Lab Assignment

Background

In electronics, a low pass filter is utilized to remove high-frequency noise from a signal. One example would be static present in a radio or cell phone transmission. A simplest low-pass filter is constructed from a resistor (R) and capacitor (C) in series. Refer to Figure 1 below.

Figure 1: Test System - Low Pass Filter with Meter

In this exercise, we will examine what happens when we "turn on" this circuit. Before we begin our analysis (initially), the switch which connects the voltage source (VDC) to the rest of the circuit is open. We will examine what happens at t = 0, when this switch closes and current begins to flow.

The equations below describe what happens to the voltage across the capacitor (vCap) and current flowing through the capacitor (iLoop) following t = 0, the moment the switch is closed.

i_Loop = (V_DC/ R) exp (-t/RC)           (1)

v_Cap = V_DC - i_Loop R

Note the definitions which are repeated below:

i_Loop = loop current flowing through capacitor
V_DC = the source voltage
R = resistance
C = capacitance
t = time
v_Cap = capacitor voltage

Problems

1. Using Excel, calculate the values of i_Loop and v_Cap every millisecond (ms) starting from t = 0 until t = 50ms. Use the following sets of values: R = 1 Ohms, C = 10 mF, V_DC = 1 V. Remember, 50 ms is equal to 0.050 s and 10 mF is equal to 0.010 F.

2. Plot i_Loop and v_Cap versus time. Remember, that i_Loop is in amps and v_Cap is in volts.

3. In order to measure the voltage across the capacitor, it is necessary to use a meter with a 3ms delay, which means that M(t) = v_Cap(t-3ms). Calculate and graph, along with i_Loop and v_Cap, this measurement (M). Remember, that M is also in volts like the value is measures.

4. Add a polynomial trendline to the measurement (M) points. Try polynomials of orders 2 through 6 and select the one that works best. Add the equation of the trendline.

5. Using the graph in your assignment and you ability to increase / decrease V_DC, R, and C, comment on the effect of these variables on the recovery of v_Cap.

Remember, you can change the variables and watch the graph change immediately.

a. How do V_DC, R, and C affect the final value of vCap?

b. How do V_DC, R, and C affect its rate of recovery (how quickly the voltage grows)?