Impedance matching

By impedance matching , and power adjustment mentioned in the will Hochfrequenztechnik the source ( output resistance ) of a signal optimal to the load ( input resistance ) adjusted.

In contrast, in which audio equipment of the entertainment industry , the voltage matching the usual adjustment . This allows several consumers to be connected in parallel to one source. The energy technology works with applied voltage; the focus here is on maximum efficiency .

In high frequency technology, loads are often complex .

root cause

Often a load impedance is not adapted to a line, which in the case of alternating currents in radio and high-frequency technology leads to standing waves on the line, which means that the full power cannot be transferred from the generator to the load. No energy can be transported on a line with a completely stationary wave. This effect can with stubs or parallel - or series circuit of capacitance (s) or inductor (s) can be prevented. Such impedance converters adapt the source impedance or a line to the load impedance.

In order to determine the optimal adaptation structure as well as component sizes, the adaptation is simulated with the help of the Smith diagram ; see also resonance transformer and line transformation .

Adaptation structures

In practice there are matching structures that can be used to match any impedance to the wave impedance of the line: L, T, as well as pi or structure. The name is derived from the appearance of the component arrangement. There can be a coil or capacitor in each branch; the configurations listed below are only examples. The selection of the adaptation structure does not only depend on the necessary transformation path and thus the adaptation, but also on the peripheral environmental conditions. ${\ displaystyle \ pi}$

Adaptation structures
T-fitting structure
L fitting structure
Pi fitting structure

When setting up, particular attention must be paid to a supply voltage coupled to the HF line, i.e. a voltage source ( direct voltage ). B. a direct connection of a coil to ground is not possible. The DC voltage must therefore be blocked by a capacitor connected in series . The greater its capacity, the less it influences the impedance of the component supplied with the operating voltage.

L fitting structure

Among matching networks, one of the most popular design methods is the lossless L-network. This applies to real impedance adjustments.

If an impedance also has an imaginary component, such as a coil or capacitor, it must first be extended with complex conjugate in order to compensate for the imaginary component. If a capacitance has an imaginary reactance of −50 Ω, it has to be compensated in series with a coil with an impedance of +50 Ω .

Impedance matching scheme

For dimensioning, the parallel element is parallel to the larger resistance, with as a source resistance and as a load resistance ${\ displaystyle X _ {\ text {p}}}$ ${\ displaystyle R _ {\ text {q}}}$ ${\ displaystyle R _ {\ text {l}}}$

{\ displaystyle Z _ {\ text {left}} = R _ {\ text {left}} + \ mathrm {j} X _ {\ text {left}} = {\ frac {R _ {\ text {q}} X _ {\ text {p}} ^ {2} + \ mathrm {j} R _ {\ text {q}} ^ {2} X _ {\ text {p}}} {R _ {\ text {q}} ^ {2} + X _ {\ text {p}} ^ {2}}}}

this results in two equations:

{\ displaystyle R _ {\ text {left}} = R _ {\ text {l}} = {\ frac {R _ {\ text {q}} X _ {\ text {p}} ^ {2}} {R _ {\ text {q}} ^ {2} + X _ {\ text {p}} ^ {2}}}}

{\ displaystyle X _ {\ text {left}} = - X _ {\ text {l}} = \ mathrm {j} {\ frac {R _ {\ text {q}} ^ {2} X _ {\ text {p} }} {R _ {\ text {q}} ^ {2} + X _ {\ text {p}} ^ {2}}}}

First is calculated from and . can be the reactance of a capacitor or a coil. The resulting reactance in now only has to be compensated with the conjugate complex element . ${\ displaystyle X _ {\ text {p}}}$ ${\ displaystyle R _ {\ text {l}}}$ ${\ displaystyle R _ {\ text {q}}}$ ${\ displaystyle X _ {\ text {p}}}$ ${\ displaystyle X _ {\ text {left}}}$ ${\ displaystyle X _ {\ text {s}}}$

Microstrip matching

For the higher frequency ranges from 1 GHz, cable lengths have ever greater influences. This can also be used to adjust impedances. There are open stub lines and short-circuited stub lines that adjust impedances.

A certain distance away from the smaller impedance " " is chosen so that the real part is adapted for the input impedance or admittance . ${\ displaystyle d}$ ${\ displaystyle Z}$ ${\ displaystyle Y}$

The length " " of the stub line is selected so that the reactive component of the input impedance or admittance is compensated and becomes zero. ${\ displaystyle l}$ ${\ displaystyle Z}$ ${\ displaystyle Y}$

literature

Thomas H. Lee, Planar Microwave Engineering , Cambridge, University Press, 2004, ISBN 978-0-521-83526-8 .