Download RLC Circuits: Understanding Low-Pass, Bandpass, and High-Pass Filters and more Lab Reports Basic Electronics in PDF only on Docsity! RLC Circuits, Page 1 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 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. Figure 1: Low-pass (a), bandpass (b) and high-pass (c) filters. R La) Vin C Vout C Lb) Vin R Vout R Cc) Vin L Vout RLC Circuits, Page 2 * 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. * 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 only the resistance of the inductor. Use an ohmmeter to measure the resistance of the inductor and use this value 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.) Calculate and measure the ratio of input and output voltages at resonance. You should find that the output voltage is greater than the input! Explain how a passive circuit like this can give a voltage gain. Measure the ratio of input and output voltages for very low frequency. From the transfer function you expect them to be the same. Are they? What is the phase shift at very low frequency? Reduced Q Reduce the Q of the filter by adding a 150 Ω resistor in series with the inductor. Measure the resonance frequency. Do you expect it to be changed? Is it? Calculate and measure the Q for this circuit. 27mH 0.047 µF Scope A Function Generator Vin Vout Scope B Figure 2: Series Low-pass Filter.
