LABORATORY 2: Bridge circuits, Superposition, Thevenin Circuits, and Amplifier Circuits

Transcription

1 LABORATORY 2: Bridge circuits, Superposition, Thevenin Circuits, and Amplifier Circuits Note: If your partner is no longer in the class, please talk to the instructor. Material covered: Bridge circuits Voltage dividers Superposition Thevenin Circuits Amplifier Circuits Part A: Resistive Bridge Circuits Vs R1 R3 Rbridge R2 R4 Wheatstone Bridge Wheatstone Bridge: A Wheatstone Bridge can be used to measure the value of an unknown resistor. It is a basic type of Ohmmeter. The bridge is shown on the in the above figure. When the bridge is balanced, no current flows through the Rbridge resistor. If that is the case, then both the left node and right node for that resistor must have the same voltage. Additionally, since no current is flowing through Rbridge, the left and right paths can be treated as voltage divider circuits with two resistors in series. Circuit analysis then gives us R2 R4 VLeft V S and VRight VS R1 R2 R3 R4 1

2 Again VLeft = VRight, so we can set these two expressions equal, perform some algebra and obtain a relationship for the resistors when the bridge is balanced (no current through Rbridge) as R1 R3 R2 R4 If one of the resistors is unknown, R4 for example, we can then use the bridge to find that value. Holding R1 and R3 fixed, we can vary R2 until we measure zero voltage drop (no current) across Rbridge. Once we have found that value for R2, we apply the above expression and determine R4. Thus, we have an Ohmmeter. A1: Wheatstone Bridge and Parametric Analysis We will use the Wheatstone bridge to determine the resistance of an unknown resistor. Pick up the unknown resistor on the podium (You can of course measure the resistor directly so that you can verify your experimental results). In the experiment, a potentiometer is the variable resistor. By adjusting the potentiometer such that the voltage across Rbridge is zero, the value of Runknown can be determined. In the LTSpice simulation, parametric analysis allows varying resistor voltages. 1) Determine the symbolic expression for Runknown when Vbridge is zero (see laboratory introduction). 2) Using values of R1 = 2.2kΩ, R2 = 4.7kΩ, Rbridge = 1kΩ, and Runknown =???. R3 is a 1K potentiometer. Note: Resistors were renamed by right clicking the given name like R4 and writing Runknown. 3) In LTSpice, plot Vbridge vs Rpotentiometer where Rpotentiometer is a parametric value. In the LTpice simulation, follow the procedure to perform a parametric analysis (details below). Using the plot and a differential voltage marker, identify the Rpotentiometer value that results in Vbridge =. The LTSpice schematic is shown below. 2

3 a) Parametric analysis: The.step command performs repeated analysis while stepping through specified values of a model parameter, global parameter or independent source. 1. Define the component parameter by right clicking the resistor R3 and entering {X} for the value of resistance (as shown in the diagram below). Note: Runknown is given the arbitrary value of 1k so the simulation can run. 2. Add a.step command using a SPICE directive (press s ) which specifies the steps for a parameter Example:.step param X 1 1k 1k steps the parameter S from 1 to 1k in 1k increments. 3

4 You may change the increments to a value that will give you more points. 3. Add.op in the SPICE directive. (Click.op far right on toolbar and add.op then place anyway on circuit) 4. Run the simulation (click Running man ) go to DC op pnt tab and click ok 5. Run the simulation again. (click Running man ). The simulation pop up window should show but without traces with resistor values as the x axis. 6. To specify the differential probes across Rbridge, click the node to the left of Rbridge (a red probe should appear), hold and click the right (a black probe should appear). 7. The trace V(Nn, Nnx) should appear (where n is some number label of node). 8. Now find the variable resistor value when VRbridge = V. Use the cursor function by clicking the trace label at the top of the diagram V(Nn, Nnx). You can drag the cursor along the curve by clicking and holding where the horizontal and vertical lines meet. 9. Include the screenshot/plot of the balanced bridge point with clear labels in your report. 1. Use the equations in the introduction to calculate the Runknown value from a balanced bridge circuit. 4

5 4) Build the physical circuit using a 1kΩ Potentiometer, as shown in the circuit below. Note, one leg of the potentiometer is floating. Turn the potentiometer such that the measured Vbridge =. Once you find that value, use an Ohmmeter to measure the resistance of the potentiometer (they are on the center table). Be careful not to turn your potentiometer and make sure you disconnect the circuit so you don t measure the other resistors. a. Compare your result to part 3). 5V R1 2.2k Rpotentiometer Rbridge 1k R2 4.7k Runknown Compare the LTSpice simulated value to the value obtained from your physical circuit. LTSpice Differential vs Nodal Measurements: In the simulations we have done with LTSpice, we have used nodal measurements which provides the voltage at a node relative to the designated ground. In order to determine the voltage across a component, we then found the voltage difference between the two nodes associated with that component. In practice, measuring the voltage across a component where neither of the nodes is connected to ground can be problematic. To safely make those kind of measurements, we use differential probes. Fortunately for us, the Discovery Board only makes differential measurements. 5

6 Part B: Analog Discovery Board Variable Sources and Superposition Discovery Board Variable Sources: In the last laboratory, we used the fixed 5V supply. This source is constant. If we want to vary the source voltage, we need to use the function generator channels instead. There are two channels available, labelled W1 (yellow wire) and W2 (yellow striped wire) on the Discovery Board. To access the software, when you bring up the Waveforms main menu a. Select WaveGen, the second item under the Welcome settings. b. We will want to use both Channels at various times during the course. (When we use only one Channel, you can turn off the other one if you want more space on your Desktop.) To enable both Channels, click on Channels pull down menu. Select both Channel 1 (AWG1) and Channel 2 (AWG2) such that there are check marks by both. Your window will probably refresh. c. We will use DC sources for now. Select the straight line from the column of waveform shapes (it should be the first icon). d. Go to the Offset pull down menu and set the DC voltage level. e. To output the voltage on the W1 (AWG1) wire, you need to select make sure the Channel is both Enabled and running. In the upper right of the window, make sure Enabled is checked. Click Run. f. Repeat steps c.-f. for AWG2 6

7 B1: Two Sources/Superposition Construct the following circuit. You will need to use both source channels (AWG1 and AWG2) on the Discovery Board to build the circuit. Note: The diagram below was created in PSpice but please duplicate this in LTSpice. V1 R1 1k R2 2.2k V+ R3 2.2k V- V2 1) Analytically, obtain an expression for the voltage across R3 in terms of the voltages V1 and V2. You should use superposition in your analysis (for practice). You are looking for an expression of the form VR3 = a(v1)+b(v2) where a and b are coefficients determined by your circuit analysis. 2) Build the circuit using the AWG wires (yellow and striped yellow) for the sources. Set V1 to 2 [V] and plot the voltage across R3 as a function of V2 for <V2<4Volts (pick a few values for V1 in that range and measure R3). 3) Repeat with V2 set to -2 [V], again plotting the voltage across R3 as a function of V1 for <V1<4Volts. 4) For both plots, compare your results with a plot of your expression from part 1). 7

8 Part C: Amplifier Circuits Overall notes: TL72CP chip (dual op-amp): The data sheet for the chip can be found online from any number of sites. One is provided below (it is long and contains several chips) A copy of the pin connections is shown below There are two op-amps on the chip, indicated by the 1 and the 2 pin labels. For example, 1IN+ is the V+ and 1IN- is the V- of the first op-amp, with 1OUT being the Vout. Power connections are +Vcc at pin 8 and Vcc at pin 4. 8

9 In LTSpice, you can use the UniversalOpamp2 component or opamp component. The opamp component does not have power levels and is assumed ideal. It is useful for simplified drawings, but your simulations will not be the same as the experiments. As such, please use the UniversalOpamp2 component, with LTSpice details shown below. A summary of the connections for LTSpice UniversalOpamp2 component: input, - (left), inverting input input, + (left), non-inverting input -(bottom), V-: Negative power, 9 V +(top), V+, Positive power, 9V Right node: Vout, output voltage The DC power sources will be the 9 Volt batteries that you have in your kit. Note the orientation of the batteries when you connect the leads. Again, for LTSpice simulations, the circuits on the following pages indicate how to power a ua741 op-amp. The input and output connections depend on the circuit. 9

10 An example of an op-amp reaching saturation is shown below. The input is a sinusoidal. If the op-amp was ideal, the output would also be a sinusoid with a scaled amplitude. However, saturation occurs and the output voltage cannot exceed (positive or negative) the source voltages. C1: Comparator op-amp circuits Build the comparator circuit shown above. V+ and V- will be your inputs and Vout will be the output. In Analog Discovery experiments, use the TL72CP chip (or 1

11 equivalent. You only need one amplifier for this part). In the LTSpice simulations use the UniversalOpamp2 component. 1) We will use W1 and W2 for out amplifier inputs. The Voltmeter channels inputs will act as the RLarge. a. Connect W1 (yellow wire) to the V+ op-amp input and ground (orange striped wire) to the V- op-amp input. b. Ground the V- op-amp input. c. To compare input voltage to output voltage, use the Voltmeter to measure the output voltage (refer to Lab 1). d. Using the Discovery board, set the W1 output voltage to DC mode and check the output voltage of the op-amp for the following input voltages Vin [V] Vout [V] e. Comment on your results and expectations when Vin = V. 11

12 2) In LTSpice, build the comparator circuit using a UniveralOpamp2 op-amp. You will need to add a load resistor at the output node since LTSpice does not allow nodes to float (be unconnected). A 1E6Ω load is fine (use exponential notation since M in LTspice is 1E-3). Compare the output voltages between LTSpice and Analog Discovery. You should see some differences, what causes these differences? Vin [V] Vout [V] 12

13 3) Remove the ground connection at V- and use AWG2 (W2, yellow striped wire) to provide a 1.5V input at the V- opamp input. Effectively, your circuit will behave as if there was a 1V source at the negative input, as shown above. If you didn t use AWG2 for the 1.5V input, what type of circuit can you use to produce the 1.5V? (Consider the 5V Discovery board connection from Lab 1.) a. Repeat the output voltage measurements again Vin [V] Vout [V] 13

14 4) Again, compare your Analog Discovery experiment to the LTSpice simulation. Vin [V] Vout [V] C2: Inverting Op-amp, Non-inverting op-amp circuits Build and test the following circuits. (Again, this schematic was created in PSpice. Recreate in LTSpice. Remember the power connections. They have been removed to simplify the drawing but they must still be included in the circuit). 5) Inverting Op-amp with a gain of -2 Vin 3 U2 + R1 2 - ua741 7 V+ 4 V- OS2 OUT OS Vout R2 a. When considering the saturation voltage, what is the maximum Vin such that Vout = -2 Vin? Choose appropriate resistors. Vin [V] Vout [V] 14

15 b. Build the circuit in LTSpice and verify that simulation is constant with experiment (within the limits of the respective saturation voltages). 6) Non-inverting Op-amp with a gain (1+R2/R1) of 3 a. When considering the saturation voltage, what is the maximum Vin such that Vout = 3 Vin? In other words, at what Vin does the output reach saturation? (Discovery Board only) Vin 3 2 ua741 U V+ V- OS2 OUT OS Vout R2 R1 Vin [V] Vout [V] 15

16 Part D: Alpha Laboratories Applications ΔΟΧ, YBAX. To continue to build a game controller, You must turn a binary on/off push of a button into voltages that differ depending on the button AND button combinations pushed. The voltage output for pushing Δ should be different from the voltage output for pushing Δ+X. How exactly do you do that? How does this relate to the Circuit fundamentals learned in Unit 1? D1: Application of Weighted Summer DAC Using LTSpice, create a 3 input weighted summer that would be used for digitalto-analog-conversion. Provide a screen shot of the schematic and the simulation. (If you find a link online to help you design one, please provide it.) a) Describe the importance of the value of the resistors in relationship to how the DAC works. b) What becomes a limiting factor when you try to build a weighted summer based DAC when you have 5+ inputs? (Hint: Try to find the resistors you design in the lab.) D2: Application of Thevenin and Superposition Circuit Analysis Better DAC 16

17 The circuit above includes 4 switches modeled as a simple voltage source (for visual simplicity) VSW, VSW1, VSW2, and VSW2. Following the switches, there is a resistor network with the Vout between resistors R7 and R8. 1) Find the relationship between each individual switch voltage to Vout using Thevenin Equivalent circuit analysis. Note: See diagram below for analyzing VSW and evaluate Thevenin at each dividing line where everything to the right of the line is the load. Find Vth and Rth and then replace circuit to the left with the Thevenin equivalent. Repeat until down to Vout. Do this analysis for each switch. Keep thevenin voltages in terms of VSWx. 2) Write the total Vout for the circuit using answers from 1) and superposition. Note: A symbolic equation should include VSW, VSW1, VSW2, VSW3 and VOUT. 17

18 3) Verify your calculated values for the following configurations using LTSpice. Button Config 1 Button Config 2 Button Config 3 VSW VSW1 VSW2 VSW3 VOUT 5V V 5V V V 5V V 5V 5V 5V 5V 5V 4) EXTRA CREDIT: Combine your push button switch simulation with pulse voltage input from Lab 1 with this ladder network DAC circuit to cycle through every possible combination of button pushes. (i.e. to 5555). Label the voltage input and corresponding output voltage on the diagram. 18