EECS 100 Astable Monostable and Bistable op amp circuits EE 100 Lab Astable Monostable and Bistable op amp circuits Theory 1 Objective In this laboratory measurement you will learn about oscillation mechanism and nonlinear wave shaping You will measure simple oscillatory and bi stable flip flop circuits 2 Introduction oscillators Oscillation is a very natural phenomenon and you can see many different examples including physics biology chemistry and electronics as well Oscillators are used in many electronic devices computers radios quartz watches wireless devices etc Their common purposes are to generate a periodic signal Every oscillator has at least one active device acting as an amplifier All rely on the same basic principle employing an amplifier whose output is fed back to the input in phase Thus the signal regenerates itself This is known as a positive feedback in contrast to previous laboratory experiments where we used always negative feedback in op amp circuits In this experiment we will focus on a special type of oscillators called relaxation oscillator A relaxation oscillator is a circuit that repeatedly alternates between two states with a period that depends on the charging of a capacitor The capacitor voltage may change exponentially when charged or discharged through a resistor from a constant voltage or linearly through a constant current source Next we will examine a simple circuit that can be easily transformed to an oscillator or a bi stable flip flop 3 Negative resistance converter Consider the following circuit shown in Figure 1 Figure 1 a A negative resistance converter and b its driving point transfer characteristic This circuit realizes a negative resistance converter incorporating both a negative feedback path via Rf and a positive feedback path via RA We will derive its driving 1 EECS 100 Astable Monostable and Bistable op amp circuits characteristic by inspecting both the linear and the saturation regions as well First assuming that the circuit works in the linear region we note that the RA and RB form a voltage divider so that vin RB v out vout R A RB Eq 1 We assumed ideal op amp model so the voltage across RB is equal to vin Applying KVL we obtain vin R f i vout Eq 2 Substituting Eq1 into Eq2 and solving for i we obtain i RA RB 1 vin Rf Eq 3 Eq 3 is drawn as the middle segment in Figure 1 b The boundary of this segment can be obtained by substituting Eq 1 into the validating inequality vout E sat so that E sat vin E sat Eq 4 By inspection of the positive saturation region vout Esat we find that vin R f i E sat so we get i E 1 vin sat Rf Rf Eq 5 Eq 5 defines the lower segment in Figure 1 b By inspection of the negative saturation region and following the same procedure as above we obtain i E 1 vin sat Rf Rf Eq 6 This equation defines the upper segment in Figure 1 b This circuit is called a negative resistance converter because it converts positive R resistance RA RB and Rf into a negative resistance equal to R f B in the linear RA region Next we show how this circuit can be easily transformed into an oscillator 4 Relaxation oscillator Let us connect a capacitor across the input terminals of the negative resistance converter Such a circuit is shown in Figure 2 Its driving point characteristic was derived earlier in Figure 1 Let us consider the four different initial points Q1 Q2 Q3 and Q4 corresponding to four different initial capacitor voltages at t 0 on this characteristic Since vin t vc t i t C and C 0 we have and vin t 0 for all t such that i t 0 vin t 0 for all t such that i t 0 2 EECS 100 Astable Monostable and Bistable op amp circuits Figure 2 a An astable RC op amp circuit and b its driving point characteristic Hence the dynamic route from any initial point must move toward the left in the upper half plane and toward the right in the lower half plane as indicated by the arrow heads in Figure 2 b Observe that there is no stable equilibrium point in the circuit because the zero i current belongs to an unstable equilibrium opposite arrowheads diverging from zero This equilibrium point cannot be observed in practice because any small amount of noise will drive out the circuit from this point Also the breakpoints QA and QB cannot be equilibrium points because i 0 Since arrowheads towards QA and QB are oppositely directed it is impossible to continue drawing the dynamic route beyond QA or QB In other words an impasse is reached whenever the solution reaches QA or QB 1 The dotted arrows show that a sudden instantaneous transition will occur also called jump For an RC circuit this transition should be always a vertical jump assuming in the v i plane that i is the vertical axis because the voltage across a capacitance cannot be changed suddenly such that vc T vc T Applying jumps at the two impasse points QA and QB we obtain a closed dynamic route This means that the solution waveforms become periodic after a short transient time starting from any initial capacitance voltage and the op amp circuit functions as an oscillator Note that the oscillation is not sinusoidal Such oscillators are usually called relaxation oscillators To figure out what kind of waveforms will be generated note that the closed dynamic route operates always in the saturation regions except for the short transient time at the very beginning These are the segments Q1 QA and Q4 QB It means that the output voltage vout will alternate between the two saturation levels Esat and Esat The output will be a square wave with a duty cycle of 50 if the saturation levels are symmetrical 1 Any circuit which exhibits an impasse point is the result of poor modeling This impasse point can be resolved for this circuit by inserting a very small linear inductor representing the inductance of the connecting wires in series with the capacitor 3 EECS 100 Astable Monostable and Bistable op amp circuits Since the output voltage will be either Esat or Esat then the non inverting input of the op amp will be biased at E sat or E sat This will drive the circuit to behave as a comparator Until the voltage of the capacitance is lower than E sat the output will remain at Esat and similarly until the voltage of the capacitance is larger than E sat the output will be always Esat The capacitor voltage will change exponentially because it is charged or discharged through the resistor Rf from a constant voltage Esat or Esat respectively The Figure 3 shows the expected waveforms Figure 3 Waveforms of RC op amp circuit
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