OP-AMPSIN LINEAR AND NON-LINEAR MODE:
OP-AMPSIN LINEAR AND NON-LINEAR MODE
Thisreport is a comprehension of the experiments that were carried out toconcerning op amps in both linear and non-linear modes, the findingsof the experiments and the conclusions from the experiments. Therewere two experiments that were carried out in this study. The firstexperiment was concerned with the non-linear operational amplifierapplication. The first objective of this experiment was toinvestigate nonlinear applications of operational amplifiers. Thesecond objective of this report was to develop design strategies thatare systematic and also combine the circuits that have beeninvestigated together in the past. The second experiment is concernedthe operational amplifier in both linear and nonlinear modes. One ofthe objectives of the experiment was to study the 741 Op-Amp in theNon-Linear mode using simulations and actual circuits. The second onewas to construct, physically, 741 Op Amp circuits in the Linear Modewith negative feedback.
Amongthe most popular functions of the operational amplifier is to buildlinear circuits that are useful eventually. However, simpleobservation has proved that when the input of a majority of thecommercial amplifiers is overdriven their performance becomespredictive and that if they are over driven in a certain way theamplifier is not destroyed by the amplifier. This phenomenon isuseful because the over driven amplifiers can be used in a very largevariety of nonlinear systems that are very useful (Terrell, 1996).
Theoperational amplifier is lost every time there is an overdrive in theinput due to a null-port property. The performance of a device atthis particular time is dependent on the type of amplifier and thearchitecture and components that are used for building the op amp(Gayakwad, 2000).
Theabove figure shows the transfer characteristics of an OperationalAmplifier showing saturation. The DC gain of the operationalamplifier is the slope of the transfer characteristics and it usuallyvery high and its gradient steeper than what is shown above. TheVSATH and the VSATL are the high and low saturation voltages and arevery close to VDD and VSS respectively. The characteristics ofnon-linear Operational Amplifier transfer would thus look like thefigure below in a graph.
Whenoperated nonlinearly the differential voltage at the input port willnot be zero but nevertheless the input current on both inputterminals still remains zero for most of the commercial Op Amps. Itis for this reason that the discussion of the study will be limitedto the application of Op Amps that have these properties. Thefollowing set of equations is what was used for summarizing thenonlinear model for the Op Amp.
TheI+ and the I- represent the input currents from the positive andnegative terminals of the operational amplifier. The followingfigures show the non-inverting comparator (a) and the inverting one(b).
Thesetwo comparators compare the input signal relative to the ground byproviding either high or low output depending on the charge of theinput. Most of the circuits that are sold as comparators today do notwork well with linear applications but performs better than Op Ampsin some respects. In this experiment the Op Amps will be applied ascomparators (Dai & Jazar, 2012).
Manytimes comparators must compare the inputs with respect to any voltageother than ground or hysteresis requirements to provide regionsaround the transition point where any small changes does not causerepeated changes in the output. Some modifications in the circuit canprovide these properties.
Thefirst circuit has the trip-point control while the second one has thehysteresis and trip-point control. Unconventionally, this sectionwill consider a without an input but still with a ouput waveform thatis useful. Most of the circuits like these ones are used for thegeneration of waveforms such as triangle waves, sine waves and squarewaves. The circuit below is one such circuit a variant of thecomparators above. This circuit has a feedback signal applied to thenon inverting terminal.
Afterthe Analysis the VOUT2 output looked like a triangle wave unlikeconventionally where it is a square wave. Although this can still beconsidered an output buffer may be needed for VOUT2 to drive othercircuits without infinite input impendence. The triangle wave’smagnitude could be modified if a non-inverting amplifier was to beused.
Equipmentand Components used
Computerwith SPICE, Signal Express, GP-IB capability, and appropriate IVIdrivers
HPE3631A or equivalent power supply (GP-IB Capable)
HP33120A or equivalent signal generator (GP-IB Capable)
HP34401A or equivalent multimeter (GP-IB Capable)
HP54602B or equivalent oscilloscope
Theparts used are
Assortmentof Resistors and Capacitors
3741 op amps
ExperimentalMethod and Procedure
Section1: Non-Linear Mode
Usingan Op Amp as a nonlinear comparator. The Op Amp is in the simulatedcircle shown below.
Use SPICE simulation to obtain the Input and Output transfer characteristics of the comparator.
Apply a 1Khz sinusoidal input voltage and set the peak amplitude to Vin=2Vp. Perform a transient analysis in SPICE and obtain the waveform of the output voltage.
Use SPICE to connect the inverting input (pin 2) to a voltage of 1.5V and repeat the transient analysis. Plot the input and output signal (voltage) and determine the duty cycle (d). What could this mean about the comparison outage voltage point.
Use real components to set up the comparator circuit. Use an input and output signal generator to apply sinusoidal input voltage with parameters and attach the Digital Storage Oscilloscope probes to the input and output ports for monitoring the input and output signals.
Theabove figures are those of Op Amp Pin diagrams and Power ConnectionDiagram.
ConnectionGuidelines for Circuit Connections
TheDC voltage sources +Vcc and –Vcc provide the voltage rangenecessary for powering the circuit. Without these, the Op Amp wouldbe totally useless. The positive terminal of +Vcc is connected to pin7 of the op amp. The negative terminal of –Vcc is connected to pin4. Now the inverting input (pin 2) is connected to the ground (0V)and pin 3 (non-inverting input) is connected to the signal source VinOutput. The reason why most circuits fail is due to incorrectconnections of the op-amp or chip. Wiring diagrams are required forall built circuits. For instance
PartB: Pulse width Modulator
Thisis a circuit that changes the width of the VH pulses to reflectchanges in the value of input analog voltage VS. Update the previoussimulated circuit to make a pulse Width Modulator. The requiredvariable input voltage, VS is supplied by a slower changing DCvoltage sweep Vs from 0 to 5V. This is easy to find in a triangularvoltage sweep source, Vs, on pin 2 of the op-amp. This varies overten periods (of the Vin sine wave source, on pin 3).
Designthe pulse width modulator so that the duty cycle responds linearly tothe value of input voltage, Vs specifically: D = 50% for Vs = 0V,D=25% for Vs = 2V, D=12.5% for Vs =3V, and D=0% for Vs>4V. Itshould however be noted that the fraction of the period during whichthe signal is high. For instance, the duty cycle with equal time highand time low is 50%.
Simulatethe circuit to verify its operation. Generate the input sweepedvoltage, Vs, and output modulated Waveform, Vout, on a single graph.Label the output waves on the circuit and graph.
PartC: Flash A/D Converter
Thecircuit used here is a four level flash A/D comparator. Use the inputvoltage, Vinrisingfrom 0V to 5V then falling back to V, to test the circuit functioning
Note the specific voltages that are lighted and extinguished by each LED.
Draw a logic table with the input voltages.
Describe how the circuit performs A/D conversion.
Section2: Linear Mode
PartA: Non-Inverting Amplifier
Thefollowing linear feedback operational amplifier should be built usingreal components.
The741 Op Amp Pin Diagram and power Connection Diagrams should be noted.
With a DC input voltage of Vin=5V the currents I1, I2, and I3 are to be measured. The results should be presented in a tabular form. Comment on what it states about the operational amplifier input terminal resistance.
Using Vin=5V as a DC input voltage, Vin=5V, measure the output voltage and note the gain in the circuit.
Measure the transfer characteristic of Vo versus Vin for the above non-inverting amplifier. Change the resistor’s value Rf to 3.3kΩ and measure the transfer characteristic again. Repeat again for Rf = 10kΩ.
Plotmanually all three transfer characteristics on the same drawn graphsand calculate the gains.
PartB: Inverting Amplifier
What is the expression for Vo in terms of the circuit components.
Build a circuit and supply a 1KHz, 1V sinusoidal input signal for Vi. Use the DSO to measure and record the input and output voltage waveforms. Determine the Gain, A, of the amplifier.
Vary the input Voltage, Vi, to a value that causes clipping in Vo. Note the effect of Op-Amp saturation and record the maximum saturation voltages.
Set the DSO to X-Y mode and obtain the transfer characteristic with saturation.
Apply a 10kHz square wave to the input, Vi, and observe the output, Vo, in comparison to the input. Determine the slew rate of the output, (in V/μs)
PartC: Analog Computing Circuits
Theabove two amplifier circuits should be built and thereafter
State the expression for Vo in terms of the circuit components.
Using a 1 Khz Sine Wave input, use the DSO to obtain the transfer characteristics.
Test the transient circuit response with Sine, Triangle and Square wave inputs. Use the DSO to measure the input and output voltage waveforms from each of the selected input waveform types and record the graphs.
Observations,Data, findings and results
Inthe first part of the first section the following comparator wasused
Thegraph for the Input and Output Transfer as characterized by thesimulation between -5V and 5V is
Thegraph below is that of an output voltage waveform for 1KHz inputvoltage with peak amplitude Vin=2Vp.
Theinput and Output voltage.
Dutycycle = tw/T*100%
T=1ms tw=0.45ms d=45%
Whatdoes this infer about the comparison voltage point? Compares twovoltages or currents and indicates the greater one.
This is the output plot
PartB: Pulse Width Modulator
PartC: Flash A/D converter
Aboveis the evidence that an A/D conversion can be converted by thecircuit to on/off values.
Section2: Linear Mode
PartA: Non-inverting amplifier
Below are the currents and measurements that have a DC input voltage of Vin=5V
Theinfinite resistance in input terminals stops the currents fromflowing through the Op-amp.
The output voltage Vo measurement with a DC input voltage, Vin=5V Vout = 9.78V. the gain of the circuit is A=2.
Below is the measurement for the transfer characteristic of Vo versus Vin
PartB: Inverting amplifier
The graphs for the input and output voltages
Thegain of the amplifier can be found below
The input and output voltages graph.
Beloware the inputs and output voltages
The Transfer Characteristic with saturation.
The Slew Rate of output Vo, in comparison the input and output with 10KHz square wave to the input, Vi.
PartC: Analog computing circuits
The Expression for Vo
The transfer characteristics using a 1 KHz sine wave input
The transient circuit response with
Thesine wave input:
The expression for Vo is
The transfer characteristics using a 1KHz sine input
The transient circuit response with:
Althoughthe circuit can work well and achieve what is expected of it, it isbeing used in the wrong area. The reason why this area is wrong isbecause it does not fully utilize the abilities of its currentapplications. For this reason it best works when used in non-linearapplications.
Terrell,D. L. (1996). OpAmps: Design, applications, and troubleshooting.Boston: Butterworth-Heinemann.
Gayakwad,R. A. (2000). Op-ampsand linear integrated circuits.Upper Saddle River, N.J: Prentice Hall.
Dai,L., & Jazar, R. N. (2012). Nonlinearapproaches in engineering applications.New York: Springer.