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# PSPICE Stuff - EE43/EE100-Lab#5 EE43/EE100 LAB#7 RC Filters...

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Page 1 of 7 EE43/EE100 — LAB #7 RC Filters Guide I. Introduction In this lab you will determine the input-output characteristics of an RC filter, and then use PSpice to simulate the RC filter behavior. RC Filter Characteristics Figure 1 below shows an RC filter connected to a sinusoidal voltage source. This circuit is termed a two-port circuit (Fig. 2) where the voltage source produces the input voltage V in and the output voltage V out appears across resistor R. + - V out V in + - R C v in v out Figure 1 : An RC filter with a series capacitor and output resistor R. Figure 2 : A two-port circuit. Recall that we customarily represent an AC voltage as a periodic function of time, such as V ( t ) = V 0 cos( ω t ) where V 0 is the amplitude of the voltage, t is time, and ω is the angular frequency, whose units are radians per second. The angular frequency is related to frequency, f , measured in Hertz, by ω = 2 π f. For example, if the frequency, f , of the ordinary power line voltage in the U.S. is 60 Hz, then the associated angular frequency, ω , is 377 radians/s (2 π× 60). Transfer Function A two-port circuit is characterized by its transfer function, whose magnitude is defined as | V out / V in |, where V out and V in are phasor voltages (as indicated by the boldface type). The variation of the transfer function with frequency characterizes the circuit, whether the circuit is an amplifier (does it amplify high frequencies more than low frequencies?) or a filter (does the filter pass the low frequencies or the high frequencies better?). If you analyze the RC circuit of Fig. 1 using Kirchhoff’s voltage law, the phasor voltages V out and V in , the resistance R and the impedance of the capacitor Z C = 1/j ω C, you can show that the magnitude of the transfer function is 2 ) ω RC ( 1 ω RC + = in out V V An approximate log-log plot of transfer function magnitude vs. frequency is shown in Figure 3. The filter characteristic has been simplified to appear as two lines that intersect at the angular frequency

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Page 2 of 7 for which ω RC = 1, or ωτ = 1, where τ is the time constant RC for this circuit. If plotted precisely,
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PSPICE Stuff - EE43/EE100-Lab#5 EE43/EE100 LAB#7 RC Filters...

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