University of Rochester Department of Electrical & Computer Engineering ECE111 Laboratory #8 RLC circuit transients week of 16 Nov 09 ------------------------------------------------------------------------------------------------------ Write-ups must provide a detailed description of the exercise, including diagrams of all circuits and descriptions of all procedures. Remember to have your lab TA sign and date each page of your lab notebook. At the front of your write-up, attach an abstract page, which (1) states the objectives of the exercise, (2) describes the methods, (3) presents the results concisely, and (4) summarizes the general conclusions drawn from the results. Your grade will be based in part upon conciseness, grammar, and spelling. Lat e work will not be accepted. ------------------------------------------------------------------------------------------------------ 0. Laboratory preparation – Upon arrival in the lab, each lab team is to hand in to the TA a completed copy of the exercise found on pg. 4. In this lab, you will investigate the transient responses of second-order RLC circuits. Prepare for the lab by using what you know about the transient behavior of R’s, L’s, and C’s circuits to complete the exercise on the last page of this assignment. On the waveforms you draw, clearly indicate all critical voltage and electric current values. Hand in a completed sheet to the TA upon arrival in the Gavett lab. I. Transient response of series RLC circuits In this laboratory assignment, you will use a square wave voltage input to excite transients in series RLC circuits, and then observe the resulting voltage and current waveforms. As in Lab #6, it is important to set the period of the square wave so that the transients have time to decay away fully, so that steady-state (asymptotic) conditions can become reasonably well-established before the next half-cycle, i.e., T ≥ 3/α. First, set up the series circuit as shown in Fig. 1 (without any resistor R), using the dual-trace feature of the scope to display the square-wave input and the voltage across the capacitor, vC(t), simultaneously. Use circuit values as follows: R = 0 Ω, inductance L ~ 10 to 50 Fig. 1. Set-up for investigating the transient response of second-order RLC circuits. Use square-wave input @ ~1 kHz & voltage magnitude of ~10 V p-p. Adjust the square-wave frequency as needed to make it easy to display the ringing transients of the ckt and to obtain the data needed to estimate the values of R, L, and C. vC(t) L R C square-wave signal generator @ ~10 kHz- 2/4 - mH, capacitance C ~ 1 nF. Once you have obtained a useable waveform display, carefully sketch it, including all important voltage levels and asymptotic limits. Also, be sure to measure the period of the transient oscillation, T, and the e-folding time of the envelope, 1/2α. For the lab write-up, you will be analyzing your data to see how close your measurements come to the predictions of circuit theory. Bear in mind that the signal generator has internal resistive impedance Rs = 50 Ω. This resistor forms part of the circuit and therefore influences the observed damping of the resonance. Furthermore, the inductor has series internal resistance rw, due to the finite conductivity of the copper windings, and in general it cannot be neglected either. Therefore, even without including a discrete series resistor in your circuit, the effective value will be R = Rs + rw. Make sure to measure all relevant component values using the LCR meter in the lab for comparison to the results from your data. For example, when measuring the inductor, use the series LR mode and record readings for both inductance and series resistance. Be sure to establish limits for the precision of each component value in ±%. After completing the measurements specified above, alter the connection to display the voltage across the inductor, vL(t), then repeat the above exercise, carefully sketching the waveform and recording all needed data. NOTE: Just as in Lab #6, it is important to recognize that (i) the initial conditions existing before each step change in voltage are controlled by the steady-state condition from the previous half-cycle and (ii) the voltage step occurring each half cycle is equal to the peak-to-peak amplitude. II. The critical damping condition Return to the series RLC circuit setup of Fig. 1, displaying the voltage across the capacitor, but with an added series resistance Rckt, where now, R = Rs + rw + Rckt. First, investigate the effect of resistance on the transient behavior as revealed by the waveform of vC(t) by changing resistor Rckt. It may be convenient to use a potentiometer instead of or in series with a discrete resistor. After you have identified the trend as Rckt is increased, see if it is possible to achieve the so-called critically damped condition, as described on pg. 321 of the text. It is probably best to approach the critically damped condition from lower values. Because the appearance of the transient does not- 3/4 - dramatically change as you approach the critical damping condition, conclusive identification may be difficult. Nevertheless, record your best estimate for this resistance value for later comparison to ! Rcritical= 2L C, the theoretical value obtained at the condition ωo = α. III. Quick look at resonant (section 14.5 of text) Apply an AC voltage to the series RLC and, while monitoring the voltage across added series resistor Rckt ~ 100 Ω, adjust the frequency to obtain the maximum voltage. The maximum is achieved at the resonant condition and the sharpness of the peak depends on the circuit quality factor: ! Q=L C R. Record this frequency and compare it to ωo. IV. Your lab write-up In your write-up, provide a systematic summary of results for each set of measurements taken. Include accurate sketches of all voltage waveforms. These sketches must depict the critical values for voltage and time used to compute the component values. You should fully explain all methods used in