Distortion in the Eye Diagrams of Synchronous Non-synchronous and 90o Bend Discontinuities

A group of well-defined equations [1] are implemented on a simulation algorithm by using a 2-DFDTD method. The method allows find behaviors in the eye diagrams not encountered by simple physical measuring [2] [3].


Introduction
The microwave circuit theory was sufficient to completely analyze structures such as microstrip with coupled load, microstrip with uncoupled load [4] [5] [6]. However, this is not the case for synchronous impedance transformers ( Figure  1), non-synchronous impedance transformers ( Figure 2) and the discontinuity at a right angle bend ( Figure 3). This discontinuity is found in many practical applications and to analyze this type of circuit is necessary to use a combination of circuit theory of low frequency and a general network analysis.

Model for a Synchronous Impedance Transformer
In this section the structure of the synchronous impedance transformer with a load of 50 ohms is analyzed. This structure consists of three transformers of a quarter wavelength. The transformers were designed for each section had characteristic impedances of 50 ohms, 34.5 ohms and 25 ohms respectively. These characteristic impedances are obtained with a dielectric thickness of 0.07874 cm and a relative permittivity of 2.25 corresponding to polyethylene. In addition, microstrip widths for section one are 2.413mm, for section two are 4.064mm and for section three are 6.096mm. The center frequency of 1.45GHz operation is taken from [1].
To calculate the length of each transformer quarter wave must meet the following condition: Therefore, by applying the equation (1), the length of each transformer quarter wave is calculated with the following equation.
As shown in Figure 1, the transformer structure is sectioned into different reference planes in which there are different input impedances. Therefore it will be necessary to make these calculations with the following equation impedance.
For Z 1 and Z 2 , the equation ( Now, having the results of the input impedance for each section of the transformer, the calculus of the reflection coefficient and hence of the output signal and the eye diagrams are possible as show in the section of Results.

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Distortion in the Eye Diagrams of Synchronous Non-synchronous and 90º Bend Discontinuities

Model for Non-synchronous Impedance Transformer
In this section, the non-synchronous transformer the same as the synchronous transformer are simulated by using a 50 ohm load. This structure consists also of the three transformers of a quarter wavelength, but different of the synchronous transformer, on this the central part is composed of the microstrip with the major thickness. However, the array keeps the same widths. The algorithm to simulate the non-synchronous transformer is similar to the synchronous one, but the positions of the quarter wavelength are interchanged.

Model for a Right Angle Bend
The right angle bend is considered a two-port network as a microstrip structure. In such structure, each segment has a corresponding equivalent circuit. All together the circuital representation of the discontinuity at a right angle bend microstrip is shown in Figure 4.
Where R1, L1, G1 and C1 correspond to the first segment of microstrip. LB1, LB2 and CB are the electric model of the right angle bend and finally C2, G2, L2 and R2 are the second segment of the microstrip.
Since inductors LB1 and LB2 are equal, from now on they shall be designated only as LB in order to calculate their values with the following equations [1]: Thus, from the Figure 4, seeing the circuit from left to right the impedances can be calculated at the different points of reference with the following equations: Now, seeing the structure as a cascaded connected array of two-port networks ( Figure 5), the reflection coefficients of each section can be calculated. The right angle bend impedance can be calculated by means of the circuit model shown in the next figure: Figure 6. Circuit model of the right angle bend impedance Then, the equation to calculate these values are as follows: The last equations are implemented in a simulation algorithm which is presented in the next section.

Results
The results of the simulation code for the synchronous impedance transformer are as follows:  The results of the simulation code for the bend discontinuities are as follows:

Conclusions
A group of well-defined equations has been implemented on a simulation algorithm by using a 2-DFDTD method. The method allows find behaviors in the eye diagrams not encountered by simple physical measuring.