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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

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Two Component Matching Network

Also called L-sections.

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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.

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Transmitter to antenna matching

• • • (maximum power transfer)

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L-type Matching Network

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Matching network using Smith Chart

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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.

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Matching networks for four different paths in the Smith Chart

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Forbidden Regions Zs = 50 ohm

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Two Designs of an L-type Matching

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Input Reflection Coefficient and Transfer Function

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Equivalent Bandpass Filter

• Matching networks can be viewed as resonance circuits with as resonance frequency

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Nodal Quality Factor

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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

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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

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T-type Matching Network for Qn = 3

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-type Matching Network for Qn as low as possible • The minimum Q is

determined by the input impedance

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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.

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Matching network with lumped and distributed components

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• 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.

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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

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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.

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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

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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.

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Smith Chart of Double-Stub Matching

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rotates the g=1 circle radians or 270 degrees

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Double-Stub Design

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