Bonus Point ENG 274 Lab 6

Bonus Point ENG 274 Lab 6 - ECE 220 Lab 6 revised April...

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ECE 220 Lab 6 © revised April 2007 by R. N. Strickland 1 ECE 220 Lab 6 Frequency Response of AC Circuits (Tone Control Ckt, Crossover Network, Tuning Ckt) This lab examines the steady-state frequency response of ac circuits. Much of the necessary theory will be covered later in the semester when we study Chapter 9 (Phasors & AC Circuit Analysis). Hence, this lab is a preview of the some of the applications of that theory. Completing the prelab and lab will help you to understand the theory when we cover it in class. The prelab consists of PSpice simulations of the following circuits: 1. Lowpass (Butterworth) RC filter, 2. Tank (or tuning) circuit, 3. Tone control circuit, 4. Loudspeaker crossover network. The main skill to be covered in the experiments is the measurement of gain and phase-shift at individual frequencies. Measuring phase-shift involves connecting two ac signals to the oscilloscope (set in X-Y Mode) to create Lissajous patterns. (See last page.) Introduction AC circuits are characterized by their steady-state response to sinusoidal inputs. In the figure, the input (shown as V1) is the sinusoid: + - Two-Port Circuit ) ft 2 cos( V ) t ( v i in π = where V i 0. The steady-state output sinusoid (i.e. after any initial transient response has died out) is given by: ) ft 2 cos( V ) t ( v o o θ + π = where V o 0, and θ (which may be positive or negative 1 ) is the phase-shift caused by the circuit, and the circuit’s gain is given by the ratio V o /V i . When V i = 1V as shown in the figure, the gain is simply equal to the amplitude of the output sinusoid. 2 Both gain and phase-shift are frequency-dependent. Plots of gain vs. frequency and phase-shift vs. frequency constitute the frequency response of the circuit. (The individual plots are often called the gain response and the phase response , respectively.) The main goal of this lab is to measure these responses and understand what they mean. One final point: gain response typically covers a very large range of values, so we use a special log scale called the dB (decibel) scale, giving the dB gain response: ) V V ( log 20 dB i o 10 = . (In ECE 320 you will study these gain curves in the form of Bode plots. ) Example Shown are the sinewave input v in (t) and the resulting steady-state output v o (t) for some linear circuit. At the frequency of the sinewave (1kHz or 6283 rads/s), the circuit has a dB gain of . The phase-shift at this frequency is given by the product: time shift × radian frequency , i.e. 0.1ms × 6283 rads/s = 0.628 radians (36 degrees). The output is delayed relative to the input, so the phase-shift is actually -0.628 radians. dB 02 . 6 ) 0 . 1 / 5 . 0 ( log 20 10 = v o (t) v in (t) T=1ms 1.0 0.5 0.1ms Summary: V i = 1.0 volts V o = 0.5 volts f = 1kHz, ω = 6283 rads/s dB gain = -6.02 dB θ = -0.628 rads t 1 When θ > 0, the circuit is said to cause a phase advance , when θ < 0, the circuit creates a phase delay . Because sinusoids are periodic, a phase advance of 160
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Bonus Point ENG 274 Lab 6 - ECE 220 Lab 6 revised April...

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