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# Electrical Engineering (Essay Sample)

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Electrical engineering research paper.

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Electrical Engineering

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Lumped Matching Networks

Consider a transmission line below that is terminated by a load ZL.

For the load to match the transmission line, the condition á´¦Type equation here.Ó¶L =0. Nonetheless a circuit with

ZL â‰ Z0 must be connected between loads ZL and Z0 to make the VSWR =1 or as least as possible.

If Ó¶L=0 , then it means that Zin = Z0. This can explained as Rin= RÄ™[Z0] and Xin=0, in a lossless TL.

Matching networks in L networks comprises of

where RL ËƒZ0:

Where RLË‚ Z0: Note that ZL = RL + jXL:

There exist about eight combinations of capacitors and inductors in an L network:

-14287552006500RL ËƒZ0:

RLË‚ Z0:

The above matching networks are lossless or the loss could be made negligible by using appropriate components (Rizzi 1988).

Consider the lumped network below when RL ËƒZ0:

Its analytic solution is given by equating

The real part of the equation is given by RÄ™LH= RÄ™RH

Z0(1-BXL)=(RL-XBRL)â†’B(XRL-XLZ0) = RL-Z0

The imaginary part of the equation is given by JmLH =JmRH

BRLZ0= XL + X(1-BXL)â†’X(1-BXL)=BZ0RL-XL

Consider network below when RL Ë‚ Z0:

The real part of the equation is given by RÄ™LH= RÄ™RH :

BZ0(X+XL) = Z0 - RL

The imaginary part is given by JmLH =JmRH:

(X + XL)= BZ0RL

In lumped matching networks, when the load admittance or impedance has a reactive part that is dominant, it can is included in the component element needed by the L network so as to obtain a maximum bandwidth. This technique of absorbing the load reactance into a matching network is a major step toward achieving broad-band matching. This technique can be used to match antennas of resistance less than that of transmission line, and whose reactance are set reducing the length of a radiating element from resonant length. The antennas resistance remains unchanged while its reactance is capacitive with its magnitude determined by the resonanceâ€™s offset. By selecting a resonant frequency above the circuitâ€™s operation frequency and ensuring the antenna admittance conductance equals Y0, addition of shunt inductor cancels out the reactive part of the admittance of the antenna. This, in turn, results to transmission line match (David 1998).

Multiple Reactance Matching

This involves matching networks that use more than two reactive components to match load impedance to the required complex output impedance. Basically, the network input involves generator impedances and complex load such as ZG= RG+jXG and ZL=RL+jXL. The reactance X1, X2â€¦..Xn are the outputs of the designed network. Usually, the matching networks change the load impedance ZL to a complex conjugate value of the generator (David 1998).

Zin=ZG : This implies a conjugate match.

Distributed Matching Networks

Distributed matching network are usually formed by open-circuit transmission line, quarter-wavelength transmission line, short circuit transmission line among other combinations.

For proper understanding, a calculation on the distributed networks is vital. Consider a case where a load of 10-j100â„¦ is matched with a transmission line of 50 â„¦. For us to design two distributed matching networks and possibly compare their bandwidth performance, the solution will be computed as shown below:

Solution

Normalized load impedance is given by: zL= ZL/50=0.2-j2

This corresponds to a point A as depicted in the impedance matching Smith Chart below:

The reflection coefficient is given by:

Ó¶=ZL-50/ ZL+50...

Name

Affiliate institution

Course

Date

Lumped Matching Networks

Consider a transmission line below that is terminated by a load ZL.

For the load to match the transmission line, the condition á´¦Type equation here.Ó¶L =0. Nonetheless a circuit with

ZL â‰ Z0 must be connected between loads ZL and Z0 to make the VSWR =1 or as least as possible.

If Ó¶L=0 , then it means that Zin = Z0. This can explained as Rin= RÄ™[Z0] and Xin=0, in a lossless TL.

Matching networks in L networks comprises of

where RL ËƒZ0:

Where RLË‚ Z0: Note that ZL = RL + jXL:

There exist about eight combinations of capacitors and inductors in an L network:

-14287552006500RL ËƒZ0:

RLË‚ Z0:

The above matching networks are lossless or the loss could be made negligible by using appropriate components (Rizzi 1988).

Consider the lumped network below when RL ËƒZ0:

Its analytic solution is given by equating

The real part of the equation is given by RÄ™LH= RÄ™RH

Z0(1-BXL)=(RL-XBRL)â†’B(XRL-XLZ0) = RL-Z0

The imaginary part of the equation is given by JmLH =JmRH

BRLZ0= XL + X(1-BXL)â†’X(1-BXL)=BZ0RL-XL

Consider network below when RL Ë‚ Z0:

The real part of the equation is given by RÄ™LH= RÄ™RH :

BZ0(X+XL) = Z0 - RL

The imaginary part is given by JmLH =JmRH:

(X + XL)= BZ0RL

In lumped matching networks, when the load admittance or impedance has a reactive part that is dominant, it can is included in the component element needed by the L network so as to obtain a maximum bandwidth. This technique of absorbing the load reactance into a matching network is a major step toward achieving broad-band matching. This technique can be used to match antennas of resistance less than that of transmission line, and whose reactance are set reducing the length of a radiating element from resonant length. The antennas resistance remains unchanged while its reactance is capacitive with its magnitude determined by the resonanceâ€™s offset. By selecting a resonant frequency above the circuitâ€™s operation frequency and ensuring the antenna admittance conductance equals Y0, addition of shunt inductor cancels out the reactive part of the admittance of the antenna. This, in turn, results to transmission line match (David 1998).

Multiple Reactance Matching

This involves matching networks that use more than two reactive components to match load impedance to the required complex output impedance. Basically, the network input involves generator impedances and complex load such as ZG= RG+jXG and ZL=RL+jXL. The reactance X1, X2â€¦..Xn are the outputs of the designed network. Usually, the matching networks change the load impedance ZL to a complex conjugate value of the generator (David 1998).

Zin=ZG : This implies a conjugate match.

Distributed Matching Networks

Distributed matching network are usually formed by open-circuit transmission line, quarter-wavelength transmission line, short circuit transmission line among other combinations.

For proper understanding, a calculation on the distributed networks is vital. Consider a case where a load of 10-j100â„¦ is matched with a transmission line of 50 â„¦. For us to design two distributed matching networks and possibly compare their bandwidth performance, the solution will be computed as shown below:

Solution

Normalized load impedance is given by: zL= ZL/50=0.2-j2

This corresponds to a point A as depicted in the impedance matching Smith Chart below:

The reflection coefficient is given by:

Ó¶=ZL-50/ ZL+50...

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