Institutt for Informatikk Ch. 8. Matching Networks • Matching networks are critical for at least two reasons: – Maximize power transfer – Minimize SWR • Primary goal of a matching network is to get no reflection INF5481: RF kretser, teori og design Svein-Erik Hamran
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Ch. 8. Matching Networks - Universitetet i Oslo · Institutt for Informatikk Matching network using Smith Chart INF5481: RF kretser, teori og design Svein-Erik Hamran 1. Find normalized
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Institutt for Informatikk
Ch. 8. Matching Networks
• Matching networks are critical for at least two reasons: – Maximize power transfer – Minimize SWR
• Primary goal of a matching network is to get no reflection
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Two Component Matching Network
Also called L-sections.
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Impedance effect of series and shunt
• The addition of a reactance connected in series with a complex impedance results in motion along a constant-resistance circle in the combined Smith Chart.
• A shunt connection produces motion along a constant conductance circle.
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Transmitter to antenna matching
• • • (maximum power transfer)
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
L-type Matching Network
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Matching network using Smith Chart
INF5481: RF kretser, teori og design Svein-Erik Hamran
1. Find normalized source and load impedances
2. Plot circles of constant resistance and conductance that pass through
3. Plot circles of constant resistance and conductance that pass through
4. Identify intersection points. 5. Find values of normalized reactances
and suceptances of inductors and capacitors by tracing a path along the circles.
6. Determine the actual values of inductors and capacitors fror a given frequency.
Institutt for Informatikk
Matching networks for four different paths in the Smith Chart
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Forbidden Regions Zs = 50 ohm
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Two Designs of an L-type Matching
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Input Reflection Coefficient and Transfer Function
INF5481: RF kretser, teori og design Svein-Erik Hamran
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Equivalent Bandpass Filter
• Matching networks can be viewed as resonance circuits with as resonance frequency
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Nodal Quality Factor
INF5481: RF kretser, teori og design Svein-Erik Hamran
At each node of the matching network, the impedance can be expressed in terms of an equivalent series impedance or admittance At each node we can find For any L-type network
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Constant Qn contours
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
T-type Matching Network
• The loaded nodal quality factor of the matching network can be estimated from the maximum nodal
• Addition of a third element into the matching network introduces an additional freedom that allows us to control the value of by chosing an approriate intermediate impedance
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
T-type Matching Network for Qn = 3
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
-type Matching Network for Qn as low as possible • The minimum Q is
determined by the input impedance
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Mixed Design TL and Discrete • At increasing frequency and reduced wavelength the parasitics in the
discrete elements become noticable. • Need to take parasitics into account. • Discrete components only available in certain values. • A solution is a mix with transmission lines and capacitors. • Possible to tune the design below by changing capacitor value and
positions.
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Matching network with lumped and distributed components
INF5481: RF kretser, teori og design Svein-Erik Hamran
• Draw a SWR circle through • Draw a SWR circle through • Transition between the two circles can
be made arbitrarly. Chose A and B. • Read off the two transmission line
lengths needed.
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Tuning Capability
• Total transmission line length is kept fixed.
• Real and imaginary parts of the input impedance as functions of the distance l between the load and the capacitor location.
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Two Topologies Single Stub Networks • Series transmission line connected to parallel combination
of load and stub (a). • Shunt stub connected to the series combination of the load
and transmission line (b). • Four adjustable parameters
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Single-stub macthing network
• Select the length of the stub such that it produces a susceptance sufficient to move the load admittance to the SWR circle that passes through the normalized input impedance.
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Balanced Stub Design • The combined susceptance of the parallel
connection of stubs has to be equal to the susceptance of the unbalanced stub.
• Susceptance of the balanced must equal half of the susceptance of the unbalanced stub.
• Length does not scale linearly: – Open stub
– Short stub
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Double Stub Matching Network
• Single-stub matching networks require a variable length transmission line between stub and input/load.
• Double-stub network overcome this drawback.
INF5481: RF kretser, teori og design Svein-Erik Hamran
Institutt for Informatikk
Smith Chart of Double-Stub Matching
INF5481: RF kretser, teori og design Svein-Erik Hamran
rotates the g=1 circle radians or 270 degrees
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Double-Stub Design
INF5481: RF kretser, teori og design Svein-Erik Hamran