# Design of Experiments

**Topics:**Factorial experiment, Main effect, Interaction

**Pages:**6 (1543 words)

**Published:**April 19, 2013

Design of Experiments (DOE) techniques enables designers to determine simultaneously the individual and interactive effects of many factors that could affect the output results in any design. DOE also provides a full insight of interaction between design elements; therefore, it helps turn any standard design into a robust one. Simply put, DOE helps to pin point the sensitive parts and sensitive areas in designs that cause problems in Yield. Designers are then able to fix these problems and produce robust and higher yield designs prior going into production. Here is a simple and practical example that walks you through the basic ideas behind DOE. This example is meant to illustrate the concept in a very easy way to understand DOE and enables you to go on and expand your knowledge on DOE further. DOE Example: Let us assume that we have designed an amplifier and we need to design an experiment to investigate the sensitivity of this amplifier to process variation. In other words, we would like to find out if there are any elements in the design that largely affect the output response due to their high sensitivities to the output measure. In ADS, the DOE tool comes with full supporting plots that enable designers to determine simultaneously the individual and interactive effects of many factors that could affect the output results in any design. Pareto plots, main effects and Interactions plots can be automatically displayed from the Data Display tool for study and investigation. However, in this example DOE is illustrated using a manual calculations approach in order to allow you to observe how the analysis and results are calculated, and what these results mean.

Let us start with our amplifier example: In this example, let us chose three elements where we want to see their effects on the Gain of the amplifier. These elements are: W (the width of the microstrip lines), a resistor (R), and a Capacitor (C). Since we chose three elements, we must construct 8 experiments (2^3) for a Full factorial experiment. We assign a -1 and +1 values to each of the elements. For example the nominal value of the Resistor is described with a “0”. A “-1” represents a -5% variation from its nominal value and a “+1” represents a +5% variation from its nominal value. Therefore if our resistor’s nominal value is 20 ohms, a “-1” represents a 19 ohms value, and a “+1” represents a 21 ohms value. Step 1

Start by choosing variables that affect the response

Choose three variables with their +1 and -1 :

Width of lines (W) Resistors (R) Capacitors (C) W=W_nominal ± .5 um R = R_nominal ± 5% C = C_nominal ± 5%

Example: For W -1 corresponds to 9.5 µm +1 corresponds to 10.5 µm 0 corresponds to nominal value, 10µm

Step 2 Next, we run the simulation eight times to get the gain (our output measure) for all the combination of +1’s and -1’s of the three elements and this is what we get:

Step 3 From the results above, let us extract the main effects of Capacitor, C on the Gain. We calculate the average Gain when C is “-1” and when C is “+1” and determine the total gain variation due to the Capacitor. The table below shows that this gain variation (due to C) is .044 dB.

Main Effect of Capacitors, C on Gain

Average gain for C=-1 13.7725 dB (yellow) Average gain for C=1 13.86 dB (blue) Slope= .044

Next we do the same thing for the Resistor. Notice that the gain variation due to the Resistor is .85 dB, which is much higher than that of the Capacitor. (See table below). This already tells us that the resistor is a trouble component and causes higher variation in the gain.

Main Effect of Resistors, R on Gain

Average gain for R=-1 12.97 dB (blue) Average gain for R=1 14.6625 dB (green) Slope = .85

The main effects can be plotted for easier view of the components’ sensitivities to Gain. Below is the main effects plot of the Capacitor and the resistor (calculated above) on the Gain variation....

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