3RCFilter-Atmel - RC Filter Laboratory RC-1 RC Filters...

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RC Filter Laboratory RC-1 © San José State University Dept. of Mechanical and Aerospace Engineering rev. 3.1 September 10, 2007 RC Filters Purpose: To introduce resistors and capacitors To introduce the concept, construction, and utility of low-pass and high-pass RC filters To introduce the Atmega 128 microcontroller and its capability to output tones. Components: Qty. Item 1 Atmel ATmega 128 microcontroller with STK500 and STK501 interface boards 1 Programming cable and power supply 1 Solderless Breadboard 1 ea. 1 k Ω and 10 k Ω resistors 1 0.1 μ F capacitor 1 10 μ F capacitor 1 Piezo speaker (Murata PKM17EPP-2002-130 (Mouser 81-PKM17EPP-2002)) Introduction: 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 is 1/(j ω C), a complex quantity, where j is the square root of -1, ω is frequency in rad/sec (2 π rad/sec = 1Hz), and C is capacitance in Farads. Equation 1 is derived using the voltage divider relationship. Equation 2 solves equation 1 for the ratio of Vo to Vi, which is called the ‘transfer function’ of the filter. Vi Vo FG ‘scope 1 k 0.1 μ F RC Low-pass filter Figure 1. RC low-pass filter. The resistor and capacitor together function 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. 1 ( ) 1 ( ) j C Vo Vi R j C ω ω = + (1) 1 1 Vo Vi j RC ω = + (2) The transfer function tells 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). We will verify equation 2 by the following experiment.
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