Lab2

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Concordia University *

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ELEC 273

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Electrical Engineering

Date

Jan 9, 2024

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LABORATORY REPORT Basic Circuits & Systems Laboratory This cover page must always be the top sheet Course: ELEC 273 275 Lab Section: ( Circle ) Experiment No.: Date Performed: 20 – – YYYY – MM – DD Experiment Title: Name: ID No.: Lab Partner Name: Lab Partner ID: I certify that this submission is my original work and meets the Faculty’s Expectations of Originality Signature: Date: 20 – – YYYY – MM – DD FL-X Prince Raphael Johnson 40153375 Faisal Quraishi 40161298

Abstract The objective of this experiment was for the students to familiarize themselves with the basics of the Operational Amplifier (or OpAmp) by constructing circuit OpAmp, as well to test the principle of Transient Response by building circuits with capacitors and inductors and measuring different responses. Introduction We begin this experiment by getting familiar with the principals of an OpAmp and how it works in a circuit. An OpAmp circuit has the objective to either obtain the output voltage Vout of the circuit for a given set of input voltages, or to find the voltage gain Av which is equal to Vout/Vin. This can be obtained via the Open Circuit (i.e., I+ = I-= 0) & Short-circuits (i.e. V+ =V- ) principles. Procedure (Methods) OpAmp circuits:  Start with checking whether the OpAmp IC is operational or not by temporarily short- circuiting one of the inverting input terminals to ground to get an output voltage of zero (if not, replace IC unit).  Then go onto building the OpAmp circuits, Non-inverting amplifier circuit and testing out various principles such as saturation and increased Gain. Transient Response  We start building 1 st an RC circuit using the RLC chassis provided, and 2 nd an RL circuit with the schematic provided, all the while making the right connection between the Function Generator and the chassis.  We then go onto try and make an RLC circuit in order to get respectively an Overdamped RLC response, a Critically Damped Response, and finally an Underdamped Response Results and Discussion Operational Amplifiers  Inverter Circuit - For the inverter circuit made from Figure 4.1 of the lab manual, we have a display of a sinusoidal wave for channel 1 and 2. - We had an expected output amplitude of V o =(-R 2 /R 1 )V i = -6.16V but observed an expected output amplitude of 6.04V. - Simply put, the inverter means that the direction of the signal is changed compared to the input of the circuit.  Saturation - We were getting a sinusoidal wave when we increased the input amplitude and looked for saturation of the op-amp output voltage and noticed the channel 1 input starting to break slightly. - Saturation for an Op-Amp would mean that the output voltage approaches the power supply voltage 𝑉 s and even exceed.

- The maximum value of the output voltage that we observed without saturation was 28.40 V and the largest input voltage that does not give rise to saturation in the output 14.80 V  Increasing gain and Saturation Value of Gain 𝐺 = 𝑅 2 ⁄ 𝑅 1 Expected Amplitude Measured Amplitude of V 0 R 2 = 1 Ω G=1 5*1=5V V 0 = 10.40 R 2 = 2 Ω 2 10 V 0 = 20.40 R 2 = 3 Ω 3 15 V 0 = 28.40 R 2 = 4 Ω 4 20 V 0 = 28.80 R 2 = 5 Ω 5 25 V 0 = 28.80 R 2 = 6 Ω 6 30 V 0 = 28.80 - The circuit built does deliver the expected Gain for all R 2 values mentioned in the table - From the table, the maximum output voltage without saturation seems to 28.80V, and we found the value to be 28.40V, which is a bit smaller than the value measured. - In this part of the experiment, we neglected the output resistance of the function generator, which is 𝑅 S = 50 Ω. The 𝑅 S resistor completely changes the expected gain when put in the circuit. Figure 1: Circuit drawn with Rs and Vs Transient Response  Charging RC Circuit - For the RC circuit, we’re getting a square wave output with the calculated frequency  Time Constant - From the scope display, we use the paired cursor to measure the time constant by setting it correctly between the channel 1 and 2 - To measure the time Constant, we follow this formula 𝜏 =RC. In this case, R=3300Ω + 50 Ω from Rs and the provided C=22nF.

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- The calculated time constant obtained after choosing the position of our x and y cursor is 220*10 -6 s. This is completely different from what we measured during the experiment . Value of 𝑅 1 from the TA 𝑅 1 =3300 Ω Measured time Constant of the RC circuit 𝜏 = 73.7*10 -6 s Calculated time Constant of the RC circuit 𝜏 = 220*10 -6 s % error in the time constant 199%  Charging RL circuit - For the RL circuit, we’re getting a square wave output with the calculated frequency.  Time Constant - On our scope display, we get the time constant by using the paired cursor and putting it between channel 1 and 2. - This time around, the calculated time constant is not that far off the one measured during the experiment. Value of 𝑅 1 from the TA 𝑅 1 = 330Ω Measured time Constant of the RL circuit 𝜏 = 123.68*10 -6 s Calculated time Constant of the RL circuit 𝜏 = 110 *10 -6 s % error in the time constant 11.06%  RLC circuit  Overdamped RLC Response - On the display we have a square wave for channel 2 and channel 1 is broken down and flat. - In order to measure the time constant, we set the display to square wave, input the calculated frequency, then use the cursor by placing it between channels 1 and 2. - The measured time constant is equivalent to 0.101ms which is found by using the damping ratio, and the calculated time constant seen on the display seemed to be 560*10 -6 s . By this, there is 99.44% error between the calculated and the measured value for the time constant  Critically Damped Response - We adjusted the resistor value so that the response is critically damped (the decrease of the Resistor value is what makes the display shows critical damping) - We found a resistor value of 1.7845 K Ω which was the value where the circuit was starting to get critically damped.  Underdamped RLC Response - Here, the resistor value has been lowered again, and we can see that the V out is being underdamped as the display shows the figure varying at precise point. - To find the damped natural frequency, we use the provided resistor value (500 Ω) and then use the V-bars to measure the period of the oscillation between the different breaks visible between channel 1 and 2.

- In order to find the time constant, we use two maxima Conclusion Overall, this experiment was tedious and long to handle. We had to figure out the various time constant for the 2 nd part of the lab in order to be able to get the proper reading on the display, and with we managed to visualize various type of response and an OpAmp in different conditions.