# Reverse Engineering - Task 2

### From Drexel University NanoEnlightment

## Contents |

## Introduction

This week at the beginning of lab, you will submit a computer-aided design (CAD) drawing of a shutter for your camera. Your design will be one that will enhance the performance of the camera by reducing the amount of time that the shutter is open, thus reducing blur. In Week 1 you were given a CAD file in ProEngineer format and asked to modify it to achieve the design goals using the modeling equation. This week you will submit to your Graduate Student Teaching Fellow your modified drawing for rapid prototype 3D printing. Your Fellow will then submit this in a batch for printing.

The as-produced part looks similar to the one depicted below. Yours will be modified in such a way that the time that the shutter is open is reduced.

If you did not collect at least nine traces from both channels last week or did not collect at least nine data points for characterizing the shutter spring, please complete this data collection this week.

This week, please also take some time to discuss ENGR 103 topics with your Faculty Laboratory Instructor and to discuss outcomes from previous modules.

## Flash Circuit Voltage Measurement

When you press the ‘charge’ button located on the front of the camera, the flash circuit (Fig. 1) begins to charge its internal capacitor to a high voltage (over 300 volts). When the flash it triggered, the charge stored in this capacitor is discharged through a flash lamp, producing a high intensity light. In last week’s lab, you measured the duration of the flash and found it to be approximately 3 ms. This is approximately the time it takes the capacitor to discharge. In your lab report, be sure to continue to use the appropriate number of significant digits. This may be determined by knowing the frequency at which the oscilloscope samples. If you have questions regarding how to determine the appropriate number of significant digits, please ask your Faculty Lab Instructor.

Today, you will observe the charging and discharging characteristics of the flash circuit’s capacitor. Using the oscilloscope, you will measure the charging time of the circuit’s capacitor.

Figure 1: Front and rear views of flash circuit.

## Experiment Setup

The circuit enclosure shown in Fig. 2 will be used in today’s measurements. The two switches are used to initiate a charge and trigger the flash lamp. The BNC connector, when connected to the scope, displays a portion (one tenth) of the voltage measured across the capacitor.

Figure 2: Circuit enclosure. (click on link for pdf).

## Charging Time Measurement

The flash capacitor charge/discharge cycle is represented in Fig. 3. Beginning in a completely discharged state (at zero volts), when the charge button is pressed, the capacitor begins to charge exponentially. Initially, the capacitor charges rapidly, but as it approaches its maximum voltage, begins to charge more slowly. This is analogous to the dynamics of students entering a classroom. Initially when there are many available seats the rate of seating is great. However, as the number of available seats diminishes, the rate at which students may sit down is reduced. Physically a similar phenomenon is occurring as electrons being "pushed" onto the capacitor plate "look" for available atoms with which to associate. Theoretically, the capacitor never approaches this maximum voltage in finite time, but approaches it asymptotically. In practice however, if we wait long enough, the voltage will get close enough to this upper value that our measurement devices cannot distinguish the changes in voltage. At this point we assume the capacitor is full.

**Figure 3.** The charging and discharging of a capacitor is described by an asymtotically rising exponential curve and an asymtotically decaying exponential curve. These curves may be characterized by a "time constant," which is represented by the Greek character tau. Tau is the amount of time it takes for the circuit to reach 63% of its maximum value and is determined by the product of the resistance and capacitance, *τ = RC* . Recalling the students entering the room analogy if there is a lot of resistance (small doors) and a lot of capacitance, (large auditorium) the amount of time to fill the lecture hall is long.

You will use the oscilloscope to measure *τ*. After properly configuring your oscilloscope (refer to the handout) press the RUN button and then press the flash circuit’s charge button. The scope will begin to capture a curve like the one shown above. The circuit reaches its maximum charge, press the STOP button on the scope. Now the curve is locked on the screen and you can measure the system time constant.

## Steps

- In determining how long it takes to charge the capacitor, first look at the equation that describes the capacitor voltage as a function of time,
*V*(_{c}*t*)=*V*(1-_{max}*e*^{(-t/τ)}). Here,*V*(_{c}*t*) is the voltage of the capacitor as a function of time,*V*is the maximum voltage attained, and_{max}*e*is the exponential function, the numerical value of which is approximately 2.71828. What does*V*equal when_{c}*t*= 0? What does*V*equal when_{c}*t*= ∞? - Measure
*V*using the_{max}*V*_{1}voltage marker. - Calculate 63% of
*V*and place the_{max}*V*_{1}voltage marker there. - Place the
*T*_{1}time marker at the point at which you pressed the charge button. - Place the
*T*_{2}time marker at the point where the*V*_{1}marker crosses the voltage curve. - From the display, read the delta-t value. This is the system’s time constant.

## Deliverables (i.e. getting graded):

The grade for your group will be based on the following criteria:

- Completing and reporting on all of the steps and questions asked above. Reminder: Take turns taking data. Each team member should take at least three data points. When finished, report on the average and standard deviation of the data. In your lab report, comment on your determination of how many significant digits to use.