matching
technique commonly employed in microwave
circuitry. It consists of two lengths of
transmission line (the stubs) connected to the
main transmission line at fixed distances from the
load impedance. The stubs are can be connected
either in parallel or series, but parallel is much
more common. The stubs may be shorted or open at
the ends, but open is more common (the only way to
go for microstrip).
The double stub tuner, like other common
impedance matching techniques such as the single
stub tuner and the quarter wavelength transformer,
has narrow bandwidth. A circuit is generally tuned
to a given frequency, and can be expected to work
well only near (10%  20%) that frequency.
The double stub tuner, like the single
stub tuner has two degrees of freedom. These are
the lengths of the two stubs. The distance of the
first stub from the load is fixed, as is the
distance of the second stub from the first. I'll
call the distance from the load to the first stub
d_{1}, and the distance from the first
stub to the second d_{2}. The lengths of
the lines will be denoted as l_{1} and
l_{2}.
 d2  d1
 load (Zl) 
 
 l2  l1
 

The lengths of the stubs may be found either by
calculation or by using a Smith chart. Since the
calculations involve complex numbers and can be
somewhat tedious, I'll describe the method for
using the Smith Chart.
The perform this procedure, you'll need to know
the load impedance you are trying to match, the
characteristic impedance of the transmission line,
the wavelength of the signal you are matching for,
and the distances of the stubs from the load.
 Normalize the load impedance by dividing it by
the characteristic impedance of the transmission
line. Plot this on the Smith chart.
 If your stub is in parallel with the transmission line, convert
the impedance to an admittance by rotating it a
quarter of a wavelength (half way) around the
Smith chart.
 Convert the distances d_{1} and
d_{2} to electrical distance by dividing
them by the wavelength.
 Rotate your load point an electrical length of
d_{1} toward generator. This gives you the
load at the point on the transmission line where
the first stub is connected. Call this point A.
 Starting at 0.25 λ, go toward the
load a distance of d_{2}. Draw a line
between the origin of the Smith chart and the
point on the outside edge you have just
found. Find the center of this line and draw a
circle around this point, so that the circle
touches the origin and the edge of the
chart. This is the unit resistance circle
transformed from the second stub toward the load
to the point where the first stub joins the
transmission line. This circle is referred to as
the L circle. We do this because we want to
have the load impedance/admittance on the unit
resistance circle when we are at the second stub,
so that we can add a pure reactance to match the
line.
 Move the load point along a line of constant
resistance until it lies on the L circle. There
will either be two possible points or none at
all. Not all loads can be matched with the double
stub technique. Assuming you find a point (call it
B) that intersects the L circle, read the
inductance / capacitance value off of the Smith
chart.
 We are now at the point where the transmission
line and the first stub from the load meet. At
this point, we want our impedance / admittance
point to be in our L circle. We know the value A,
and the value of B. B = A + C, so find the complex
part of C. This is the value you have to cancel
out with the first stub.
 If the first stub is open, start at the point
of infinite impedance (zero admittance) and rotate
toward generator until you reach 0  jA. If the
first stub is shorted, start at zero impedance
instead. The distance around the chart to get to
this point is the electrical length of the stub;
multiply by the wavelength to get
l_{1}.
 Now we want to examine the impedance /
admittance at the point where the second stub from
the load connects to the transmission line. To do
this, we have to move point B along a circle of
constant VSWR (a circle centered on the origin of
the Smith chart) until it is on the circle of unit
resistance. Call this point on the circle of unit
resistance D.
 Now read off the complex part of D. This is
the value we have to cancel out with the second
stub. Find the negative of the complex part of D
on the edge of the Smith chart. If the second stub
is open, start at zero admittance (infinite
impedance) and rotate toward the generator until
you come to the aforementioned point. The distance
traveled around the Smith chart, when multiplied
by the wavelength for which we are tuning, gives
l_{2}.
The double stub tuner is slightly more
complicated to design than the single stub
tuner, the quarter wavelength transformer, or
reactive matching. The main difference is that
when finding the length of the first stub, you
have to add the transformed load impedance or
admittance to the stub impedance or admittance
such that the result is located on the L
circle.