Download RLC Circuits: Understanding Low-Pass, Bandpass, and High-Pass Filters and more Lab Reports Basic Electronics in PDF only on Docsity! RLC Circuits Note: Parts marked with * include calculations that you should do before coming to lab. In this lab you will work with an inductor, a capacitor, and a resistor to demonstrate concepts of low-pass, bandpass, and high-pass filters, amplitude response, phase response, power response, Bode plot, resonance and Q. Series RLC Circuits *1. Simple filters: Figures 1 (a), (b), and (c) show low-pass, bandpass, and high-pass filters. Write the transfer function H(ω) for each of these filters, showing the ratio Vout/Vin as a Figure 1: Low-pass (a), bandpass (b) and high-pass (c) filters. function of the angular frequency ω of the input voltage. *2. The low-pass – calculations: Show that the low-pass filter in (a) above has a power response function: ! H(") 2 = " 0 4 (" 0 2 #" 2)2 +" 2(R /L)2 * Explain why this is a low-pass filter by finding the limits ω = 0 and ω =∞. * Explain why we say that resonance occurs when ω = ω0. * Find the half-power points. That is find the frequencies ω where the value of |H(ω)|2 is reduced to half the value at resonance. You may use the approximation that the resonance width is small compared to the central value ω0. * The difference between half-power frequencies is the bandwidth of the resonance. The Q of the resonance is equal to the resonance frequency divided by the bandwidth. Show that Q = ω0L/R. 3. The low-pass – experiment Set up the series low-pass filter shown below: Notice that there is no discrete resistor. The resistor in this circuit is the resistance of the inductor plus any resistance contributed by the Function Generator. Normally the Function Generator has an output impedance of 50 Ω. Verify that this is the case by measuring the resistance of the function generator output with the generator turned on but the output voltage set to 0 V. Measure the resistance of the inductor, add the value contributed by the Function Generator and use this sum in your calculations below. Calculate the resonance frequency and measure it by changing the oscillator frequency. Using the measured resonance frequency and resistor value, calculate the Q. Vary the oscillator frequency to find the half-power frequencies and calculate the Q from the measurements. (Note: At the half-power frequencies the output voltage is smaller than the output at resonance by a factor of 1/√2.) Figure 2: Series Low-pass Filter.
