STEP RESPONSE OF 1 ST AND 2 ND ORDER CIRCUITS YOUR NAME GTA S SIGNATURE LAB MEETING TIME Objectives: To observe responses of first and second order circuits - RC, RL and RLC circuits, source-free or with the DC excitation THE HP IMPEDANCE ANALYZER The HP Impedance Analyzer is found in the Circuits Lab (Engineering C105) on a table next to the hallway connecting C105 and C107. You can/should use it to determine a circuit element s value, whether it be a resistor, capacitor, or inductor, and also measure the magnitude and phase of an element s impedance. The machine will also show how these quantities vary with frequency. Chapter 3 of the instruction manual (on the table) describes the front panel functions but you probably can just figure them out by trial and error. Get any capacitor and measure its value: a) Set the frequency of the analyzer to 1 khz. b) Insert the capacitor into the test fixture and measure the impedance magnitude and its angle. The angle of your capacitor should be near -90. If the angle is not close to one of these values, get a different capacitor. Impedance angle (measured) = deg c) Now change the analyzer s settings so that capacitance is displayed. C (measured) = F You might be curious to explore how the capacitance value depends on frequency from 0.1 to 100 khz. You might also like to try measuring inductor values with the Analyzer; the impedance angle of an inductor should be near +90. It is particularly interesting to see how the inductor s impedance angle varies with frequency; often, the value improves with increasing frequency.
RC CIRCUITS 5. Build the two circuits shown below and observe their output waveforms when you apply a 5 khz square wave input that changes from 0 to 5 V. a) Set the function generator to 5 khz, 5 V pp and 2.5 V DC level. b) To begin, choose values of C to satisfy: 5(RC) = T 1 /2 for the differentiator, and RC = 5(T 1 /2) for the integrator, where T 1 is the period of v i (t). a) Differentiator b) Integrator Note: This is called the 5 time constants rule of thumb and gives a good estimate of the time required for the output signal v(t) to achieve steady state during one period of the input signal (one half in the case of the square wave). c) Now change the input square wave frequency by a factor of five, decreasing f for the differentiator and increasing it for the integrator, and record your observations on the graphing paper. f differentiator = f integrator = Attach sketches of v i (t) and v(t) for each case (a total of four graphs). d) Do these circuits justify their titles? Explain.
6. Assemble the circuit shown using the values given and calculated in the PreLab homework. a) To obtain a repetitive output waveform that can be seen on the oscilloscope, use a 5 V amplitude square wave at the input. Set the function generator to 5 V pp with 2.5 V DC level. The period of the square wave should be long enough to achieve steady state, at least five time constants of the circuit. Calculate the square wave frequency f for this condition to be satisfied, using the 5RC rule of thumb. Equation and value for f: b) Now measure the output steady-state voltage V x and the time constant τ. V x = τ = c) What is the equation which describes the measured voltage step response of this circuit? d) Attach sketches of the observed v i (t) and v(t) waveforms.
GENERAL SECOND ORDER CIRCUIT 7. a) Draw circuit that your team has decided to examine during the lab session today. b) Write characteristic equation of the examined circuit. c) Fix values of all elements except one. Change values of the element that is not fixed to obtain the best possible appearance of the response. You may have to try multiple values in order to be able to nicely display on the oscilloscope your circuit s response. What were the measured values or elements you have used? d) Preparing to demo your circuit: Arrange three values of the changing elements on the breadboard in such a way that you can quickly switch between different responses (moving wires around). Use oscilloscope to capture all three responses and include them in your lab report. Do not forget to write which current or voltage you have measured. e) Walk-around / Circuit Expo (time allowing): All teams will walk-around during the last 10 minutes of their session and each team will present about their circuit. One team per lab session will get 10 bonus points for the nicest appearance of the response. TA may decide to award bonus points to another team, if two teams have excellent displays. Remember GTA s signature for 2 nd order circuit operation:
POSTLAB ASSIGNMENT: 8. Use Cadence to simulate your circuit for all three responses. Use measured values of elements from 7.c Include a printout of your circuit and current or voltage you have captured on the oscilloscope during the lab session. Comment how well do the actual measurement and simulation agree.