RC Filter Laboratory RC-1 RC Filters Pre-lab Questions 1. What are some typical uses of RC filter circuits? 2. Given a low-pass filter with a 2 KΩ resistor and a 0.2 µF capacitor, find the corner frequency. 3. Design an RC filter that removes the high frequency noise from the signal seen below. -1.5-1-0.500.511.5Voltage, VTime, ms10 Purpose • To introduce resistors and capacitors • To introduce the concept, construction, and utility of low-pass and high-pass RC filters • To introduce the Basic Stamp microcontroller and its capability to output tones Components Qty. Item 1 OEM Basic Stamp II microcontroller 1 ea. 1 kΩ and 10 kΩ resistors 1 0.1µF capacitor 2 10µF capacitor 1 30 ohm resistor 1 8 ohm speaker Introduction Resistor-Capacitor Filter Circuit: The impedance of a capacitor 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. The following equation relating input voltage, Vi and output voltage, Vo for the circuit shown in Figure 1 is obtained by using the voltage division formula: San José State University Department of Mechanical and Aerospace Engineering Fall 02 12SEP00RC Filter Laboratory RC-2 Vo = 1/(jwC) R + 1/(jwC) Vi orVoVi = 11 + jwCR The frequency dependent term 1/(1+jωCR) is called the Transfer Function of the circuit. 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). We will verify this relation by the following experiment. Vi VoFGScope1K ohm0.1uFRC Low-pass filter Figure 1 RC low-pass filter Procedure 1. Construct the single-stage RC Low-pass filter circuit shown in Figure 1. 2. Set Vi to 5 volts p-p at 500Hz and record the amplitude of Vo. Repeat this measurement with the frequency of Vi set to 1.6 kHz and 10 kHz. Compare the ratio of the input voltage and the output voltage (i.e., Vo/Vi) with the magnitude of the Transfer Function 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. The phase lag of the circuit shown in Figure 2 is the angle of the transfer function, 1/(1+jωCR), evaluated at the frequency of the signal. We will verify this relation by the following experiment. 3. Set the scope to dual-trace mode. Display both Vi and Vo on the scope at the same time. (Ask the TA for help if needed). Measure the phase lag of this circuit as shown in Figure 2 at Vi=1.6 kHz. Does the theoretical value match the observed value? 360 degree~ 45degreeViVo Figure 2 Phase lag of Vo. San José State University Department of Mechanical and Aerospace Engineering Fall 02 12SEP00RC Filter Laboratory RC-3 4. Construct the single-stage RC High-pass filter circuit shown in Figure 3, and verify (using the voltage division formula) that Vo/Vi for this circuit is as follows: Vo = R R + 1/(jwC) Vi orVoVi = jwCR1 + jwCR 5. Repeat step (2) and (3) for this high-pass filter. Vi VoFGScope1K ohm0.1uFRC High-pass filter Figure 3 High-pass filter 6. Add a DC offset (any value) to the function generator output. Does this DC offset affect the output (Vo) of the filter? This is the reason that a capacitor can be thought of as a device that blocks a DC component, but allows the AC component to go through. This is called “AC coupling.” 7. Now we want to use the Basic Stamp microcontroller to output a tone and see the effect of filtering a Pulse Width Modulated signal. First let’s get familiar with the Basic Stamp hardware and its connections. Remove the OEM Basic Stamp from its anti-static bag, being careful to avoid touching the exposed pins. It is always a good idea to hold a card like this by its edges, and avoid touching the pins or circuit traces unless you are properly grounded for electrostatic discharge (ESD). See Figure 4. Carefully plug the OEM Basic Stamp into the lower right or left corner of the solderless breadboard with the solder pins facing away from the breadboard. Looking at the Stamp, from the left side (the left side has the DB9 serial cable connector), the third pin marked Vin is the pin to which power must be connected in order to run the Stamp. The Stamp has a voltage regulator onboard that will accept 5.8 V to about 15 V comfortably and regulates that to 5 V, which is what the Stamp IC needs to run. It will be best to supply 9-12V to the Vin pin. Thinking ahead toward self-contained projects you might build, it will be easy to power the Basic Stamp using a 9 V battery. So keep life easy for yourself here in the lab, and use 12 V from the fixed supply to power Vin. (As recommended in the previous lab, make sure the power supply is turned off when you are wiring or making any changes to the wiring. Make connections from the power supply to the screw terminal posts on the solderless breadboard using the banana-to-banana test leads. Then, from the screw terminals, run short lengths of hookup wire to the bus strips that run the length of the breadboard. Finally, use short lengths of hookup wire to connect the appropriate pins to power or ground. This not only saves hookup wire, but it makes your circuits more robust, and less sensitive to noise.) San José State University Department of Mechanical and Aerospace Engineering Fall 02 12SEP00RC Filter Laboratory RC-4 The common connection is marked Vss. It is the second pin from the left side. This is the common ground connection for the Stamp. Make this connection to the common ground of the power supply (through the bus on the solderless breadboard) Figure 4 OEM Basic Stamp II ViVSS8. Build the circuit shown below in Figure 5. Note that the 10 µF capacitors are POLARIZED. If you look at the side of the capacitor body, you will see one leg marked with a minus sign. IT IS EXTREMELY IMPORTANT THAT THE MINUS LEG ALWAYS BE KEPT AT LOWER POTENTIAL THAN THE OTHER LEG! If you reverse the polarity, the capacitor can explode, so take extra precaution and double-check how you wire the capacitors before you apply power to your circuit. Not all