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### Design Notes

**ARBS AND PRBS HARMONIC BALANCE SOURCE **

This example shows how to use the Harmonic Balance engine to view eye diagrams and waveform metrics (rise time, jitter, etc.) using both the pseudo random bit sequence source (PRBS) and the user defined bit sequence source (ARBS). The effects of a non-ideal transmission line on eye shape are explored.

__Overview__

Eye diagrams and the associated time domain waveforms are shown for two different sources, a pseudo random bit source and an arbitrary (user defined) bit source. These sources allow for fast, frequency domain analysis of time varying signals by automatically configuring the source to supply the spectral representation of the desired waveform. To run the circuit simulation, click on the **Analyze** button on the tool bar.

Note that the PRBS eye is “closed” while the ARBS eye is “open.” This was intentionally set up to demonstrate that the two sources are different. The PRBS source always generates random data based on its parameter settings (i.e. number of symbols). The ARBS source takes in a user-defined bit sequence (can be defined as an array on the schematic or file-based). The initial setting of this array is a series of “1’s” followed by a series of “0’s,” so it’s more of a “step function” than random data. Therefore, there is only one “transition” seen in the eye. A more random data array is also defined on the "Global Definitions" page and can be activated to see the effects of random user defined waveform.

By varying the line length, the effects of dispersion can be seen. Make the line very long and the shape of the pulse gets distorted because higher frequency components are propagating slower than the lower frequency components.

By varying the line width, the effects of impedance mismatch can be seen. As the impedance changes from 50 ohms (W ~ 0.49 mm for 50 Ohms), reflections will start to become apparent. This is effect is more pronounced with longer lines than shorter lines.

By varying the filter cut-off frequency you can see the effects of filtering the input signal harmonics. The eye will become more square as the cut-off frequency is taken higher in frequency.

The line length, width, and filter order are already set up for tuning. Click on the **Tune** button on the toolbar to tune these variables.

__Displaying Masks in Eye Diagrams__** **

The equations in the **Output Equations** window create the mask in the "PRBS Eye Diagram" graph (black trace). Eye mask specifications vary widely. Please modify the equations as necessary for your specification. In this case, the mask is proportional to the final eye diagram amplitude (see picture, below). The Eye_Corners measurement is used to get the mean 0 and 1 voltage levels and crossing times (red trace in the "PRBS Eye Diagram" graph). The equations can be much more compact, but are written explicitly to make description of each variable easier, below:

ctr(x) = function definition; calculates the mid point between the maximum and minimum values of arbitrary vector, x

ECy = output equation assigning the Eye_Corners measurement to this variable

ECx = x values of ECy

T = Bit width in seconds (time scale factor of mask: it is simpler to scale the mask than the eye diagram)

t0 = time at center of eye (to shift mask in x direction)

Ampl = difference between 0 and 1 levels in ECy (y scale factor of mask)

y0 = y value at center of eye (to shift mask in y direction)

X1, X2, Y: mask specification parameters, please see the picture below.

x1,x2,x3,x4: x values of mask vertices

yl and yh: minimum and maximum mask values

mask_x and mask_y: vectors of x and y values for the vertices, scaled and shifted to center them at t0,y0.

mask: plots mask_y vs. mask_x, and specifies the x variables to be in time units.

(Select **Help > Contents and Index**, click **Index **tab, type "eqn" (no quotes), double-click "built-in functions" under "Equations" for details.)

__ARBS Circuit Eye Circuit Schematic__

This schematic uses arbitrary bit sequence harmonic balance source "PORT_ARBS", which can is found in the “Elem” tab under Ports/Signals. The waveform used by the source is an array called “DataSeq” which is defined in “Project” tab under “Global Definitions.”

__PRBS Circuit Eye Circuit Schematic__

Same as ARBS schematic, but uses a pseudo-random generator instead of an arbitrary wave generator. The “PORT_PRBS” element is found in the “Elem” tab under Ports/Signals.

__SAMP Setting Effects__

Since Harmonic Balance is used to create a waveform type of signal, FFTs are used to create the waveforms. The time resolution of the waveforms will be controlled by the **SAMP** setting on both the "PORT_ARBS" and "PORT_PRBS". Try setting this number to 2 to see its effect on the eye diagrams. Note that this number must be a power of 2.

__Filter Circuit Schematic__

This is the circuit that contains the dispersive microstrip line model used to look at the effects of metallization on digital signals. Note that the length and width of the line are both blue on the schematic, indicating that they are enabled for tuning.

__Voltage vs Time Graphs__

There are 2 graphs showing the voltage vs. time waveforms that generate the resulting eye diagrams shown on the schematics. These are called “ARBS Circuit Waveform”, and “PRBS Circuit Waveform."

__Spectrum Graphs__

There are 2 graphs showing power vs. frequency spectral displays for both the ARBS and PRBS source. These are called “ARBS Spectrum” and “PRBS Spectrum.”

__Eye Diagram Graphs__

There are 2 graphs showing the eye diagrams for both the ARBS and PRBS schematics. These are called "ARBS Eye Diagram" and "PRBS Eye Diagram". Note that the "PRBS Eye Diagram" graph also has some additional measurements on it. These measurements show the voltage levels, crossing points, rising edge, and falling edge that are used for the eye diagram metrics described below.

__Eye Metric Tables__

There are 6 tables (under Graphs) showing the different eye diagram metrics that can be calculated in AWRDE. These consist of Amplitude, Height, Width, Level, Rise Time, Fall Time, Overshoot, Undershoot, Extinction Ratio, Inverse Extinction Ratio, Q, and Jitter. Note that the input data used to calculate all of these metrics (voltage levels, crossing points, rising edge, and falling edge) are graphically displayed on the "PRBS Eye Diagram" graph. All of these measurements are available in the Nonlinear>Waveform category