RC Filter Laboratory RC-1 ©San José State University Dept. of Mechanical and Aerospace Engineering rev. 3.2 10SEP2010 RC Filters and Basic Timer Functionality Learning Objectives: The student who successfully completes this lab will be able to: • Build circuits using passive components (resistors and capacitors) from a schematic diagram. • Explain the concept of a high or low-pass filter and what its corner frequency is • Construct a low-pass or high-pass RC filter with a given corner frequency. • Explain terms associated with counter/timers, such as clock, top, bottom, overflow, and clock prescaler. • Explain how the hardware timer integrated with an ATmega16 can be used to output a square wave with a given frequency. Components: Qty. Item1 Atmel ATmega16 microcontroller with STK500 interface boards 1 Programming cable and power supply 1 Solderless breadboard 1 1 kΩ resistor 1 0.1μF capacitor (may be polarized) 1 10μF capacitor (electrolytic, so it is polarized) 1 Piezo speaker (Murata PKM17EPP-2002-130 (Mouser 81-PKM17EPP-2002)) Introduction RC Filter Theory You will begin this laboratory using the function generator connected to a simple circuit consisting of a resistor and capacitor. Details of the construction are given in the Procedure below. First, consider the circuit shown in Figure 1. The impedance of a capacitor, ZC, is 1/(jωC), a complex quantity, where j is the square root of -1, ω is frequency in rad/sec (2π rad/sec = 1Hz), and C is capacitance in Farads. Equation 1 can be derived from the voltage divider relationship formed by the resistor and capacitor. Equation 2 solves equation 1 for the ratio of Vo to Vi (VO/Vi), which is called the ‘transfer function’ of the filter. Vi VoFG ‘scope 1 k 0.1μF RC Low-pass filter Figure 1. RC low-pass filter. The resistor and capacitor function together as a frequency-dependent voltage divider. The function generator will provide a time varying signal whose frequency can be varied, and the oscilloscope will enable you to measure the signal at the output of the circuit. Make sure that you use ‘scope probes with the ‘scope. Ask your lab instructor if you are unsure about which probes are ‘scope probes.RC Filter Laboratory RC-2 ©San José State University Dept. of Mechanical and Aerospace Engineering rev. 3.2 10SEP2010 1( )1( )jCVo ViRjCωω=+ (1) 11VoVi j RCω=+ (2) The transfer function is a measure of how much of the input voltage is ‘transferred’ to the output. What happens to the value of the transfer function as the frequency of the input voltage increases? Does it increase or decrease? For a given sinusoidal input voltage Vi, the magnitude of the output voltage Vo is given by the product of Vi and the magnitude of the transfer function (evaluated at the frequency of Vi). An important property of filters is the corner frequency, or cut-off frequency. This is the frequency at which the attenuation of the signal through the filter starts to increase sharply. For a passive RC filter, (high or low-pass) the corner frequency is 1/RC radians/sec. By substituting ω=1/RC into equation 2, you can see that the denominator goes to 1+1j, and consequently the magnitude of Vo/Vi becomes 0.707. We will verify equation 2 by the following experiment. Procedure: [Note: the lab stations are set up so that half of the lab team can work on the circuit on the left side of the bench, and the other half of the team can work on programming the microcontroller on the right side with the computer. Be aware that exams will include information on both aspects, so all team members should switch roles and be familiar with what the other team members are doing.] 1. Construct the single-stage RC Low-pass filter circuit shown in Figure 1 above. Pay attention to the connection of the leads of the capacitor. The curved line on schematic shows that the capacitor is polarized (which may or may not be the case depending on the type of capacitor you were given by your lab instructor). Not all capacitors are polarized, but electrolytic (‘lytic, for short) capacitors are. ‘Lytics look like little aluminum cans. If you look at the side of the can, you should see a minus sign. The lead closest to the minus sign corresponds to the lead with the curved line on the schematic. It will also be the shorter of the two leads on a polarized capacitor that has not had its leads trimmed. It is extremely important that the lead nearest the minus sign always be kept at a lower potential (toward ground) than the other lead of the capacitor. If you reverse the polarity, the capacitor can explode, so take extra precaution, and double-check how you have wired the capacitors before you apply power to your circuit. There are other capacitors, such as ceramic capacitors, which are not polarized, and the connection to the leads are interchangeable. Discern what kind of capacitor you have, and connect it accordingly!2. On the function generator, output a sine wave, and set the amplitude of Vi to 5 volts peak-to-peak (Vp-p) at 500 Hz (What termination should you set the function generator output to, 50 ohms or High Z?). Measure and record the amplitude of Vi and Vo using the ‘scope. Repeat these measurements with the frequency of Vi set to 1.6 kHz and then 10 kHz. Compare the ratio of the input voltage and the output voltage (i.e., Vo/Vi) with the magnitude of the transfer function (from equation 2) evaluated at the corresponding frequency. What can you conclude from this comparison about the relationship between the magnitude of the transfer function and the ratio of the input and output voltages? Explain. Why is this circuit called a “low-pass filter”? The phase lag of a circuit can be thought of as the amount of delay in the signal as it goes through the circuit. Phase lag is measured in degrees as shown in Figure 2. Recall that since theRC Filter Laboratory RC-3 ©San José State University Dept. of Mechanical and Aerospace Engineering rev. 3.2 10SEP2010 transfer function from equation 2 is a complex quantity, you can think of it as a vector in the complex plane. As you know, vectors have magnitude and direction. The phase lag of the circuit shown in Figure 2 is the angle of the transfer function vector, 1/(1+jωCR), evaluated at the frequency of the signal with respect to the real axis in the complex plane. We will verify this relation by the following experiment: 3. Set the ‘scope to dual-trace mode.