Lab Procedures Part A) Frequency Response Data The objective of Part A) is to show how you can get a Bode plot manually. In Lab 7, you took measurements of the response of this same circuit at two frequencies: 2000Hz and 9000Hz and found the output amplitude and phase. This information can be used to find | H(f)] and ZH(f) at those frequencies using the method in the background section. In a real situation, you would take a lot of measurements, say 15-20 frequencies. Here, we will demonstrate the procedure with just one frequency. 1. Find the response of the RLC circuit to an input of 2cos(2000πt). First, use the protoboard to build the RLC circuit shown BELOW. Voltage source provided by the function generator, FGEN, passed through the buffer circuit +15 Scope Channel 0 FGEN IN PIN 8 Al: 0+ PIN 3 OUT Scope Channel 1 AO:0 PIN 1 www Al: 1+ 3.3mH 1ΚΩ + -15 0.22μuf PIN 2 PIN 4 AO: AGND Al: 1- Al: 0- Channel AO of the scope displays the input voltage, V., and Channel A1 of the scope displays the output vc. 2. Measure the steady-state output v. sine wave of your circuit to an input of v = cos (2лft) for f = 1000 Hz. Follow these steps for this measurement: a. FGEN Settings • Set the frequency on FGEN to 1000 Hz • Set the amplitude to 2 Vpp (that is, peak to peak), so A; = 1v b. SCOPE Settings • Enable Channel 1 and set to Al 1 • Turn on the cursors (box is in the bottom left of the SCOPE) and set C1 to CHO and C2 to CH1 • Trigger set to edge (on AO) Aicos (wit) A。cos(@it+6) H() Figure 1: Input Output behavior of a linear circuit in steady state. The output amplitude, A., and the output phase, o, depend on H() as follows: A₁ = A¡ |H[1]] and $=ZH(1) To determine H(@) from experimental measurements of a circuit, find the steady-state sinusoidal response to a wide range of input frequencies. From each sinusoidal response, measure A. and . Fill in a table such as the one below for each input frequency. @₁ | 0=H(@1)||H(@1)|=A。/A₁| 20log | H(1)| Consider, for example, the response, y(t), of a system with input x(t)=sin(3лt) shown below. For this input, ₁=3л, and A₁ = 1. For the signal in steady-state, measure A. and AT, the time lag. The phase lag in degrees is calculated from == 360° AT T if the output is shifted to the right and $ = 360° where T is the period of the signal. AT T if the output is shifted to the left